For that belief to exist one would have to exist to believe it. Similarly [...]
in Descartes' argument, it's not the cause of the thought that is relevant. Even if the thought was thought by the evil demon, the one that holds the belief about thinking it, the one that is conscious of the thought and experiences it, must exist in order to do so. — BlueBanana

As a meta-example of what I’m saying: I uphold that fallibilism is true. It fallibilism is indeed a true belief (a belief which conforms to the ontic given which it references, namely our psychological/mental capacities), then it will be justifiable, at least in principle (it will not contradict any other epistemically established, believed truths and will cohere into such truths which are related). So here the onus is on me to justify that my belief is in fact ontically true (and not merely a believed truth that is in fact false, i.e. not true).

Some will uphold the Buddhist stance of no-self to signify that we do not exist--more particularly, that there is no ontic given which the pronoun "I" references. (Something which is not in keeping with what the Buddha stated; he said, “neither is there a self nor is there not a self” … or something along these lines, which need not be a contradiction if not at the same time or in the same way. More recently saw a documentary, “Compassion in Emptiness,” in which it is stanchly affirmed that self-worth is crucial for compassion—thereby acknowledging there being a self while yet maintaining a no-self thesis … different issue though.) As a different example, others will argue for one form or another of hard-determinism and, in so doing, will denounce all agency … as in “I did this (I caused this to happen)” or “Descartes thought things (Descartes caused his own particular thoughts to hold presence)" … which can also result in an argument against the presence of selves (minimally as pertains to the agency involved with thoughts, beliefs, interpretations (which are essential to the meaning/significance that either accompanies or is embedded with perceptions), etc.—and what is a self when deprived of all agency? … but I won’t play the devil’s advocate in arguing for this).

Feel like my hands are tied. I, for example, don’t want to rely upon a hard-determinist argument because I disagree with it. But I’ll conclude with this: until one can demonstrate with infallible certainty that all such alternatives are false, or impossible, there will remain some degree of possible error in our appraisals that we exist … even that anything exists (for it is we who make such appraisals).

Here’s a justifiable possibility (as compared to possibilities that are for example contradictory, thus unjustifiable, thus invalid--such as the possibility of a square composed of three sides) with which to more formally back this up: we humans are not the pinnacle of what intellect can existentially be, such that if our species survives some 100 millennia from now, it will then obtain some instances of knowledge which we currently cannot fathom. No one can prove a) that our species will go extinct and b) that 100 millennia from now some sapient descendent of our species will not discover some strongly justified alternative to our needing to be/exist (or to anything needing to be/exist). The very potential for such justifiable alternative being someday discovered in itself makes our current convictions that we exist less than perfectly secure from all possible error—therefore, our belief that we exist is yet technically fallible.

This is all taken to an extreme--though I so far find it to be a sound argument. But again, the onus is now on me to justify fallibilism as currently being ontically true (though maybe not at some future period of our awareness as sapient beings given all universal time that is yet to come … For, if fallibilism is currently true, the impossibility of this scenario could not be demonstrated with infallible certainty).

As you may notice, falliblism does away with the crutch of absolute/infallible subjective certainty. But this is not to say that it denies there being such a thing as the ontic, as well as conformity to that which is ontic.

But what if the teapot is not only small, but also invisible and does not interact with the Universe in any way - it can't be perceived and does not influence anything? How could its existence be proven even in theory? — BlueBanana

To keep this short for now: Why presume that such a teapot is an ontic given to begin with? If it’s not an ontic given, then all beliefs affirming its truth would be false … and thereby unjustifiable.

There's always a possibility of being wrong, so can you claim that your belief is justified if that claim isn't justified? Then you couldn't make that claim. In your belief, you can't have an idea that can't be justified and be justified in making the claim that it is justified simply as the belief justified by the justification is believed to be justified. — BlueBanana

It's not the claim "this is justified" which makes a belief justified, it's to demonstrate the correctness of the belief to others and have them agree with the demonstration, as correct, which makes it a justified belief. One's claim that a belief is justified or not, is meaningless and irrelevant except in arguments of whether or not the belief has been justified. But anyone can claim any belief as justified, so I don't see your point.

Responses to Gettier along the lines of, "Well, he had a false belief -- garbage in, garbage out," rather miss the point, I think. Do we allow falsehoods to have real connections? Traditional logic says yes, valid but unsound, But how can this be? If our reasoning mirrors the rationality of the universe, those connections must also be only seemings, conditionals that cannot ever be perfected, for there is no truth underlying them. — Srap Tasmaner

The issue I take against Gettier is that he seems to be arguing that an unsound (because it's based in a false premise) conclusion, may be a justified conclusion. I think that's contradictory nonsense. If you can honestly state that the conclusion is unsound then you cannot honestly state that it is a justified conclusion.

The issue I take against Gettier is that he seems to be arguing that an unsound (because it's based in a false premise) conclusion, may be a justified conclusion. I think that's contradictory nonsense. — Metaphysician Undercover

He doesn't argue for this position; he asks us to accept it as a premise. You don't.

The word "justified" is really not particularly important here -- you can substitute any epistemic virtue you like. What Gettier discovered is that if we assume, what seems reasonable, that material implication preserves epistemic virtue in much the same way it preserves truth, then it is trivial to construct counterexamples where our intuition is that the conclusion is not known even though it is believed, true, and has whatever virtue it inherited from the premise (that it is reasonable, rationally believed, that we have warrant to believe it, that we are justified in believing it, whatever). What the conclusion doesn't inherit from the premise is truth -- that it usually gets somewhere else.

If you can honestly state that the conclusion is unsound then you cannot honestly state that it is a justified conclusion. — Metaphysician Undercover

In the Gettier literature this is the "no false lemmas" view, I believe. So you would say that material implication only preserves epistemic virtue when the premise is true. I'm inclined to disagree. If I have good reason to believe my keys are in the kitchen, then I have good reason to believe they're in my house. If I can't say that sort of thing, of what use is material implication?

The word "justified" is really not particularly important here -- you can substitute any epistemic virtue you like. What Gettier discovered is that if we assume, what seems reasonable, that material implication preserves epistemic virtue in much the same way it preserves truth, then it is trivial to construct counterexamples where our intuition is that the conclusion is not known even though it is believed, true, and has whatever virtue it inherited from the premise (that it is reasonable, rationally believed, that we have warrant to believe it, that we are justified in believing it, whatever). What the conclusion doesn't inherit from the premise is truth -- that it usually gets somewhere else. — Srap Tasmaner

I think you'll have to lay out for me what you mean by "material implication". In any case, you don't seem to be getting at the point here. The issue is not the relationship between truth and epistemic virtue, it concerns the relationship between falsity and epistemic virtue.

In the Gettier literature this is the "no false lemmas" view, I believe. So you would say that material implication only preserves epistemic virtue when the premise is true. I'm inclined to disagree. If I have good reason to believe my keys are in the kitchen, then I have good reason to believe they're in my house. If I can't say that sort of thing, of what use is material implication? — Srap Tasmaner

Again, this does not address the point. It is implied by the op, that Gettier believes that a particular argument is an unsound argument (having a false premise), and he also believes that the conclusion of this argument is a justified conclusion. This is what I see as irrational. If you recognize that the argument uses an incorrect premise, you cannot recognize the conclusion as justified. Your example of a conditional is irrelevant because it doesn't utilize a false premise.

I think you'll have to lay out for me what you mean by "material implication". — Metaphysician Undercover

Just the usual. I think Gettier actually talks about "entailment" but it's not clear whether he means something special by that. We can come back to this.

Your example of a conditional is irrelevant because it doesn't utilize a false premise. — Metaphysician Undercover

Let's start there. How do you know the premise isn't false?

All I said was "IF I have good reason to believe my keys are in the kitchen, THEN I have good reason to believe they're in my house." I think this conditional is true whether or not I do in fact have good reason to believe my keys are in the kitchen. Do you disagree?

Let's vary the example slightly. Suppose I remember leaving my keys in the same place I always do, and that memory is veridical, I really did that. There's my reason for believing they're where they usually are. Now I could be wrong -- maybe I'm forgetting that later I put them in my coat pocket when I went out. I still have reason to believe they're where I usually leave them, just not conclusive reason. Does that reason suddenly become conclusive if I didn't move them later? Do you see anything here, in either case, you'd consider me justified believing?

The Gettier version would be this: you grab my keys to head out, recognize your mistake and put them back, all unbeknownst to me. Now I have that original reason to believe the keys are where I left them, and they are, but now my belief about where my keys are is true by luck.

Let's start there. How do you know the premise isn't false? — Srap Tasmaner

That's irrelevant, what I'm talking about is when one believes that the premise is false, and also that the conclusion drawn from it is justified. Look at the op. Gettier believes that a person has a false belief, belief (a), from which a conclusion is drawn, belief (b). It is stated (1), that belief (b) is justified. My claim is that it is impossible to believe that a conclusion drawn from a belief which is believed to be false, is a justified conclusion. An unsound argument is not justifiable. Therefore the proposition (1) is nothing better than irrational nonsense at the best, or outright deception at the worst.

My claim is that it is impossible to believe that a conclusion drawn from a belief which is believed to be false, is a justified conclusion. — Metaphysician Undercover

What about just the premise?

Is it possible (whatever you mean by "possible") for me to believe that your claim is reasonable but wrong?

No. Do you think that being wrong could be reasonable? Isn't this how we define "unreasonable", as wrong? I think so. And if unreasonable is wrong, then how could wrong be reasonable? To say that something which is wrong is reasonable is simply contradictory. By designating it as "wrong" you are declaring it unreasonable.

My so far favorite Gettier case is this one (I’ve only read about Gettier cases online):

The pyromaniac (Skyrms 1967). A pyromaniac reaches eagerly for his box of Sure-Fire matches. He has excellent evidence of the past reliability of such matches, as well as of the present conditions — the clear air and dry matches — being as they should be, if his aim of lighting one of the matches is to be satisfied. He thus has good justification for believing, of the particular match he proceeds to pluck from the box, that it will light. This is what occurs, too: the match does light. However, what the pyromaniac did not realize is that there were impurities in this specific match, and that it would not have lit if not for the sudden (and rare) jolt of Q-radiation it receives exactly when he is striking it. His belief is therefore true and well justified. But is it knowledge? — Stephen Hetherington

I find it far more realistic than most others. For the record, I too sponsor a no false lemmas resolution to the Gettier problem. If a premise or observation is false, that it cannot be rationally used to obtain a true conclusion, thereby making all Gettier cases epistemically unjustifiable derivative beliefs that, thereby, are held due to luck and are hence not instances of knowledge.

But in saying that, this quoted example illustrates the tentative nature of what we presume, or uphold, to be knowledge. Such that were you or I to be in the same position, we’d of course maintain that we knew that the match would light (in absence of the information regarding the specific match we pick and of the perfectly timed jolt of Q-radiation [have no idea what this is but I’m rolling with it]).

As the IEP article points out, one problem with the no false evidence resolution is that it can result in methodological doubt of what is true knowledge (the one form of skepticism which has been commonly understood for some time by the term, “skepticism”). Yet to the other form of skepticism that is subjectively certain/sure of there not being anything which is demonstrably infallible (the non-Cartesian form of skepticism which holds no doubts about this being so—e.g., Pyrrho, Academic, Cicero, Hume, etc.—not here addressing the subsequent differences between these--a form of which Descartes was not), the technically tentative nature of knowns is just an intrinsic aspect of what knowing is all about. Yes, like many in history, this second form can wind its way towards a negating fallibilism where all knowledge becomes denied, but here I’m addressed a Pragmatist-like stance of a positing fallibilism (illustrated, for example, by Cicero and Hume … and, in at least some measure, the Pragmatist Pierce who came up with the term “fallibilism” [ I haven’t read his works to figure out if the guy was a closet skeptic]).

So in looking back at the example, most everything we do and know could hold intervening causal elements that are not those which we use to epistemically justify our knowledge. But until we discover that our premises are false, we then hold all the reasoning in the world to conclude that we know.

That said, in Gettier’s Case I, for example, one here discovers that one was wrong in that which is used to justify the conclusion … so, again, I agree that the conclusion here is then not knowledge.

The Gettier problem is, in a general form, as follows: a person has a false belief a, from which a conclusion b is drawn. It is then found out that a was false, yet b is true (although only when interpreted in some different way). — BlueBanana

Have you got an example of this?

In Gettier's original example, a person called Smith is applying for a job. Another person, Jones, whom is known to have 10 coins in his pocket, is applying for the job as well, and Smith (for a justified reason) believes Jones will get the job. This is the belief a. The conclusion b is that the person who gets the job has 10 coins in his pocket. What happens is that Smith himself gets the job, but also, although he didn't know this, had 10 coins in his pocket.

↪charleton In Gettier's original example, a person called Smith is applying for a job. Another person, Jones, whom is known to have 10 coins in his pocket, is applying for the job as well, and Smith (for a justified reason) believes Jones will get the job. This is the belief a. The conclusion b is that the person who gets the job has 10 coins in his pocket. What happens is that Smith himself gets the job, but also, although he didn't know this, had 10 coins in his pocket. — BlueBanana

You mean belief 'a' is falsely confirmed by a co-incidence of fact.

Like a black cat walked across my path and I subsequently tripped over and broke my leg, falsely confirming the black cats are unlucky?
post hoc ergo propter hoc fallacy.

JTB is not valid. — BlueBanana

Depends on the justification surely? If I continued to have bad luck after seeing black cat it could be confirmation bias. Eventually I'd have to ignore the sighting of a black cat that was not followed by bad luck.

You mean belief 'a' is falsely confirmed by a co-incidence of fact. — charleton

No, the reason for a is not specified in the example, although iirc, the example was given of the employer telling Smith that they're going to hire Jones.

Like a black cat walked across my path and I subsequently tripped over and broke my leg, falsely confirming the black cats are unlucky?
post hoc ergo propter hoc fallacy. — charleton

I don't see the connection tbh.

↪charleton In Gettier's original example, a person called Smith is applying for a job. Another person, Jones, whom is known to have 10 coins in his pocket, is applying for the job as well, and Smith (for a justified reason) believes Jones will get the job. This is the belief a. The conclusion b is that the person who gets the job has 10 coins in his pocket. What happens is that Smith himself gets the job, but also, although he didn't know this, had 10 coins in his pocket. — BlueBanana

Uh... No. No. No.

Read the paper...

I don't see the connection tbh. — BlueBanana

1) I have abelief that black cats are unlucky.
2) One walks across my path.
3) After that I break my leg.
4) I know justify my belief that black cats are unlucky because I broke my leg. Justifed and believed true. JTB

However the breaking of the leg and the cat are not connected, therefore JTB is false.

How is your example different?

Your example doesn't seem at all like a Gettier case. In Gettier cases, the general form is:

1. P is justified
2. P entails Q
3. Q is true
4. P is false

What are P and Q in your example?

1. P is justified
2. P entails Q
3. Q is true
4. P is false — Michael

a person called Smith is applying for a job.
Another person, Jones, whom is known to have 10 coins in his pocket, is applying for the job as well,

and Smith (for a justified reason) believes Jones will get the job. This is the belief a.
The conclusion b is that the person who gets the job has 10 coins in his pocket.

What happens is that Smith himself gets the job, but also, although he didn't know this, had 10 coins in his pocket.

How does P entail Q in this example. Having 10 coins in your pocket is not relevant to employment opportunities and so that would mean that P does not entail Q.

How does P entail Q in this example. Having 10 coins in your pocket is not relevant to employment opportunities and so that would mean that P does not entail Q. — charleton

P is "Jones will get the job and has 10 coins in his pocket" and Q is "the person who gets the job has 10 coins in his pocket".

If P is true then Q is true. P entails Q.

P is "Jones will get the job and has 10 coins in his pocket" and Q is "the person who gets the job has 10 coins in his pocket". — Michael

Neither of those examples deserves the words "justified" or "entails".
Maybe Gettier expressed the situation more clearly?
So unless there is a more convincing example I'll bow out.

So you would say that material implication only preserves epistemic virtue when the premise is true. I'm inclined to disagree. If I have good reason to believe my keys are in the kitchen, then I have good reason to believe they're in my house. If I can't say that sort of thing, of what use is material implication? — Srap Tasmaner

What about when multiple premises are concerned? I am justified in believing a, I am justified in believing b, and c follows from a and b. Am I justified in believing c?

A particular counterexample is that of a lottery. Given the high odds, I am justified in believing that any given ticket won't win. But I am not justified in believing that no ticket will win, even though that no ticket will win follows from the conjunction of each given ticket not winning.

Perhaps we just need the additional qualification that ¬c isn't justified?

A particular counterexample is that of a lottery. Given the high odds, I am justified in believing that any given ticket won't win. But I am not justified in believing that no ticket will win, even though that no ticket will win follows from the conjunction of each given ticket not winning. — Michael

Hmmmm.

1. Is there a hidden premise here that some ticket will win? Because the way the big lotteries work here in the States, it's quite common for no ticket to win for months, and that's how the jackpot grows into hundreds of millions.

2. Given some such premise, you just have to be careful with quantifiers and sums, I think. If you have ye olde urn of a hundred marbles, 99 white and 1 black, the chances of having drawn a black marble are 1/100 for as many individual trials as you'd like, but obviously if you draw more marbles per trial your chances are better, right up to guaranteed success if you draw all of them. I don't think there's a problem here.

((Btw, this slippage from individual to collective can be really interesting. It's thought one of the earliest examples of a game-theoretical problem is a story somewhere in Plato about a soldier who reasons thus: we're either going to win or lose this battle; my participation can't make much difference to the outcome and I run the risk of dying; therefore I should desert. The reasoning isn't bad for an individual, but doesn't scale up very nicely.))

Is there a hidden premise here that some ticket will win? — Srap Tasmaner

Yes, sorry.

Given some such premise, you just have to be careful with quantifiers and sums, I think. If you have ye olde urn of a hundred marbles, 99 white and 1 black, the chances of having drawn a black marble are 1/100 for as many individual trials as you'd like, but obviously if you draw more marbles per trial your chances are better, right up to guaranteed success if you draw all of them. I don't think there's a problem here. — Srap Tasmaner

Let's say that 100 people have each picked out a ball. Given the high odds, I am justified in believing that Person 1 doesn't have the black ball. But then I am also justified in believing that Person 2 doesn't have the black ball, given that he is just as unlikely to have it as Person 1. And the same for each individual person.

It's perhaps explained better here:

There are also multiple premise closure principles. Here is an example:

If S knows that p and knows that q, and S comes to believe r by correctly deducing it from p and q, then S knows that r.

That is, if I know two things to be true and can deduce a third thing from the first two, then I know the third thing to be true. There is good reason to be dubious of multiple premise closure principles of justification, such as

If S is justified in believing that p and justified in believing that q, and S correctly deduces r from p and q, then S is justified in believing that r.

Lottery examples reveal the difficulty. Given that there are a million lottery tickets and that exactly one of them must win, it is plausible (though not obvious) that for any particular lottery ticket, I am justified in believing that it will lose. So I am justified in believing that ticket one will lose, that ticket two will lose, and so forth, for every ticket. But if I know that there are a million tickets, and I am justified in believing each of a million claims to the effect that ticket n will lose and I can correctly deduce from these claims that no ticket will win, then by closure I would be justified in concluding that no ticket will win, which by hypothesis is false.

Right, I had forgotten about this.

My hot take is still that this is a muddle that arises from ambiguity over what constitutes a trial. The closure principle relied on here is no substitute for doing the math right. That can mean the math seems counterintuitive (e.g., the Monty Hall problem), and that's interesting as a fact about our epistemic biases but nothing more.

Maybe @fdrake could chime in.

I'll think about it some more...

Nitpicking, the case is practically the same.

Lottery examples reveal the difficulty. Given that there are a million lottery tickets and that exactly one of them must win, it is plausible (though not obvious) that for any particular lottery ticket, I am justified in believing that it will lose. So I am justified in believing that ticket one will lose, that ticket two will lose, and so forth, for every ticket. But if I know that there are a million tickets, and I am justified in believing each of a million claims to the effect that ticket n will lose and I can correctly deduce from these claims that no ticket will win, then by closure I would be justified in concluding that no ticket will win, which by hypothesis is false.

P(at least one ticket wins) = 1
P(any particular ticket does not win)=very high

Keep multiplying 'very highs' together, they're all <1, and you end up with 'very low' - IE, take enough tickets and you can become very confident that your selection of tickets contains the winner.

Trying to map probabilistic reasoning, which in some respects is an uncountably infinite valued logic, onto a set with two values 'is justified' or 'is not justified' corresponding to probability thresholds doesn't really represent anything about our reasoning. This kind of logic always has difficulties dealing with iterated disjunction and conjunction. If you take many 'very certain' things together conjunctively (they all must happen), you end up with 'very uncertain', if you take many 'very uncertain' things together disjunctively (at least 1 must happen) you get something 'very certain'.

You are justified in believing any particular ticket loses, you are not justified in believing the entire sample of tickets loses; especially if it's set up a priori that there is always and only 1 winner.

Always and only 1 winner is the same as 'if you take them all, the probability that you take the winner is 1', if there isn't an 'all' then the probability that a sample of size n contains the winner is a function of n and the probability of winning the bet for each ticket (under the usual equiprobability assumptions this is obtained by the cumulative distribution function of the binomial distribution with n trials up to k successes with ticket winning probability p).

You are justified in believing any particular ticket loses, you are not justified in believing the entire sample of tickets loses; especially if it's set up a priori that there is always and only 1 winner. — fdrake

It's true that you're not justified in believing that the entire sample of tickets loses, and I think that shows that justification isn't necessarily inherited, which is the issue under consideration.

If a is justified, b is justified, c is justified, and d follows from a, b, and c then d is not necessarily justified.

So epistemic closure for justification can fail where there are multiple premises. Presumably because, as you say, for each additional premise the degree of justification for the set decreases.

It's true that you're not justified in believing that the entire sample of tickets loses, and I think that shows that justification isn't necessarily inherited — Michael

Wait -- does it? I think in this case, it's that the inference that would preserve justification is faulty. (You just can't go from "each individually" to "all taken together" like that. It's like the Logic 101 example of inferring there's someone everyone loves from everyone loving someone.)

I think it's resolved by breaking it into 2 cases. The cases being A) where someone knows that a given selection is the entire selection of tickets and it contains 1 and only 1 winner and B) where they don't know at least one of these things. If someone is justified in believing the entire selection is present then they're justified in believing it contains the winner. If they don't know, the strength of their belief should probably depend on the state of their knowledge regarding total number of tickets and the number in the batch (under the assumption that the reasoner knows how to reason probabilistically).

Wait -- does it? I think in this case, it's that the inference that would preserve justification is faulty. (You just can't go from "each individually" to "all taken together" like that. It's like the Logic 101 example of inferring there's someone everyone loves from everyone loving someone.) — Srap Tasmaner

Assuming a lottery of n tickets, the premises are:

P1. Ticket 1 won't win
P2. Ticket 2 won't win
P3. Ticket 3 won't win
...
Pn. Ticket n won't win

From this we can deduce:

C1. No ticket will win

It's a valid inference.