The JTB Analysis of Knowledge is the best analysis of knowledge that I know of, and it often remains reliable despite it's occasional (seldom) failing, for it informs us of the necessary conditions of knowledge, and though it's not always sufficient, it often is.

But there is no JTB+ Analysis of Knowledge.

The + simply tells us that knowledge either has at least a fourth necessary condition or that the justification condition needs to be tweaked.

Conveying to us that the JTB Analysis of Knowledge fails to give us the jointly sufficient conditions of knowledge isn't an analysis of knowledge in itself, so the JTB Analysis of Knowledge is still the best analysis of knowledge that we have.

It is what I would call an "analysis sketch" since it would need to be filled in. But it is possible that JTB are sufficient conditions under some unknown analysis of J. I doubt it, though. There have been too many unsuccessful attempts at it. (Including one by me).

How did yours go? I recall that you said that you defended the "was not inferred from a falsity" at sometime.

That's substantially it. But, there are counterexamples to that, too.

Yes, non-inferential justification. That's not inferred from a falsehood. Not inferred at all. Perhaps not just a single additional necessary condition is needed but multiple. In that case this condition for inferential justification and some other condition for non-inferential justification.

Did you invent that one or did you just defend it?

Here are my thoughts on the Gettier essay.

If (1) the man who will get the job is Jones, and
(2) Jones has ten coins in his pocket,
then
(3) the man who will get the job has ten coins in his pocket.

But does it logically follow that if Smith is justified in believing (1) and (2), then he is justified in believing (3)? Consider the following case:

Being familiar with the alphabet, I am justified in believing that the letter A is followed by B, B by C, C by D etc, up to "T is followed by U". Now, if all these relationships between adjacent letters are correct, it necessarily follows that U comes 20 letters after A. But if I am justified in believing that A is followed by B, B by C etc, it does not follow that I am justified in believing purely on that basis (without keeping a count of the letters) that U comes 20 letters after A. So justification is not transitive.

If this is correct, then Gettier's argument fails, because Smith's belief that the man who will get the job has ten coins in his pocket is not justified.

We are not directly aware of trees, but so what?

We are indirectly aware of trees, because we know there are trees because we have subjective experiences of trees. And, as I already have pointed out, the very best explanation of why we have subjective experiences of trees is that there are trees. I have already asked you whether you have as good an explanation of our subjective experiences of trees than that we observe trees? Why do you think we have experiences of trees?

That knowing is a mental event means that it happens solely in the mind. But it doesn't knowledge implies truth and truth is often not in the mind. (It can be.) For instance, that I know the capital of Denmark is Copenhagen implies that (given JTB):

• I believe that Copenhagen is the capital of Denmark.
  
• I am justified in my belief that Copenhagen is the capital of Denmark.
  
• It is the case that Copenhagen is the capital of Denmark.
  

The third requirement is not something that has to do with my mind. It is not a mental fact. If knowing was a mental event, then all requirements for it would be mental facts. But that is not the case, thus knowing is not a mental event.

It is clear that belief is a mental fact. I think that justification is also a mental fact, but I'm not very sure about it.

In any case, I think the phrase "knowing is a mental event" should not be used, since it is far from clear that that means solely mental.

I'm pretty sure this analogy is confused but I can't quite put my finger on it. How about:

You talk of "following" as if it is some kind of property that letters in the alphabet can have. But it isn't. That something follows from something else is just a way of talking about logical implication. Logical implication is a truth-functional concept and it does not make sense with mere letters "following" (in a complete non-related sense) each other. Of course in the everyday sense of "following" letters can follow each other. But that's not the kind of following that Gettier is talking about.

You say that "justification is not transitive". That's right. But Gettier does not claim in the paper that it is. I imagine that you think that he does because you think that he argues that: If (2) follows from (1) and (3) follows from (2), then (3) follows from (1). (This interpretation makes sense with your alphabet analogy.) But he doesn't.

Basically, the premise that you ought to question in the Gettier essay is this:[INDENT]For all persons, a person is justified in believing that P and justified in believing that Q, and P and Q logically implies S, logically implies that that person is justified in believing that S.

(∀x)(Jx(P)∧Jx(Q)∧((P∧Q)⇒S))⇒Jx(S)
[/INDENT]("Jx(P)" means x is justified in believing that P.)

I'm not terribly read on the matter but I'm pretty sure this principle has a name. Kennethamy properly knows.
Does it not seem true to you? It definitely seems true to me.

We have free will, we don't have free will, we can know truth, we cannot know truth, the soul exists, there is no soul....so what? Who cares right? :sarcastic: What is the name of this forum? Questions like those above do matter, if philosophy matters. And so does the question of what is meant by 'tree' when sometime says 'I kick the tree.' If you want to stop at the solution of common sense ('if I kick a tree, it is a tree I kick'), which suffices for practical purposes, that's perfectly fine, but then you aren't any longer philosophizing.



Who ever claimed to have a 'better explanation?' And what do you mean by that anyway? If you mean some better, more useful way of thinking about the world, then certaintly the concept I'm proposing is not that. It is in no way practical. If you mean, have I offered an alternative to the simplistic, common sense, answer to 'what is a tree' (answer: 'a tree'), then yes I have.



I contend that 'knowing that Copenhagen in the capital of Denmark' does not neccessary suppose either the second of third bullet point above. E.g. I might 'know' that I am in fact a wristwatch. Does that mean that I am justified in this belief or that, in fact, I am a wristwatch? Clearly neither.



I would agree. Belief as such is existent only 'in the mind,' or 'in the phenomenological world: i.e. existent in the same way that a sensation of cold or a desire to have a drink exists, and not in the way in which a tree exists (i.e. if we are referring to the 'real tree,' which I have problems with as already noted, but ignoring that for now..). Through observation from a third person perspective it may be possible to determine what relation that belief bears to 'objective' reality, but that does not change the fact that the belief itself is purely a mental event.



I suppose it's a matter of taste, but I think 'mental event' will do. Sure, it might be more clear if it read 'only a mental event,' but isn't that implied? If I say, 'this animal is a chicken,' it's implied that it is not also a horse or anything else. Anyway, the only problem I have with the phrase is that 'mental' connotes the mind-body duality, which I feel is imaginary. Ideally, I'd probably use 'phenomenological event' in place of 'mental event,' to mean exactly the same thing, but without that Cartesian implication: i.e. making no distinction between a mental and a bodily (raw sensory) event, but rather thinking of them all as experience.

I think your principle is better phrased as: if p entails q, and if p is justified for A, then q is justified for A. (I do not like the phrase, "justified in believing" because it is ambiguous, since A may be justified in believing p even it p is not justified for A). So the principle is that every proposition, q entailed by a proposition p justified for A, is, itself, justified. I think that is true. But, note that the above principle is different from the principle that every proposition q, which is entailed by a proposition, p, which is believed by A, is believed by A. That is the principle that A believes every proposition entailed by a proposition A believes.

I think the name of your principle is just, "the transitivity of justification". And I think it is true.

You talk of "following" as if it is some kind of property that letters in the alphabet can have. But it isn't. That something follows from something else is just a way of talking about logical implication. Logical implication is a truth-functional concept and it does not make sense with mere letters "following" (in a complete non-related sense) each other. Of course in the everyday sense of "following" letters can follow each other. But that's not the kind of following that Gettier is talking about.

Basically, the premise that you ought to question in the Gettier essay is this:

For all persons, a person is justified in believing that P and justified in believing that Q, and P and Q logically implies S, logically implies that that person is justified in believing that S.

Does it not seem true to you? It definitely seems true to me.

I did not mean to imply that the two senses of "following" were in any way related. Look at my alphabet analogy again, replacing "follows" with "comes immediately after".

Yes, this is exactly the premise I am questioning.

No, it not seem true to me.

Let's go back to my alphabet example. I have enough experience of the alphabet to have a justified belief about which letter comes next after any given letter. But (unless I have learned it by rote at an early age) I am unlikely to be able to reliably tell the order-number of the letter U (21) without a quick count through the alphabet. So if someone asked me "U comes how many letters after A?" and I replied "20" without bothering to count, it would be a lucky guess; and if I actually believed it (for some wrong reason) without counting, then my belief (though true) would not be justified.

Now:

(1) B comes next after A,
(2) C comes next after B,
and so on up to
(20) U comes next after T

together logically imply

(21) U comes 20 letters after A.

But, as I have argued above, the fact that I am justified in believing all of (1)-(20) does not logically imply that I am justified in believing (21) (without the additional step of counting).

NB: By "justified" I mean "epistemically justified".

I had to read that post very carefully to understand it.

Right. The phrase "justified in believing" is dangerous. What about "epistemically justified in believing" (e-justified)? That seems to avoid other possible types of justifications (pragmatic? prudent?).

I have a potential problem with you formulation and that is that it only works for single-proposition entailment/implication. Can that be fixed by simply forming conjunctions?
I suppose it can. It's misleading to say that (1) and (2) together logically imply (3) if one is not talking about the conjunction of (1) and (2). I can't think of another analysis.

For clarity I shall formalize Ken's version:[INDENT](∀x)(Jx(P)∧P⇒Q)⇒Jx(Q)
For all persons, that a person is e-justified in believing P, and that P logically implies Q logically implies that that person is e-justified in believing that Q.
[/INDENT]This seems true to me.

Belief principle
Formally:[INDENT](∀x)(Bx(P)∧P⇒Q)⇒Bx(Q)
For all persons, that a person believes that P, and that P logically implies Q logically implies that that person believes that Q.
[/INDENT]Yes, I agree that they are different. I disbelieve that the belief principle is true. It implies that we believe in an infinite number of things which is false. (Given a mental state theory of beliefs which I believe in.)

Transivity
Transitivity is a property of binary relations and justification is not a binary relation in the right way (it is a binary relation since it uses two arguments (I hate using "argument" in that sense but I haven't found a replacement word)). See Wikipedia's examples. It doesn't make sense at all to even state an example of justification as a transitive relation!
There may be some other sense of "transitive" but it seems not. This is the same sense as my logic textbook was talking about.

Why is transitivity a two-term (binary) relation, only? The hypothetical syllogism illustrates a transitive relation, doesn't it? And it illustrates a three-term (argument) relation. Yes, the belief principle is clearly false. For the reason you give. ("Transitivity" not, "transivity")

But then, do you actually believe these all the time? I think not. It seems to me that the only time that anyone ever believes all these is when one is counting through the alphabet and probably not every time one is counting through. The only time that one actually believes all of these simultaneously is when one has spent a lot of time (that day) to intensively practicing the alphabet. And when one has intensively practiced the alphabet (that day), it seems to me that one is justified in believing things such as (A).

I certainly don't go around believing all these and I couldn't answer questions like "what comes after S?" without counting the alphabet or at least that part of the alphabet.

But then, do you actually believe these all the time? I think not. It seems to me that the only time that anyone ever believes all these is when one is counting through the alphabet and probably not every time one is counting through. The only time that one actually believes all of these simultaneously is when one has spent a lot of time (that day) to intensively practicing the alphabet. And when one has intensively practiced the alphabet (that day), it seems to me that one is justified in believing things such as (A).

I certainly don't go around believing all these and I couldn't answer questions like "what comes after S?" without counting the alphabet or at least that part of the alphabet.

But maybe it is possible with enough practice to believe (1) though (26) (or (n)) without studying the alphabet intensively (that day). And I'm not sure in such a case that one is justified in believing (A). Especially if we consider a similar but much larger set. But recall that the more members between (1) and whatever chosen number in that set, the less chance that someone can (physical possibility or intentional possibility) actually believe all of them.

Interesting case.