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
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
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
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. — Metaphysician Undercover
If you can honestly state that the conclusion is unsound then you cannot honestly state that it is a justified conclusion. — Metaphysician Undercover
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
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
I think you'll have to lay out for me what you mean by "material implication". — Metaphysician Undercover
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? — Srap Tasmaner
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
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
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
↪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
JTB is not valid. — BlueBanana
You mean belief 'a' is falsely confirmed by a co-incidence of fact. — charleton
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
↪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
I don't see the connection tbh. — BlueBanana
a person called Smith is applying for a job.
1. P is justified
2. P entails Q
3. Q is true
4. P is false — Michael
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". — Michael
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
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
Is there a hidden premise here that some ticket will win? — Srap Tasmaner
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
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.
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.
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 — 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.) — Srap Tasmaner
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