Knows: A person a knows that q iff (a believes q) and (q).
Note that this is meant in the sense: a has a belief to the effect that q, and as a matter of fact q is true, regardless of a's reasons for believing in q, and also regardless of whether or not it is in fact widely known that q is true.
1. As defined, knows is a propositional attitude defined in terms of believes, and things are intentionally left simple.
One common widely accepted definition of "knowledge" is "justified true belief", but there are several problems with the "justified" part, that is left out above.
One reason is that one may be justified in quite a good sense yet be mistaken, as happens in science, and as may happen to oneself if one believes one's car keys are in the trash-can because one's little daughter has put them there, whereas they are there but for another reason, and a third is that the whole notion of justifying a belief is none too clear.
2. A complication of the above, that is in fact quite welcome for many ends, is that (q) itself may be a proposition that attributes some sort of probability, as in "a knows that this fair coin has a probability of falling heads of 1/2".
This is a complication because it makes the analysis of what is involved in knowing more complicated, but it is welcome because the analysis is more subtle and anyway all thinking human beings believe in many probabilistic propositions.
3. It is quite consistent with the given definition that a sincerely believes that a knows q, and that a is completely mistaken - that is, a is right in maintaining (a believes q) but as a matter of fact (~q). In brief, one may believe one knows and be mistaken.
Indeed, since it seems quite true of everyone that one knows about some of one's earlier beliefs that they turned out to be mistaken, it follows that everyone knows something, if only about one's own beliefs, one's own lack of knowledge, or one's knowing the natural language with which one can state claims to the effect that one knows almost nothing and knows one knows this.
Now the proposed minimalistic definition of knows is interesting also in that it is a conjunction of a propositional attitude of a person (a belief) and a statement of fact - while it would seem as if the latter, even if true, cannot be known by the person except in the form of a propositional attitude.
For the reasons just given it seems quite sensible to assume that every living person knows something, if only that one is often mistaken about what one believes one knows. That is formally: (a)(Eq)(aKq), where "K" is short for "knows".
And this again is quite compatible in principle with knowing one knows some things without knowing which, except for this, or - far more realistically - with knowing that one probably knows some things and certainly is mistaken about others, without presently knowing which.
Incidentally, in these formulations a non-constructive use is made of the existential quantifier: If one knows one is mistaken about some things and doesn't know which, one cannot instantiate them other than by artiticial formulas like "Let t* be something I believe I know but am mistaken about while I don't know more about it". (The tip of the tongue phenomenon - "There is a name for this thing, I know, but I just now can't recall it" - is another example of such an existential quantifier.)
4. There is a tradition that adds to the given definition a clause to an effect like this "(a has justifiable reasons for believing q)". This has been defended by Ayer, after Ramsey have his version "(a found q by a reliable process", and attacked by Gettier, who showed that for many such additions examples may be thought of that made the reasons both plausible and mistaken - making the knower believe something that was true and that he justifiably believed himself to have good reasons to believe, except the knower was mistaken about his reasons.
t seems: Many have drawn more radical conclusions, such as that the analysis of "knowledge" as "justified true belief" has been overthrown or shown to be mistaken. All that has been shown, it seems to me, is that one's reasons for believing one knows may not be as good as one believes, and one may believe one knows, and indeed does know, but not for the reasons one believes it.
This is in line with what is a more serious difficulty with the concept of knowledge:
5. Much of what a person, or indeed what human beings, once believed he knew, or they knew, perhaps also for what they all thought were very good reasons, and indeed may have been so, has been shown to be false. One example is Newton's theory of space, time and gravity, that was overthrown or at least corrected by Einstein's theory of general relativity.
And this in turn may be found to have been mistaken, even though presently it counts as very well confirmed.
There are various ways to deal with the problem that what seems firm and justified knowledge may - perhaps long after one has died - turn out to have been mistaken.
Since there are many kinds of knowledge and many kinds of justifications of knowledge, probably the best answer to this problem is to admit it for the case of scientific knowledge, and therefore also for any other kind of knowledge, on the ground that scientific knowledge has the best justifications compared to other justifications, and to hold on to five general points
- First, any scientific knowledge that has been used for manufacturing artefacts - cars, lamps, dynamos, bridges, airplanes, computers - that did not exist without it, must have gotten most things right even if some things may, after all, be found to be mistaken or not quite correct. See adequacy.
- it makes sense to keep two general qualifications in mind
(1) Even the best laid foundatiions of some specific claim to knowledge may be mistaken
(2) Generally, mistakes in scientific knowledge that technologically worked were partial and local.
- Third, in many ways, human knowledge has been accumulative: Newer knowledge generally built on and arose from older knowledge, which it often did not so much overthrow, though this happened too, as corrected in some detail, and extended in a hitherto unknownn direction.
- while one may be mistaken in many details and convictions about facts, and while one is always ignorant of much that will be known eventually, if mankind keeps existing, thinking and doing real science, it is unlikely that a person with a scientific outlook, and good knowledge of mathematics, logic, physics, biology, and history, is mistaken in all major ways: This has never happened to such persons (with a scientific outlook, and good knowledge of with a scientific outlook, and good knowledge of mathematics and science).
- What tends to get overthrown radically, in nominally scientific traditions, which are the only ones to take rationally serious in this context of "justified true belief", are for the most part specific theories, that specify specific things, such as Priestly's phlogiston (that was a mistaken theory about what is now called oxygen), and sometimes branches of some science, either because they did involve assumptions of things shown to fail to exist in fact, or else because their got to be better ways to do that branch of science.
Finally, those who desire logical reasons should consider that there is much any adult person knows, in terms of mere natural language and some basic mathematics and logic: One cannot even say cogently that "one knows one does not know anything", for the least one needs to know to claim that, are the rules and terms of the natural language that one states this incoherent claim in.