ON PROBABLE GROUNDS
Probabilistic Thought and the Principle of Reason
in Law and Data Science
JULY 2010

Katja de Vries – 9823611 – Leiden University – Department of Philosophy (degree: doctoraal Philosophy of Law)
Supervisors: prof. Th.C.W. Oudemans and prof. Th.J.M. Mertens.

PREFACEP

robably this thesis could have turned out differently. There are simply too
many butterflies in this world to believe that there is an immutable andforeseeable determinist chain of causal necessities leading from the bigbang to this bundle of paper. For instance, I can easily imagine myself handing in a thesis
entitled ‘The Lockean Proviso in Nozick’s Anarchy, State and Utopia’ or ‘The rule ofrecognition in Hart’s The Concept of Law: merely a matter of fact or a metaphysical foundationin disguise?’’. Such topics would have tied in nicely with some of the interests I pursued
during the past years and would have been a perfectly befitting pinnacle for a degree inphilosophy of law. This raises the question: why this thesis and not another? The current
text appears to be neither a random outcome (which would have been the case if I had
flipped a coin to decide on which topic to write or rented a monkey to bang its fists on
my keyboard) nor an iron necessity written in stone. If one is to compare my typing
fingers striking the keys to a pair of dice rolling on a casino table, the dice in thismetaphor are of the loaded type: tendencies, preferences, allowances and allurementsskewed the probabilities of their course but the actual outcome stayed accidental. As
Popper (1990) writes: “Looking at my own long life, I find that the main allurements
which led me on and on […] were preferences. The solutions were accidents.” (p. 26) So
which are the hidden weights, the altered edges, the bumps in the table?
hidden weights:
the world folded
within myfingers

What ‘loads’ my body in its actions is not, as is the case with loaded dice, a little
lump of metal, but my environment as it is folded into me. This ‘environment’ or ‘world’appears through the encounters it has with my body and becomes mine through thetraces it leaves in it. For instance, in the case of my fingers, the folded environment
consists out of the books whose pages they turned, the people they touched, theconversations which made them gesticulate, the objects which scarred them, the first
disciplining pencils which made them write, the sunrays which stroke them, andinnumerable other elements. Clearly, this thesis could not have been written without anyof these elements. However, as it is uncommon to thank inanimate things in a preface(Thank you sun, air, laptop, and desk!), I will stick to some names that cannot be left
unmentioned: in Leiden prof. Oudemans, in Brussels prof. Gutwirth, dr. Hildebrandt andNiels van Dijk, and, always and everywhere, Sebastian Abrahamsson.

a posteriestablishedtendencies

A second observation is that the tendencies or biases, whether towards a certain
number in a crooked die or towards a certain style of reasoning in a piece of writing,emerge from a specific constellation of ‘hidden weights’ and can only be inferred aposteriori. Thus, in retrospective (for the reader the preface is the first part of the thesis, to—1—

me it is the last) it appears that there are at least three important biases that might have
had a significant impact on the paths followed in this thesis:
1. a philosophicalhunch:
thinking certainty
and uncertainty atonce

1. A philosophical hunch: to think certainty and uncertainty at once within the notion of‘probable grounds’
In 1897 Mallarmé wrote and published the poem Un Coup de Dés Jamais N'Abolira Le
Hasard (‘A Throw of the Dice will Never Abolish Chance’). Hacking (2004) calls thispoem the “most subtle and many-layered expression” of the “self-conscious conceptionof pure irregularity, of something wilder than the kinds of chance that had been excludedby the Age of Reason” (p. 10). It arose in the nineteenth century, “[p]arallel to the tamingof chance” (p. 10), as an “ultimate backlash, a sort of statistical nihilism” (p. 147).
Hacking argues that the first poignant articulations of this philosophical experience of an
absolute and blind chance, which is always primordial to the “approximate Law” (Hacking,
2004, p. 215) into which it stabilizes, can be traced back to two philosophers: Peirce (whocoined tychism as the name of the doctrine that absolute chance is the primordial factorof the universe1892) and Nietzsche (e.g.: “I gave it [chance] back to all things, I redeemedthem from their servitude under purpose”, 2006, p. 132). In the second half of thetwentieth century Deleuze and Badiou (e.g. Badiou, 2000, pp. 72 ff.; Brassier, 2000;
Deleuze, 1983, pp. 25-7) both claimed to be the true heir of this primordial experience ofchance. Leaving aside the differences which divide these authors, I will focus on thequestion how to gain philosophical access to this ‘absolute chance’ and articulate it without
ending up in a romantic, anti-calculative discourse. Thus the hunch – or: thephilosophical itch – that has been guiding me in this thesis is whether the concept of‘probable grounds’ might offer the possibility to think at once both this pure chance andthe relative certainty following from statistical methods – which in itself seems as difficult
a feat as perceiving Wittgenstein’s duck-rabbit (1997, p. 194) as both a duck and a rabbit.

2. a doublebind

2. A double bind towards philosophy of law and philosophy of science
When I enrolled for the degree Philosophy of a specific discipline at Leiden University I did notknow what this “specific discipline” would be in my case. Having a background in both
civil law and cognitive psychology (specializing in research methodology) allowed me to
explore philosophy of law as well as philosophy of science. At first this double bindtowards two disciplines – each with its own distinct style of reasoning – appeared as acomplicating factor that I had to get rid of, but at second thought (inspired by the idea ofan ‘ecology of practices’: Stengers, 2005) it also seemed that such a non-place as the in-—2—

between of two practices might actually turn out to be a fertile ground for doing
philosophy.
3. a tendency
towards
semantics

3. A tendency towards semantics
I have often tried to do ‘practical’ or ‘applied’ philosophy in the hope to advance anotherdiscipline. But whenever I try to formulate a constructive ethical opinion or a thoughtprovoking cultural critique I always get stuck in ‘fundamental’ or ‘semantic’ questions(what is a ‘critique’, ‘culture’, ‘use’, ‘practical’, ‘fundament’, ‘logic’, ‘philosophy’, etc.?) thatare mere philosophy for philosophy’s sake. Both for me and for the reader this can be afrustrating experience – the endless dabbling in semantics feels as if one never leaves
square one. However, while such an approach is of little help in answering questions (“Shall
we go right or left? Based on a logical analysis and ethical assessment I say: to the right”), it mighttransform them in to more interesting questions (“Why do we think in the dichotomy right andleft, and is it possible to think differently?”).
The tendencies described above correspond to the matters discussed in the three firstchapters. The first chapter, informed by the philosophical hunch that there might be apossibility to think probability and the principle of ground together (1), explores thehistorical and philosophical grounds of the notion ‘probable ground’. In the second chapter– here the disciplinary double bind (2) enters the stage – a research question is formulated
by placing the notion of ‘probable ground’ against the background of law and data
science. Last but not least, the tendency towards semantics (3) is elaborated in moredetail in the third chapter, which presents the philosophical methodology of this thesis.
Now that these important cards are on the table, it is time to roll the dice: in the second
half of this thesis the relatively distinct themes of the first three chapters begin to overlap,
blend together and interact. In chapter four the way wherein the principle of ground moves
the course of my thoughts comes to the fore as I give a historical account of the world
which preceded the seventeenth century emergence of probability. In chapter five I present
law as a practice of probable grounds and attempt to retrace their functioning within thisdiscipline. Following Spinner’s (1977) analysis of some of Parmenides’ fragments, I
reformulate the role of probable grounds as a legal settlement following from an assumed
correspondence between the subjective belief of the judge and the legal proof indicating
reality. Retracing the functioning of probable grounds within the practice of law showsthe efforts that have to be made in order to establish the seemingly so effortless paths ofcorrespondence between ‘subjective’ and ‘objective’ probabilities. Chapter six shows how
probable ratios function within the practice of data science, i.e. as ratios that do not claim—3—the status of grounds. I argue that one of the implications hereof is not only that the
opposition between the subjective and objective interpretation of probability looses muchof its edge, but also that probability can no longer be conceived as ‘a gradation of
possibility’ (Leibniz, 1999, p. 94) and, consequently, does no longer fall under thevenerated Aristotelian metaphysics of potentialities striving towards actualisation. Afterall, the rationality of probable ratios only reigns in the present future and can be considered
independent of the question whether they actualise in the future present. Finally, in chapter
seven the concepts which emerged during the process of writing this thesis, i.e. not only
‘probable ground’ but also ‘affection’, ‘before’ and a ‘parallax between practices’, arerecapitulated and evaluated. This concluding chapter also returns to the pivotal question
whether it is possible to reformulate the deadlock dichotomy certainty-uncertainty in sucha way that it becomes possible to think them at once.

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TABLE OF CONTENTS

Preface1chapter 1

Introduction: the rationality of probable grounds

6

chapter 2

Research question: how do probable grounds movereasoning in law and data science?

19

Method: a parallax view on the affections of probablegrounds in law and data science22

chapter 4

A prelude to the parallax: before probable grounds

28

chapter 5

The probable grounds of law – solid/uncertain
encounters of being and thought

32

Probable ratios in data science – the eternal sunshineof the present future

41

Conclusion – new affections

52

Bibliography

57

chapter 3

chapter 6
chapter 7—5—chapter 1

INTRODUCTION: THE RATIONALITY OF PROBABLE GROUNDST

his is a thesis on probable grounds. Because knowledge exempt of any doubt
is scarce – or maybe even impossible 1 – most decisions which are taken
are based on probable grounds. To take a decision on probable grounds

means to act rationally under uncertainty. Such rational decision-taking on probablegrounds is omnipresent: the judge convicts the suspect because the evidence makes ithighly probable that he or she is guilty as charged; the researcher writes that it is likelythat the studied drug is effective because it is highly improbable that the measured effects
are due to chance; the broker invests money in a stock whose value is most likely to grow;the military airplane drops a bomb from a spot where it is probable to hit the target; andthe rational consumer – an intuitive statistician (Brunswik, 1943; Gigerenzer, 2000) –chooses the car which is probably the best buy because it received the highest averagerating from other consumers. In none of the aforementioned cases there is certainty thatthe right decision is made: against all odds the suspect can turn out to be innocent, thedrug ineffective, the stocks worthless, the bomb a miss, and the car a lemon. Thus,
probable grounds always have to come with a disclaimer: improbable does not mean impossible(cf. Esposito, 2007). In case of uncertainty relying on probable grounds seems the mostrational thing to do but it also implies a risk since improbable events do happen
sometimes 2 . Or, to put it differently: it is not probability but possibility which lures thegambler in to irrational behaviour.
rationality
independent of
actuality in the
future present

However, as Esposito (2007) convincingly argues, the fact that an improbable
event occurs does not affect the rationality of taking decisions on probable grounds 3 :even if things will turn out differently than expected the probable grounds guarantee ajustification. She builds this argument on the distinction (2007, pp. 50-67) between the

1 Following the ‘Popperian’ method of trial and error, science does not produce certain knowledge but merely

working hypotheses. As the amount of attempts to falsify these hypotheses grows they become more powerful(corroborated). Yet, notwithstanding the extent of corroboration, a future falsification of a hypothesis can never be
excluded. (Popper, 2002b)
2 The fallacy that improbable events are impossible played an important role in a recent criminal case in the
Netherlands. In 2003 Lucia de B., a nurse, was sentenced to life imprisonment for multiple murders. The mostimportant proof of her guilt was statistical ‘evidence of attendance’ (dienstroosterbewijs) : during several of her shifts astatistically remarkable high amount of patients had died. The court relied on statistical expertise and concluded thatthe repeated coincidence of these deaths with Lucia de B.’s presence as the nurse on duty could not be attributed tochance. The judgement was highly criticised (Derksen, 2006) and received wide media coverage. In March 2010 thecase was reopened and in April 2010 Lucia de B. was acquitted. Hoge Raad (Netherlands Supreme Court),
LJN: BD4153 (Lucia de B.), 11 March 2010; Hof Arnhem, (Court of Arnhem), LJN: BM0876, (Lucia de B.), 14 April
2010. Van Asperen de Boer (2007) gives a good account of the statistical and legal details of the case.
3 Many financial models contain probabilistic elements. Even though these models, which were one of the importantcauses of the current economic crisis, have been heavily criticised as being too complicated, opaque and risky, therationality of taking decisions on probable grounds is not disputed as such. Esposito draws a parallel between the—6—present future (‘gegenwärtige Zukunft’), i.e. the future as it presents itself in the now, andthe future present (‘zukünftige Gegenwart’), i.e. a now that will take place in the future.
According to Esposito the rationality of a decision which is made on probable grounds isbased upon the present future 4 and thus can never be refuted by a future present. The future
actualisation of an improbable event does not make the probable ground less rational. On
the contrary, when one calculates and plans the future on probable grounds one has toreckon with the possibility – although hopefully very small and improbable! – that things
will turn out differently than expected or hoped for. 5 Even though Hume already pointed
out that induction, and its underlying supposition “that the future will be conformable to thepast” (Hume, 2000, p. 31), is mere “custom and habit” (Hume, 2000, p. 37) and not
rationality 6 , the world would probably be less rational if the probabilities of the present
future would be structurally ignored because the future present is fundamentally open andundecided. As we all know: success in the past does not guarantee success in the futureand from the fact that the sun has risen every morning for millions of years it does notfollow that we can count on it that it will continue to do so. Still it would be irrational not
to take probable grounds into account. It simply seems undeniable that probable grounds
are indispensable in order to take rational decisions – not only because they often workout quite well in the future present, but even more because they are the rational thing to doin the present future.
probable grounds:
a contradiction interms?

Yet the notion of probable grounds seems not only opaque, but even paradoxical toa certain extent. Since Hume’s formulation of the problem of induction there has been an
endless amount of attempts to show that a probable ground is as much a contradiction interms as a round square. Most of these arguments rest on two assumptions: firstly that aground is a rational, certain and solid step in deductive thought, and secondly thatmodern probabilistic models and oracles in Antiquity: both are irrefutable by future events. When a prophecy did notoccur it was not the oracle that was to blame but its interpreter (Esposito, 2007, p. 65).
4 The notion of a present future also can help to overcome the distinction between a probability which refers to whatsomething already is (e.g., the woman is pregnant or non-pregnant – but given the test results of the pregnancy test in
the present future it is improbable that she is pregnant) or to what something will become (e.g. the bomb will be a hit ora miss – but in the present future it is improbable that it is a miss). However, this does not imply that the present future
should be understood as some kind of pseudo-Aristotelian potentiality (cf. Hermes is already present qua dunamis in
the block of wood before the artist has begun to cut the sculpture out of it: Aristotle, 1947, book IX, section 6)
which becomes actualised in the future present, because according to Esposito the rationality of a probable ground is
the likelihood of an event in the present future and is independent of its actualisation in the future present.
5 “Diese können dazu führen, dass man eine in der Vergangenheit eingenommene Position, so rational undwohlüberlegt sie auch immer gewesen sein mag, bereut – auch mit dieser Möglichkeit rechnet man bereits in derGegenwart. […] Obwohl man die Zukunft nicht kennen kann, verspricht die Berechnung ihre Planbarkeit. Diese
sollte, wie wir sahen, garantieren, daß man in der Zukunft nichts würde bereuen müssen, und in der Gegenwart den
Konsens mit andere Akteuren ermöglichen”. (Esposito, 2007, pp. 53-4)
6 “…that all our experimental conclusions proceed upon the supposition that the future will be conformable to thepast. To endeavour, therefore, the proof of this last supposition by probable arguments, or arguments regarding
existence, must be evidently going in a circle, and taking that for granted, which is the very point in question”.
(Hume, 2000, p. 31)—7—

probability is a mere inductive habit of thought without any rational justification, andthus uncertain and shaky 7 . With these assumptions in mind it is unsurprising that Leibniz,
the intellectual father of the ‘principle of ground’, never spoke of probable grounds. In
those instances where Leibniz specifies the ratio which according to his principle has to be
sufficient grounds

given, it is always with the adjective sufficient (‘sufficiens’):“…, the principle of Sufficient Reason, in virtue of which we believe that no fact
can be real or existing and no statement true unless it has a sufficient reason why
it should be thus and not otherwise”. (Leibniz, 1992, p. 74)
Thus, the principium rationis suffientis, the Principle of Sufficient Reason 8 , states that every
contingent fact must have an underlying reason which explains it (see, e.g., Pruss, 2006),
or as Schopenhauer reformulated it: “that everything must have a sufficient reason forbeing as it is, and not otherwise” (1889, p. 20). Like Descartes, the other famous
rationalist, Leibniz was looking for something solid to ground one’s reasoning. Clearlystern deductive reasoning, which led Descartes to the absolute certainty of his
fundamentum inconcussum, is very different from a probabilistic way of thinking which
revolves around the notions of uncertainty and induction. Still, when a determinist(whose doctrine says that every event has a cause) fails to find sufficient grounds,
probable grounds might be the next best thing to ease epistemological uncertainty. In
fact, one could argue that probability and statistics reconcile “Scientia to her arch-rival
Fortuna” (Gigerenzer et al., 1990, p. xiii). Probability turns Fortuna – who only shows hertrue colours, according to the sobering warnings of Boethius’ Lady Philosophy, “when sheshows herself to be inconsistent and changing” (1973, p. 225) – from fickle and pureuncertain certainty

uncertainty into (even though often uncertain) certainty. Uncertain certainty: again we end
up in a contradiction in terms.

7 For example, in the Theaetetus, 162e, Socrates says: “ἀπόδειξινδὲ καὶ ἀνάγκην οὐδ᾽ ἡντινοῦν λέγετε ἀλλὰ τῷ εἰκότιχρῆσθε, ᾧ εἰ ἐθέλοι Θεόδωρος ἢ ἄλλος τις τῶν γεωμετρῶν χρώμενος γεωμετρεῖν, ἄξιος οὐδ᾽ ἑνὸς μόνου ἂν εἴη.
σκοπεῖτε οὖν σύ τε καὶ Θεόδωρος εἰ ἀποδέξεσθε πιθανολογίᾳ τε καὶ εἰκόσι”. In translation (Plato, 2002, 162e, p. 81):“…; but you do not advance (legetè) any cogent proof (apodeixin de kai anagken) whatsoever, you base your statements(chresthe) on probability (eikoti). If Theodorus, or any geometrician, should base his geometry on probability, he would
be worth nothing. So you and Theodorus had better consider whether you will accept arguments founded onplausibility and probabilities (pithanologia te kai eikosi) in such important matters”. In general this translation is rather
anachronistic: not only because of the use of ‘probability’, but also expressions like ‘base statements’, ‘found onarguments’, etc. Quoted in: Franklin, 2001, p. 195, who translates eikoti (derived from ἔοικα) as ‘likelihood’, which
seems to me a less anachronistic translation than ‘probability’. Franklin also refers to similar passages in Plato, e.g.
Phaedo 92d and Pheadrus 229e.
8 Paradoxically, Leibniz deemed his principle to be so obvious, that it was not in need of any further explanation or
grounding : “On a pretendu d’abord que je commets une petition de principe. […] Ce principe est celuy du besoind’une Raison suffisante, pour qu’une chose existe, qu’un événement arrive, qu’une vérité ait lieu. Est ce un principe
qui a besoin de preuve? […] J’ose dire que sans ce grand Principe, on ne sauroit venire à la prevue de l’existence deDieu, ny rendre raison de plusieurs autres verités importantes. Tout le monde ne s’en est il point servi en milleoccasions?”. (Leibniz, 1890, p. 419)—8—

How did those seemingly opposite concepts of ground and probability end up in
their unlikely alliance? A first observation which could help to explain this entanglement
is the almost simultaneous emergence of probability and the so called principium rationis(“principle of ground”) in the second half of the seventeenth century. According toprinciple ofground(Leibniz, 1671)

Heidegger (1997, p. 49), who argues that this latter principle has paved the road for the
calculating thought which defines the science and technology of our modern age 9 , thefirst published record of the principium rationis is contained in a treatise written by Leibniz
in 1671. In this treatise (Theoria motus abstracti) the principle, which Leibniz characterizes
as “most noble” (nobilissimo illo), is only mentioned as an aside: Nihil est sine ratione – Nothingis without ground (Leibniz, 1880, p. 232; 1969, p. 142).
probability
By the time that the principle of ground was formulated for the first time, the(Pascal-Fermat, 1654
Bernoulli, 1692)
modern notion of probability was already seventeen years old. Its official moment ofbirth took place in the summer of 1654 when Pascal and Fermat sent each other fiveletters concerning the so called ‘problem of points’ 10 . Inspired by this correspondence(Stigler, 1999, p. 239) Christian Huygens wrote the booklet Rekeningh in Spelen van Geluck(written in 1656, published in 1660), which was immediately translated into Latin as De
ratiociniis in ludo aleae (1657). This text was the point of departure for Jacob Bernoulli’s
famous Ars conjectandi (The art of conjecturing) which “presents the most decisive
conceptual innovations in the early history of probability” (Hacking, 1975, p. 143) andcompletes the emergence of probability. The law of large numbers 11 , which is the chief
theorem of the Ars conjectandi, was proved in 1692 (Hacking, 1975, p. 143) but the bookwas only posthumously published in 1713.
In Ars conjectandi Bernoulli underlines that probability does not contradict the ideathat every event has a cause: all uncertainty is epistemological. For if all causes could be
9 “…we, who live in this age, stand under the reign of the claim of the mighty principium reddendae rationis. We who live
today are who we are only insofar as the mighty claim of rendering reasons bepowers us” (Heidegger, 1957, pp. 5960; 1991, p. 30). With regard to science Heidegger writes: “The authority of the powerful fundamental principle ofreason is the element in which the sciences move just as fish do in water and birds do in air” (1991, p. 123), and,
“Science responds to the demand of ratio reddenda and does so unconditionally. Otherwise, it couldn’t be what it is”.
(1991, p. 30)
10 The ‘problem of points’ questions how the stakes in a dice game should be divided when it is prematurely cut off,i.e., whether there is a fair division of the stakes based on the probability of each player to win the total game (given
the results of the previous rounds). The Pascal-Fermat correspondence concerning the problem of points has beentranslated to English (David, 1962) and practically every book on probability mentions them as the origin ofmathematical probability (e.g. Daston, 1988; Gillies, 2003; Hacking, 1975; Maistrov, 1974; Oosterhuis, 1991; Schuh,
1964; Vlis & Heemstra, 1988).
11 The Law of Large Numbers states that the average of the results obtained from a large number of trials should beclose to the expected value, and will tend to become closer as more trials are performed. Bernoulli’s version of thelaw is called the weak law of large numbers. In a letter to Leibniz (3 October 1703) Bernoulli writes: “…it must be
inquired whether the probability of an accurate ratio increases steadily as the number of observations grows, so that
finally the probability that I have found the true ratio rather than a false ratio exceeds any given probability; orwhether each problem, so to speak, has an asymptote — that is, whether I shall finally reach some level ofprobability beyond which I cannot be more certain that I have detected the true ratio” (Bernoulli, 1966, p. 24).

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determined the future could be determined with certainty: “All things which exist or are acted
upon under the sun – past, present, or future things – always have the greatest certainty in themselves andprobability as adegree of certainty

objectively”. (1966, p. 3) Bernoulli, just like all the other classical probabilists of his era(Daston, 1988), considers probability to be a degree of certainty: “For probability is a degreeof certainty and differs from absolute certainty as a part differs from the whole”. (1966, p. 3)
Moreover, when something is so very probable that its “probability nearly equals thewhole certainty” it should be considered morally certain: “Thus, if one thing is considered morally
certain which has 999/1000 certainty, another thing will be morally impossible which has only 1/1000
certainty”. (1966, p. 3) Bernoulli continues that, “[b]ecause it is still rarely possible to obtain total
certainty, necessity and use desire that what is merely morally certain be regarded as absolutely certain”.
(1966, p. 7) Thus the Ars conjectandi exemplifies why Daston calls the classical probabilist a‘rationalist manqué’ (1988, p. 241): although Bernoulli embraces rationalism he also
acknowledges that given epistemic uncertainty you have to cut your coat according to
your cloth. However, before we endorse the concept of the classical probabilist as a‘rationalist manqué’ we should not merely focus on his ‘defect’ but also on the ‘rationalism’
itself: what is the ratio that a rationalist manqué like Bernoulli was looking for? In order toanswer that question we will first have to take a closer look at the ratio of the principium
rationis which, according to Leibniz, underlies every event.

ratio – bothcause and reason

How to translate the principium rationis (or, in its more fully fledged formulation,
the principium reddendae rationis sufficientis) from Latin into English? The sufficient ratio whichshould 12 be rendered is both an epistemological (relating to how we think and know) andan ontological (relating to what is) ground: it is both a reason of thought for the subject
and a cause of being for the object 13 . However, in the standard translation in English of
the principium rationis sufficientis as the principle of sufficient reason – in fact this translation is somuch standardized that it is often used in the abbreviated form PSR (see, e.g., Pruss,2006) – this Janus-faced character of the ratio (as a ground that is both cause and reason)
is erased. This is why I have spoken, in accordance with the German translation as derSatz vom Grund, of the ‘principle of ground’. Lilly, in his translation of Heidegger’s Der Satzvom Grund (‘The Principle of Reason’), uses ‘reason’, ‘foundation’, ‘ground’, ‘grounds’, oreven ‘ground/reason’ to translate the equivocal Grund (1991, p. xiii). In the present,‘atomic’ (Heidegger, 1991, p. 121 ff.) age, the principle of Grund or ratio has not only

12 Reddendae is the gerundivium, which has to be translated as ‘should be rendered’.
13 When read together with the Leibnizian understanding of truth, namely as a proposition in which the predicate is

contained in the subject, the principio rationis can be reformulated as “all predication has a foundation in the nature of things”(Smith, 2005b, p. 130): “The principle of sufficient reason says not only that the notion of a subject contains everything that happens tothe subject, all its difference – that is, everything that is truly predicated of the subject – but also that we should be able to demonstratethat this is the case” (Smith, 2005b, p. 131 ), “just as we can demonstrate that the predicate “three sides” is contained in the concept of
the triangle”(Smith, 2005a, p. 6). Discussing the Leibnizian notion of truth in more detail is beyond the scope of thisintroductory chapter, but I refer the interested reader to: De Bakker, 2008.

—10—

become an imperative to give an ‘account’ which justifies a judgement (Heidegger, 1991,
p. 119 ff.), but also to secure the establishment of objects through calculation andreckoning.
probability – bothdegree of belief
and stochastic
frequency

It is worth noticing that the seventeenth and eighteenth concept probability has
the same kind of duality as the ratio in Leibniz’s principle: “On the one side it is statistical,
concerning itself with stochastic laws of chance processes. On the other side it is epistemological, dedicatedto assessing reasonable degrees of belief in propositions quite devoid of statistical background” (Hacking,
1975, p. 12). During the first two centuries of its existence nobody really seemed to beconcerned by this equivocal nature of probability, but in the last 150 years it has divided
probabilists and statisticians in two irreconcilable camps: Bayesians who say thatprobabilities are subjective degrees of belief and, on the other hand, Frequentists who holdthat probabilities are objective frequencies 14 . Bayesian statisticians attribute probabilities
to hypotheses (‘this hypothesis has a probability of 0.85’), whereas their objectivist
counterparts hold that – given a certain hypothesis that in itself is either completely false
or true – only data can have a probability (‘given this hypothesis these results are highly
unlikely: they have a probability of 0.001’). A nice illustration of the depth of this divide is
the reaction of Popper, who belonged to the camp of the objectivists, on his discovery
that his former ally Carnap also had begun to defend a subjectivist position:“Carnap was then [in 1934], and for some years afterwards, entirely on my side,
especially concerning induction […]. Carnap and I had come, in those days, tosomething like an agreement on a common research programme on probability,
based on my Logik der Forschung. […]This was the state of the discussion reached in 1934 and 1935. But 15 years later
Carnap sent me his new big book, Logical Foundations of Probability, and, opening it,
I found that his explicit starting point in this book was the precise opposite – thebare, unargued assumption that the degree of confirmation is a probability in thesense of probability calculus. I felt as a father must feel whose son has joined theMoonies; though, of course, they did not yet exist in those days”. (Popper, 1990,
pp. 4-5)probability –an approximationof the underlying
true ratio

Not only was the classical concept of probability Janus-faced, but so were the true ratios,or ‘reasons’, that these probabilities were supposed to approximate: ratios between black
and white pebbles in an urn 15 , between boys and girls in a population, between different

14 In 2010 the prestigious Von Dantzig price for Statistics in the Netherlands was awarded to prof. Grünwald andprof. Van Zanten for their attempts to bridge the gap between Bayesian and frequentist statistics. See:
http://www.vvs-or.nl/
15 “…if, for example, we replace the urn by the atmosphere or the human body (both of which contain—11—

diseases in a human body, between guilty and innocent people etc. In the two centuries
following its discovery degrees of belief and observed frequencies coincide within the concept ofprobability because they are supposed to be natural indexes of the underlying true ratios.
Because the true ratios are hidden in the urn of nature we can merely know them
indirectly from the observed frequencies of similar cases. In this way the a priori ratio canbe deduced from a posteriori observed frequencies (which correspond to the degree ofbelief):“But indeed, another way is open to us here by which we may obtain what issought; and what you cannot deduce a priori, you can at least deduce a posteriori –i.e., you will be able to make a deduction from many observed outcomes ofsimilar events. For it must be presumed that every single thing is able to happen
and not to happen in as many cases as it was previously observed to have
happened and not to have happened in like circumstances. For if, for example, anexperiment was once conducted on 300 men of the age and constitution ofwhich Titius is now, and you observed that 200 of them had died before passing
the next ten years and that the others had further prolonged their lives, you could
safely enough conclude that the number of cases in which Titius must pay his
debt to nature within the next ten years is twice the number of cases in which hecan pay his debt after ten years. And so, if anyone has observed the weather forthe past several years and has noted how many times it was calm or rainy; or ifanyone has judiciously watched two players and has seen how many times thisone or that one has emerged victorious: in this way he has detected what the ratio
probably is between the number of cases in which the same events, with similar
circumstances prevailing, are able to happen and not to happen later on.”(Bernoulli, 1966, p. 12)
Bernoulli does not merely posit that the a priori ratio can be deduced from a posteriori
observations, but with his ‘law of large numbers’ he also gives a practical guideline to findthese true ratios. The basic idea of this law is that the approximation of the hidden true
ratios becomes more precise as the number of observations grows (Basel, 3 October 1703,
letter to Leibniz):“…it must be inquired whether the probability of an accurate ratio increases
steadily as the number of observations grows, so that finally the probability that I
have found the true ratio rather than a false ratio exceeds any given probability;
fuel for various mutations and diseases as the urn contains pebbles), we will in the same way be able to determine byobservations how much more easily this or that event can take place in the regions of the atmosphere or the humanbody”. (Bernoulli, 1966, p. 13)—12—

or whether each problem, so to speak, has an asymptote – that is, whether I shallfinally reach some level of probability beyond which I cannot be more certainthat I have detected the true ratio. […] if the former is true, we will investigate
the ratio between the numbers of possible outcomes a posteriori with as muchcertainty as if it were known to us a priori. And I have found the former condition
is indeed the case; whence I can now determine how many trials must be set up
so that it will be a hundred, a thousand, ten thousand, etc., times more probable(and finally, so that it will be morally certain) that the ratio between the numbersof possible outcomes which I obtain in this way is legitimate and genuine.”(Bernoulli, 1966, p. 24).
Though the law of large numbers seems to be intuitively sound it took Bernoulli great
pains to come up with the mathematical proof:“Moreover, although – and this is amazing – even the stupidest man knows, bysome instinct of nature per se and by no previous instruction, that the more
observations there are, the less danger there is in straying from the mark, it
requires not at all ordinary research to demonstrate this fact accurately andgeometrically.”. 16 (Bernoulli, 1966, pp. 23-4)
Leibniz’s ratio =Bernoulli’s ratio?

Summarizing we could make two observations about the ratio in classical probability andLeibniz’s principium rationis. Firstly, we notice a difference: the ratios of the probabilists are
not simply grounds in general, but they are grounds that are proportions between different
cases 17 . However, the second observation is that this difference is relatively small
compared to what Bernoulli’s and Leibniz’s ratio 18 have in common: in both ratios the
subject and object coincide.

Leibniz andprobability

Leibniz cannot be credited for the invention of the modern notion of probability, but as
an important “witness to the transformation” (Hacking, 2004, p. 9) and “the first
philosopher of probability” (Hacking, 1971b, p. 597) he nevertheless is the main
protagonist in Hacking’s (1975) seminal book on the seventeenth century emergence of

16 “Quanquam autem, quod mirabile est, etiam stupidissimus quisque […] quo naturae instinctu per se & nulla

praevia institutione norit, quod quo plures observations fiunt, hoc minus a scopo aberrandi periculum sit; hoc ipsum
tamen accurate & geometrice demonstrare minime vulgaris indaginis est” (Bernoulli, 1993, p. 117). Part of thisfragment is also discussed by Daston (1988, p. 229). See also: Bernoulli, 2006, p. 35 ff.
17 In 1933 Kolmogorov came up with the axiomatic formalization of probability which states that the probability ofan event is a non-negative real number:
0≤ P(E) ≤1∀E ∈F
where F is the event space and E is any event in F. Kolmogorov’s axiom does not elucidate probability in aphilosophical way (Hacking, 1976, p.), but it merely provides a mathematical tautology: probability is what fits theaxioms of probability.
18 In this regard it is worthwhile to notice that in the index of the most recent volume of the Akademie-edition of
Leibniz’s philosophical writings (1999) there are three main entries for the word ratio: ‘ratio (Grund)’, ‘ratio (Vernunft)’,and ‘ratio (Verhältnis, proportio)’.

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probability. Contrary to Descartes (who had “no truck with the nascent concept ofprobability”, Hacking, 1975, p. 45), Leibniz showed a lively interest in the ideas springing
forth from the probabilistic revolution. Not only did he write quite extensively on
probability in matters concerning aleatory contracts and testimony in court (see e.g.
Leibniz, 1996, book 4, chapter xiv, ‘Judgment’, chapter xv, ‘Probability’, and chapter xvi,
‘The degrees of assent’), but he also entertained a lively correspondence (consisting of 21
letters 19 ) with Jacob Bernoulli during the period from 1687 until the latter’s death in 1705
(Sylla, 1998).
no probability
without the ratio of
the principium
rationis?

In this thesis I will try to take Hacking’s argument even further. The argument I
will develop is that Leibniz – by formulating (firstly in 1671) the principle of reason with
its Janus-faced ratio – was not only a witness but also a crucial facilitator in the emergenceof probability (approximately from 1654 to 1692). This might be what Heidegger hints at
when he remarks:“Parenthetically, Leibniz, the discoverer of the fundamental principle ofsufficient reason, was also the inventor of ‘life insurance’” (Heidegger, 1991, p.
124)
Although this statement is historically incorrect – not Leibniz but Johan de Witt can beconsidered to be the inventor of life insurance – it might be true in a philosophical sense.
Heidegger’s parenthetical remark suddenly would make sense if it could be proved thatthe two pivotal elements of life insurances, i.e. probabilistic grounds and the desire forcertainty and security, follow from the Leibnizian reason that is requested by his principle

being andthought:
the sameof reason.
Leibniz’s ratio belongs both to the realm of thought and being 20 . The hypothesis
which I propose is that this theme of ‘co-originality’ (Cristin, 1998, p. 88 ff.), that posits aco-belonging (“aeque originaria”: of the same origin) between “thinking self” (“cogito”) and“things thought” (“varia a me cogitantur”) 21 , as it is also to be found in the principle ofreason, facilitated the emergence of probability. As Cristin (1998) notices, the Leibnizian
co-originality of being and thought announces “an ontological rediscovery of Pre-Socratic
themes (especially those of Parmenides) which was later to reach its full development in
Heidegger”. (p. 89)

19 These letters can be found in Bernoulli, 1993; Leibniz, 1855. Some letters have been translated into English:

Bernoulli, 1966.

20 Cristin differentiates Leibniz’s co-originality from Heideggers: the former posits a co-belonging of “thinking self”

and “things thought”, whereas the latter transfers it fully to the ontological plane by speaking of the “thought” and“being” (1998, p. 88-89). However, I will not develop this distinction as it would lead us on too many side-ways..
21 “prima Experienta nostra constat esse ipsas internas perceptions, nempe non tantum me esse qui cogitem, sed etvarietatem esse in meis cogitationibus (quae due a se invicem independentia et aeque originaria judico”) ab ipsis
Scepticis est inculcatum, […]” (Leibniz, 1880, p. 327). (For an interpretation of this fragment see: Cristin, 1998, p. 89
ff.)

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To assume a relation between the ratios expressed in probabilities and those thathave to be rendered according to Leibniz’s principle, is far from self evident. Yet, maybe
probableratio as a
calculative
proportion

probable ratios are an instance of ratio as such? Probabilistic ratios are quantitative or
calculative proportions 22 that transform uncertainty in less uncertainty, whereas Leibniz
ratio is an almost infinite regress 23 (in the end everything leads back to the final ratio) of
solid, ‘made-in-one-piece’ reasons that lead to absolute certainty. According to Heidegger
quantitative calculation is merely one of the instances (“…reckoning in the sense of an
operation with numbers is a special kind of reckoning distinguished by the essence ofquantity”, p. 100) of this Leibnizian ratio which is both “reckoning” as “a deed” and as

sufficient orprobablereason?

“what is reckoned, the presented calculation, the account” (1991, p. 100).
When the focus is shifted from the seeming opposition 24 between probability
and ground (inductive and uncertain v. deductive and certain) to the Janus-faced ratio that
underlies both, the notion of probable grounds is not so paradoxical any longer. From thevery first formulations of the principium rationis it is clear that in practice the imperative
reddendae (should be rendered) cannot always be satisfied by sufficient grounds: “Mostfrequently, however, these reasons [i.e, sufficient reasons why it should be thus and not otherwise]cannot be known by us” (Leibniz, 1992, p. 74). The imperative to bring the ratio of‘thinking itself’ in accordance with the ratio of ‘things thought’ will not always becompletely satisfied. When the sufficient reason cannot be known, insufficient (i.e.
probable) reason is the next best thing. Although one can argue whether it was Leibniz or
Bernoulli who formulated the probabilistic Principle of Insufficient Reason 25 (which is likely to

22 Even though in, for instance, post-eighteenth century law these calculative proportions have become very implicit.

Thus most modern Western lawyers would consider it an impossibility to express ‘proof beyond reasonable doubt’
and the intimate conviction of a judge in precise quantitative terms (i.e., as a number between 0 and 1). Franklin(2001, p. 362-72) even argues that in procedural law a totally unquantified, archaic kind of probability has survived.
The manifold attempts that were made in the seventeenth and eighteenth century to quantify legal proof andconviction in probabilistic terms have been largely superseded by more hermeneutic approaches in the nineteenth
century.
23 Because of this regress of reasons (an “infinitely infinite seriality”, p. 25) Deleuze calls Leibniz a very Baroquethinker (Deleuze, 1993, p. 49): “The individual notion, the monad, is exactly the inverse of God to the degree thatreciprocals are numbers that exchange their numerator and their denominator: 2, or 2/1, has as a reciprocal 1/2. And
God, whose formula is ∞/1, has as its reciprocal the monad 1/∞”. Deleuze thus opposes the classicism of Descartes
to Leibniz’s Baroque Mannerism: “Essentialism makes a classic of Descartes, while Leibniz’s thought appears to be a
profound Mannerism” (p. 56).
24 The assumption that there is an opposition between Leibniz’s probabilistic ideas and his principium rationis has beenchallenged in recent research (see e.g. Dascal, 2001; Dascal, 2005; Roinila, 2007).
25 It is not completely clear who gave the principle this name, but as far as known it is first mentioned as such in aprobability textbook by Von Kries (1886). Bernoulli does not name the principle as such but describes it, forinstance, in the fourth chapter of Ars conjectandi (Bernoulli, 1966, p. 9): “… all cases are equally possible, or that they
all can happen with equal ease” (“…omnes casus aequè possibiles esse, seu pari facilitate eveniri posse”). Though the principle
of insufficient reason is commonly attributed to Bernoulli, Hacking argues that the latter got the idea from Leibniz(1975, p. 125): “Before the 1713 publication of Ars conjectandi no well-circulated work makes use of equipossibility.
Bernoulli himself did not employ it much. He got it from Leibniz, who had long associated it with probability”.

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be a play on Leibniz’s principle and that was later renamed the Principle of Indifference), it isinsufficientreason:a supplement
to sufficientreasonclear that insufficient reason seems to be a necessary supplement of sufficient reason.
The Principle of Insufficient Reason says that not knowing can also be a ground forreasoning: when the mind is ‘tabula rasa’ about the occurrence of certain events, then therational thing to do is to assign equal probabilities to each of several alternatives if there is
no known reason for preferring one to another (see, e.g. Hald, 1998, p. 159). Thus, forinstance, if one has no knowledge 26 whatsoever to base one’s beliefs on the a priori
probability of a rainy day is equiprobable 27 with a sunny day (50% : 50%). Even though
the original Principle of Insufficient Reason has been critiqued intensely (Hacking, 1971a;
Howson, 2002; Sober, 2002), the idea which still stands is that uncertainty can betransformed into something which at least has a certain semblance of rational certainty.
By departing from an assumption of equi-probability, uncertainty can be transformed in
to something more or less rational and reliable:“Let us take a set of events configured in such a way that there is a priori no reason
why any one of them should occur rather than any other. […] When, armed withthis hypothesis, we attempt to calculate the likelihood of one event occurring(understood as this or that outcome of throwing the dice), we implicitly assume
the following a priori principle: whatever is equally thinkable is equally possible. It isprecisely this quantitative equality between the thinkable and the possible thatallows us to work out the probability or frequency of an event when we play agame of chance”. (Meillassoux, 2008, p. 96)
the downfallof sufficientreasonOver time probable grounds have outgrown their status of supplements. In fact one
could even argue that, whereas sufficient grounds are past their prime, probable grounds
continue to make the principio rationis important for our current age. After all, from thesecond half of the twentieth century the principle of sufficient reason has been under heavy
attack – both scientifically 28 (e.g. Popper, 1979, ‘Of Clocks and Clouds’, p. 214) andphilosophically 29 (e.g. Meillassoux, 2008) – as too determinist and onto-theological (there
has to be an ultimate reason or final cause which cannot be anything else but God: “This26 In Leibniz the principle of insufficient reason is only epistemological because there is an underlying causality that is‘indifferent’: ‘It is not we who are indifferent, but the objective tendencies […]’. (Hacking, 1971b, p. 602) Thus, thestate of ‘no knowledge’, i.e. epistemological insufficient reason, coincides with the objectively equipossible grounds.
27 Leibniz speaks of “aequalibus aequalia” (Leibniz, 1882, p. 448), i.e. “giving equal weight to equal suppositions(Hacking, 1971b, p. 601).
28 “Indeterminism, which up to 1927 had been equated with obscurantism, became the ruling fashion; and somegreat scientists, such as Max Planck, Erwin Schrödinger, and Albert Einstein, who hesitated to abandon determinism,
were considered old fogies, […]”. (Popper, 1979, p. 214 )29 See for instance: “Quentin Meillassoux […] saves necessity, including logical necessity. But like Hume, he grantsthat there is no acceptable ground for the necessity of the laws of nature. Meillassoux’ proof - for it is indeed a proof- demonstrates that there is only one thing that is absolutely necessary: that the laws of nature are contingent”.(Preface by Badiou in: Meillassoux, 2008, p. vii)

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reason must be in some sort of real being, or in its cause […] and is usually named with one word:
GOD” 30 , (Leibniz, 1890, p. 289, translation in Heidegger 1991, p. 26). For instance,
Meillassoux, in reformulating Hume’s induction problem, argues that the necessitating
the primacy
of probable(insufficient)reasonprinciple of sufficient reason did only emerge because the universe appeared as aprobabilistic ‘dice-universe’:“Every time it [the dice] is thrown, this dice-universe invariably results in thesame physical universe – mine, the one I have always been able to observe on adaily basis. […] The latter has never infringed the principle of uniformity; it has
always presented me with the same result given the same initial conditions. The
improbability of this stability in the outcome seems so aberrant that I do noteven pause to consider the possibility that it might be solely the result of chance.
Consequently, I infer from it – via an inference which is generally executed too
quickly even to be noticed – the existence of a necessary reason, but a necessitythat is extra-logical as well as extra-mathematical. […] if physical laws could actuallychange for no reason, it would be extraordinarily improbable if they did not change
frequently, not to say frenetically”. (Meillassoux, 2008, pp. 97-8)
Pruss, belonging to the minority of defenders of the principle, wails that “a significant
amount of work in the twentieth century was put into discussions of attempts to disprove
the PSR, whether by counterexample or by reduction to absurdity” (Pruss, 2006, p. 13).
Thus it might seem surprising that Heidegger says of this ‘outdated’ principle that it iswhat makes our current age tick. However, in this respect it is telling that Heidegger did
not call his famous course “On the principle of sufficient reason”, but merely “On theprinciple of reason”. The kind of reason is left open 31 .

what is leftof the PSR
in science
andtechnology:
probabilistic
ratiosIn fact in contemporary science and technology it is not only the sufficiency ofreasons and causes which appears anachronistic, but also ‘reason’ and ‘cause’ as a groundsounds a bit rusty. Of course, science and technology still look for causes and reasons,but these have long lost their metaphysical aura of foundational Grounds with capital ‘G’.
Causes and reasons are more and more often only probabilistic ratios in algorithmically“Ea ratio debet esse in aliquot Ente Reali seu causa. […], et uno vocabulo solet appellari DEUS” (Leibniz, 1890,
p. 289). Similar conclusions can be found in contemporary accounts of the principle as well: “This means that this
PSR, if true, is strong enough to ground the Cosmological Argument for the existence of a necessarily existing First
Cause. Of course, it is a separate question what the nature of this First Cause is, though, as I have noted in Chapter
5, there are considerations in favor of a theistic answer.” (Pruss, 2006, p. 321) Unsurprisingly, the recommendation
algorithm of the website Amazon suggests that customers who look for books on the principle of sufficient reason
might also be interested in theological books which argue for the existence of God. However Heidegger notes thatwhile in our atomic age, as Nietzsche says, God is dead, “the calculated world still remains and everywhere includes
humans in its reckoning inasmuch as it reckons up everything to the principium rationis” (Heidegger, 1991, p. 101).
When there is no God that can function as the summa ratio, the rendering of reasons becomes truly infinite or, as
Deleuze would say, even more ‘Baroque’. (1993)

30

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adjusted working hypotheses – probabilistic temporary models that have to be eternallyadjusted and whose accordance with the data can never be proved conclusively. A new
discipline that seems to be exemplary of this shift away from the foundational reading of
the principle of sufficient reason to the principium rationis as the mere reign of probabilistic
ratios is data science (Hand, 2007), whose practitioners combine “the skills of a software
programmer, statistician and storyteller/artist to extract the nuggets of gold hidden undermountains of data”. (The Economist, 2010, February 27th, p. 2)
data science:a pragmatic
view onprobability

One of the striking novelties of this new discipline is the fact that it has anextremely pragmatic approach that makes the distinction of subjective and objective
probability of no importance. Most 32 data scientists shrug their shoulders in indifference
towards the Popperian ban on Bayesian (i.e. subjectivist) probability and either fully
embrace Bayesianism 33 or use both branches of statistics as they please. Let us recall theirreconcilable quarrels between those who adhere to the position that probability isobjective and those who hold that it is subjective: adherents to the former argue that one
can never attribute a probability to a hypothesis itself and that probabilities only relate to
the likelihood of observed data given a certain hypothesis, whereas the latter maintainthat the higher the probability of a hypothesis, the more reason there is to believe that itis true. However in the many applications of data science, e.g., automated speech
recognition systems and spam filters, both the probability of the data and the probabilityof the hypotheses are calculated! The multiplicity of probabilistic hypothesis (e.g. ‘ thesound **** has a probability of 0.65 to mean head and a probability of 0.23 to mean hat’,or, ‘an email with VIAGRA in the subject line has a probability of 0.999 to be spam’) is
subjected to an algorithmically infinite process of negative feedback, probabilistic
adjustment of the hypotheses and falsifying scrutiny. It is an endless shuttling hence andforth between data and probabilistic hypotheses to fine tune thought (the categorization
in folders, as words, etc) towards being (the sounds, the emails, etc). The question what
the probabilities express (e.g. is there an objective propensity of VIAGRA-emails to havea probability of 0.999 to be spam or is this probability the rational belief we have toattach to the hypothesis that it is spam?) recedes into the realm of irrelevant metaphysicalwonder – what counts is how well the spam filter or speech recognition system works.

31 Meillassoux takes this to its extreme and argues that the principle of sufficient reason has to be replaced by theprinciple of unreason (2008).
32 The status of this new discipline, its methods and its implications is still highly debated. See, for instance, the Wired(2008) article by Anderson and the abundance of replies that it has provoked.
33 One of the most important data scientists at Microsoft proudly shows pictures of his pilgrimage to the tomb ofReverend Bayes: http://research.microsoft.com/en-us/um/people/horvitz/revbayes.htm—18—chapter 2

RESEARCH QUESTION: HOW DO PROBABLE GROUNDS MOVE REASONING IN LAWAND DATA SCIENCE?

summarizingB

efore proceeding to the research question I will first recapitulate some ofmain ideas formulated in chapter one. Where have the introductory

remarks on probable grounds/ratios brought us so far? Following Hume’s problem of
induction the notion of probable ground seemed to lack rationality or even to be acontradiction in terms: a probable ground is like an uncertain certainty. The assumptions
on which this conclusion rests is that a ground is a rational, certain and solid step in
deductive thought, whereas probability is a mere inductive habit of thought without any
rational justification, and thus uncertain and shaky. However, on closer inspection boththe notion of probability and ground seemed to be too equivocal to allow for such aprobability andrationality aresuch equivocal
notions that
simplejuxtaposition is
impossible

simple juxtaposition. Following Esposito I argued that the rationality of probability does
not depend on the actualization of a probable event: an event that is probable in thepresent future but never occurs in the future present does not disproof the rationality of
relying on probable grounds. Moreover the notion of ratio can be translated in manydifferent ways such as ‘ground’, ‘reason’, ‘foundation’ or ‘cause’. Also the notion ofprobability is far from unequivocal. How can we say that a ‘probable ratio’ (or: ‘probableground’) is an incoherent imbroglio in which the constituent parts annul each other incontradiction (e.g. a probable ground is neither rational nor probable), if these“probable
grounds” as thepoint ofdeparture

constituents themselves are opaque to us? Thus the point of view is reversed: by tracing
the emergence of probable grounds from a historical and philosophical perspective 34 thismight also allow us to shed some light on rationality and probability. The historicalperspective brought me to the second half of the seventeenth century, wherein both theclassical concept of probability (Bernoulli) and the principle of reason (Leibniz) emerged.
What both have in common is a Janus-faced ratio – even though in probabilistic thinking
this ratio is a proportion and in the principium rationis sufficientes it is not, both create acoinciding identity between the ratios of thought and those of being. Another thing thatis common to both probabilistic and sufficient ratios is their reckoning nature – eventhough in the former it is more explicit – that produces certainty.
Not only do the principle of reason and the classical concept of probability sharea similar ratio, but also their histories are intertwined. From the days of its conception
and onwards probabilistic ratio has been the supplement to sufficient ratio. The
probabilistic principle of insufficient reason would offer a way out if the sufficient reasons

34 See the following chapter for more details on the methodology of this thesis.

—19—could not be unearthed. Thus the lack of reason could be turned into, even thoughinsufficient, reason after all. From the 1920s and onwards the principle of sufficientreason has been increasingly criticized – logically, scientifically and philosophically.
Inversely proportional to this downfall, probable ratio has emancipated itself from its
supplementary role. Probable ratio is no longer the humble ancilla of sufficient ratio.
law as thefirst and thelast greatbastions offoundational
grounds andreasons

Yet there is a field wherein things have not progressed in the same way. That
field is law. In law, at least in all its modern Western varieties, the whole legal process
always revolves around finding the right grounds (justifications) and the establishment ofsufficiently convincing causal connections. In law the principle of sufficient ground stillrules in a way that has been long lost in most contemporary scientific and technologicalpractices. Moreover, law is not only one of the last bastions of sufficient reason but it wasalso its first: both the emergence of the most archaic 35 form of the principle of sufficientreason in the writings of Parmenides (Spinner, 1977) and the fully-fledged Leibnizianvariety came about in a context of legal thinking. As I argued before, Leibniz’s principleof sufficient reason has been supplemented from its inception with probable reason.
Thus, unsurprisingly, law – with its eternal epistemological uncertainty of the judge, theinescapable need to give a decision, the indirectness of legal evidence, the possibility toassign numerical weight to different kinds of proof (e.g. half or full proof), etc. – was not
only the cradle of sufficient reason but also of its supplementary twin: probable reason(Daston, 1988; Franklin, 2001; Hacking, 1975). Consequently we could say that law is theratio asground – ameaningpreserved inlaw‘practice of origin’ of the principium rationis: both its sufficient and probable variety.
However in law, contrary to e.g. data science, the ratio of the principium rationis still
continues to be more than mere ratio as a proportion. In law ratio is both proportion andground.
Ratio, a simple word, shapes how we think. However, how it makes us think, i.e.
relate to the world around us, is subject to change. This evolvement – over time, between
languages, disciplines, practices, etc. 36 – questions whether we can speak of an ‘us’ at all.
Even though Janus-faced ratio tends to appear as universal and timeless, this is a position
that is both historically and philosophically untenable. In order to be able to think how

35 Although the first archaic version of the principle of sufficient reason can be found in Anaximander it isParmenides (On Nature, fragment 8) who gives the principle its logical grounding (Pruss, 2006, pp. 20-26). Thisfamous ex nihilo nihil fit reads: “I shall not permit you to say or to think that it grew from what-is-not, for it is not tobe said or thought that it is not. What necessity could have impelled it to grow later rather than sooner, if it beganfrom nothing? Thus it must either fully be, or be not at all. Nor will the force of conviction ever allow anything,from what-is, to come-to-be something apart from itself; […]”. (Parmenides of Elea, 1996, fragment 8a)
36 To trace the evolvement of words that are important for how we think has been is a way of doing philosophy thathas become very important in twentieth century continental philosophy. Heidegger and Derrida have become theexemplary philosophers of the ‘etymological’ way of thinking; Stengers has coined the notion ‘ecology of practices’and focused on thinking in between different practices and disciplines (see e.g.
http://www.imbroglio.be/site/spip.php?article43 or (Stengers, 2005).

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probable ratio – whose reign is quickly spreading itself over a vast amount of domains –thinking
ratio throughlaw and data
sciencemoves thought, I will trace it through two practices. Firstly there is law: the practice that is
supposed to be the cradle of both the principle of reason (Spinner, 1977) and probableratio (Daston, 1988; Franklin, 2001; Hacking, 1975). Secondly there is data science: thepractice in which being and thought fully coincide in algorithms with probabilistic ratios.

researchquestion

After this concise recapitulation of the pivotal questions raised by the notion‘probable ground’, it is time to present my research question: How does the reckoning
and Janus-faced ratio of probable grounds move reasoning in law and data science? 37 I
hypothesize that in answering this question it will be impossible to avoid an issue that was
raised at the beginning of this chapter: the relationship (or lack of it) between probability
and the actualization of possibilities in time (cf. the questions raised by Esposito, 2007).
Yet, before I can proceed with tracing answers to the central question of thisthesis – how does the calculative and Janus-faced ratio of probable grounds movereasoning in law and data science? – I will have to present the methods which will help
me to pursue this question. After all, probable grounds do not only shape thought in law
and data science, but also my own reasoning 38 in this thesis. Method and object of study
overlap and coincide. To ask how probable grounds shape reasoning (e.g., can one think
philosophically if one reasons on probable grounds?) while my own thoughts on thismatter are also shaped by these probable grounds: it seems a task worthy of Von
Münchausen who escaped from a swamp by pulling himself up by his own whig. Thus,
unsurprisingly, the matters raised in the following chapter on method will not be
unrelated to the questions raised in this chapter.

37 I do not assume any causal direction, as it would be misguided to assume that there is a law or data science
independently of reckoning and Janus-faced ratio, or the other way around, that this ratio exists outside theembodiment in a practice. In fact my research question could thus be posed in two ways. Not only “How does thereckoning and Janus-faced ratio of probable grounds move reasoning in law and data science?”, but also “How does
the reasoning in law and data science move the reckoning and Janus-faced ratio of probable grounds?”
38 Meillassoux calls this correlationalism: “Correlationism consists in disqualifying the claim that it is possible toconsider the realms of subjectivity and objectivity independently of one another. Not only does it become necessary
to insist that we never grasp an object ‘in itself’, in isolation from its relation to the subject, but it also becomes—21—

chapter 3

METHOD: A PARALLAX VIEW 39 ON THE AFFECTIONS OF PROBABLE GROUNDS IN
LAW AND DATA SCIENCE“…S

pinoza will affirm strongly, in book two, that we can only know [connaître]ourselves and we can only know external bodies by the affections that theexternal bodies produce on our own. […], this is the basic anti-Cartesian

proposition since it excludes every apprehension of the thinking thing by itself, that is it excludes all
possibility of the cogito. […] a body must be defined by the ensemble of relations which compose it, or,what amounts to exactly the same thing, by its power of being affected. […] A body has something
fundamentally hidden: we could speak of the human species, the human genera, but this won't tell us what
is capable of affecting our body, what is capable of destroying it. The only question is the power of being
affected. What distinguishes a frog from an ape? It's not the specific or generic characteristics, Spinozasays, rather it's the fact that they are not capable of the same affections”. (Deleuze, 1978, 24th
January, p. 6)

the before
that allows anaffect to emerge

To live is to be affected 40 : the flower is affected by the sun, the lover is affected by his
beloved, the ear is affected by the scream, the scientist is affected by the microbe below
his microscope, and as Jakob von Uexküll famously showed: the tick has only three waysof being affected 41 . Before an affection can arise there always has to be something which

necessary to maintain that we can never grasp a subject that would not always-already be related to an object”. (2008,
p. 5)
39 ‘Parallax view’ is a reference to Žižek’s (2006) book by the same name. Though my theoretical andmethodological stance differs in many respects from Žižek’s (e.g. there is no Lacan, Hegel or Marx to be found in
this thesis, nor do I endorse the dialectical understanding of the ‘parallax’) I adopted the term – as I explain later inthis chapter - to express a philosophical way of thought that is ignited by the “confrontation of two closely linked
perspectives between which no neutral common ground is possible”. (Žižek, 2006, p. 4)
40 The word affection is used here in a Deleuzian sense. Following book 2 and 3 of Spinoza’s Ethics, Deleuze
distinguishes between affect (‘affectus’) and affection (‘affectio’). Contrary to the former an affection has to be understoodas a specific form of an idea: “the trace of another body on my body” (Deleuze, 1978, 24th January, p. 5). According
to Spinoza there are three kinds of ideas: affections, notions and essences. Affections are the lowest form of this trio“…because these ideas of affection know [connaissent] things only by their effects: I feel the affection of the sun onme, the trace of the sun on me. It's the effect of the sun on my body. But the causes, that is, that which is my body,that which is the body of the sun, and the relation between these two bodies such that the one produces a particulareffect on the other rather than something else, of these things I know [sais] absolutely nothing” (Deleuze, 1978, 24th
January, p. 5). A similar difficulty to give a proper English word for affection can also be seen in the translation ofsection 13 of Leibniz’s Monadology: “…; et par consequent il faut que dans la substance simple il y ait une pluralitéd’affections et de rapports quoyqu’il n’y en ait de parties”(Leibniz, 1885, p. 608). In translation by Bennett: “Soalthough there are no parts in a simple substance, there must be a plurality of states and of relationships” (Leibniz,
2004). Deleuze reformulates: “And even when the monad will be the subject without parts, predicates will continue
to be “affections and relations”, at least in the lexicon of the Monadology” (Deleuze, 1993).
41 “In this particular case, the Umwelt is reduced to only three carriers of significance or Merkmalträger : (1) the odor of
the butyric acid contained in the sweat of all mammals; (2) the temperature of thirty-seven degrees corresponding tothat of the blood of mammals; (3) the typology of skin characteristic of mammals, generally having hair and being
supplied with blood vessels”. (Agamben, 2004, p. 46)—22—

comes before, that is to say an a priori which is a relational constellation or a landscape which
attunes the affector and the affectee in such a way that there is a space where they can meetand become what they are (e.g., only within a complex network of organs, words,
laboratory instruments, etc., the microbe and the microbes researcher can arise as such: asa microbe and a researcher).
That there is such a before that allows the affect to emerge is both a very obvious
and a very counterintuitive idea. In twentieth century philosophy it has been pointed out
over and again that feeling, speaking, writing or doing research is never immediate – every
sensation, utterance, letter or research paper has to traverse a ‘before’ (an ‘a priori’) before
it comes into being. Yet, because this before of every affection is so close to our skin (or,sometimes because it simply is our skin) it is easy to overlook it. Moreover, the argumentof the before has often been misconstrued as a relativist assertion (Latour, 2002) which
corrupts the pureness of the observation, the truthfulness of the feeling, the reality of thefact, etc. But how can one corrupt something – direct sensations, an original or mentalese
language of thought, etc. – that would not have existed without this ‘corruption’? There isno pure input which precedes the before. Only in a so called before something can emerge.
It is important to underline that the before does not mediate an immediate, but that it is amediation without original input. Retracing the paths traversed by such mediations without
an immediate origin has been the endeavour of many thinkers in different fields. Just to
give a flavour of the vast range of fields which have been covered one could think of theutterance of speech (in On Grammatology, 1997, Derrida famously debunked the fallacy
that so-called direct speech is more immediate, pure, natural and original than written
language), the experience of one’s self (Ricoeur, 2008, p. 143, argued that selfunderstanding is never an ‘‘immediate intuition of the I’’ as it always involves mediation
by a ‘‘long detour through objectification, making reflection an interminable Odyssey’’)and the production of scientific knowledge (Latour, 1999, became famous for his
ethnological studies wherein he opened the black box of scientific mediators and showedthat scientific knowledge, however real and effective it might be, is never pure scientificobservation: no microbe without microscope).
the affection ofprobable ratio

Since the seventeenth century affections have emerged that traverse a before of probableratio. For example, however different they may be in many respects, both the judge who
has to decide whether the suspect is guilty or innocent and the spam filter that has tocategorize an incoming mail into either the spam or the inbox folder, traverse this beforeof probable ratio. Probable ratio is the element that both the judge and the spam filter—23—

traverse before they are affected by what something is – for the is (e.g. ‘the suspect is
guilty’), which is opened up by this affection, is an affection of probable ratio.
what is the‘what is’ofprobableratio?

What is this probable ratio they traverse? In asking this question the difficulty is how to
ask it. If it is indeed true that in law and data science the question of ‘what is?’ traverses
the before of probable ratio, we have to ask ourselves if this is the case in philosophy as
well. When we ask philosophically after the ‘what is’ of probable ratio in law and data
science, we cannot simply assume that we ourselves do not traverse this probable ratio
when thinking philosophically. Or, to reformulate the question: is the ‘what is’ ofphilosophy different from the ‘what is’ of law and data science? Does it also share in theaffection of reckoning and Janus-faced ratio? Because if this would be the case thequestion would coincide with what is questioned. To be affected by philosophicalthought is to ask for the ‘what is?’ of thinking. If one, as I did in the beginning of thischapter, posits that thought is a way of being affected, one is inclined to answer thisquestion affirmatively. After all, one could in fact hold that the whole notion of the word
‘affection’ is exemplary of a reckoning and Janus-faced ratio. Meillassoux (see above,footnote 32) calls this correlationism:“Correlationism consists in disqualifying the claim that it is possible to consider
the realms of subjectivity and objectivity independently of one another. Not only
does it become necessary to insist that we never grasp an object ‘in itself’, inisolation from its relation to the subject, but it also becomes necessary tomaintain that we can never grasp a subject that would not always-already be
related to an object” (Meillassoux, 2008, p. 5)
Even though philosophical thinking might not be affected by probable ratio, it most
likely is affected by ratio as such: “Thinking appears as rationality”. 42 Heidegger writes:“The principium rationis as thought by Leibniz not only determines, by the sort of demand
it makes, modern cognition in general, but it permeates in a decisive manner that thinking
known as the thinking of thinkers – philosophy” 43 (Heidegger, 1991, p. 43).

a manifesto of
methodHow to proceed? The method proposed in this thesis is one of utmost indirectness. The
problem of circularity should not be belittled – but it is possible to pay attention to themediators (such as words) that guide us when we think about thinking. Let me (clearly
not everybody will agree with this manifesto of method, so it is time to abandon the all

42 “Das Denken erscheint als das Rationale”. (GA8, Heidegger, 2002, p. 213)
43 “Das von Leibniz gedachte principium rationis bestimmt in der Art seines Anspruches das neuzeitliche Vorstellennicht nur im allgemeinen, sondern es durchstimmt in entscheidender Weise jenes Denken, das wir als Denken der
Denker kennen, die Philosophie”. (Heidegger, 1957, pp. 80-1)—24—encompassing we, the colloquial you and the impersonal one by which I have tried to lure
the reader into this text) declare the way in which I will try to proceed.
the before(1)

To think the before – but how?

Where to look for the probable grounds as the before? At the beginning of thisparagraph I wrote: “…to pay attention to the mediators (such as words) that guide us when we think
about thinking”. Yet, it is clear that mediators are not only words but the whole of therelational constellation that precedes thought – which consists out of a heterogeneous
assemblage of actants (cf. Latour, 2005) such as my body, its technological prostheses(e.g. a pencil, a typewriter and an external hard drive: Kittler, 1999), the words (which aretechnological prostheses as well: Stiegler, 1998) in which I speak and the landscapes andarchitectures in which I move. Should one follow the Heidegger-Derrida ‘method’ ofretracing the words through which one thinks? Or maybe the ethnographic-semiotic‘method’ of Actor-Network theoreticians like Latour (for instance, retracing the very
particular network of scientists, microscopes, pipettes and coffee machines which allow a
microbe to emerge)? Before I can attempt to answer this question I will first need to havea look at the other methodological imperatives.
breaks andinterruptions(2)

Looking for breaks and interruptions in the before of thought.

The relational constellation that precedes thought, i.e. the before, evolves over time, bothwithin and between languages, within and between practices. The fact that the before ofthought is neither static nor eternal allows me to create a certain distance to my thought.
Although similarities and differences which emerge in evolutions and translations do notoffer a way out of the circularity of thinking about thinking, they nevertheless create astance wherein the thinker does not necessarily have to coincide completely with what isthought. In the in-between of a difference there can be a reason to start to think
differently. The ‘before’ or ‘always-already’ cannot be avoided, but the way in which it
moves us can become more noticeable.

a parallax
between twopractices(3)

Practices: going hence-and-forth between the parallax of law and data science.

Though I can never be outside the before of the questioning of what is, in going henceand-forth between different ways of thinking I could become affected by the difference
and similarities between them. As Jacques Rancière said in an interview: “Philosopy isalways a discourse between something and something” 44 . Such a philosophical way ofthought which proceeds by “putting two incompatible phenomena on the same level”, iswhat Žižek baptized the “parallax view”:

44“D'une manière générale je ne pense pas que la philosophie soit une philosophie de quelque chose. La philosophie
est toujours un discours entre quelque chose et quelque chose […] La philosophie est pour moi un travail sur
l'homonymie.” (Blouin, During, & Zabunyan, 2005, p. 142)—25—

“…the illusion of being able to use the same language for phenomena which aremutually untranslatable and can be grasped only in a kind of parallax view,
constantly shifting perspective between two points between which no synthesis
or mediation is possible. Thus there is no rapport between the two levels, noshared space—although they are closely connected, even identical in a way, they
are, as it were, on the opposed sides of a Moebius strip. […] although they arelinked, they are two sides of the same phenomenon which, precisely as two sides
can never meet”. (Žižek, 2006, p. 4)
A parallax view is something of a paradox: it allows one to become affected by theunaffected, the unmediated. The question which follows is of course: a parallax between
what and what? Which practices, which modes of thought? In the first chapter I argued
that probable grounds have become ubiquitous – not only the judge or the statistician
rely on probable grounds, but everyone of us while being ‘intuitive statisticians’(Brunswik, 1943; Gigerenzer, 2000). Is this true? Are you an intuitive statistician when
you look into the eyes of your beloved or mourn for the loss of a relative? Is the ‘we’ ofthinking on probable grounds restricted in some way, for example, does is only concern
Western thought or technological-scientific actions? Or, to pose a question that might beeven more difficult, are the probable grounds which direct thought the same in different
practices? For instance, Jonathan Cohen (1977) famously argued, that probable grounds
in legal reasoning (“Baconian probability”) are fundamentally different from those incalculative (or as Cohen calls it: “Pascalian”) probability. To put it in more abstract terms:
which ‘unit’ or ‘system’ should one study? In this thesis I will try to think between law
and data science: both practices are affected by probable ratio in a way that is at the sametime both very similar and yet abysmally different. I do not claim that this is the only or
best way to question what probable ratio is, there are many roads that lead to Rome, but
given my own background thinking through these two practices suits me.
looking for a
before that
affects mythought(4)

To think is to reshape the before of thought – the Deleuzian imperative ofcreation of new philosophical concepts.
After three methodological imperatives I still do not have a clear answer how and where
to begin. The first methodological imperative was to look for the before – but which before
is relevant? The second demanded to look for the breaks and interruptions of the before –but how to know where to encounter them? And while I declared in the third imperativethat I would look at law and data science, the choice for these two particular practices
might seem rather arbitrary. So, how to begin? I answer this question in a pragmatic way:—26—

I do not look for the before ‘in itself’ 45 , but for a before that affects the way I think andwhich opens up possibilities for new affections. I cannot define this ‘before’ beforehand,neither predict where the breaks will be, nor say beforehand which modes of thought areencompassed in the ‘we’ of probable grounds: if I would know that this whole exercise
a beginningwithout
grounds

would be superfluous. Without any grounds, not even probable grounds, to guarantee its
outcome this is an uncertain journey. Thus my beginning is not very well grounded: I
simply start by thinking the words ‘before’ and ‘probable grounds’ and I can only hopethat by closely following the mediations which make me think, in particular theinterruptions and breaks which I might encounter, the trajectory which I traverse could
affect the way I think and open up possibilities for new affections. Yet, as became clear inchapter 1, the words surrounding both ratio in general and probable ratio in particular(cause, reason, ground, possibility, correspondence of subject-object, reckoning, etc.) are
philosophical slippery slopes. This is a promising sign for me who has set myself the task
to have a parallax view (2006) at probable reason in order to find new words or concepts(Deleuze & Guattari, 2003) that will allow for new philosophical affections and relations.

45 Of course there is no ‘before in itself’: the ‘before’ is never ‘just’ out there. In the same way as the ‘microbe’

emerges as an ‘artefact’ or ‘invention’ from microscopes, scientists, words and pipettes, the attempt to retrace the‘before’ of probable ratio will also necessarily traverse its own ‘before’. Still this does not imply that it is my
subjective creation (and neither is the microbe a mere figment of imagination), because this ‘before’ is not the
subjective me who thinks, but the whole which is traversed and which steers my thoughts. The before is neither
objective nor subjective, but an affection.

—27—

chapter 4

A PRELUDE TO THE PARALLAX: BEFORE PROBABLE GROUNDS

In the first chapter I followed Hacking’s thesis (1975) that probability in themodern understanding of the word, that is Janus-faced (aleatoryepistemological) and reckoning, only emerged in the second half of theseventeenth century. However, the word as such emerged at least 46 a century earlier when
probabilism

Jesuits 47 developed the so-called method of ‘probabilism’ or ‘probabilistic casuistry’(Byrne, 1968) to decide in morally equivocal matters: it is “a form of moral reasoning
aimed at interpreting and solving the practical issues of every-day life posed by theunprecedented changes of the early modern era” (Maryks, 2008, p. 3).
“What is to be done when authorities, especially the Fathers of the Church, arefound to disagree? The problem became pressing in the Renaissance as more andmore texts were discovered and more and more interpretations of existing texts
were invented. […] Probabilism says that one may follow some probable opinion
or other, even a less probable opinion. The word ‘probable’ here does not meanwell supported by evidence. It means supported by testimony and the writ ofauthority. When a doctrine is disputed, and you are in doubt how to act, you may,according to the probabilists, follow a course of action that is recommended bysome authority, even when weightier authorities counsel the opposite course ofaction. […], from the point of view of the Jansenists, the probabilists would firstof all decide on a course of action for its social and moral expediency. Then theywould find some old text that could be interpreted as approval of that course ofaction”. (Hacking, 1975, p. 24)
As Hacking (1975, pp. 18-30) shows, the relationship between this kind of moral
probabilism and modern probability is far from evident. The fact that Pascal, a Jansenist

46 Garber & Zabell (1979) argue that the word ‘probability’ has been around much longer and point, e.g., to the useof ‘probabilis’ in Cicero. In a similar vein Franklin (2001, p. 103-4) argues that the seventeenth century emergence ofmathematical probability is an offshoot of a much older uninterrupted tradition of unquantified probability whichreaches from antiquity till our present day, and he stresses that even in ancient Greek two words were in use that wetoday often (anachronistically) translate as ‘probability’: πιθανόν (pithanon) and εἰκός (eikos). Pithanon is a word that wasparticularly common in rhetorics, meaning something like ‘persuasive’, ‘plausible’ or ‘convincing’. Eikos (from ἔοικα =‘to resemble’) was normally used in the sense of ‘like’ or ‘likely’, but Plato (see also above, footnote 7) used it in thespecific sense of ‘like truth, but not truth’. Aristotle’s Poetics (1995, 1460a, chapter 25, p. 134-5, lines 11-2) contains aline of advise to poets that nicely illustrates the use of both words: “What is convincing though impossible (ἀδύνατα
εἰκότα, adunata eikota) should always be preferred to what is possible but unconvincing (δυνατὰ ἀπίθανα, dunata
apithana).”Though such accounts (Franklin, 2001; Garber & Zabell, 1979) are very enlightening with respect to the prehistoryof probability, and even show that in some particular cases such proto-probability was associated with a rudimentaryfrequentist understanding (‘when things happen often they are more probable’), they do not challenge the fact that
Janus-faced and reckoning probability only arose in the second half of the seventeenth century.

—28—and one of the main founders of modern probability, was an extremely fierce opponentof Jesuit probabilism, exemplifies this troubled relation. Probabilism never recoveredfrom Pascal’s devastating attack in his Provincial Letters (1962) and it became forever“associated with hypocritical minds and the alleged backwardness of the CounterReformation” (Maryks, 2008, p. 3). Nevertheless the word ‘probable’ in the sense of‘approvable’, ‘worthy of approval’ or ‘trustworthy’ 48 still lingered on for a few centuries:“A couple of centuries ago one readily spoke of a ‘probable doctor’, apparently
meaning a medical man who could be trusted. We no longer speak that way”.
(Hacking, 1975, p. 18)
The reason why probabilist casuistry seems so backwards from a contemporary
perspective is precisely because it lacks the two major characteristics of modern
probability: it does not base itself on clear-cut calculations, which makes it appear as lax,
permissive or even opportunist, and instead of being equivocally objective-subjective it
relies fully on the approval by an authoritative opinion, which surrounds it with a very
medieval aura. And yet probabilism and modern probability are not unrelated.
the book of
Nature:from Jesuitprobabilism tomodernprobability

As Hacking (1975) convincingly argues, it was the late Renaissance understanding of
Nature as a book 49 which allowed for the large leap from probabilism into modern
probability.
“Nature is the written word, the writ of the Author of Nature. Signs haveprobability because they come from this ultimate authority”. (Hacking, 1975, p.
30)
This new understanding of Nature led to the slow dissolution 50 of the medieval
distinction between the demonstrative high sciences, “such as optics, astronomy, andmechanics” (Hacking, 1975, p. 35), where effects could be demonstrated from firstcauses, and low sciences such as medicine, astrology or alchemy, where one has to rely on
the indirect evidence from signs (effects) to diagnose an underlying state (hypotheticalfirst causes). The understanding of the world as a text written by God and the need tofind the right way of reading it, made the notion of the sign ubiquitous and respectable.
For modern probabilists the signs which are to be found in the ‘text’ of nature provide
evidence and testimony that overrules every other authoritative opinion: probability is no

47 Though originally developed by a Dominican theologian, Bartolomé de Medina (1527–1580), probabilist casuistrybecame particularly popular among Jesuits.
48 Probabilis in classical Latin meant, among other things, ‘having the appearance of truth’ or ‘seeming likely’ and wasthus closer to the modern colloquial, non-mathematical sense of ‘probable’ (Garber & Zabell, 1979, p. 45).
49 Galileo (2008, p. 183) famously writes in The Assayer (1623): “Philosophy is written in this all-encompassing bookthat is constantly open before our eyes, that is the universe; but it cannot be understood unless one first learns tounderstand the language and knows the characters in which it is written. It is written in mathematical language, […]”.

—29—

longer an attribute of persons and their opinions but of signs which can be found in
Nature, that is the written opinion of the Creator. In 1686 Leibniz underlines in
Recommandation pour instituer la science générale that he does not speak of probability as
understood by the Casuists, which relies on the reputation of scholars, but of aprobability that can also be called verisimilitude (vraisemblance) because it draws upon thenature of things to the extent (proportion) that they are known:“Je ne parle pas ici de cette probabilité des Casuistes, qui est fondée sur lenombre et sur la réputation des Docteurs, mais de celle qui se tire de la naturedes choses à proportion de ce qu’on en connaît, et qu’on peut appeller lavraisemblance”. (1890, p. 167; 1999, p. 707)
Sullerot (2006), who gives a nice overview of the ideas concerning probability in the New
Essays (Leibniz, 1882, 1996), proposes to call this approach the naturalisation or realisationof the probability: it is nature and the things (res) themselves that give testimony of theirnature through signs which can be understood in terms of probability. Nevertheless,probability in Leibniz is – as it is in the writings of other seventeenth century probabilists– not fully naturalised but always Janus-faced. Even though the foundation of probability“is always grounded in likelihood or in conformity to truth”, this “resemblance between
the probable and the true comes either from the thing itself or from ‘something
extraneous’ [‘conformity with something we know or on the testimony of those whoknow it’, KdV]”. (Leibniz, 1996, book IV, chapter 15, p. 457)
So far I looked at two phenomena in this chapter that preceded the emergence ofJanus-faced and reckoning probable grounds: old-school Jesuit probabilism and a shift
towards a calculative textualization of nature. However, at least one crucial ‘ingredient’
proof

still seems to be missing: proof. Hacking (1986) opens his British Academy lecture of1973 by stating:“Leibniz knew what proof is. Descartes did not. […] Leibniz’s concept of proof
is almost the same as ours. It did not exist about his time. […] Leibniz was surethat mathematical truth is constituted by proof while Descartes thought thattruth conditions have nothing to do with demonstration. […] The modern reader
tends to equate intuition and deduction with axiom and theorem proved, but thisis to see matters in a Leibnizian mould. The Cartesian distinction is chiefly
psychological. One man might require deduction where another would intuit. In
either case the end product is perception of truth”. (p. 47 and 51)

50 Hacking (1975, p. 35 ff.) underlines that he merely describes this dissolution in order to clarify the origin of theconcept of ‘inductive evidence’, and not the origin of the highly complex and equivocal concept of the ‘experimental
method’.

—30—

For Descartes there can be direct access of truth and certainty by intuition, whereas forLeibniz truth and certainty can only be reached indirectly – through proof (which often
will turn out to be a ‘Baroque’, Deleuze, 1993, chain of proof-upon-proof). From proof
to probability it is only a little step 51 : “finite proofs and probability” are “coarse andinadequate” reflections of “the very nature of truth, the infinite proof” (Hacking, 1986, p.
59). As I will argue in the following chapter the emergence of this concept of proof might
have emerged in the context of legal thought.
grounds
after allHowever, before going to the next chapter, it is time to pause for a moment andlook at my own style of reasoning: in this chapter I explored the state of affairs before
there was anything as ‘probable grounds’. And in the next chapter, on law and probablegrounds, the before involves the role of law in the shaping of modern probability as well as
the Parmenidian ‘principle of reason’ avant la lettre. While I declared the death of theprinciple of sufficient reason in chapter one, and argued in the previous chapter that myown approach is not very well grounded – at least not in the classical sense – but only
traverses ‘mediation’ without immediate origin, here I am: unearthing origins, pointing toproto-forms of probability, contaminated by the bewilderment of so many other scholars(e.g. Franklin, 2001; Garber & Zabell, 1979) about the fact that probability seemingly
appeared ‘out of nothing’ (“But that is impossible – nothing comes out of nothing!”, say
the little Parmenides and Leibniz within me). In fact, there is a curious contrast between
the style of this chapter, presenting grounds (probabilism, a textualization of nature, etc.)of the principle of probable ground, and the fact that this chapter describes a time before
the principle of ground (both the sufficient and its supplementary, probabilistic, variety).
Maybe it is therefore better to say that probabilism, the calculative textualization and thelegal setting (see infra, chapter 5) allowed for the emergence of an affection that makes them
now appear to me as grounds.

51 The words “proof” and “probability” are etymologically closely related through the Latin verb “probare” (to test,

prove worthy).

—31—

chapter 5

THE PROBABLE GROUNDS OF LAW – SOLID/UNCERTAIN ENCOUNTERS OF BEING
AND THOUGHT

groundsL

aw is the discipline of grounds. For instance, most German case law begins
by a heading called “grounds” (Gründe or Entscheidungsgründe), in Dutch
judgments the legal arguments (middelen) are enumerated and followed bywhether they are grounded or should be rejected, a format which is also common in
France (where they speak of moyen 52 ), and also the verdicts in other Western societies 53
abound with ‘reasons’ and ‘grounds’. A legal verdict without any factual and legal
grounding to justify it does not deserve its name. Even during Stalinist show trials
allegations were invented to create the illusion of grounded judgments, i.e. of law. A judge
who does not even pretend to ground his or her decisions, openly declaring the verdict tobe fully ungrounded, belongs to the realm of the absurd. The chains of factual and legal
grounds that form the foundation of a legal decision create the expectancy, or at least thehope, that it is correct. Thus it will not come as a surprise that Leibniz’s principium rationis
and the law are not unrelated. The only question is: how are they related? Was law alreadya discipline of grounds before the formulation of the principle of reason? Or is it as
Berkowitz (2005) argues only after Leibniz’s principium that law developed its obsession
with reasons and grounds?
“[…] Leibniz’s metaphysics, and specifically his embrace of the principle ofsufficient reason (nihil est sine ratione), shifted the inquiry into law from a knowingof law itself to a knowing of the reasons, grounds, and justifications for law. Law
comes to be subordinate to its justification or rationalizations; in other words,
law is emptied of any independent meaning and authority”. (p. 7)
Notwithstanding the question when law became the discipline of grounds, it is clear that
uncertainty

this is not the only aspect that characterizes it: law is also the discipline of uncertainty.
While the same might go for other areas of life, in law it is particularly evident that a judge
never has direct access to the matters under dispute but always has to rely on testimonies
and other kinds of proof. Judgments that turn out to be incorrect, especially in criminalcases such as Lucia de B. (2010), where an innocent person is presumably wrongly
convicted, cause public outrage 54 . Yet, in law there is always a certain amount of

52 As Latour (2010) shows the word moyen ( which can be translated as ‘legal mean’, ‘ground’, ‘argument’ or ‘reason’)is crucial in the creation of legal arguments.
53 I have limited myself to Western legal systems. For some seminal descriptions of non-Western legal systems, seee.g.: Gluckman, 1965; Malinowski, 1926; Moore, 2005.
54 See above, footnote 2, on the case of Lucia de B. Hoge Raad (Netherlands Supreme Court), LJN: BD4153 (Lucia deB.), 11 March 2010; Hof Arnhem, (Court of Arnhem), LJN: BM0876, (Lucia de B.), 14 April 2010—32—

uncertainty. No legal system requires the judge to be fully certain, but ‘merely’ toestablish, e.g., a ‘conviction beyond reasonable doubt’. Hence, Van Asperen de Boer
writes about the use of statistical evidence:“How did one dare to use a [statistical] number to convict somebody? Is it notpossible that something very improbable could take place nevertheless?
However, one has to realize that decision-making under uncertainty is inherent tocriminal procedure. You never know for sure. It has to be ‘beyond reasonable
doubt’ that the criminal offence is committed by the suspect. But when thisuncertainty is expressed in a number, many people become very alarmed”. (Van
Asperen de Boer, 2007, p. 66, transl. mine)
What is exemplified by a case like Lucia de B. is that in law, contrary to e.g., data science,probable ratio can never be merely a probabilistic proportion, but always also has to be aprobable ground.
proof

In law the way to overcome uncertainty and generate solid grounds is by meansof proof. This might sound counterintuitive as proof itself is often inconclusive or evenfully lacking. However, this is not an insurmountable barrier as long as one can rely on
presumptions and add up several pieces of partial proof (such as ‘half proof’) to create
sufficient legal grounds. Such methods were already conceived by the Romans (Daston,
1988; Franklin, 1991, 2001; Hacking, 1975) and became particularly advanced after thetwelfth century (Daston, 1988, p. 42 ff). Leibniz, a lawyer himself, was also very wellaware of this:“When jurists discuss proofs, presumptions, conjectures, and evidence, they havea great many good things to say on the subject and go into considerable detail.
They begin with common knowledge, where there is no need for proof. They deal
next with complete proofs, or what pass for them: judgments are delivered on thestrength of these, at least in civil actions. In some places they are more cautious
in criminal actions; in these there is nothing wrong with insisting on more-than-full
proofs, and above all for the so-called corpus delicti if it is that sort of case. […]Then there are presumptions, which are accepted provisionally as complete proofs– that is, for as long as the contrary is not proved. There are proofs which are,strictly speaking, more than half full; a person who founds his case on such a proof
is allowed to take an oath to make up its deficiency (juramentum suppletorium). And
there are others that are less than half full; with these, on the contrary, the oath isadministered to the one who denies the charge, to clear him (juramentum
purgationis). Apart from these, there are many degrees of conjecture and ofevidence. And in criminal proceedings, in particular, there is evidence (ad—33—torturam) for applying torture […]. The entire form of judicial procedures is, infact, nothing but a kind of logic, applied to legal questions. (Leibniz, 1996, pp
464-5; also quoted and discussed in: Franklin, 1991, p. 133; Roinila, 2007, p. 155;
Sylla, 1998, p. 49)
Thus the argument that I present in this chapter is that law, with its inherent uncertainty,
its need for grounds and its rudimentary methods of quantifying inconclusive evidence,
the role of law inthe emergenceof probability: awell-documented
factallowed for the unlikely marriage between probabilistic casuistry and the calculative
textualization of nature. This is in itself not a very novel or original idea: the role of law 55
in the emergence of seventeenth century probability is almost impossible to overlook(Daston, 1988; Franklin, 1991, 2001; Hacking, 1975). Even when writing aboutprobability in seemingly a-legal contexts, such as chance games, probability’s role isalways to guarantee a just or fair game setup or division of the stakes. For instance,
Huygens speaks in his Rekeningh in Spelen van Geluck 56 (1660) of ‘fair play’ (‘rechtmatighspel’, Daston, 1988) and Leibniz (1999, p. 92-101) opens De incerti aestimatione (September
1678) by writing that a game is fair (justus) when hope and fear have the same ratio 57 .

a new dimension:
not just the
emergence of
probability orof theprincipium
rationis, but of
probablegrounds

As I do neither want to simply repeat or refine this well-established picture of law (inparticular its way of coping with uncertainty through proof) as the facilitator of theemergence of probability, nor merely elaborate on the role of legal reasoning (the role offactual and legal grounds) in the constitution of Leibniz’s principium rationis, I try to bringthese two lines of research together. What I add to the existing research on either
probability or the principium rationis, is an attempt to retrace the relation between law andprobable grounds, i.e. the probabilistic or insufficient ratios which supplement Leibniz’s
principium rationis sufficientis. I hope to show that law did not just contribute, on the one
hand, to the emergence of probability because it had developed ways to quantify
uncertainty and cope with situations where only inconclusive proof was available, and on
the other hand to the principle of ground because it is a discipline of grounding, but thatlaw gave raise to the Janus-faced nature which characterizes both insufficient andsufficient ratios.
First I will try to substantiate this claim by taking a closer look at the legal andJanus-faced (a coincidence of being and thought) nature of Parmenides’ ‘principle ofreason’-avant la lettre. Secondly I will try to retrace a similar trajectory in the constitution

55 Not only the legal way of copying with evidence helped the shaping of probabilistic calculus, but also the modular

logic which plays a role in the fair execution of conditional rights. Leibniz described the latter in his early works De
conditionibus (Leibniz, 1930, pp. 99-15, originally published 1665) and Specimina Juris, (1930, pp. 367-430, originallypublished 1667-69). See also: Thiercelin, 2008.
56 First appeared in translation as De ratiociniis in ludo aleae, 1657. See further above, chapter 1.
57 “Justus ludus est si spes et metus utrinque eadem ratio sit”, Leibniz, 1999, p. 92.

—34—

of Leibniz’s principium rationis sufficientis and its supplementary principle of insufficientreason.

Parmenides

Twenty five centuries separate us from Parmenides – the man who is considered to be
one of the earliest and most important fathers of Western thought, and in particular ofphilosophy, logic and science. Henceforth the little of his writings that has survived – acollection of fragments, in total approximately 160 lines, of a didactic poem (Burnet,
1920, pp. 126-45; Diels & Kranz, 1959, pp. 227-45) – belongs probably to the mostanalyzed texts of the world. There are at least two famous parts which cannot be left
unmentioned when writing about the prehistory of the principium rationis.. Firstly (see also
above, footnote 35) there is fragment 8, in which the ex nihilo nihil fit, which is often

Parmenides’
principle ofground?

understood as a rudimentary version of the principle of reason 58 , can be found:“I shall not permit you to say or to think that it grew from what-is-not, for it is
not to be said or thought that it is not. What necessity could have impelled it togrow later rather than sooner, if it began from nothing?” 59 (Parmenides of Elea,
1996, fragment 8, line 7-10)
and“[…]: either it is or it is not.” 60 (Parmenides of Elea, 1996, fragment 8, line 16)

Parmenides’
adequation ofthought andbeing

Secondly, there is fragment 3, which contains the adequation of thought and being:“for it is the same thing that can be thought and that can be” 61 (Burnet, 1920, p.
129, fragment 3)
From the contemporary perspective both themes, the ‘something-cannot-come-out-ofnothing’ and the adaequatio rei et intellectus, are of course easily understood as precursors ofmodern rationality 62 . While the aforementioned fragments might sound very familiar andmodern to the contemporary reader, the poem of which they are part has nothing incommon with the style of modern scholarship. Not only because of the curious form of a

58 It is important to underline that it is only in retrospect that Parmenides’ writings are understood as containing arudimentary version of the principle of reason. Parmenides does not speak of anything even vaguely related to words
like ‘ratio’, ‘ground’, or ‘reason’, nor does he formulate any ‘principles’.
59 “οὔτ΄ ἐκ μὴ ἐόντος ἐάσσωφάσθαι σ΄ οὐδὲ νοεῖν· οὐ γὰρ φατὸν οὐδὲ νοητόν
ἔστιν ὅπως οὐκ ἔστι. Τί δ΄ ἄν μιν καὶ χρέος ὦρσεν[10] ὕστερον ἢ πρόσθεν, τοῦ μηδενὸς ἀρξάμενον, φῦν;”, Diels & Kranz, 1959, p. 235-6, fragment 8, lines 7-10.
60 “ἔστιν ἢ οὐκ ἔστιν”, Diels & Kranz, 1959, p. 236, fragment 8, line 16.
61 “. . . τό γάρ αυτό νοεϊν εστίν τε και είναι.”, Diels & Kranz, 1959, p. 231, fragment 3.
62 See e.g Popper (2002a, p. 549), who turns Parmenides in a critical-rationalist avant la lettre: “He [Parmenides] is arevolutionary thinker, […] his revolution consisted, partly, in trying to prove a doctrine of immobility or invarianceof reality, the non-existence of change. Some of his other revolutionary innovations were: his discovery of the
distinction between appearance and the reality behind the appearances; and his onslaught upon common sense,
empiricism, and traditional belief which he thought was based upon mere convention (name-giving) rather thantruth: upon doxa, the mere opinion of the mortals. In all of this he had, of course, predecessors, but he went far
beyond them”.

—35—‘didactic poem’ – neither fully poetic, nor truly abstract (Heidegger, 1992, p. 2-3) – but
also because the quoted lines are part of a revelation given to Parmenides by a goddess toa goddess

whom he has travelled in a chariot after he has entered through “aetherial gates”(fragment 1, line 14) the “roads of day and night” (fragment 1, line 11). This
‘mythological’ side to Parmenides’ writings is a bit of an embarrassment to the modern
reader and many interpreters prefer to ignore or understand it as a simple allegory(Spinner, 1977, p. 96 ff). Who is this goddess and what is her role within the text?
Heidegger calls her the goddess of truth (1992, p. 5), but it is more likely 63 that she is

Dikē

Dikē, the goddess of law and truth, who is named twice in Parmenides’ fragments: first as
the Dikē polupoinos 64 (“avenging Dikē”, fragment 1, line 14) who keeps the keys to thegates of day and night, and secondly it says that Dikē is the one who “does not loosen her
shackles so as to allow it to come-to-be or to perish, but holds it fast” (Parmenides of Elea, 1996,
fragment 8, lines 14-5) and thus guarantees the ex nihilo nihil fit. Moreover, the goddess
also says that it was not ill chance (moira), but themis and dikē 65 (fragment 1, line 28) thatbrought Parmenides on this path.

a perplexity:
why are there
so many legal
terms inParmenides?

Here we might be struck by a perplexity: why do the founding fragments of all Western
philosophy, logic and science abound with what seem to be (at least from the modern
perspective) legal terminology? What are the roles of the goddess Dikē,, and the words
themis 66 and dikē 67 a in this text? Let’s begin by the question whether Dikē is a legal
goddess. Translating Dikē simply with Justice does not seem to be very helpful 68 – notpaying any attention to the particularities of the Greek notion Dikē might lead one astray
into a swamp of anachronisms – completely ignoring 69 the fact that this goddess stands in alegal context seems to be too radical as well. A rare exception to this tendency to fully
ignore the legal connotations of Dikē is presented, with the proverbial deutsche
Gründlichkeit (‘Teutonic thoroughness’), by Spinner (1977) who argues that in its

63 See also Popper, 2002a, pp. 545-7.
64 “Δίκη πολύποινος”
65 “θέμις τε δίκη”

66 Themis a very particular word, meaning something like ‘approved behaviour’ or “law”, and often anachronisticallytranslated as ‘justice’ or ‘order’; see e.g. Gagarin, 1989.

67 Dikē is another word that has no clear equivalent in English, originally meaning “ruling” or “settlement”, i.e. “whatone gets as the result of a judgment”, later more broadly “plea, case, trial, court” or even “legal process”, and finallybecoming in Heraclitus and Parmenides “a cosmic force” of unity which is implied in the legal process and its
outcome; Gagarin, 1974, p. 187-8.
68 “Just as impossible[…] is an interpretation of δίκη on the basis of the modern concept of justice and the Roman
iustitia”, Heidegger, 1992, p. 96.
69 For instance, Popper (2002a, p. 12) describes Dikē as the “divine guarantor of truth”. Heidegger (1992, p. 92 and96) is slightly more subtle, but also prefers to disconnect Dikē from the legal context and understand it through thewords deiknumi (‘demonstrate’) and aletheia (‘truth’, ‘unconcealedness’):“ […] δίκη (which for the Greeks immediately resonates with δεικνυμι, to demonstrate, to indicate, and δίκειν, tothrust)” and “Δίκη, understood as the order which ordains, i.e., assigns, to humanity its relations and comportment,takes its essence from a relation to ἀλήθεια, […]”.

—36—

Spinner: a legal
reading of
Parmenides

Parmenidean articulation the ‘principle of sufficient reason’ is in the first place a legal, andnot a logical, principle:“The principle of sufficient ground is according to its nature not a logicalprinciple of epistemology, but a cosmic principle of law with a translogicalcharacter” 70 (p. 109)
In order to explain how Spinner reaches this surprising conclusion, I have to clarify theoften heard position which he criticizes: that Parmenides is a precursor of Leibniz who
almost says that everything has a ground but who simply fails to make the final step ofarticulating the notion of ‘ground’ because he formulates his ‘principle’ in a negative way(ex nihilo nihil fit). What makes Spinner’s reading of Parmenides thought provoking is thatinstead of considering the negative formulation as arbitrary (“Saying that nothing is without
ground is basically the same as saying that everything has a ground”) or as a failure, he argues
that the negative formulation of the ‘principle of ground’ is of essential importance andthat this can be understood from a legal procedural perspective. In a nutshell Spinner’s
hypothesis is that Parmenides’ ex nihilo nihil fit follows from a legal way of shifting theburden of proof during a procedure: when both parties cannot produce sufficient proof,
one of them will have the advantage of a presumption while the other will have thedisadvantage of the burden of the proof, or to put it more precisely – the burden of anotherwise irresolvable uncertainty which implies losing the case.
“In Parmenides the principle of sufficient grounding comes into force, when the‘ex nihilo nihil
fit’understoodas a legalprocedural
principle: the‘groundingavoidance
principle’

logical possibility for grounding has ended” 71 (p. 129)
One could call this a Begründungs-Vermeidungsprinzip (‘grounding-avoidance principle’, p.
129): a deadlock (Patt-Situation, p. 129) is avoided or circumvented by assuming that thecontrary of what cannot be proved must be true. After all, independent of the amount of
uncertainty, in law a case has to be decided. Crucial in Spinner’s argument 72 are theaforementioned lines 9-15 of fragment 8:

70 “Das Prinzip der zureichenden Begründung ist seiner Natur nach kein logisches Erkenntnisprinzip, sondern ein
kosmisches Rechtsprinzip translogischen Charakters”.
71 “Das Prinzip der zureichenden Begründung tritt bei Parmenides in Aktion, wenn die logische
Begründungsmöglichkeit endet”.
72 “This is indeed an astonishing line of argumentation: From the lacking necessity of the contrary, the inevitablecorrectness of [Parmenides’] own doctrine is concluded. Because there is no knowable ground that says that it isotherwise, it necessarily follows that the state of affairs with regard to Being has to be as stated. Lack of necessity of
the contrary is a sufficient ground for the correctness of the opposite position of the alternative grounds. It is like
this, because there is no compelling reason that it is not like this. What Parmenides staged here, with extremely
skillful direction of the discussion, and by making use of the principle of sufficient ground, is not an argument ofjustification (in the sense of a positive proof of truth) in favor of the proper point of view, but rather a shift in theburden of proof to the detriment of the opposite position, combined with the rigorous exploitation of this effective
shift of the problem”. (Spinner, 1977, p. 128-9, tranl. mine, original below)“Dies ist nun in der Tat eine erstaunliche Argumentation: Aus der fehlende Notwendigkeit des Gegenteils wird auf
die zwangsläufige Richtigkeit der eigenen Lehre zurückgeschlossen. Weil kein erkennbarer Grund vorliegt, daß esanders sei, muß es sich mit dem Sein notwendigerweise so verhalten, wie behauptet wird. Mangelende Notwendigkeit—37—

“What necessity could have impelled it to grow later rather than sooner, if itbegan from nothing?” (Parmenides of Elea, 1996, lines 9-10)
Spinner reads: as it can not be proved that something comes out of nothing, the burden of
proof can not be fulfilled and hence Parmenides has to conclude that the contrary is true.
“Thus it must either fully be, or be not at all” (line 11)
Henceforth it is not the stalemate which has disappeared, but Dikē requires there to be asettlement, i.e. a krisis (‘judgment’ or ‘decision’, line 15) according to dikē, whether
something is or is not:“Nor will the force of conviction ever allow anything, from what-is, to come-tobe something apart from itself; wherefore Dikē does not loosen her shackles so
as to allow it to come-to-be or to perish, but holds it fast. The decision on thesematters depends on this: either it is or it is not. (lines 12-5)
So where has Spinner’s legal reading of Parmenides brought me? Although Spinner’s
reading is problematic in many respects, mostly because of his abundant use of words
such as ‘Grund’ or ‘Patt-Stellung” that are completely alien to Parmenides’ text and era ingeneral, it is thought-provoking in at least three respects. Firstly because the legal outlook
gives a way, though not followed by Spinner himself, to read the ex nihilo nihil fit without
the need to take recourse to a language of reasons, grounds, rationality and logic. Instead
it allows one to think the ex nihilo in its negative formulation, that is, in terms of legal
uncertainty, the burden of proof, dikē, and krisis. Read in this way the line “Thus it mustthe lack of proof
constitutes thenecessity of being

either fully be, or be not at all” does not deny the existence of non-being or of a twilightzone between being and non-being, but only says that dikē cannot allow it because there
is a lack of proof in its favour. The lack of proof constitutes the necessity of being:“It is like this, because there is no compelling reason that it is not like this”.
(Spinner, 1977, p. 128)a legal thought
which does notcoincide with‘justitia’ and‘rectitudo’

Secondly, Spinner also allows one to think about the legal dimension of Parmenides
without reading it as contemporary legal ‘metaphors’ or expressions (justification, criticaljudgement, correctness, etc. – almost every word related to rationality is in some way
related from ‘justice’ and ‘right’ 73 ) to describe rational thought. Finally, Spinner helps tozugunsten der Gegenseite ist ein zureichender Grund für die Richtigkeit der anderen Seite der Grundalternative. Es
ist so, weil kein zwingender Anlaß besteht, daß es nicht so ist. Was hier von Parmenides in äußerst geschickter
Diskussionsregie mit Hilfe des Prinzips der zureichende Begründung in Wirklichkeit inszeniert worden is, ist keine
Begründungsargumentation (im Sinne eines positiven Wahrheitbeweises) zugunsten des eigenen Standpunktes,
sondern eine Verschiebung der Beweislast zulasten der Gegenposition, verbunden mit der rigorosen Ausbeutung dieser
folgenreichen Problemverschiebung”. (Spinner, 1977, p. 128-9)73 While being a tendency beginning in Roman, and maybe even ancient Greek thought (Spinner, 1977, p. 102), it is
only in the modern period (with its acme in Nietzsche’s notion of ‘Gerechtigkeit’ or justice) that juridici and veridici havefully converged. Heidegger (1992, p. 53) notes: “In the age in which the modern period finds its completion in ahistorical total state of the globe, the Roman essence of truth, veritas, appears as rectitudo and iustitia, as ‘justice’.”
Heidegger also poses that this adequation is not present as such in Parmenides notion ‘aletheia’ (‘truth’): “It seems as—38—

An adequationof thought andbeing which has
not solidified yet

see that the adequation of thought and being in Parmenides, especially when thought ofas an encounter between being and the thought of a judge under the denominator of dikē(legal settlement), does not yet have the self-evidency or the solidity of Janus-faced ratio.
It will take another twenty centuries until Leibniz formulates his principle that will bringthe encounter between thought and being under its modern and decisive Janus-faced
denominator of ‘ratio’ or ‘ground’. While it is unnecessary to repeat what I have alreadydiscussed in chapter one – how Leibniz articulated the principium rationis and how hebecame the first philosopher of probability – it is interesting to restate what I noted in the
beginning of this chapter: that Leibniz’s ratio is strongly related to the practice of law. In
a way Leibniz’s articulations of sufficient and probable ratio traverse a similar but much
more explicit path through law than Parmenides writings: there is a similar movement ofcreating an encounter between being and thought in order to create a settlement of theuncertainty that is in accordance with dikē (Parmenides) or fairness (Leibniz, e.g. ‘justus
ludus’). Of course it must also be noted that such a comparison cannot be straightforward
because seventeenth century legal reason consists out of completely different terms thanthose that made up the legal universe of ancient Greece: instead of themis, krisis and thegoddess Dikē, there are justice, jurisprudence, proof, evidence, law, reasons, grounds, andlots of calculation. Thus I certainly do not argue that Leibniz’ articulations of sufficientand probable grounds simply repeat Parmenides, but what I try to show is that there is aforgotten Eleatic and legal “inheritance” (Spinner, 1977, 130) or ‘before’ that offers words
such as Dikē or “natural Jurisprudence” 74 to think ‘probable grounds’ in a way that is not
self-evident, or even paradoxical, to the modern mind: as solid-uncertain encounters(whether as aletheia under the denominator Dikē, as Janus-faced ground construed fromif ἀλήθεια has withdrawn itself from the history of Occidental humanity. It seems as if the Roman veritas, and thetruth which evolves out of it as rectitudo and iustitia, correctness and justice, have commandeered the field of theessence of ἀλήθεια”. (p. 53)
74In a letter to Burnett, from February 1697 (Original in French in: 1887, p. 194), Leibniz call probabilistic calculus a“natural Jurisprudence” and underlines the immense importance of it – not only for law but also for other field oflife: “But practical Philosophy is founded on the true Topics or Dialectics – that is to say, on the art of estimating thedegrees of proofs, which is not yet found among the authors who are Logicians, but of which only the Jurists havegiven samples that are not to be despised and that can serve as a beginning for forming the science of proofs properfor verifying historical facts and for giving the meaning of texts. For it is the Jurists who are occupied ordinarily withthe one and the other in [legal] processes. Thus […] a natural Jurisprudence [is needed], by which the way to estimate
the degrees of proofs may be learned demonstratively. For several probable arguments joined together sometimes
make a moral certainty, and sometimes don't. There is therefore need of a sure method to be able to determine it. It
is often said, with justice, that reasons should not be counted, but weighed; however no one has yet given us thatbalance that should serve to weigh the force of reasons. This is one of the greatest defects of our Logic; we feel theeffects of it even in the most important and most serious matters of life, which concern justice, the peace and wellbeing of the State, human health, and even religion. It is almost thirty years since I made these remarks publicly, andsince that time I have done a quantity of research, to lay the foundations of such works; but a thousand distractions
have prevented me from giving final form to those Philosophical, Juridical, and Theological Elements that I had—39—

inconclusive proofs and presumptions, or as self-adjusting probabilistic ratios) of being
and thought. This brings me to the following chapter on data science: whereas in law
ratio is still both ground and proportion, in data science ratio seems to be merely thelatter 75 .

projected. If God still gives me life and health, I will make it my principal business”. (transl. from: Sylla, 1998, pp. 667, which is a slightly adjusted adaptation of Adams, 1994, pp. 198-9).
75 This shift towards ratio as merely probabilistic proportion, instead of ground and proportion, also explains why the
Bayesian-frequentist debate (as described in chapter one) between those who hold probability to express objective
frequencies (‘frequentists’) and those who argue that probabilities represent justificatory subjective degrees of belief(‘Bayesians’) is losing its edge within data science: instead of looking for a ground in either falsification through the
improbability of the data or through justificatory induction which makes a belief more probable, this division is oflittle importance for the workings of the probabilistic proportions tumbling through the negative feedback loops
created by data scientists. See for the Popper-Carnap controversy on probability: Michalos, 1971. For the discussionof the question whether corroboration (a hypothesis that resists many attempts of falsification becomes increasingly‘corroborated’) is in fact the pseudo-inductive justificatory grounding of a belief: Watkins, 1984.

—40—

chapter 6

PROBABLE RATIOS IN DATA SCIENCE – THE ETERNAL SUNSHINE OF THE PRESENTFUTUREIn data science, as I wrote in chapter one, probabilistic ratios are not so much‘grounds’, but ‘algorithmically adjusted probabilistic temporary models’. In
order to substantiate this claim I will take a closer look at the way in which

probable ratio appears within data science. In the second half of this chapter myexplorations in this regard will lead me to the question how probability (i.e., probabilistic
ratios) within data science is related to the concept of possibility.
However, before I can develop any thoughts on the working and appearance of probableratios within data science, I will first have to clarify some of the notions involved. I will
do this in three consecutive steps: firstly, I will explain the relation between probability
and statistics, secondly what data science and data mining is, and thirdly how statistics
compares to the analytical part of data science and data mining (the data analysis
algorithm).
step 1:what hasprobability to
do withstatistics?

Step 1: What has probability to do with statistics?
The word ‘Statistik’ was first used by the German ‘statist’ Gottfried Achenwall in his
book Staatsverfassung der heutigen vornehmsten europäischen Reiche und Völker im Grundrisse(1749). This ‘Statistik’, ‘Staatswissenschaft’ or ‘Kameralwissenschaft’ was the practice ofgathering demographical data, such as the amount of fertile women or conscriptable men,which expressed the power, wealth or strength of a state and contributed to theeighteenth century emergence of the nation state (Desrosières, 1999; Porter, 2003).
Mostly such ‘Statistik’ would be what we call today descriptive statistics: straightforward
counting that does not involve the drawing of any conclusions beyond what is expressedby the actual data, but only the reformulation in a concise or visually attractive manner

fromdescriptive toinferential
statistics(tables, percentages, charts, etc). However, if one wants to extend one’s conclusions
beyond the immediate data 76 , one has to weigh the gathered data with probabilistic
assumptions (e.g. ‘if we assume that this is a fair die, these data are extremely unlikely tooccur by chance’). This extension from descriptive to inferential statistics is one of theimportant reasons why statistics have “already overrun every branch of science with arapidity of conquest rivalled only by Atilla, Mohammed, and the Colorado beetle”

76 When the Royal Statistical Society was founded in 1834 its emblem was a wheatsheaf adorned with the motto Aliis
Exterendum – “to be threshed out by others” or “for others to interpret” – but already in 1857 this caption wasremoved because it was considered to limitative. (Hilts, 1978; Kendall, 1942, p. 79; Poovey, 1998, p. 310-11) This
nicely exemplifies the shift from mere descriptive statistics to inferential statistics.

—41—

(Kendall, 1942, p. 69). Enzensberger calls probability and inferential statistics two sisters:the ‘ugly
sister’:what is thevalue ofstatisticalinferences?

the first one being very pretty, the other ugly but practical (2009, p. 26). Just like geometryor algebra (2009, p. 44) pure probability is a beautiful but self-enclosed logic, whereas ininferential statistics its axioms are used to draw inferences from actual data. Althoughmost scientists do not question the statistical methods they use, recently some doubts
have been raised about the value of statistical inferences (Biau, Jolles, & Porcher, 2010;
Ioannidis, 2005; McCloskey & Ziliak, 2008). These doubts are connected to a problem
which was already noted by Popper in the first edition (1934) of his magnum opus (Popper,
2002b), namely that probabilistic statements are in principle not falsifiable!

probabilistic
statements
areunfalsifiable“For although probability statements play such a vitally important role inempirical science, they turn out to be impervious to strict falsification”. (Popper,
2002b, 133)
For instance, the non-probabilistic –famous and infamous (Popper, 2002b; Taleb, 2007)–
statement that all swans are white can be easily falsified by one single black swan;
however, there is no analogous method to falsify the hypothesis that a coin is unbiased,i.e., has a probability of ½ to turn up tails. Only if we would be able to produce an infinite
sequence of tosses with this coin – which is of course impossible! – and the relative
frequency of tails would turn out to be for instance ⅓, we could falsify a probabilistic
hypothesis: only “an infinite sequence of events […] could contradict a probability
estimate” (Popper, 2002a, p. 182). One could think that this would be a major problem
for scientific research because the majority of hypotheses formulated in science arestatistical, i.e., probabilistic: for instance, when a scientist wants to know if a certain
medical treatment has a statistically significant effect, his or her situation can be comparedwith a person tossing a coin and hoping to find out whether the coin is biased, viz. that
there is a difference between the treatment group and the control group. However, theonly way to falsify the null hypothesis that the treatment has no effect would require an
infinite sequence of trials. Nevertheless, the empirical sciences are very successful in deciding
when to accept and when to reject a hypothesis. Assume for instance that a scientist,
whose hypothesis is that a coin is unbiased, has made 10.000 tosses and only 5 times tails

practical
falsification

turn up. Given the hypothesis this result, i.e. these data, are highly improbable (although
not impossible!) and therefore the scientist may decide to consider his or her hypothesis
as “practically falsified” (Popper, 2002b, p. 182):“It is fairly clear that this ‘practical falsification’ can be obtained only through amethodological decision to regard highly improbable events as ruled out – asprohibited. But with what right can they be so regarded? Where are we to draw
the line? Where does this ‘high improbability’ begin?” (Popper, 2002b, p. 182)
—42—

Most sciences have answered Popper’s question by establishing the famous p-values of
0.01 or 0.05: if, given a certain hypothesis, observed data have a probability that is lower
the trouble
withstatisticalsignificancethan 0.01 or 0.05 the result is considered to be statistically significant and the hypothesis
is rejected because it is “practically falsified”. However, this approach of course gives
raise to a certain arbitrariness (McCloskey & Ziliak, 2008) – for instance, why use p≤ 0.05
as a cut-off point and not p≤ 0.07843? Moreover, a ‘statistically significant’ falsification
always brings along the uncertainty that it was wrong – after all unlikely things do happen.
The ground or reason on which to decide whether to reject a hypothesis is always
uncertain because improbable does not mean impossible. Yet, a highly statisticallysignificant result is not meaningless either. It is, to use an expression which I introducedin chapter one, an uncertain certainty.

step 2:
what aredata scienceand data
mining?

Step 2: What are data science and data mining?
The present age is often characterized as the information age (Castells, 2000a, 2000b,2009): as “a new kind of capitalism” (Himanen, 2001, p. 12). Whereas most pit-coal mines
have been closed down during the last decades, transforming raw data into valuable
information has become the new booming industry (e.g. Hand, 2007; Tanaka, 2010, 1stApril; The Economist, 2010, February 27th). The software industry “specialising in data
management and analytics” has an estimated value of “more than $100 billion and [is]growing at almost 10% a year, roughly twice as fast as the software business as a whole”(The Economist, 2010, February 27th, p. 2). Increasing computing power, and processing

managing theavalanche ofdata

and storage capacity have created a need to manage and analyse the avalanche of data inmodern society. Especially when data are available in bulk it can become close toimpossible to see the wood for the trees. A nice example hereof can be seen in thecurrent debates around the SWIFT agreement, which allowed US intelligence service tosift through all international bank transfers in order to detect suspicious transactions
which could be possibly related to terrorism (Barrett, 2010, 8th April; Traynor, 2010, 11th
February). Whatever stance one takes in these debates, which are focused on whether thetransfer of SWIFT data is an infringement on the sovereignty of the EU and civil liberties
such as privacy, they also made clear that it is far from self evident to find golden nuggetsof useful information in the records of the approximately 11 million financial transactions
which are made every day. This explains that new disciplines that help to extract “useful
information from large data sets or databases” such as data mining, (also known asdata mining &KDD“Knowlegde Discovery in Databases” or KDD) which lies “at the intersection of
statistics, machine learning, data management and databases, pattern recognition, artificial
intelligence, and other areas” (Hand, Mannila, & Smyth, 2001, p. xxvii) and the even—43—data science

broader discipline of data science (Hand, 2007), whose practitioners combine “the skills ofsoftware programmer, statistician and storyteller/artist to extract the nuggets of gold
hidden under mountains of data” (The Economist, 2010, February 27th p. 2), havebecome new and upcoming fields. Apart from the fact that the overlapping fields of data
mining and data science both deal with very large volumes of data, they also share a verya practical
approachpractical outlook – maybe ‘data engineering’ would in fact be a more appropriate namethan ‘data science’. For example, a topic such as experimental or survey design is clearlyoutside the scope of data mining (Glymour, Madigan, Pregibon, Smyth, & Fayyad, 1997,
p. 11; Hand, 1999, p.17). Shalizi (2010, June 17) describes data mining as:“[…] the art of finding and extracting useful patterns in very large collections ofdata. […] the aim is to directly guide action (praxis!), rather than to develop atechnology and theory of induction. In some ways, in fact, it’s closer to what
statistics calls ‘exploratory data analysis’, though with certain advantages andlimitations that come from having really big data to explore”.

step 3:what hasstatistics to
do with data
science?

Step 3: What has statistics to do with the analytical part of data science (i.e., the data
analysis algorithm)?
Large parts of data science do not concern the actual analysis of data but the preparationof the analysis and the visualisation of the results:“What differentiates data science from statistics is that data science is a holistic
approach. We’re increasingly finding data in the wild, and data scientists are
involved with gathering data, massaging it into a tractable form, making it tell its
story, and presenting that story to others” (Loukides, 2010, June 2)
However, for the sake of the argument I will not discuss these parts of data science but
rather focus on the analytical part wherein useful patterns are extracted from the data. In
this respect statistics and data mining clearly have much in common: both “are concernedwith discovering structure in data” (Hand, 1999, p. 16) and deal with uncertainty by
quantifying it (Glymour et al., 1997).
One difference between statistics and data mining is that the datasets in the latter are
sometimes so big that they cover the whole population and not just a sample: thus data

models instatistics,
algorithms indata mining

science tends to be more about “model fit rather than its generalisation” (Hand, 1999, p.
17) from sample to population. Nevertheless, probable ratios are as much an importantfeature in data science as in statistics, particularly when patterns are used to generalize
towards the future (forecasting and anticipatory predictions). Another importantdifference between statistics and data science is that the latter is not primarily about—44—

models 77 but about algorithms (Hand, 1999). This difference needs more clarification as it
is a source of endless misunderstandings. For instance, in a much criticized but widely
read article Anderson (2008) declared that the new data science means the end of models
and theory as patterns would be self-emergent from correlations found in large data sets:“‘Correlation is enough.’ We can stop looking for models. We can analyze thedata without hypotheses about what it might show. We can throw the numbers
into the biggest computing clusters the world has ever seen and let statisticalalgorithms find patterns where science cannot”. (Anderson, 2008)
As was correctly noted it is wrong to say that merely looking for correlations in data sets
will do the trick:“[…] anyone who thinks the power of data mining will let them write a spam
filter without understanding linguistic structure deserves the in-box they’ll get.”(Shalizi, 2008, 25 June)
However, contrary to the classical statistical approach in data mining the data aresubjected to an “on-going process (even if the data set is fixed)” (Hand, 1999, p. 18) inalgorithmic
automationof discovery

which large parts consist out of algorithmically automated 78 discovery (Glymour, 2004) in“an attempt to discover the unexpected” (Hand, 1999, p. 18). Thus the issue is not that
there is a lack of hypotheses, models, or theories in data mining but, quite the opposite,that there is an abundance: there is an endless algorithmic hence and forth between data
and malleable, probabilistic hypotheses. Whereas models in statistics tend to be static,mathematical descriptions, data science draws on computer science and artificial
intelligence 79 , giving “pseudocode descriptions (simplified versions of computer
programs) of algorithms, telling you how to process data to reach a conclusion”. (Hand,
2007, pp. 113-4) Hence, data mining techniques can also be described as belonging to thedomain of “machine learning”:

77 “In statistics, a model is a description of the data as it occurs, summarizing its distribution, relationships between
observed characteristics, and so on, […]”. (Hand, 2007, p. 113) Thus a model could look, e.g., something like “testscore= (0,2)*(age) + (0,6)*(years of education)” or “Yi = b0 + b1Incomei”.
78 The fact that part of the on-going process in data mining is automated, does of course not imply that being a data
scientist is a simple job that only involves pushing a ‘start’-button – on the contrary! Developing algorithms andfollowing up on the on-going process of data mining (“One examines the data one way, interprets the results, looks
more closely at the data from a related perspective, looks at them another way, and so on”, Hand, 1999, p. 18) is acomplicated job that requires many skills. (Loukides, 2010, June 2)
79 “For the typical computer scientist, the statistics literature is relatively impenetrable: a litany of jargon, implicit
assumptions, asymptotic arguments, and lack of details on how the theoretical and mathematical concepts are
actually realized in the form of a data analysis algorithm. The situation is effectively reversed for statisticians: thecomputer science literature on machine learning and data mining is replete with discussions of algorithms,
pseudocode, computational efficiency, and so forth, often with little reference to an underlying model or inference
procedure. An important point is that both approaches are nonetheless essential when dealing with large data sets.
An understanding of both the “mathematical modeling” view, and the “computational algorithm” view are essential
to properly grasp the complexities of data mining”. (Hand et al., 2001, p. xxviii)—45—

How tomakemachines
find theregularities
in a data
set?

“There’s a place where AI, statistics and epistemology-methodology converge, orwant to anyhow. ‘Machine learning’ is the AI label: how do we make a machinethat can find and learn the regularities in a data set? (If the data set is really, reallybig, and we care mostly about making practically valuable predictions, thisbecomes data mining, or ‘knowledge discovery in databases,’ KDD.) The
statisticians ask very similar questions about model-fitting and hypothesis-testing.
The epistemologists are mired in the problem of induction, and ‘inference to thebest explanation’ […]. The fields over-lap in the most crazy-quilt and arbitraryway.” (Shalizi, 2010, June 3)

statistics as
the grammarof datascience

Keeping all of this in mind, “one should not overlook that the model and algorithm
approaches are two sides of the same coin” (Hand, 2007, p. 114). Hence, the role ofstatistics within data science should not be belittled:“[…] statistics is the ‘grammar of data science.’ It is crucial to ‘making data speak
coherently.’ […] it takes statistics to know whether this difference is significant,or just a random fluctuation. Data science isn’t just about the existence of data,or making guesses about what that data might mean; it’s about testing hypotheses
and making sure that the conclusions you’re drawing from the data are valid.”(Loukides, 2010, June 2)

data science:quite much
like statistics
but moreprocessual,inventive,
algorithmic,
and
agile

However, the deeply processual, algorithmic and inventive nature of data science (it is notabout finding ‘Scientific Truth’, but about an endless re-ordering of the data to findinteresting or profitable patterns), makes even the scientific hypothetico-deductive
method look as a rather “confirmatory” 80 practice:“To many, the essence of data mining is the possibility of serendipitous discovery
of unsuspected but valuable information. This means the process is essentiallyexploratory. This is in contrast to the rather optimistically styled ‘confirmatory’analysis. (Optimistic because one can never actually confirm a theory, only
provide supporting evidence or lack of disconfirming evidence.) Confirmatory
analysis is concerned with model fitting – establishing that a proposed model
does or does not provide a good explanation for the observed data. Thus much,perhaps most, statistical analysis addresses confirmatory analysis.”(Hand, 1999, p.
17)Hence, what is important in data science is “agile” data analysis: “Faster computations
make it easier to test different assumptions, different datasets, and different algorithms”.
(Loukides, 2010, June 2)

80 This statement would, of course, make Popper turn in his grave.

—46—

Now that all relevant terms have been introduced and clarified in the three steps above, it
is time to return to the question how probable ratios appear and work within data science.
summary:
what do welearn from thethreeaforementioned
steps?

The image that appears is of a practice in which probable ratios produce a never-ending
sequence of present futures (see above, chapter one, and Esposito, 2007, pp. 50-67) which
can never be refuted by a future present. Firstly, there is the inheritance of statistics which
replaces the possibility to get an unequivocal ‘no!’ of classical refutation by the much moreopaque ‘probably not…’ and ‘…in the present future a refutation would definitely be the mostrational option as long as one reckons with the disclaimer that improbable does not mean impossible in a
future present’ of so-called “practical falsification” (Popper, 2002b, p. 182). Thus not only

probableratios indata science:a doubled
independenceof
actualizationis the rationality of the probable ratios independent of its actualisation in the future
present, but it also excludes the impossible: however improbable things are, one can neverfully exclude the possibility of their actualisation. Secondly, the algorithmic and processual
nature of data science takes this impossibility of refutation and the irrelevance ofactualisation in the future present even a step further: the probable ratios are no longer
conjectural ‘models’ that can or cannot be refuted, but are better described as elements ofevolution (“Evolutionselement”, Esposito, 2007):“[…] Forecasts [are] themselves a result and a moment of evolution, which itprocesses in building a more complex world”. 81 (transl. mine, p. 108)

probableratio:
not a groundbut anevolutionary
element

To give a concrete example: the temporary emergence of the probable ratio 0.945 (e.g., asin: ‘this email with VIAGRA in the subject line and 78 undisclosed recipients has a probability of
0.945 to be spam’) is neither a ground for thought (i.e., a ‘reason’ for the belief of the spam
filter) nor a ground for being (i.e., a ‘cause’ or ‘propensity’ of the email to be spam) but
simply an intermediate result that functions as an ‘evolutionary element’ within theapplication of the algorithm. This is no longer about the growth of scientific knowledge,
but about adaptation in a rapidly changing environment. Here probable ratio goes beyond
the notions of subject and object, and beyond the notions of ground, cause and reason,
becoming an ‘event’ in its own right, that is in own present future.

Leibniz’s
metaphysics:
the equationofprobability,
possibility,andfeasability

Let me pause here for a while: is it not extremely strange that I reached the conclusionthat probable ratios in data science are not about their possibility for actualisation? Is it
not common sense that something that is probable (e.g., “It is very probable that tails willshow up more than once if I toss this coin ten times”) is also equally possible? The
alienating aura that surrounds this conclusion probably follows from our attachment to

81 “[…] Prognosen [sind] selbst ein Ergebnis und ein Moment der Evolution, die sie beim Aufbau einer komplexeren

Welt verarbeitet.” (Esposito, 2007, p. 108)—47—

Leibniz’s equation of probability, possibility, and feasibility. In De incerti aestimatione (1678)
Leibniz is unequivocal about the relationship between possibility and probability:“Probability is a gradation of possibility” 82 (transl. mine)
Earlier, in the Vorarbeiten zur Characteristica Universalis (1671-1672) Leibniz had alreadyclarified that he equates possibility with that which is facile (‘easy’, ‘feasible’ or ‘doable’):Quod facile
est in re, id
probabile est
in mente“Facile is what is very possible, that is to say, for which little is required” 83 (transl.
in: Hacking, 1975, p. 127)
In the following sentence of the same entry Leibniz continues:“What is easy in reality [facile in re] is probable in the mind” 84 (transl. in: Adams,
1994, p. 203)
Thus one could say that for Leibniz probability reflects the propensity (Popper, 1990) or
proclivity 85 (Hacking, 1971a) in things themselves to come into existence. However, bytranslating “facile in re” simply by propensity or proclivity, one could easily overlook the close
etymological relation between facile and faire (‘to do’, ‘to make’) – a relation that is muchstressed by Leibniz himself. In 1714 Leibniz elaborates on how a degree of facility(‘makeability’ or ‘doability’) should be understood:“The art of conjecture is based on what is more or less easy (facile) or, better,more or less doable (faisable), for the Latin facile derived from faciendo literallymeans doable; for example, with two dice, it is as doable to throw a twelve as tothrow an eleven for each can only be done in one way; but it is three times more
doable to throw seven, for that can be done by throwing six and one, five andtwo, and four and three, and one of these combinations is as doable as theother” 86 . (letter to Bourguet, March 1714, in: Leibniz, 1887, p. 569-70; transl. in:
Sylla, 1998, p. 50-1)
Looking at all of the aforementioned quotations one can conclude that Leibniz’s Janusfaced conception of probability is not only a “degree of assent” (belief) but that it also

Daseinsstreben

corresponds to the level of “effective propensity towards existence” (Krüger, 1981, p. 49)
or what Wilson (1971) has called “Daseinsstreben”:

82 “Probabilitas est gradus possibilitas”, (Leibniz, 1999, p. 94).
83 “Facile est valde possible, seu cuius pauca sunt requisita”, (Leibniz, 1966, p. 492).
84 “Quod facile est in re, id probabile est in mente”, (Leibniz, 1966, p. 492).

85 When probability emerged in the second half of the seventeenth century, “proclivity” also emerged as one of its
synonyms. For instance, Huygens writes in proposition III of De ratiociniis in ludo aleae (1657) that there are “casus
aeque in proclivi, namely events, or chances (translating the Dutch kans) that have an equal proclivity to occur”.
(Hacking, 1975, p. 125)
86 “L’art de conjecturer est fondée sur ce qui est plus ou moins facile, ou bien plus ou moins faisable, car le latin
facilis derivé a faciendo veut dire faisable mot à mot: par exemple, avec deux dés, il est aussi faisable de jetter douze
points, que d’en jetter onze, car l’un et l’autre ne se peut faire que d’une seule maniere; mais il est trois fois plus
faisable d’en jetter sept, parce que cela se peut fair en jettant 6 et 1, 5 et 2, et 4 et 3; et une combinaison icy est aussi
faisable que l’autre”. (Leibniz, 1887, p. 569-70; 2010, p. 144-5)—48—

“The possible demands existence by its very nature, in proportion to its possibility,that is to say, its degree of essence” 87 (transl. in: Hacking, 1971b, p. 603)
Such a notion of “Daseinsstreben” 88 , i.e., a predetermined degree of possibility or
probability in the essence of every thing 89 , does of course not sound very credible to themodern mind (Hacking, 1971b, p. 603; Wilson, 1971, p. 610).
…dans l'etat
present deschoses …

And yet, if we continue reading Leibniz’s aforementioned letter to Bourguet (1714) one
sentence suddenly seems very modern:“One also evaluates plausibilities (vraisemblances) a posteriori, by experience; one
should have recourse to this in the absence of a priori ratios (raisons); for example,
it is equally plausible (vraisemblable) that a baby about to be born will be a boy or a
girl, because the numbers of boys and girls are found to be nearly equal in thisworld. We may say that what is done more or done less is also more or lessdoable in the present state of things, putting all the considerations together whichmust concur in the production of what is done (d'un fait).” 90 (transl. in: Sylla, 1998,
p. 51, bold emphasis mine)
Once one reads these sentences without the idea of a God who guarantees that there is atrue and unchangeable nature of probable ratios to be discovered, it suddenly becomesdifficult to say how Leibniz can speak of “dans ce Monde” and “dans l'etat present des choses”.
Lacking a bird’s-eye view over eternity or a God to guarantee that the “vraisemblances aposteriori” will continue to correspond to the “raisons a priori”, Leibniz’s “etat present desfrom onepresent
future…tothe next

choses” begins to appear as Esposito’s “present future”: a construction in which therationality of the probable ratio is irrefutable, but with the imminent “future present”(which is, as the classical problem of induction tells us, completely indifferent to the“present future”) always lurking at its borders. How to stay within the rays of the eternal

87 “Haec autem aliter reddi non potest quam ex generali essentiae seu possibilitatis ratione, posito possibile exigere
sua natura existentiam, et quidem pro ratione possibilitatis seu pro essentiae gradu ”(Leibniz, 1890, p. 194)
88 “God must be able to do what can be seen to be best in a rational consideration, i.e. in an intelligible comparisonof essences. And a such consideration is essentially not a matter of all or nothing but a measurement and evaluationof degrees or essence or perfection. […] God’s assent follows perfection, ours follows conjectured perfection”,(Krüger, 1981, pp. 52 and 54). Hacking (1971b, p. 603) summarizes Leibniz’s metaphysics in similar terms: “God’srole is to conceive possibilities. The creatability of the things will correspond to the degree of possibility in the divinemind. Similarly, in our world the objective propensities of different outcomes to occur are the foundation of ourmental expectations, the probabilities, which, as Leibniz had said, are degrees of possibility”.
89 The modern propensity interpretation of probability as developed by, e.g., Popper, locates the propensity or
probability not in the essence of things but in a situation (Popper, 1990). Thus it is argued that probability is not
subjective (a degree of belief), but an objective tendency within a certain situation: “…that the propensity of a penny
to fall on a flat table with heads up is obviously modified if the table top is appropriately slotted. Similarly, one andthe same loaded die will have different propensities if the table top is very elastic rather than marble, or if it is coveredby a layer of sand”. (p. 15)
90 “On estime encore les vraisemblances a posteriori, par l'experience, et on y doit avoir recours au défaut des raisonsa priori: par exemple, il est egalement vraisemblable que l'enfant qui doit naistre soit garçon ou fille, parce que lenombre des garçons et des filles se trouve à peu près egal dans ce Monde. L'on peut dire que ce qui se fait le plus ou—49—

sunshine of the present future, where there is always a rational (even if only ‘certainuncertain) way to proceed? One way to hold the constantly imminent ‘future present’ atbay can be seen in modern data science: an on-going process of the production (onewould almost be tempted to say with Leibniz: “…mettant toutes les considerations ensemble qui
doivent concourir à la production d'un fait”) of present futures.

summary

Where does this leave us? First I tried to describe the workings of data science and toshow that the way in which probable ratio unites being and thought in this practice has
little to do with the terms in which we normally think about probability and probableratio: grounds, reasons, causes, the possible, actualisation, etc. Thought from a common
sense approach one would expect that data scientific applications are about predicting thefuture, i.e. about establishing which possibilities are most prone to come into existence.
In a popularising article in Forbes magazine it says:“Thus predictive analytics is emerging as a game-changer. Instead of looking
backward to analyze ‘what happened?’ predictive analytics help executives answer‘What’s next?’ and ‘What should we do about it?’” (Rich & Harris, 2010)
However, using Esposito’s distinction between the ‘future present’ and the ‘present
future’ it became clear that probabilistic ratios do not predict the ‘future present’ but only
relate to the ‘present future’, i.e. the future as it shows itself in the present. Moreover,because of their probabilistic nature the rationality of probable ratios is irrefutable. Hence
probable ratios can be better described as ‘evolutionary elements’ in an on-going adaptive
production of new ‘present futures’. While we still might tend to think in terms of

enclosed in
the endlesssequence ofpresent
futures

Leibniz’s metaphysics, equalling makeability, possibility and probability, this triad fits
badly with the actual practice of probable ratio in data science. Yet, when reading Leibniz
closely, already there we see expressions (such as “dans l'etat present des choses”) that seem toanticipate the endless sequence of ‘present futures’ in which the probable ratios of data
science enclose us.
As such an ‘endless sequence of present futures’ might still sound rather abstract I will try
to illustrate this in a more concrete manner. Popper, when explaining his propensity
interpretation of probability, i.e., that every situation has a certain objective propensity
than can evolve over time, gives a nice example of what I would call, following Esposito,
a sequence of present futures:“How probable is it that you will live another 20 years? This has its own little
mathematical problems. Thus, the probability that you will live another 20 years

le moins est aussi le plus ou le moins faisable dans l'etat present des choses, mettant toutes les considerations
ensemble qui doivent concourir à la production d'un fait”. (Leibniz, 1887, p. 570; 2010, p. 145)—50—

from today – that is that you will be still alive in 2008 – increases for most of you
every day and every week as long as you survive, until it reaches the probability 1on the 24th of August 2008. Nevertheless, the probability that you will survive
for another 20 years from any of the days following today goes down and downwith every sneeze and with every cough; unless you die by some accident, it is notunlikely that this probability will become close to 0 years before your actual
death. […] Nevertheless, the view that the propensity to survive is a property ofthe state of health and not of the situation can easily be shown to be a serious
mistake. As a matter of course, the state of health is very important – animportant aspect of the situation. But as anybody may fall ill or become involvedin an accident, the progress of medical science – say, the invention of powerful
new drugs (like antibiotics) – change the prospects of everybody to survive,
whether or not he or she actually gets into the position of having to take any
such drug. The situation changes the possibilities, and thereby the propensities”(Popper, 1990, pp. 8 and 14-5)
Of course, what Popper tries to show is that his objective understanding of probability is
not as essentialist as Leibniz’s: Popper underlines that he is talking about the propensityof situations, not states, and that these situations can change. However, when read throughthe lens of ‘future presents’ and ‘present futures’ one sees how the ‘situations’ or ‘present
futures’ have to be adapted and reconstructed all the time to incorporate accidents anddiscoveries, immunizing life against the ‘truly’ unexpected.
Moving away from the ingrained language of grounds, reasons and the actualization of
possibilities, allows me to question the relation between the probable and the possible inpresent future
future present

a way that I could not have before, namely, what is the relation between the ‘present
future’ and the ‘future present’? The obvious answer is of course that there is no relation.
In fact, how can I even talk of a future present if it is so fully and completely excluded
from the ‘present futures’ generated by the algorithms of data science? Maybe one could
say that the ‘future present’ is absent from the ‘present future’ in a way which Deacon
calls “constitutive” or “specific absence”, that is to say that it “is not so much the absence
itself that is critical, but how it affects what is left and how this may relate to otherthings” (Deacon, 2006, p. 120). Thus the ‘future present’ presents itself as an absence
against which the endless sequence of present futures is built, presenting itself as
uncertain-certainty, or to put it differently, a certainty “dans l'etat present des choses” with an
inerasable birthmark of the pure uncertainty which it excludes.

—51—

chapter 7

an experimentin thinking
betweensomething andsomething…

CONCLUSION – NEW AFFECTIONST

his is thesis is an experiment in thinking a parallax, of evocating a kind ofthought that only arises when one thinks “between something andsomething”. (Blouin et al., 2005, p. 142, transl. mine) Thus both the lawyer,

looking for practical advise how to deal with probabilistic reasoning in the courtroom, or
the data scientist hoping to find arguments that will help in the decision whether to put…in order tofind howprobable ratio
give rise to aphilosophicalaffect“Bayesian”, “Frequentist” or “Undecided” on his or her business card, will bedisappointed.
By letting myself become affected by ‘the same’ (‘probable ratio’) through two different‘befores’ or ‘mediations’ (law and data science), I tried to find ways in which probableratio could also begin to affect me in a philosophical way.
So did the experiment succeed? Did the traversed trajectory give rise to new affections tothink probable reason? My own cautious answer would be: “Maybe – sometimes”. The
process of thinking was full of pitfalls and slippery slopes. Sometimes, despite all of myoutflanking movements to avoid that, I would notice that an attempt was falling flat as
my sentences were walking down trodden paths of thought, while on other occasions thenotion ‘probable grounds’ would suddenly appear in the text in ways previously
unthought of. For instance, in chapter four, I felt the danger of anachronistic conclusions
lurking in Spinner’s (1977) reading of Parmenides, and in chapter five it turned out to bedifficult to provide the necessary terminological precision without diverting attention
from the main questions. Both chapters show that the question how to present a practice(law and data science), and the role played in it by certain notion (probable grounds) in it,
is far from a unequivocal enterprise. Not only in the two aforementioned chapters but

crossroads

also in other parts of this thesis have I found myself standing hesitant on theoreticalcrossroads – unsure about the direction to take. At the same time these moments often
also proved to be the most decisive ones, opening possibilities to think things differently.
At these points I would also be forced to introduce unusual or novel notions in order toproceed in the intended direction. Thus, before evaluating the philosophical ‘harvest’ ofthe parallax between law and data science, I will first recapitulate and defend some of theturns and twists which I took while writing this thesis.

1. probablegrounds

Crossroad 1: Probable grounds
Many things have been said about probability, and maybe even more about the principium
rationis. Why not simply write about probability or the principium rationis? While the—52—historical and philosophical intertwinement between those notions is undeniable, there
has not been, as far as I know, any serious philosophical attempt to think them together
as probable grounds. On the one hand the supplementary nature of probability and theprinciple of ground seem quite obvious: not only do the calculus of probabilistic ratios
and the principium rationis emerge more or less simultaneously, but they also share in thesame Janus-faced and reckoning ratio. On the other hand I also clearly see that I risk theallegation that ‘probable grounds’ or ‘probable ratio’ are paradoxical jackstraws of myown making. However, introducing the term ‘probable ground’ has been helpful inseveral respects. Firstly, because it dissolves the not very fruitful opposition between
probability and ground as inductive and uncertain v. deductive and certain. Secondly, it
allowed me to move away from the many and often tedious debates about the principleof sufficient reason, towards its supplement, the principle of insufficient or probable reason,
which in our modern era seems to have become more important than its counterpart.
Last but not least, ‘probable ground’ is a tool that provides a starting point to think therelation between probability and the principium rationis – and more in particular the relation
between probability and the volatile yet resilient word ‘ratio’.
2. affection

Crossroad 2: Affection‘Affection’ is the word used in this thesis to point to the fact that ‘probable grounds’ arenot ‘things’ or ‘objects’ but ‘relations’ through which being and thought meet. To speakof probable ratio as an affection could appear controversial – after all, is affection not thecounterpart of ratio? Although, as I explain extensively in chapter three, I use affection ina very specific, Spinozian sense (i.e., as the relation which arises from a relational
constellation or a landscape which attunes the affector and the affectee in such a way that there isa space where they can meet and become what they are), I also welcomed the possibility
that thinking of ratio as an affection could be a refreshingly disruptive side-effect which
could be of help to avoid stepping in all too trodden paths of thought.

3. before

Crossroad 3: Before
In this thesis I named the aforementioned “relational constellation or a landscape which
attunes the affector and the affectee” the before. Of course, I could have used its Latintranslation, i.e., the more philosophically common a priori, but I feared that its heavy
burden of metaphysical connotations would lead me astray. Also I considered using
mediations, yet was concerned that the word would point me into the direction of‘immediate origins’ and ‘input-before-mediation’. However, in the process of writing thebefore began to double as both “relational constellation” and as the before in time. Starting of—53—

with the good intention to explore two practice and traverse each of their befores fromwhich the affection of probable grounds or ratios appears, I ended up digging forhistorical origins – talking about Parmenides’ ‘principle of reason’-avant la lettre andCasuist probabilism.

4. a parallax

Crossroad 4: A parallax
If doing philosophy, as I think, always regards the ‘before’ or ‘a priori’ through whichthought and being meet, philosophy will always have to struggle with a certain circularity:
method and ‘object’ of study will always, at least partly, coincide. How to proceed?
Drawing upon Stengers’ notion of the ‘ecology of practices’ (Stengers, 2005) and Žižek’sparallax view (2006), I tries to address this pivotal philosophical-methodological problem.
However, a parallax view is like navigating between Scylla and Charybdis. On the one
hand there is the risk that one ends up making a comparison between two practices inwhich the incommensurability of the ‘before’ of each practice disappears as they aremeasured by a common standard (“Probable ratio in law and data science are very similar
is this respect, while in that other respect they show the following differences”, etc., etc.).
On the other hand there is the risk that nothing happens between the two separately
traversed trajectories.

5. sticking to
the practiceitselfCrossroad 5: Sticking to the practice itself
A parallax between practices would seem to imply that these practices are relatively clearlydelineated. For instance, when philosophers try to think a parallax between languages (e.g.
“ratio” in Latin, “raison” in French and “Grund” in German) the question “Does thisword belong to the French language or not?” is less complicated than when one wants toknow whether something belongs to a practice. Talking about the practice of law or thepractice of data science is of course rather abstract, and forces one to give more detailed
information such as “When?”, “Where?”, “Which school?” and “Which branch?”.
As becomes immediately clear when reading chapter five (on law) and six (ondata science) I have not been much of a purist in this respect. When writing aboutprobable grounds in law, I refer to matters as disparate as ancient Greek Dikē,seventeenth century views regarding proof, and the use of statistical evidence in a recent
Dutch criminal case. With regard to data science things are not much better. The firstproblem is that the boundaries of this upcoming field are still very much in flux. A
second issue is that, similar to what I did in the chapter on law, I easily jump between
very different matters: from Leibniz’s musings on possibility-probability, to statistics and—54—

data science, while rephrasing their modus operandi in terms (e.g., “future present” and“present future”) which the practitioners themselves would probably never use.
One explanation was given above: sometimes the tendency to explain things interms of historical causes and avant la lettres (a matter of ‘old habits’ and that it is far fromobvious how to write differently) would simply get the better hand of me. However, from amore pragmatic perspective we could ask – is that really a problem? After all, theintention has never between to give correct, exhaustive or representative descriptions of thepractice of law and data science, but to use them to allow for philosophical thought inbetween them.
Apart from this pragmatic outlook there are also two other justifications forhaving these bric-à-brac assemblages instead of clearly delineated practices.
Firstly, as readers familiar with the history and philosophy of probability might
have noticed, the chapters on law and data science show certain similarities with how the
emergence of probability is often presented. This account (see e.g. Hacking, 1971b;
Hacking, 1975; Sullerot, 2006), in a very simplified and caricatured form, goes as follows:
first Leibniz discovers probability through law, in which probability has already a slightly
Janus-faced status but still is predominantly epistemological (degrees of belief), then hedevelops a more ‘naturalised’ and objective understanding of probability, as a proclivity
within things themselves, but he never fully disentangles the two sides which have turned
later into the subjective and objective interpretation of probability. What I wanted to avoid in
writing chapters five and six was exactly this: to write a law-chapter on the origin of thesubjective interpretation and a data science-chapter on the origin and unfolding of theobjective interpretation, as if already I knew what subjectivity and objectivity are insteadof trying to retrace these notion through probable ratio.
Not only did I face the challenge to avoid a reduction towards the subjective andobjective, but in the chapter on law I also struggled with the fact that in modern thought
the words of law and truth are so conflated (‘judgment’, ‘justification’, ‘correctness’,‘ground’, ‘reason’, etc.) that it becomes very difficult to talk of ‘the-legal-as-it-gave-rise-toprobable-grounds’ instead of ‘the-legal-that-is-already-taken-in-by-probable-grounds’. In
taking recourse to Parmenides, who does not speak of grounds, I hoped to encounterwords that would help me to avoid this pitfall.
After these two final justifications of my rather peculiar presentation of thepractice of law and of data science, I come to the final point: is there a parallax between
them? And did any new affections arise?
A parallax between law and data science—55—

a parallax
between law
and data
science –did something
happen?

While trying to stay away from the words objective and subjective when thinking about law
and data science something else emerged: a before of probable grounds which still lingers onin law but is slowly vanishing, and a before of probable ratio which is upcoming in data
science, for which we not have yet found the right words to describe it. Looking at the
trajectory of twists and turns through which ‘probable grounds’ and ‘probable ratio’ wereconstituted – with words like ‘Dikē’, ‘fairness’, ‘proof’, ‘opinion’ and ‘authority of Nature’– the words ground, ratio and probability began to lose something of their self-evidence.
In both law and data science the words that we use and the metaphysics that they bring along(ground as a solid reason for thought and a cause for being, probability as degree of
possibility or propensity towards actualisation, etc.) do not seem to fit very well with whatis actually happening. Only, how can I notice or say such a thing if my all my thoughts always
traverse those exact same words? In thinking through law and data science I encountered
new directions and new words that allowed me to notice and articulate this misfit.
Let me first look at chapter five (on law). In the notion of ‘proof’ and in
Parmenides I found a language that while seemingly saying the same – ‘proof’ as ‘ground’
and Parmenides as the father of the ‘principle of ground’-avant la lettre – allowed me tothink ‘ground’ differently, namely as always already founded in (legal) uncertainty and both
required and guaranteed by a legal need of dikē or fairness. Hence, the paths taken
throughout chapter four (on probabilist casuistry) and five (on law) allowed me toarticulate ground in a way that is a new affection: ground as “solid/uncertain encounters of
being and thought” under the denominator of something legal like dikē or fairness.
Chapter six (on data science) took a fully different route. When realizing that‘possibility’ and ‘actualization’ did not manage to put the right words to what ishappening in data science, I was able to restate the practice in Esposito’s notion “present
future” and “future present”. Turning away from the idea that data science tries to predictthe degree of possibility that something will actualise in the future present, the probableratios of data science started to affect me in a novel way: as ‘evolutionary elements’ in thegeneration of endless present futures.
But what about the parallax between law and data science? The parallax occurs when one
notices that one field of ‘legal’ words (‘dikē’, ‘fairness’, ‘legal ground’) surrounding
probable grounds has slipped away, while another field of ‘data scientific’ words(‘evolutionary element’, ‘present future’, ‘probabilistic ratio’) is upcoming but not yet fully
articulated. In the lack of these words lies the parallax which allows for probable grounds
to affect us philosophically.

—56—

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