Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid inferences. — creativesoul
I accept that your premises are true, and I accept that your conclusion may be validly inferred from those premises, but that is all; I do not accept that your conclusion is in fact true.
Does it make sense to say that "London is the capital city of England or I am a woman" is an invalid conclusion? — creativesoul
It is nothing less than knowledge that (p v q) follows from p. The truth conditions of p and q are irrelevant to knowing that (p v q) follows from p. — creativesoul
Either an inference is not inferred, or being inferred doesn't count as being an inference. — creativesoul
So then, g, h, and i are only valid inferences when you say so? What sense does this make? — creativesoul
Smith believes that f is true. Smith knows that g, h, and i follow from f as per the rules of correct inference. Therefore, Smith knows that g, h, and i are valid inferences. Because Smith knows that g, h, and i are valid, his belief is not that g, h, and i are all true unless he conflates being valid with being true. Smith is rational and knows the rules, so doesn't do this. Rather Smith knows that g, h, and i are all true if and only if his belief that f is. — creativesoul
So then, let's say that Smith is just a regular joe, and says with unshakable certainty "Well, either Jones owns a Ford or Brown is in Barcelona" even though he knows that he's ignorant regarding Brown's whereabouts.
He would believe that f, but would not know that h followed. Thus, his assertion would be unjustified, and the case ends there. — creativesoul
Gettier's claim is that if an inference is valid, it preserves justification as well as truth, and thus even though there was no truth to preserve, what justification Smith had for his belief that (f), is passed to (g), (h), and (i) by modus ponens.
...And Smith believes that g, h, and i are true.
Smith's justification for (f) is all relevant to (f). Smith's inferring (g), (h), and (i) from (f) has nothing to do with the justification for (f). This is obvious because Smith could have correctly inferred (g), (h), and (i) even if it were the case that (f) was unfounded. — creativesoul
Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q. — Gettier
Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f). — creativesoul
I would disagree with Gettier's claim. — creativesoul
1. London is the capital city of England
2. London is the capital city of England or I am a woman
2 follows from 1. 1 is true and 2 is true.
3. London is the capital city of France
4. London is the capital city of France or I am a woman
4 follows from 3. 3 is false and 4 is false.
5. London is the capital city of Germany
6. London is the capital city of Germany or I am a man
6 follows from 5. 5 is false and 6 is true.
What makes the following claims true? — creativesoul
Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.
Michael wrote:
1. London is the capital city of England
2. London is the capital city of England or I am a woman
2 follows from 1. 1 is true and 2 is true.
3. London is the capital city of France
4. London is the capital city of France or I am a woman
4 follows from 3. 3 is false and 4 is false.
5. London is the capital city of Germany
6. London is the capital city of Germany or I am a man
6 follows from 5. 5 is false and 6 is true.
I replied:
What makes the following claims true?
"1 is true and 2 is true"
"3 is false and 4 is false"
"5 is false and 6 is true"
"2 follows from 1"
"4 follows from 3"
"6 follows from 5"
Srap asked:
What kind of answer are you expecting here?
Because it looks like you are asking, in so many words, for a theory of truth.
I would say that that would be the case if, and only if, P and Q have the same truth conditions. — creativesoul
However, I am teasing out the differences between statements that are called 'true' by virtue of being a valid inference, and those that are true. — creativesoul
I strongly suspect that there is conflation between the two at work. — creativesoul
I wrote:
Rather, (g), (h), and (i) are justified by virtue of Smith knowing the rules and applying them accordingly to his belief that (f).
You replied:
The trouble with this view is that valid inference from unjustified belief would confer justification upon the conclusion of the inference. Inference isn't supposed to do that...
I wake up on a Tuesday morning, groggy, remembering that I didn't have to get up yesterday, and thinking it's Monday and I have to be at work at 9. As it happens, Monday was a holiday and I have forgotten. I have a true belief that I need to be at work at 9, but it is in not justified, as it is a valid inference from my unjustified belief that it is Monday, not Tuesday.
You replied:...There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true...
Disjunctions are unique. — creativesoul
Gettier asserted:
Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.
I commented:
I would say that that would be the case if, and only if, P and Q have the same truth conditions.
You replied:
That would make them the same proposition.
You think/believe that every proposition has it's own unique set of truth conditions? — creativesoul
I do not accept Gettier's notion of belief. — creativesoul
Disjunctions are unique. — creativesoul
(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules. — creativesoul
You see what's happening here regarding the clear distinction being drawn between believing that a proposition is validly inferred, and believing that a proposition is true? — creativesoul
I wrote:
(g), (h), and (i) all consist of (f) and different statements about Brown's location. None of those statements (Q's) are believed by Smith. Smith derives them all by virtue of knowing the rules.
You replied:
And you've not shown why this matters. At no point does Gettier attribute to Smith a belief in any of the "Q's".
nothing at all to do with his belief except his belief that (p v q) follows from p. — creativesoul
I wrote:
But I have shown why it matters. Assuming sincerity in speech, statements are statements of belief. Smith's lack of belief in Q shows that his belief that (p v q) has nothing at all to do with his belief except his belief that (p v q) follows from p.
You replied:
... and is therefore true.
I wrote:
Regarding the difference between being called 'true' as a result of being the conclusion of a valid inference and being true, I expressed suspicion of conflation...
You replied:
...There might be if you persist in thinking that being the conclusion of a valid inference makes a proposition true...
That Smith believes (g), (h), and (i) -- i.e., believes all of them to be true -- is a premise of the argument.
Believing (f) and properly inferring (g), (h), and (i) from (f), why on earth should he not believe any of his own conclusions?
Disjunctions are unique — creativesoul
You wrote:
So let's say that I know that my girlfriend is in the bathroom washing. I believe that the disjunction "she's having a shower or she's having a bath" is true. Let's also assume that this isn't a dichotomy, and that she could in fact just be using the sink.
According to you, to believe that this sentence is true is just to believe that it follows from "she's having a shower" (and/or from "she's having a bath")? That's quite clearly wrong.
Believing that a disjunction is true is no different in kind to believing that a conjunction is true, or to believing that a simple proposition such as "she's having a shower" is true.
I can believe that p is true, I can believe that if p is true then r is true, and I can believe that r is true. In our case, r is p ∨ q.
Belief that a disjunction such as "she's having a shower or she's having a bath" is true, is to believe that one statement or the other corresponds to what she's doing in the bathroom. — creativesoul
Gettier asserted:
Secondly, for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.
I commented:
I would say that that would be the case if, and only if, P and Q have the same truth conditions.
You replied:
That would make them the same proposition.
I then asked:
You think/believe that every proposition has it's own unique set of truth conditions?
You answered:
I think that's a pretty reasonable way to define propositions, yeah. You can express the same proposition in multiple ways, in multiple languages, and there will be all sorts of differences that logic just doesn't care about. Insofar as they have the same truth conditions they are different ways of expressing the same proposition.
Belief that a disjunction such as "she's having a shower or she's having a bath" is true, is to believe that one statement or the other corresponds to what she's doing in the bathroom.
And belief that a disjunction such as "Jones owns a Ford or Brown is in Barcelona" is true is to believe that one statement or the other corresponds to some fact about the world.
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