(author’s final draft)

Vagueness of Free Will
Masaki Ichinose
Professor of the University of Tokyo, Japanichinose@l.u-tokyo.ac.jp

Abstract
I aim to bring the idea of “degree of free will or freedom” into philosophical debates on free will by
rejecting the two choices formulation, ‘we are either free or not’. This idea is based upon myviewpoint of regarding free will as a realistic phenomena actually occurring.

First of all, I focus

on the fact that it is vague whether an agent is free or not. This vagueness is interpreted as
ontic vagueness, corresponding with the status of freedom as real. However, Evans’s argument
regarding ontic vagueness must be considered as, according to his argument, ontic vaguenessabout identity and objects are impossible.

I point out that this argument assumes thetruth-value gap position in borderline cases, hence we can avoid Evans’s argument by adopting
truth-value glut position.

Of course, the truth-value glut approach has serious difficulties, but I

conclude with sketching out a possibility to develop this approach in the free will debate via theintroduction of probabilistic valuation.

Body
1 Degree of Free Will
I will begin with pointing out the strange discrepancy between the philosophical discussion1

on free will and our ordinary notion of freedom.

Philosophers traditionally have raised thequestion, ‘how is free will compatible with necessity?’, which has motivated a metaphysicaldebate between so-called compatibilism (e.g.Hume) and incompatibilism (e.g.Kant). Basically,
the debate is backed up by this two choices disjunction, ‘we are either free or we are not free’,together with the idea of determinism. Indeterminism is sometimes considered in this debate, buteven in that case the disjunction is retained. On the other hand, when we talk about freedom inordinary conversation, it is not unusual to mention the degree of free will or freedom we have.
For example, we can say we have more degree of freedom in selecting jobs when we have adriver’s license than when we don’t have one, or that a mentally disordered person is less free tocontrol their actions (including offences) than a healthy one.

If so, it seems that thephilosophical debate on free will has to take the concept of degree in free will more seriously;
otherwise the debate will have no practical applicability or reality.

2 Ontic VaguenessHow, then, can we reflect the concept of degree in the free will debate?

There are somepossible routes, but here I will pay attention to the fact that it is often vague whether an agent isfree or not.

This is easily confirmed by the example of the mentally disordered offendersuggested above.

If the offender is so disordered as to make no sense of even basic logicalrules, the offender is judged to act not from autonomous free will but just from mechanicalimpulses. However, there are borderline cases.

What about the case in which the offendermostly understands logical rules and moral norms, but is brain-washed by a cult that condones
2killing, or the case in which the offender is normal but suffering from personality disorder partly
caused by brain disease?

If we admit the core meaning of free will or freedom lies in the factthat the agent isn’t controlled by the external causes, we will hesitate in the cases above todecide whether the offender had free will or not when committing the offence, for in those cases
the offender seems to be partially governed by the external causes.

Probably this decision

depends upon how much they are brain-washed or suffer from the personality disorder.

In aword, this situation is so vague that we can’t definitely declare whether it is true or false that theoffender acted from their own free will.
What sort of vagueness appears here? As is well known, there are two types of vagueness,
i.e. linguistic vagueness and ontic vagueness.

As regards free will I want to take ontic

vagueness to matter as, as I described, I hope to highlight the issue about the practicalapplicability or reality of freedom, which should be discussed by regarding free will as a sort ofrealistic phenomenon that actually occurs. Ontic vagueness usually matters in discussions
about material objects like mountains or clouds, whose boundaries are vague, but if we could
take freedom (at least a part of its mode) to be a natural phenomenon actually occurring in nature,
perhaps as a brain state able to cause human actions, it is not inappropriate to employ theconcept of ontic vagueness in this context.

3 Evans’s Argument
However, vagueness brings about some puzzles. The sorites paradox is the most famous,but, as far as ontic vagueness is concerned, we mustn’t overlook a classical puzzle given by3

Gareth Evans in 1978. He argues about whether the concept of a vague object is possible or
not by analyzing vagueness of identity.

His argument proceeds as follows.

Suppose (1) it isindefinite whether b is identical with a. Then (2) b is such that it is indefinite whether it is identical
to a. But (3) it is not indefinite whether a is identical to a. So (4) a isn’t such that it is indefinite
whether it is identical to a.

So, from (2) and (4) by Leibniz’s Law, (5) b isn’t identical to a. But theconclusion (5) contradicts the assumption (1). Therefore, by reduction to absurdity, vague
identity and thus vague objects should be impossible (Evans 1978. p.208).
This argument was so shocking that many reactions arose immediately. Initially, somephilosophers argued that its conclusion is simply a mistake as a matter of ordinary and quantum
theoretic facts (e.g. Lowe 1994 et al.).

I agree with this point, since my discussion supposesthat ontic vagueness is a realistic matter, as exemplified by the issue of free will. But, if so, there
must be something wrong with Evans’s argument. Why is that? There are quite diverse pointsof view as to this, raised by many philosophers.

4 Truth-Value Glut Approach
It seems to me, however, that a naïve reaction against Evans’s argument is that (1) and (5)aren’t contradictory. The assumption (1) seems to mean “’a = b‘ doesn’t have definite truthvalue”, which implies “’a = b‘ isn’t true”. Then, this is nothing but the consequence (5). This
reaction is motivated by the standpoint which regards indefiniteness as a truth-value gap.
Actually many philosophers analyze Evans’s argument from the viewpoint of a many-valued
logic (e.g. Broome 1984).

But, truth-value gap approach implies as to (1) “’a = b‘ isn’t false” as4well, while (5) seems to mean “’a = b‘ is false”, according to a natural interpretation of negation.
Thus, it seems that (1) and (5) aren’t consistent after all.
However, there could be another direction to lead our naïve reaction. That is to say, thetruth-value glut approach, which provides the alternative that, “’a = b‘ is both true and false”. If weadopt this view, (1) and (5) are perfectly consistent so we could avoid the conclusion of Evans’sargument, because we can deduce “’a = b‘ is false” from “”a = b” is both true and false”.

Inreality, the truth-value glut approach seems to indicate the existence of a positive state of affairs
in borderline cases, and hence conforms to my point that freedom is a sort of real phenomenon
actually occurring which can cause human actions. On the other hand, the truth-gap approach
can refer to only the negative status of borderline cases which is causally inert. In other words,
both of the approaches of truth-value gap and truth-value glut may be theoretically equivalent as
a dual, but are practically different from each other.

5 Probabilistic Valuation on Degrees of Free Will
Even if this is so, however, it’s not an easy option to adopt the truth-value glut approach.
First of all, this approach calls a contradiction into my argument. As to this, I want to introduce
the concept of ontological contradiction that Patrick Grim suggests, which admits that a state ofaffairs can both have a property and lack the property (Grim 2004, p.53). That sort of conflict isbrought about from a different point of view, which is quite suitable to describe the issue of theborderline case of free will (probably in the court).

Second, as far as the logical status of thetruth-value glut is concerned, we have to encounter some quite controversial theories.
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Paraconsistent logic and dialetheism are its representatives, and in particular subvaluationism(as Dominic Hyde developed it) must be considered in connection with the problem ofvagueness. However, I set those aside now, as all of those are basically semantic theories,
whereas I’m now focusing on ontic vagueness.
Instead, I want to propose a probabilistic approach to treat cases of ontic vagueness likethat of free will. Actually, the concept of probability concept will harmonizes with the truth-value
glut, since, for instance, when we judge the agent was free by probability 0.4, we affirm that 0.4
weight and negate 0.6 weight. Namely, the concept of probability concept admits that bothaffirmation and negation of one proposition somehow actually obtain, which conforms to thetruth-value glut scheme. Additionally, the probabilistic approach reacts to the law of excluded
middle in the same way as the truth-value glut approach, which is quite different from thereaction of the truth-value gap approach.
How, then, can we valuate the degree of free will in terms of probability?

I offer a brief

sketch as my tentative conclusion. When we face some borderline cases about whether anagent acted from their free will or not, we can collect (i) their physiological data -maybe about
their brains, (ii) and other data i.e., about time taken for them to give a primary and independent
answer to the question “why did you do that?” If they give an answer immediately, we cansuppose that the degree for them to be controlled by the external causes will be less, so theywere freer.

On the basis of those data we can valuate the degree of free will of a particular

agent. This is a sort of probability whose value 1 should apply to the state of perfectly freesituation, although ideally.

I think that this probability can be interpreted as either degrees of6belief, or a kind of objective propensity that people who valuate have. Although the free will I
analyzed here may be just a prima facie free will or only a part, it is one possible route forbringing the concept of the degrees of free will into philosophical discussions.

References
Broome, J. 1984. Indefiniteness in identity. Analysis 44: 6-12.
Evans, G. 1978. Can there be vague objects?
Grim, P. 2004. What is a Contradiction?

Analysis 38: 208.

In The Law of Non-Contadiction: New PhilosophicalEssays. 2004. eds. G. Priest, JC.Beall. and B. Armour-Garb. Oxford University Press.
Hyde, D. 1997. From Heaps and Gaps to Heaps of Gluts. Mind 106: 641-660.
Lowe, E. J. 1994. Vague Identity and Quantum Indeterminacy. Analysis 54: 110-14.

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