The simplified answer, as for most seemingly simple philosophical questions, is both "Yes!"and "No!". It all depends on just what you mean by "justified".
Philosophers studying epistemology generally distinguish between three different kinds of "knowledge". There is what is called "acquaintance knowledge", "ability knowledge", and "propositional knowledge".
Acquaintance knowledge is the kind of knowledge we claim when we are familiar with a person, place, or thing. It is "knowledge of . . .". This kind of knowledge allows us to recognize things again, or to take advantage of our familiarity in various ways. For example, I can claim to "know" London if I can navigate my way from place to place, or find a particular night spot. Acquaintance knowledge is not considered "justified true belief" because it is not considered to involved beliefs. Acquaintance knowledge is considered a skill or ability of the memory.
Ability knowledge can be exemplified by such examples as "I know the violin", or (again) "I know London". The sense of the word in this context implies some special skill or ability. It is "knowledge how . . .". I can play the violin, or I can find that particular restaurant in Soho. The key distinguishing criteria for ability versus acquaintance is that I must be able to employ my special skill or ability to some standard. Thus, if I can play the violin to my mother's standards, then to her I can say that "I know the violin". But if I cannot play well enough to satisfy anyone else, then I cannot say to them that "I know the violin". Ability knowledge is also not considered "justified true belief" because again it is not considered to involve beliefs. Ability knowledge is also considered a skill or ability of the memory -- but to some standard.
Given the context within which the question is posed (a course on epistemology), it is "propositional knowledge" that is intended as the subject of the title question. It is "knowledge that . . .". Propositional knowledge appears in statements that have the general format "S knows that P", where "S" is any particular subject of interest, and "P" is some belief (usually conceived as a proposition or other truth carrier -- philosophers differ) that describes some characteristic of Reality. If a teacher tells her class that she knows one of her students left the apple on her desk, is that merely her opinion, or is it knowledge? Just what is the difference between a person's belief or opinion that the ball is read, and a person's knowledge that the ball is red. What has to be added to the belief in order to qualify it as "knowledge"? It is this kind of propositional knowledge for which the title question about "justified true belief" is relevant.
The analytical process of determining just what the
difference is between some subject S believing that P and that subject "knowing" that P, involves the identification of the conditions that are individually
necessary and jointly sufficient to warrant the claim to knowledge. The
"Tri-Partite" or "Justified True Belief" (JTB) theory posits that for S to know
that P, it is individually necessary and jointly sufficient that
(a) P be true;
(b) S believe that P; and
(c) S be justified in believing that P.
It is generally agreed by almost all who ponder this issue that for it to be said that S knows that P, P must be true. Obviously, it is possible that I might believe some proposition that is not in fact true. But it would certainly be counter intuitive for me to claim to know things that are not in fact the case. It is common practice to expect that for me to claim to know that London is in England, it would be necessary that London is in fact in England. If I were to claim to know that London is, instead in Ireland, most people would claim that I am mistaken in my belief, and that I do not in fact know that. A claim to propositional knowledge, is a claim that the proposition is in fact true.
It is also generally agreed by almost all who ponder the issue that for it to be said that S knows that P, S must believe that P. Again, it would be counter intuitive for me to claim to know something that I do not believe is the case. But something further can be said on the question of belief. For a claim of knowledge to be generally accepted, the belief involved must be more than a weak form of acceptance. If I claim to know that London is in England, you would expect me to have a firm and committed belief that London is in fact in England. If I were to add to my claim that I am quite doubtful of this fact, or that I am simply accepting your unsubstantiated word for this fact, then most people would seriously challenge my claim to know the fact. Therefore, as long as one understands that the "belief" that is being referred to in the title question is intended to denote a strong and committed belief, then the condition that the proposition at issue is believed is consistent with the manner in which we employ the concept of knowledge.
This leaves us with the third of the conditions referenced in the title question. There are many propositions that I might believe on a whim, that just happen to be true. No one would accept my claim to know any of these propositions. Something extra is clearly required. The extra condition referenced in the title question is that of justification. And it is the issue of the nature of justification that has occupied epistemologists at least since the time of Plato's dialogue between Socrates and Meno. There are many different theories of just what "justification" means in the context of the extra condition that needs to be added to true beliefs to warrant calling them knowledge.
Some theories are termed "internalist" because their concept of justification is based on things that are directly available to the subject S. Their basic argument is that when you list all the evidence you believe justifies your belief that P, what you are listing is other beliefs along with the associated second-order belief that the supporting evidence actually does imply P, or make P more probable. Internalist theories focus on the manner in which we employ reason to infer conclusions from the evidence.
However, internalist theories have their difficulties. One difficulty is the potential for infinite regress. If your knowledge is justified on the basis of other beliefs, and those are justified based on further beliefs, you can see that an infinite regress quickly develops. Similar regress occurs with the second-order beliefs that the evidence supports the likelihood of P. Two other difficulties arise from the notion of non-inferential beliefs based on sensory experience, and the common practice of attributing knowledge to animals and pre-rational children.
The two most popular Internalist theories of knowledge are "Foundationalism" and "Coherentism". Foundationalism addresses the problem of infinite regress by positing that some beliefs are non-inferential, and therefore foundational. Non-inferential beliefs are those that are "infallible" -- beliefs that are true just in case we have them. For example, perceptual beliefs can be called infallible because, it is supposed, we form the belief that the ball is red if and only if we perceive the ball to be red. However, this still leaves the problem of the manner in which S's belief in P "rests" on the foundational beliefs. If it is necessary that P be logically entailed by some foundational beliefs, then what happens if our foundational (for example perceptual) beliefs are contradictory? This is certainly possible. For instance, it is not uncommon for our eyes to give us one message of what is out there, while our ears or fingers give us another. Alternatively, perhaps our belief in P relies on defeasible evidence. Defeasible evidence is simply evidence that justifies, but does not logically entail. It is always possible, no matter how much evidence we accumulate, that defeasible evidence may be defeated by the addition of more (and counter) evidence. If this is the hypothesis, then Foundationalism more or less devolves to Coherentism.
Coherentism is internalism without foundational beliefs. The hypothesis is that S's belief in P is justified if and only if S's belief in P coheres with the rest of S's beliefs. Unlike foundationalism, the coherence concept of justification is holistic rather than linear or hierarchical. Yet the coherence theory also suffers from a number of difficulties. Chief among these is the nature of the coherence involved. It surely cannot be logical consistency, since most people believe at least some contradictory beliefs. Perhaps the criteria is logical consistency within some sub-domain of beliefs. But that only raises the question of how to delineate the relevant sub-domain. Most coherentist theories leaves open the question of how some beliefs qualify for supporting status while others are disqualified. They also often leave open the question of how to distinguish between beliefs that are more, better, or properly justified from those that are less, poorly, or improperly justified. If the coherence is not logical consistency, just what is it?
Another difficulty faced by coherence theorists is that in principle, a coherent belief structure could be totally disconnected from reality. The only way to avoid this disconnect potential is to grant perceptual beliefs some special status in grounding the rest of the web of beliefs. But to do that, the coherence theorist is migrating towards a foundationalist theory which the coherence theorist initially denies.
Finally, the coherence theorist faces the challenge of explaining why the coherence of a set of beliefs should converge on truth. It is not at all obvious that the coherence of a set of beliefs should track reality. Yet, as noted above, it is commonly accepted by all thinkers that for a belief to be accepted as knowledge, that belief must at the very least be true.
In response to these (and other) challenges to the internalist theories of propositional knowledge, there are some theories that deny the basic premise of internalism. These are (naturally enough) termed "externalist". They base their concept of justification on elements that are not directly available to the subject. There are externalist variants of both Foundationalism and Coherentism that draw upon external features of the web of beliefs to delineate the foundational beliefs, or the sub-domain of relevant beliefs. But most prominent among the externalist theories is the theory of reliablism.
Reliablism is the thesis that propositional knowledge consists of a true belief that is arrived at through some reliable process. Reliabism is an externalist theory because the reliability of some belief forming process is a feature that is external to the subject, the subject is not in a position to be aware that the processes involved are reliable.
In parallel with the "justified true belief"(JTB) theories,
reliablism posits that for S to know that P is it individually necessary and
jointly sufficient that
(a) P be true;
(b) S believe that P; and
(c) S's belief in P be produced by a reliable process.
Unlike the other theories described above, pure (or hard) reliablism does not admit that knowledge demands justification. In short, pure reliablism would deny the definition posed in the title question. On the other hand, of course, it is always possible to understand the word "justification" as a broad enough concept that it would consider a belief formed by some reliable process as suitably "justified". So from a reliablist theory perspective, how we answer the title question would depend on just what is meant by "justification".
It is worth noting that reliablism is much more consistent than the JTB theories with the evolutionary development of human intellect. In positing only the existence of some unspecified reliable belief forming process, reliablism is ambivalent to any specific process. This allows reliablism to accommodate an evolutionary sequence of ever more reliable processes. Such an evolutionary conception of knowledge generating processes also provides an explanation of why knowledge is valuable -- an issue that the standard JTB theories do not directly address. On any theory of knowledge, knowledge is "assured true belief", and is thus the best bet when pursuing evolutionary survival. It is better, in the long evolutionary run, to know behind which tree the tiger lurks, else one is liable to become lunch rather than enjoy it. From the perspective of reliablism, however, it is largely irrelevant how one comes to know the necessary knowledge. The processes of evolutionary selection will ensure that those with the more reliable belief forming process will be the ones to populate the future.
For similar reasons, reliablism is also fully consistent with our common practice of employing the term "knowledge" when describing animals and pre-intellectual children. Both internalist and externalist versions of JTB theories demand a sophisticated intellectual ability to reason and draw logical inferences from the evidence. On this basis, it is difficult to see how I can properly say that my dog "knows" that I have cookies in my pocket, or that a baby "knows" when its mother is smiling at it. Most JTB theorists would deny that non-intellectual mentalities (animals, young children, brain-damaged patients, senile seniors, etc) have "knowledge" in the proper meaning of the word. They only seem to have knowledge, and our application of the word "knowledge" to their circumstances is convenient metaphoric short-hand.
On the other side of the fence, if Reliablism is viewed with a more loosely conceived boundary, Reliablism can be said to subsume the justified true belief theories. Reasoned inference from the evidence simply becomes another of the reliable methods of belief formation. From this perspective, the category of "propositional knowledge" can be seen to divide further into what might be termed "animal knowledge" and "intellectual knowledge". Intellectual knowledge would cover all those beliefs formed by intellectual reasoning from the evidence. Animal knowledge would cover all those beliefs formed by other reliable but non-intellectual means. This would allow a looser conceived theory of Reliablism to treat both the kinds of beliefs that are justified by the available evidence, and the kinds of beliefs that are formed quickly without a reasoned analysis of the justification.
So, to return to the title question -- is knowledge justified true belief? Certainly knowledge is true belief. But it is justified true belief only if one holds one of the JTB theories of knowledge. Or it is justified only if one holds a looser conception of "justification" that considers a reliable belief forming process as properly justifying a true belief.
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