Why Knowledge is not "Justified, True Belief"

 

No serious philosopher, indeed no reasonably intelligent person who has given the matter sustained thought, believes that knowledge consists of nothing but justified, true beliefs. 

It's wrong on all counts.  For something to be knowledge, it doesn't need to be justified.  Furthermore, it doesn't even need to be true.  But most importantly, it doesn't even have to be a belief.  

Let's take each of these, one at a time.

Justification

Does knowledge need to be justified?  Of course not.  The idea that knowledge has to be justified is silly on its face.

For one thing, this leads to a logical regress, which could potentially be infinite.  Let's say that you want to know a potential piece of knowledge- call it "A".  But in order to know "A," according to this theory, you have to justify it - you can call the justification "B".  But this justification would also be a piece of potential knowledge.  So in order to know "A," you would have to know "B".  But in order to know "B," you would have to be able to justify it, and so you would need another piece of knowledge, "C".  It's not hard to see that you would need "D," "E," "F," and... well, would this ever end?

There are two possibilities: either this ends, or it doesn't.  If it doesn't end, there are a couple of possibilities: either knowledge forms a circle of justification (where, let's say, A is justified by B, which is justified by C, which is justified by D, which is justified by E, which is justified by A), or the chain of justification simply goes on forever without repeating.  (Of course there's also the possibility of a complex web of justification, rather than a linear progression, but this web must either contain repeating cycles of justification or go on forever.)  If there is a cycle of justification, this implies that a piece of knowledge must (indirectly) justify itself - which seems like it would undermine the very meaning of justification.  If it goes on forever, this too seems like a failure of justification.  On the other hand, if the chain of justification ends, that means one of two things: either there is a piece of unjustified knowledge, or there is such a thing as self-justifying knowledge.  If there is such a thing as unjustified knowledge, then we have proven that knowledge isn't always justified.

All of which leaves only one possibility: that there is such a thing as self-justifying knowledge.  Now on the one hand, if self-justifying knowledge exists, then it seems we are facing the same problem where we have cycles where we question whether a certain piece of potential knowledge can exist, and we notice that it can be justified by a chain of pieces of potential knowledge which end back at that original piece of potential knowledge that is under investigation - though in a much more concentrated form.  So it seems that the very meaning of self-justifying knowledge is dubious in the extreme.

On the other hand, if self-justifying knowledge does indeed exist, if there is at least one piece of self-justifying knowledge, then why can't we say that other pieces of potential knowledge are self-justifying?  Or even that all knowledge is self-justifying?  Why does 2+2=4?  Because 2+2=4.  How could you distinguish between the self-justifying forms of knowledge and the non-self-justifying forms?  (And if you do know how to distinguish them, wouldn't that be a form of knowledge?  And would it be self-justifying?)

There are, in fact, potential examples of self-justifying knowledge that philosophers have proposed over the centuries.  Perhaps one of the most prominent is Descartes' famous "cogito ergo sum" ("I think, therefore I am") - the general sentiment of which had already been offered by Aristotle in his Nicomachean Ethics: "to be conscious that we are perceiving or thinking is to be conscious that we exist," and somewhat similar ideas had been expressed even earlier by Plato and Parmenides.  Descartes believed that it was possible to deduce much more on the basis of this self-justifying knowledge, beginning with the existence of God and the existence of the external world.  But even if we accept that the cogito is self-justifying - a somewhat dubious claim itself, in my opinion, but one which I will explore in detail elsewhere - I reject the logical steps that Descartes takes beyond the cogito, and it's difficult for me to what, if anything, can be reliably deduced from the existence of one's own consciousness.  If anyone has any ideas, I'm open to listening to any and all arguments either taking steps beyond the cogito or considering other candidates for self-justifying knowledge besides the cogito, but those arguments that I've seen have not been particularly convincing and alternative arguments are not very obvious.

To make an already long story a bit shorter: even if self-justifying knowledge exists, somewhere, somehow, and even if some other pieces of knowledge can be derived from it, surely it seems somewhat implausible that all knowledge can be derived from this self-justifying knowledge?  There are other kinds of knowledge out there.  More on that in a moment.

Truth

But first, let's consider the next question: in order for something to be knowledge, must it be true?  I think the answer is no.  

In my opinion, some things are true, and some things are knowledge, and there is an overlap between the two, as in the classic Venn diagram.  But not all knowledge is true and not all truths are known.  In other words, I wouldn't go so far as to say that knowledge is unrelated to truth.  But I would say that truth is neither necessary nor sufficient for knowledge.

Consider fiction: I know that Tom Sawyer had an aunt named Polly.  But is it true that Tom Sawyer had an aunt named Polly?  No- both Tom and Aunt Polly are made up characters, invented by Mark Twain.  But do I know Tom Sawyer's aunt's name?  Yes, I do.  

Some of you out there may be objecting: well, this is just a kind of shorthand.  When I say that I "know" that "Tom Sawyer has an aunt named Polly," what I really mean is: "According to the novel, 'The Adventures of Tom Sawyer,' Tom Sawyer has an aunt named Polly," but for simplicity's sake, I left out the opening (italicized) prepositional phrase of that sentence.  But the sentence is only true when this crucial bit of context is added back in.

Very well.  But I contend that all (or at the very least, most) propositional knowledge is of this form - that it has important context, which is usually left unspoken.  (Again, more on this in a moment.)  For instance: if I say that the formula for the kinetic energy of an object moving in a straight line is 1/2 mv^2, I am leaving out the phrase "According to Newtonian mechanics".  In a different context - namely Einsteinian mechanics - we would of course use E=mc^2.  So, in a sense, it is not "true" that kinetic energy=1/2 mv^2.  And yet it would be absurd for anyone to say that knowing that kinetic energy=1/2mv^2 does not constitute a form of knowledge.  Of course it does.  You have to study to learn that KE=1/2mv^2.  Simply memorizing this formula constitutes knowledge - and being able to use this formula to solve problems is a greater degree of knowledge, which requires practice.  Just because Einstein showed that KE=1/2mv^2 does not hold true for every possible context did not suddenly and automatically render all of the knowledge of Newtonian physicists and engineers and designers and architects into non-knowledge.  They still had just as much knowledge after Einstein published his discoveries as they'd had before.

(By the same token: E=mc^2 closely approximates KE=1/2mv^2 at sufficiently low velocities and in regions of relatively low space-time curvature, and yet E=mc^2 is the more general equation that gives accurate results even at velocities close to the speed of light and in regions of high space-time curvature, such as areas near black holes.  But who knows?  Maybe, one day, it may turn out that another Einstein-like genius will come along, and will come up with another formula that is even more general than Einstein's formula and which holds true in even more extreme contexts - at the singularity at the center of a black hole, for instance.  Would that make all of Einstein's special theory and general theory of relativity into non-knowledge?  Of course not.  Would that make all of the physicists who still use Einstein's formulae into ignorami?  Not at all.)

It may not be "true" in some absolute sense that kinetic energy equals 1/2mv^2, but pragmatically we continue to study and learn this principle, and it is still very useful.  Not only that - it is a foundational kind of knowledge, through which we, as students, build up to more difficult kinds of knowledge, such as those discovered by Einstein.   

This brings us back to the question of justification: in order to know that KE=1/2mv^2, is it necessary to understand why KE=1/2mv^2?  In other words, in order to use this formula, do you need to be able to derive it from first principles?  Not at all.  You only need to know that it works - and practice, practice, practice.

In fact, in the history of science, it has occurred more than once that scientists have "stumbled onto" important truths.  Charles Goodyear discovered the process of vulcanization without fully understanding the chemical process involved.  Alexander Fleming noticed that bread mold producing penicillin and that it retarded microbial growth without fully understanding how.  You only need to discover a pattern, and notice that it works, and be able to apply it in useful ways: this constitutes knowledge, even if you don't know why it works.  Often, expanding human knowledge is more about tinkering than it is about deriving truths from first principles - it is more "perspiration" than "inspiration" as Edison put it.  The Wright Brothers developed the airfoil, and for decades we misunderstood how they work - the popular explanation, about air flowing faster above the wing than below it - did not account for the fact that, for instance, trick pilots are able to fly upside down.  You find out what works first, and then you develop an explanation for it.

And just as, in physics, there are often unspoken contextual conditions such as "according to Newtonian mechanics," "according to Einstein's special theory of relativity," "according to the Copenhagen interpretation," and so on, so it is in every science and, as far as I can tell, in every form of human knowledge.  Take, for instance, math: according to standard analysis, there is no such thing as an infinitesimal quantity.  But according to non-standard analysis, infinitesimal quantities can exist.  Well, which one is "true"?  It's not clear, and it's not even clear what that question means.  (That doesn't mean it's not worth thinking about.  On the contrary, I think this is a very interesting and important question.)  But in any case, if one is true, and the other is false, or even if they are somehow both false, and some other understanding of mathematics is more accurate, would that make any difference as to whether studying any of the above produces something that constitutes knowledge?  I say no: they are all forms of knowledge.  

Mathematics offers us a very pure example of this philosophical concept, because in math, unlike in, say, literary analysis, there is a right answer, and there are wrong answers.  And yet a correct answer is only correct given a set of axioms, either implicit or explicit.  In some cases, an implicit axiom may become explicit, after the fact - a perfect example of this was the axiom of choice, which countless mathematicians were using without realizing that they were using it.  Who knows what other axioms we may be using, without knowing we are using them?  To my mind, the very essence of the progress of the history of math is the discovery of its own axioms, in and through the practice of doing math.

Belief

But I'd almost go so far as to say that all of the above is beside the point.  Unfortunately, philosophical debates about whether all knowledge is justified true belief usually tend to focus on the "justified" part, or occasionally the "true" part.  But to my mind, the most important problem with the "justified true belief" model of knowledge is the "belief" part.  Of the three conditions, this is the one that is most wrong.

Not all knowledge consists of beliefs - justified, true, or otherwise.  In fact, I would argue that beliefs constitute an extremely small part of knowledge - if there is any overlap between beliefs and knowledge at all.

Consider the ability to ride a bike.  Is this a belief?  Does it consist of beliefs?  If I believe something about bikes, will this belief give me the ability to ride a bike?  I can read every book about bikes, memorize every aspect of their history, manufacture, maintenance and mechanics, and yet I still won't know how to ride a bike.  If took these memorized facts and believed them, scrunched up my forehead and concentrated and put all my faith in them, and believed them as hard as I could, would that bring me any closer to knowing how to ride a bike?  Clearly not.  Yet I know how to ride a bike. The only way to learn how to ride a bike is... to ride a bike.  The essence is practice.  

The same is true for a vast number of human activities: swimming, playing basketball, sewing, playing the cello....  In order to learn a language - say, Swedish - do you need to believe something about Swedes?  Do you need to believe something about Sweden?  Do you need to believe something about language?  Do you, in fact, need to believe any particular thing at all, in order to speak this language?  No, you need to practice speaking, listening, reading, and writing the language.

Knowledge and belief are not the same.  An example, from my own life: I took what is normally called "Civics" in high school.  (In my school, growing up, as I've mentioned elsewhere on this blog, it was called "PIG".)  This was an absolutely terrible class, with a terrible curriculum, and a terrible textbook, taught by a terrible teacher.  It was, through and through, nothing but propaganda - and I knew it at the time.  I was a teenage anarchist.  

I did pretty well in this class.  I studied, and I was able to do well on the tests.  But I hated it.  I correctly filled in the little scantron bubbles with a number 2 pencil for the multiple choice portion, and I wrote clearly and comprehensively for the essay portion.  I knew exactly what they wanted me to say.  But I didn't believe a word I was writing.  I had the knowledge, but not the belief.  The belief had nothing to do with the knowledge.  In the meantime, my opinions have mellowed a little.  Maybe my beliefs are now closer to what they taught back then, in some ways.  But that really doesn't matter.  The knowledge stays the same.  The degree of belief, or lack thereof, makes no difference.

I had friends who were various kinds of religious fundamentalists: Evangelical Christians, Mormons, Jehovah's Witnesses, and so on.  Some of them were Young Earth Creationists.  I'll bet they felt the same way, in biology class, answering the quizzes on evolution, that I felt during PIG.  They had the knowledge, but they didn't believe it.  And that's fine.  You don't have to, as long as you do it.  I'm tempted to say that for knowledge, all that is necessary is that you "go through the motions".

Even math, I would argue, is something that you learn by practicing solving problems.  It is not necessary to believe anything in particular, so long as you do the work.  The practice is what matters.

In fact, it makes sense to be skeptical whether there are any justified, true beliefs - or, if there are, that any of these justified, true beliefs constitute knowledge.  Maybe there are, and maybe they do - or maybe not.  I don't have a strong belief either way.  I don't know.  

(I mean, we could argue forever about, say, "2+2=4".  I'm willing to say that I believe that 2+2=4, and that I consider this a kind of knowledge.  But then some pedantic person could point out that 2+2 does not equal 4, mod 3, or in ternary numbers, etc., etc..)  But I think these arguments are beside the point.  The main point is: even if there are justified, true beliefs, and even if they do constitute knowledge, not all knowledge consists of justified, true beliefs.  Indeed I think that the vast, overwhelming majority of knowledge does not consist of justified, true beliefs.

I suspect that belief and knowledge are related to each other somehow - or at least I hope so.  My guess is that beliefs can sometimes arise as a kind of byproduct of the process of learning various forms of knowledge, as a kind of epiphenomenon.  Take, for instance, chess.  As a person learns to play chess, they might, along the way, come to the belief that "In order to win at chess, it's important to control the center of the board."  Note that it's possible that a person, at a certain level of the development of their proficiency, might go through a phase of having that belief, only to discard this belief as a hasty overgeneralization once they have learned more.  

Maybe even I would go so far as to make some speculations about this, such as: maybe some people sometimes spontaneously come to have certain beliefs, based on the experience of their practice, whereas other people (or even the same people) at other times only acquire beliefs because someone told them such-and-such.  Maybe these are quite different phenomena, which only have the superficial appearance of being the same thing.  So for instance, in our chess example, perhaps "In order to win at chess, it's important to control the center of the board" means something different when you have arrived at that belief spontaneously arising out of your own practice, rather than when you hear someone else say it.  Maybe even if you do hear someone say it, you don't really know what it means until this has arisen out of your own practice - and then you have that "aha" moment, in which you say to yourself, "Oh, so that's what they meant."  Maybe even when you hear someone else say it, and then you have the experience that gives it meaning, and then you pass it along to someone else who is trying to learn chess, anything you can say about this kind of strategy is merely a rough - and necessarily incomplete, not to say, ultimately, incorrect - summary of the real content that you have learned.  In short, perhaps the parts of knowledge that can be expressed as justified, true beliefs are still ultimately nothing but hearsay.

In any case, I am convinced - I believe! - that whatever the relation between knowledge and belief might be, what matters most for knowledge is practice.  It's not just that "justified, true belief" is not necessary for knowledge.  More importantly, it is not sufficient for knowledge.  A justified, true belief is (theoretically, at least) something that you can acquire at once: someone simply has to give you the convincing justification, and then you have it.  But knowledge is not like that - it has to be done over and over and over again, in order to be learned.  (I would even argue that persuasion is not a matter of justified, true beliefs - even in this realm, it requires (at least) repetition - and probably more than that, such as experience, problem solving, practice, personal psychology, and an entire set of complex social relations, to persuade a person of something, even if that thing is true and justified.)

Language

Which brings us to an underlying issue - an unspoken assumption, ironically enough - which is that knowledge requires true, justified opinions in language.  When an academic tells you that knowledge is a belief that is true because it can be justified, what they usually mean is that it can be justified in words.  And when a wanna-be Socrates asks an innocent person - a violinist, say, to justify their knowledge of how to play the violin in words, and after repeated questions demonstrates that they can't, the wanna-be Socrates will conclude that the violinist has no knowledge, when he has done no such thing.  The violinist will go on knowing how to play the violin, their knowledge unaffected by the wanna-be's annoying questions.  It's actually the wanna-be Socrates that has demonstrated his lack of knowledge.

I might even be more open to the idea knowledge is justified, true belief, if the concept of "justification" were expanded to include forms of justification that are non-verbal - and if we expand the concept of "belief" to include non-verbal beliefs, and if we expand the concept of "truth" to include non-verbal truths.  But I'm not sure exactly how that would work.  It's more complex than it sounds.