At least since Plato’s Theaetetus, philosophers have had a standard definition and understanding of knowledge (although there are a wealth of specifics to argue about within this understanding).
What is knowledge?
Knowledge is true belief plus a third quality called warrant or justification, or for short “warranted true belief” or “justified true belief.”
Let’s look at these:
1. Knowledge is always of something true. If P is not true, then I cannot know that P. I can believe that P, because a belief can be either true or false. If I falsely believe a man is 45 years old, when he is really 47 years old, I do not and cannot know he is 45.
2. Knowledge, subjectively, involves belief, that is, mental affirmation of the truth of something. It is senseless to say “I know that P … but I don’t believe it!”
3. If I believe that P is true, and P is true, then don’t I know that P? No, because I might believe that P by some means that has nothing to do with the truth of P. In other words, the fact I believe that P and the fact that P is true might be merely accidentally connected.
I believe many things simply on the grounds that I have been told them. Sometimes being told something by someone is a sufficient warrant to believe it: for example, a person we have just met telling us their name. And yet, we also know that it is possible the person telling us their name is using a false name, for whatever reason. More commonly, we know that human beings like to tell sensational tales; hence, the many urban legends we have all heard at one time or another, or the common cultural myths that circulate popularly, but are known to be false by historians. Once he had a reputation for saying witty, quirky things, for example, people were quick to attribute many witty, quirky things to Yogi Berra, leading him to say “I never said most of what I said.”
Thus, philosophers hold that there is a third element to knowledge which rules out lucky guesses and other merely accidental connections between belief and truth, and this is what we call warrant or justification (hereafter I am simply going to speak of warrant. The two terms are interchangeable).
Certain interpretations of warrant are subject to what is called the Gettier Problem, named after philosopher Edmund Gettier, who threw a wrench in the standard model of knowledge as “Justified True Belief” in what is probably the most influential paper of its length in the history of philosophy. You can read more about Gettier cases in the links above, if you feel so inclined; nowadays, most philosophers are inclined to think either that Gettier cases can be dealt with via a more adequate specification of warrant (which is already a difficult problem, so that Gettier simply added yet another condition that needs to be met in this specification) or else consider Gettier cases to be intrinsic anomalies similar to division by zero: You cannot divide by zero, as you can be any other number. Why not? It’s just an ad hoc rule mathematicians use so as not to break mathematics. We certainly aren’t going to abandon the operation of division just because zero presents a problem: so, to save division, we just exclude zero from division. If that’s what we have to do to save warranted true belief, simply exclude Gettier cases, then we should do that (Note: I lean to the former camp, that thinks a sufficiently nuanced account of warrant can address Gettier problems.)
Warrant has something to do with evidence. In the broadest sense, evidence is what supplies warrant to a belief. As David Hume wisely said, “A wise man proportions his belief to the evidence,”—although Hume himself falls rather short of exemplifying this principle.
Many philosophical positions can be challenged either de facto or de jure. That is, if someone makes a knowledge claim, one can challenge the truth of the claim, which is a de facto challenge, or one can challenge the claim de jure, which is to challenge the warrant of the claim. Matters are not so simple as this, since one must often challenge the warrant of a claim in order to challenge its truth—if a claim is both warranted and false, one needs to supply a reason that undermines the apparent warrant.
For example, if the earth does not stand still, but moves around the sun, one needs to defeat the seemingly warranted beliefs that, if this were the case, things would fly off the earth due to this motion and that stellar parallax would be observed. Both are entirely reasonable beliefs, that is, seemingly warranted beliefs. It required Newton’s development of the law of inertia to deprive the first one of its seeming warrant, and the purely speculative postulation that the stars were too far away to display parallax—which was a guess, and also true, so a true belief, which we could say became knowledge when it was finally measured by Bessel in 1838—a measurement that came a bit late to assist Copernicus, Galileo, Tycho, and Kepler in making their case for heliocentrism. The battle over Copernicanism is interesting in this regard, since its first proponents, Copernicus and Galileo, had almost no warrant for asserting the position as true. Copernicus died before he faced any serious blowback, and was shielded by an anonymous and unauthorized preface to his De revolutionibus erbium coelestium written by Andreas Osiander, which stated that the model described in the book was not necessarily true, or even probable, but was useful for computational purposes—and most people naturally assumed that the unsigned preface was Copernicus’ own view of the matter. Whether Osiander was wise or foolish to have attempted this pre-emptive protection of Copernicus is not known, but perhaps one might conjecture somewhat on the basis of Galileo’s startlingly dogmatic and doctrinaire assertion of the absolute truth of Copernicanism. Galileo was demanding belief in the truth of something for which he was consistently unable to produce warrant. Galileo’s failure to convince the world of Copernicanism is a credit to the good sense of the rest of the world, not evidence of its intransigent stupidity and resistance to scientific progress. Galileo’s main “proof” of Copernicanism was the 24 hour cycle of the tides—he utterly dismissed Spanish sailors who told him, from experience, that the tides have a 12 hour cycle rather than a 24 hour one, and he heaped scorn on Kepler’s theory that the tides were caused by the moon as “occult” and “childish”—even though Kepler was entirely correct in the matter. Kepler himself is an excellent case in point, because he propounded a number of true things, such as the elliptical orbits of the planets and the lunar cause of the tidal sequence, which he could not explain. He had merely discovered things which remained, for him, brute facts. It was not until Newton’s publication of Philosophiæ Naturalis Principia Mathematica that Kepler’s ideas were given a deeper and systematic grounding.
Arguments about warrant and truth, de jure and de facto, although in many cases separable, are sometimes not separable, as when one makes truth claims about warrant itself: knowledge about warrant must itself be warranted to be knowledge, and when there is basic disagreement about what confers warrant, there often appears to be no “neutral” way in which to settle such disagreements, since each side will appeal to evidence that the other side will dismiss, the one side seeing it as evidence because it confers warrant, the other dismissing it as non-evidence because in does not confer warrant. Each side accuses the other of a cognitive mistake: the one for accepting something as evidence, as warrant-conferring that is not, the other for rejecting something warrant-conferring, as evidence, that is.
This situation is explanatorily important in debates between theists and atheists. Atheists will often insist that theists do not have evidence for their beliefs, that is, that they believe what they believe without warrant. But for theists, it is atheists who hold the unwarranted belief that certain of our natural cognitive powers are not warrant-conferring, on the basis of arbitrary metaphysical assumptions about the nature of human beings and their cognitive powers, and so of the nature of warrant. In this situation, the atheists are effectively arguing “If atheism is de facto true, then theism is de jure without warrant,” which claim is, as a hypothetical, entirely correct. Unfortunately, the claim “If theism is de facto true, then atheism is de jure without warrant” is also, as a hypothetical, entirely correct. The problem arises because atheists typically present their claim as “theism is de jure without warrant“; the trouble with this claim is that its warrant depends upon the de facto truth of atheism: if atheism is de facto true, then theism probably does de jure lack warrant. BUT if theism is de facto true, then then it is very probable indeed that theism possesses de jure warrant and atheism is de jure either an unwarranted belief or an irrational (unwarranted) rejection of a warranted belief.
What follows from this is simple: atheists cannot make the claim that theism is de jure without warrant without first making the case for the de facto truth of atheism, because if theism is true, then the claim that it is without warrant is so improbable as to remove all its effective force as a real objection to theism. Atheists who wish to refute theism cannot do so by means mere de jure objections to the warrant of theism, but must make the positive de facto case for the truth of atheism, since any evaluation of the warrant conditions of theism depend upon the truth or falsity of theism. Unless and until atheists have done this, their de jure objections are without force, since they all contain the unspoken caveat “If atheism is true, then it is the case that …”