Why Knowledge is not "Justified, True Belief"

 

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.

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.

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 axioms, in and through the practice of doing math.