# One man's look at epistemology

This article by Dan Polansky contains various notes on epistemology, the philosophical inquiry into knowledge. A key inspiration is Karl Popper. Various observations will be sort of trivial, but one may sometimes benefit from going over platitutes.
Epistemology is to cover both any knowledge in general and scientific knowledge in particular. It therefore overlaps with philosophy of science.
Epistemology can be a worthwhile exercise. Its results can be at least in part counterintuitive. To me, the Popperian doctrine that we can never really conclusively verify scientific theories and that any genuine verification is an attempted falsification is very instructive and revealing. (Popper sometimes uses the word corroboration instead of verification to emphasize the inconclusive character.)

## Certain knowledge

One doctrine states that mathematics possesses certain knowledge whereas empirical sciences possess uncertain knowledge. Einstein made a point to that effect. Lakatos extended Popperian falsificationism in part to mathematics, in his Proofs and Refutations. Thus, there can be certain tentativeness even in mathematics.
The uncertainty of knowledge is demonstrated by the overcoming of Newtonian mechanics with Einstein's mechanics. Newtoning mechanics seemed to be so convincing verified and final, yet it turned out to be merely approximate, failing e.g. for high velocities. (One does not need to study philosophy to note as much; study of physics suffices. One may thus claim that this result does not stem from the field of philosophy and that philosophers merely reflect on what physics would have made clear without them anyway. But it is perhaps still useful to drive the point home as forcefully as Popper did, against Marx, Freud and Adler. Popper does not state that all that e.g. Freud states is wrong; his point is that it is not scientific.)

## Everyday knowledge

There are countless examples of everyday knowledge for which we feel certain from direct sensory experience that we know something. Thus, we think to know that e.g. there is a domestic cat over there or that the tree over there is a fir. In addition to sensory experience, we also often rely on verbal reports (whether auditory or in writing) and call the result knowledge, but this use of the word knowledge appears rather debatable to me. Nonetheless, Wikipedia aims to collect knowledge, or so it says.
A simple heuristic scheme one can sometimes find in literature is this:
* To see --> to know.
* To have heard --> to believe (without necessarily knowing).
Of course, the mapping is merely heuristic; one can read something (and thus see) and merely believe what one sees and one can hear the sound of the motorcycle engine and thus know (rather than being subject to hearsay).

## Knowledge in mathematics

Mathematics is thought to have certain knowledge due to using conclusive proofs. But one can put this to doubt, as is suggested by Hofstadter. Since, we do not have perfect certainty (in principle) that the systems of proof that we are using are consistent, meaning contradiction free.
One can also argue as follows: human minds are mammalian brains evolved as part of natural selection. Human methods of knowing may be merely adequate for survival and reproduction (and other gene support). It may turn out that the human brain hardware contains platform-wide defects that would lead all practicing mathematicians to recognize the same kinds of proofs as conclusive which in fact were inconclusive. I find this line of argument interesting and thought-provoking but very hard to accept. I tend to side with those who claim that mathematics has certain knowledge. Or at least some mathematics; Lakatos criticism is to be taken seriously. And one can recall that Newton's and Leibniz calculus was originally in, say, somewhat provisional state, lacking the rigor that modern mathematics requires. Perhaps the picture is more complicated and varied than one would want to believe.

## Unprovable knowledge

Unprovable knowledge exists. If I roll a die, observe the result, remember the result, and roll the die several times again, I know the outcome bar failure of memory but I have no way of proving it to anyone. This applies to a range of situations. It seems plausible that someone may succeed in committing, say, a murder and hiding all traces or traces of having done so.

## Documented knowledge

Above, I noted the thought experiment with rolling a die, and then having no means of proving the outcome. I can improve my chances of proving that by taking a record of the outcome. I could then show the record in the court of law. The proof/evidence would be inconclusive since I could have cheated or make some wild mistake when taking the record. But the record is stronger evidence than memory, since human experience generally shows human memory to be all too often frail. I can use the record later not only to convince the court but also myself. Since I too know that human memory is frail, whereas sheets of paper with writing or typing do not undergo a change in which some words get changed or similar.
Textual record necessarily leads to considerable loss. Knowledge obtained through eyesight about an object is much richer than the propositional knowledge captured in sentences. This is in part addressed by photography and videorecording as well as sound recording.

## Induction

I believe Popper is correct in stating that induction does not work to demarcate science from non-science. Moreover, it seems to me that induction hardly ever works at all. That is to say, if we have a predicate F, no amount of affirming instances of F would alone lead us to conclusion that for all x, F x (F is true of X). This also obtains for the more narrow form where F is in fact F ==> G. This is obvious in mathematics: we can have an arbitrarily large number of even numbers, but this does not lead us to conclude that all positive integers are even numbers; in this case, F is positive integer and G is even number. That is to say, we have a large set of examples meeting F and G, and thus meeting F ==> G, but that does not lead us to generalize that for all x, F x ==> G x. The situation is similar in sciences. Since, let us take F to be mammal and G to be domestic cat. Our seeing additional cats (examples of F and G) does not lead us to conclude that universally F ==> G, that is, that all mammals are cats. Instead, we consider the existence of refuting instances (e.g. dogs) and close the case as rejected.
A meaningful investigation of a hypothesis of the form for "all x, F x ==> G x" involves above all considering the store of all observations (in the mind or elsewhere) to check whether there are refuting instances. Additional step involves trying to find as many or varied instances of F since these are the ones that can lead to discovery of additional falsifiers, F x and not G x.
That's how it seems to me. A proper research in the literature on induction could perhaps lead me to a different conclusion or a correction of the above.
By induction I here mean induction in sciences, not mathematical induction. I constrained the concept of induction to exclude extrapolation and interpolation; it could perhaps be used more broadly to include those.

## Incompleteness of knowledge

Some of the Gödel's results are sometimes used to point out necessary incompleteness of mathematical knowledge. Thus, not only cannot human mind achieve all mathematical knowledge, not even machines can ever achieve it. One may trivialize the matter by pointing out that we cannot even know all the statements of the form X + Y = Z for three integers for lack of memory and such, but that is not the point.
It seems also likely that we will never have complete (empirical) scientific knowledge. At a minimum, predictive knowledge about future will be out of bounds dues to chaos or computational irreducibility. One could still hope to discover the ultimate fundamental physical laws, without being able to use them to predict everything.

## Authority and sourcing from publications

One often uses sourcing from publications. Interestingly enough, Popper scorns this as a method of doing science at least in one piece of writing. The theory of scientific method is not usually concerned with sourcing from publications. Einstein's famous special relativity paper does not contain much sourcing, if I remember correctly; better find the paper.
I view sourcing with a heavy dose of skepticism. Yet I cannot do without it. Things can be improved by differentiation: are we sourcing math or are we sourcing nutrition science (spinach has iron?). One can investigate various fields and their history of success and treat them accordingly, with higher skepticism as justified by the experience with the field. One can for instance suspect that math results will be more international or interculturar than history, where nations have strong interest to skew things or spin them in their favor or direction.
In mathematics classes in the high school and university, we almost never worked with "reliable sources"; we instead proved everything or almost everything. The teachers hardly ever invoked their authority, if at all; the authority was there of the proof, and the student had to verify the proof. Of course, this is perhaps somewhat idealized; the authority of the teacher perhaps does play a role, even in mathematics.

## Justified true belief

Knowledge is sometimes defined as justified true belief. That is to say, I know X if I believe it, X is true and I am justified in believing it. There is criticism of this definition/characterization. For one thing, as long as we use the word knowledge to refer to uncertain knowledge, things known to be true are not logically necessarily true (which seems like a paradox or contradiction since the word to know implies perfect certainty, but that cannot really be the case). Another criticism concerns the requirement of justification. Popper denies that knowledge is justified. But the idea of justification is plausible; in mathematics, we only know a theorem to be true if we have a proof. One could counter that axioms are not proven, to which one may respond that axioms are definitions in disguise and that theorems in ultimate analysis point to statements of the form, if axioms such-and-such are true, the following theorems are true. Yet another criticism applies to the genus of belief. As long as knowledge can be contained in a book, it does not seem to be belief. By contrast, knowledge in a mind does seem to be species of belief if one extends the concept of belief enough to include knowledge. This extension is perhaps required since otherwise, one would say that if one believes something, it implies one does not know it; and thus, knowledge and belief would be coordinate terms rather than one being subordinate to the other.

## Knowledge in plants

From what I remember, Popper indicates innate expectations of organism to be something like knowledge. Thus, a plant adapted to presence of sunlight via chlorophyl as if states, there is sunlight in the environment. I find this point interesting, but it perhaps stretches the concept of knowledge.

## Knowledge in animals

Knowledge in some animals, e.g. chimpanzees, seems plausible, including concepts. The concepts would be there, but not names for concepts.
Even simple animals can have knowledge or quasi-knowledge, including innate one in the form of innate expectations about the environemnt.

## Knowledge of historical statements

According to Popper, existential statements in sciences are not falsifiable and therefore not scientific. This seems rather counter-intuitive, but has some force. Thus, the statement that there is a teapot orbiting the Earth (Russell? Dawkins?) is not falsifiable/testable and does not have a scientific character.
This can be extended to historical statements. The statements of historiography would then be non-scientific. This seems strange but also not entirely so. Since, e.g. Newton's mechanics applies at all locations and all time points, so it runs the risk of being refuted in future. By contrast, the statement that the battle of Waterloo took place in year so-and-so and was between parties so-and-so does not directly run the risk of being refuted by a future event; it is not universally quantified. The textul historical record becomes an important source of (putative) knowledge, but that is not so in physics, chemistry or biology. I should perhaps learn more about the matter by studying methodology of historical and historiographic fields.

## Reason vs. experience

There is some kind of discussion about reason vs. experience in how we know things, relating to rationalism vs. empiricism. I cannot make much sense of it. I would argue that all or nearly all epistemic processes contain both elements of experience and reason.
Since, concerning everyday knowledge, we recieve perceptual objects in the mind, e.g. the visual perception of a cat. The visual perception appears raw in a sense, uninterpreted. But in fact, what is really uninterpreted is the retinal image; what enters the mind is merely based on that retinal image, enriched with inferred physical properties. And thus, something like reason (inference) is part of the perceptual cat, before anything like reason in narrow sense was applied.
Let us consider mirage. The raw sensory experience tells us we see something we do not see. And we use reason (informed by other experience) that what we see cannot be real. Both elements are present.
In mathematics, one could argue that it is based on reason and not experience. But I do not find that convincing. We know that our proving methods work in part from experience. That said, I fully recognize the contrast between mathematical knowledge and empirical knowledge.
We know very little by reason or critical thinking alone. Never direct your eyes to the sky and never engage in careful observation. Instead, lock yourself in an ivory tower and have a computer to do large-scale speculative simulations and analysis. You may find out about e.g. mathematical fractals or the road to chaos, but never about the stars. No amount of analysis can compensate for missing observation and experiment and for the missing observational and experimental instrumentation.

## Instrumentation

Large portions of science do not get very far without instrumentation, including telescopes, microscopes, measuring devices but also computers (computing and information storage and retrieval devices). These instruments enhance our getting to know, or make it possible in the first place.

## Revisionism and scientific revolutions

Inspired by Kuhn and Popper. In general, scientific knowledge does not grow merely by extension/expansion but also by modification. It is in general not cumulative in this sense. One cannot hope to establish a method so good that it will only lead to statements in no need of revision. In a geographic analogy, one could naively think of science as map maping where one only fills in the white blanks and never has to redraw any parts of the map. History of science shows that redrawing is necessary once in a while. But the cumulative character is far from absent. The filling of periodic table was probably not a process of continual scientific revolution; once the concept of chemical element was well established, the process of finding additional chemical elements was probably relatively cumulative. (But I would need to check relevant literature to learn more and be sure I know what I am talking about.)
Kuhn makes the point that a certain degree of resistance to refutation and sticking to theories that appear to be refuted by observation does not need to be a bad or unscientific thing. The apparent refuting observation may later turn out not to have been refuting after all. On the other hand, the contrast between religious dogma and scientific successive modification of tentative knowledge is real, and one characteristic of good science is that it does not stick to refuted theory beyond what is reasonable (for some value of reasonable).

## Proof and evidence

As part of inquiry into knowledge, one can include inquiry into what serves as proof and evidence, in relation to the justified part of the characterization of knowledge. This concerns not only science but also courts of law. Courts accept witness evidence although it is logically very inconclusive.
Mathematics provides one idea for what a proof is. This idea does not seem to directly carry over to other fields.
In the field of software, automatic test suite run against the software is a form of proof or evidence that the software meets the requirements/works as required. Educational examination provides something like a proof or evidence that the student has learned the matter. Industrial testing is another case.
In another section, I supported Popperian falsificationism as a standard. There, one does not prove things; one tries to refute them. How, then, can one substantiate corroboration (attempted falsification) of a hypothesis? For instance by submitting documentary or data evidence indicating what attepts at refutation were attempted, what observations and experiments and with what results. That is the first idea; a better elaboration would be preferable.
Further reading:
* evidence, britannica.com
* proof, britannica.com

## Certificates

Certificates seem to be something like evidence or proof. They can perhaps be thought of as written testimonies of the entity issuing the certificate. Educational diplomas are one class of certificates, it seems. Identity documents are a related concept.
Certificates are subject to the risk of forgery. This is one source of their being less than fully conclusive as evidence. Even so, one may say: I know that his name is so-and-so since he showed me his identity card. This is one piece of evidence supporting a weakened use of the verb to know. The utility of certificates depends in part on our willingness to run the risk of being deceived by them. Indeed, if authorities and other organizations did not see any addition of certitute resulting from their use, they would not use them. Obtaining a forged document requires additional effort and expenditure compared to merely making an untrue statement.
Further reading:
* Identity document forgery, wikipedia.org

## Procedural knowledge

Apart from declarative knowledge (e.g. knowing there is a cat over there), there is also procedural knowledge or know-how. Procedural knowledge can have a non-propositional form; thus, one may know how to dance jive without being able to give verbal instructions. Even human ability to walk can be seen as a procedural knowledge. Tigers can be thought of knowing how to run, thus having procedural knowledge. Alternatively, one could distinguish knowledge from skil and consider ability to dance jive to be skill, not knowledge.
Some procedural knowledge does have a propositional form, form of sentences.

## Innate knowledge

Some knowledge is innate, given by the genes. Knowledge-acquisition aparatus (e.g. eyes and the visual cortext) is innate. Knowledge being innate does not make it necessarily accurate. Thus, it seems likely that the innate geometry in human vision and understanding of space is approximately Euclidean; the human environment under which it evolved seems unlikely to contain anything to give stimulus to evolution of Einstenian geometry (which is needed in GPS).
These considerations can lead to deep skepticism. One may think that human knowledge acquisition faculties are only good enough for survival and reproduction (and other support of the genes) and that they may fail miserably when used outside of their bounds. Part of this skepticism is perhaps healthy. One can launch a defense: how do you know that humans originated by evolution by natural selection? If the human faculties are so frail, you should not be so certain. And then you should not be so certain about your skepticism either. It is an entersting twist, pointing to certain apparent circularity in attempts to reason about knowledge with the use of Darwinism. Since, one needed an initial knowledge theory to learn about evolution by natural selection, but the results can then impinge on the knowledge theory itself. I sense this is not a grave defect, but I acknowledge the line of reasoning as not without merit.

## Knowledge of word meaning

The knowledge of word meaning is an interesting problem. In order to formulate an observation in language, one needs to have knowledge of word meaning. But word meanings are not trivially objectively observable entities, unlike e.g. cats or rivers. The knowledge of word meaning does not need to be explicitly represented in words; thus, one may be able to use language productively without being able to give plausible definitions.
Lexicography seems to posit that word meaning can be extracted from quotations of use. But this seems to be far from trivially obvious. It seems one has to insert a lot of conceptual interpretive analysis to extract the word meaning.
Knowledge of word meaning cannot be innate since words are not innate. But some general concepts could be innate rather than obtained from experience. A child could be trying to map the words heard to the naive observational ontology (or entitology?) given by the senses, especially sight, and then refine the ontology based on the language use. It seems doubtful that the child's naive observational ontology would contain the nodes of mammal or feline, but it could well contain animal and cat. The node of animal could be innate; cat perhaps not. These questions would need to be seriously investiated.

## Cybernetics

One could use the ideas from cybernetics to investigate knowledge. Thus, one could set up two abstract systems, one trying to learn about the other and try to figure out what that learning would consist in. In relation to that, I seem to remember that Ashby indicates that being a model is given by isomorphism or homomorphism.

## Scientific models

The concept of a scientific model seems to point to the idea that elements of scientific knowledge are rather imperfect representations of reality. Both Newtonian and Eistenian mechanics can be seen as models. But also Ptolemaic astronomy can be seen as a model, one that has been made increasingly observationally adequate by subsequent modifications during its use.
A visual analogy for the concept of scientific model can be a toy model of a car. The toy model bears some resemblance to the real thing, but key aspects are missing. To what extent this analogy is apt would need to be clarified.
Further reading:
* Models in Science, Stanford Encyclopedia of Philosophy

## Counting and calculation

Counting and calculation are both epistemic processes.
Counting is additional to seeing. Thus, one can see e.g. many cows, but to know exactly one many, one has to count, unless the cows are only few.
Calculation with numbers can answer arithmetic questions. Some indicate this results in no true additional knowledge, which makes sense from the perspective of empirical knowledge, but sounds strange anyway.
Logical derivation using logical calculus is an analogue to calculation with numbers. In any case, it is a mechanical manipulation of symbolic encodings.
Calculation is a key part of computed tomography and magnetic resonance imaging. Without calculation, the medical doctor would not be able to see much. Revisiting the argument sometimes made that calculation adds no true knowledge, that is all nice and perhaps superficially plausible, but here calculation makes a difference between seeing something (on the display or other visual representation) and seeing nothing at all.
Humans are rather bad at calculation, too ready to make calculation errors. This can be addressed by verification. One may do the same calculation multiple times. One may let another person do the same calculation independently (the person doing the first calculation may have a blinder that will lead to the same error when he tries to make a 2nd calculation). And one may calculate the inverse function, e.g. first do long division, and then multiply the result back. There seems to be a host of various other partial plausibility checks, depending on what one calculates.

## Measurement

Measurement is an epistemic process. Like counting, it yields a quantitative characterization of something.
There seems to be the field of metrology concerned with this subject.
Measurement adds information beyond mere visual inspection. Thus, there is a difference e.g. between estimating the length of a table from looking at it and measuring the length using meter.

## Knowledge of the knowing agent and apparatus

Something like metaknowledge can contribute to epistemology, knowledge of the knowing agent and apparatus. Thus, one may empirically study limitations of human cognition, limitations of measuring instruments and measuring procedures, etc.
One could object that part of such inquiry is no longer philosophical but rather psychological. Nonetheless, I am wary of strictly separating philosophy from psychology. Perhaps someone can execute such a separation well enough; let them then present what they have done and how and let us see whether the result is satisfactory.

## Epistemology vs. history of knowledge

One could want to separate epistemology from history of knowledge and history of science. One could want to prohibit input from the latter to the former; the former would be purely philosophical. I can see the attraction of doing so from something like architecture of inquiry standpoint, but I do not think it a good idea. For instance, one can hardly fail to observe the impact of Einsteinian special relativity on the philosophy of scientific knowledge. The history of human theories about the world is very instructive, revealing incredible fallibility and openness to wrong suggestion.
One can say: I am fallible. My analyses of knowledge are tentative. Their being philosophical is not a good thing per se. If findings of special sciences can shed some light on the questions being asked, so much better. Thus, it is e.g. all fine to use Darwinian thinking to speculate about quasi-knowledge embedded in plants.

## Failed epistemic methods

It is instructive to consider not only what is likely to work well but also what has demonstrably failed. Torture is one thing that does not necessarily make one say truth. There are other absurd methods that were sometimes used in history, to be added later.

## Epistemology of philosophy

If philosophy contains a key non-empirical element, one can wonder whether there is a separate epistemology of philosophy, different from epistemology of empirical sciences.
For philosophy, one can use something like proposals and refutations, arguments and counter-arguments. The basis for making them is not constrained, but it usually contains both empirical and deliberative element. It is understood that the proposals are too likely to be wrong too often. It is also understood that running the proposals through the acid test of counter-arguments does not establish anything like certainty or validity. The results do not resemble science with its marked progress, e.g. from before the concept of chemical element to the concept and discovery of the individual chemical elements.
Be it as it may, the human brain has this remarkable capacity of coming up with ideas formulated as sentences, without knowing whether they are true or right. The brain seems to use some fantasy or inventive method: figure out something half-plausible and say it. And then, see whether we can refute or effectively criticize the thing said. This is hardly satisfactory. We should have something better.

## Reviewing

Reviewing is a powerful method for reducing mistakes. A review can take place when there is something to be reviewed, e.g. a document such as a draft of a scientific article. One can review one's own writing, but bringing in other people generally makes a remarkable difference. There may be a subliminal block or resistance to seriously and earnestly looking for mistakes in one's own creation; other people may be more openly adversary (and pointing out mistakes is adversary in principle). Moreover, other people may happen to see things from a different perspective. And they may be more experienced and know better.

## Evolutionary epistemology

The phrase evolutionary epistemology could refer to epistemology informed by biological evolution, e.g. one emphasizing the evolutionary origin of organs that play a key role in knowledge acquisition, including eyes and the brain. Or it could refer to epistemology that sees scientific theories are objects undergoing evolution somewhat similar to biological evolution. It seems to refer to both, as per SEP.
Further reading:
* Evolutionary Epistemology, Stanford Encyclopedia of Philosophy

## Artificial intelligence

One would expect artificial intelligence to be able to produce something like knowledge from observation. Sufficiently capable artificial (general) intelligence should be able to use e.g. camera to produce observational reports in natural language. One would naturally ask whether the machine really knows anything or merely imitates knowledge or pretends to know. Study of design of an AGI machine would seem to be a contribution to study of knowledge processes. One would be forced to technically clarify issues instead of waffling about them. One would be forced to discover sets of technically formulated principles, rules and algorithms. Alas, one thing one would discover would be artificial neural networks, which can be trained, but from which it seems hard to extract anything like human-intelligible sets of rules or principles.
Machines can produce mathematical knowledge without having anything like human-like subjective knowledge states. Thus, machines can do arithmetic calculations. Moreover, machines can do computer algebra, including derivation. There are theorem provers. That is to say, whenever the knowledge production (reliable production of true statements) can be supported by a reasonably small set of mechanical rules, it can be done by a machine.
One may look at a human as a gigantic lumbering (biological) robot (to use Dawkins phrasing) and wonder whether the human intelligence and cognition is after all also a collection of mechanical rules embedded in neural and endocrinal anatomical structures. Many of these rules would be heuristic, rules of thumb.
Recalling the section on instrumention, current production of human knowledge is an effect of biotechnosphere, of a combination of humans (bio-) and machines (techno-). For instance, astronomy uses telescopes as well as computers.

## Knowledge about knowledge sources

Knowledge about knowledge sources/providers is key for distinguishing reliable from unreliable sources and thus reducing chance that one ends up in error.
For instance, one may have good experience with a particular geographic map publisher, having learned first-hand that their maps match the terrain visited. One may then say: I know there is a bridge over the river at that location since a map published by a reliable publisher indicates as much. Alternatively, there may be an indirection: one may not have first-hand experience with the map publisher but one may know a reliable assessor of publishers, and the reliable assessor may indicate the publisher is reliable.
He who trusts unreliable sources and makes reports based on them is himself unreliable. Thus, one may feel to have a duty to only trust sources for which one may have good reason to believe they are reliable. And if not because of duty, one may dislike being considered unreliable.
In an ideal world, one would simply divide sources into reliable and unreliable, trust the reliable ones and be done with it. Unfortunately, there hardly exist any perfectly reliable sources completely free from mistakes. One may know about a source that it contains remarkable number of mistakes but continue using the source anyway for lack of better alternatives, mentally marking the information as having an increased uncertainty. Moreover, one may differentiate what kind of statements are more likely to contain mistakes in the source class, e.g. mainstream media. For instance, when mainstream media report that so-and-so was elected a president, that is perhaps much more reliable than when they report that scientists found such-and-such.
One can increase confidence by considering multiple independent sources instead of only a single source. However, true independence may be hard to come by. Even so, consulting multiple sources is often a meaningful exercise that reveals how the sources differ.