Wasn't he criticizing you in that post? — Terrapin Station

I don't think so. @unenlightened, care to weigh in on this?

I don't think so. — Michael

Oh. Well, that would look bad for him then.

You can just use 1) "if something is a raven then it is black" and the logically equivalent 2) "if something is not black then it is not a raven". The paradox still holds. Evidence for 2) is evidence for 1). — Michael

Fuckin ell Micheal. You can if you want, but if you don't say anything that populates the world, you ain't saying anything about the world, and no evidence from the world applies. And then the statements are equivalent and there is no evidence for any of it and thus no paradox, because it is just a declaration about language.

A raven is evidence that there are ravens. If there aren't ravens, I really don't care what you say about them or what evidence you produce.

Fuckin ell Micheal. You can if you want, but if you don't say anything that populates the world, you ain't saying anything about the world, and no evidence from the world applies. And then the statements are equivalent andthere is no evidence for any of it and thus no paradox, because it is just a declaration about language.

A raven is evidence that there are ravens. If there aren't ravens, I really don't care what you say about them or what evidence you produce. — unenlightened

I don't understand this. If I were to say "if you are from Wales then you are a woman" then you can provide evidence (or even proof) against this claim by showing me that you're from Wales but not a woman. So evidence from the world certainly does apply to if/then claims.

So evidence from the world certain does apply to if/then claims. — Michael

It certainly can, but it doesn't necessarily, especially not based on simply playing a logic game that we've constructed. It depends on just what the claim is, the meaning assigned, the context, etc.

By the way, this is also the problem with arguments like the Gettier objections to jtb. Gettier's argument hinges on how we play particular logic games conventionally, but it makes the mistake of assuming that that's all there is to person's beliefs.

I don't understand this. If I were to say "if you are from Wales then you are a women" then you can provide evidence (or even proof) against this claim by showing me that you're from Wales but not a woman. So evidence from the world certain does apply to if/then claims. — Michael

Only if I exist. Are you claiming I exist? Then there can be evidence.

Only if I exist. Are you claiming I exist? Then there can be evidence. — unenlightened

And that's the point. According to the paradox, the existence of green apples is evidence for the claim "if something isn't black then it isn't a raven", and because of contraposition is also evidence for the claim "if something is a raven then it is black".

And that's the point. According to the paradox, the existence of green apples is evidence for the claim "if something isn't black then it isn't a raven", and because of contraposition is also evidence for the claim "if something is a raven then it is black". — Michael

What people count as evidence for something doesn't hinge on logic games in that way. Most people would say--and I'd agree--that green apples have nothing to do with ravens. So green apples aren't evidence of anything about ravens.

If we go by the definition here, "Evidence, broadly construed, is anything presented in support of an assertion. This support may be strong or weak. The strongest type of evidence is that which provides direct proof of the truth of an assertion. At the other extreme is evidence that is merely consistent with an assertion but does not rule out other, contradictory assertions, as in circumstantial evidence."

As the maths shows, each successful observation increases the probability of the assertion being true, and so seems to me to count as evidence (even if weak evidence).

The paradox still holds even if the existence of green apples is only weak evidence that if something is a raven then it is black.

Two statements have the same truth value in every model iff they mean the same thing. — Michael

Again, I think you're mistaken. You've applied an unjustified condition to "mean the same thing".

Here's a little example. Let's say that 2+2=4. There is a logical equivalence between (2+2) and (4). Now we can have a look at what each of those means. I assume that (2+2) means that one group of two is added to another group of two. I also assume that (4) means one group of four. I see a difference between the meaning of (2+2) and the meaning of (4). You have applied an unjustified principle, to say that because the two are equivalent they have the same meaning.

Here is the result of your application of that unjustified principle. If we observe, and therefore have evidence, that one group of two objects was added to another group of two objects, we can claim to have evidence of a group of four objects. But if we have evidence that there is a group of four objects, this does not constitute evidence that a group of two objects was added to another group of two object.

If we go by the definition here, "Evidence, broadly construed, is anything presented in support of an assertion. This support may be strong or weak. The strongest type of evidence is that which provides direct proof of the truth of an assertion. At the other extreme is evidence that is merely consistent with an assertion but does not rule out other, contradictory assertions, as in circumstantial evidence." — Michael

Anything can be evidence of anything if you use a definition that stipulates that it's evidence, no?

What does that prove though?

Here's a little example. Let's say that 2+2=4. There is a logical equivalence between (2+2) and (4). Now we can have a look at what each of those means. I assume that (2+2) means that one group of two is added to another group of two. I also assume that (4) means one group of four. I see a difference between the meaning of (2+2) and the meaning of (4). You have applied an unjustified principle, to say that because the two are equivalent they have the same meaning. — Metaphysician Undercover

Neither "2 + 2" nor "4" are truth-apt propositions. Therefore it's wrong to say that "2 + 2" and "4" are logically equivalent.

Again with the previous example, "I am both British and a man" is logically equivalent to "I am neither not British nor not a man". This is contraposition. Evidence for one is ipso facto evidence for the other.

As the maths shows, each successful observation increases the probability of the assertion being true, and as such counts as evidence (even if weak evidence). — Michael

What probability would you ascribe to Newton's theory of gravitation in 1915?

All you are saying is that logical equivalence is not "the same" as numerical equivalence. You have just provided evidence for my argument, that "equivalent" does not mean 'the same".

All you are saying is that logical equivalence is not "the same" as numerical equivalence. You have just provided evidence for my argument, that "equivalent" does not mean 'the same". — Metaphysician Undercover

I didn't just use the word "equivalent". I used the term "logically equivalent" which has a strict definition in logic.

The vast majority of people have a relevance requirement for evidence. The purported evidence needs to have something to do with what it's evidence for.

What I would like to see, is if you can justify the following claim. If this can be justified, then you might have an argument:

Two statements have the same truth value in every model iff they mean the same thing. — Michael

The vast majority of people have a relevance requirement for evidence. The purported evidence needs to have something to do with what it's evidence for. — Terrapin Station

Newton's law of gravitation accumulated a vast amount of evidence in support over many years. Applying the purported probability calculus to it, it must have achieved the status of a highly probable theory by 1915.

Then what happened? Is it still a highly probable?

The vast majority of people have a relevance requirement for evidence. The purported evidence needs to have something to do with what it's evidence for. — Terrapin Station

That's the paradox. The existence of green apples is relevant to and so is evidence for the truth of "if something is not black then it is not a raven". But because of the law of contraposition it is also evidence for the truth of "if something is a raven then it is black" even though it doesn't seem to be relevant.

What does your comment have to do with what you quoted from me? (Maybe it was an example of something without relevance? Haha)

The existence of green apples is relevant — Michael

No it isn't. I explained what I meant right after that. The purported evidence needs to have something to do with what it's evidence for. That's an explication of the first sentence.

The purported evidence needs to have something to do with what it's evidence for. That's an explication of the first sentence. — Terrapin Station

Yes, and the existence of green apples does have something to do with the claim "if something is not black then it is not a raven", given that it isn't black and isn't a raven.

Yes, and the existence of green apples does have something to do with the claim "if something is not black then it is not a raven" — Michael

Not with a claim per a logic game.

It needs to have something to do with ravens--the creatures.

Actually, what we are looking at is two statements which have the same truth value within the same model. So you need to adjust your claim to read:
"Two statements have the same truth value in the same model iff they mean the same thing."

Are you just not reading what I'm writing?

I should be asking you the same thing.

Actually, what we are looking at is two statements which have the same truth value within the same model. — Metaphysician Undercover

No, that would be material equivalence. We're discussing logical equivalence.

the existence of green apples does have something to do with the claim — Michael

Not with a claim per a logic game. — Terrapin Station

You seem to parse things as if you're a computer and you can only do exactly what the code you've been programmed with specifies.

It needs to have something to do with ravens--the creatures. — Terrapin Station

Why must it have something to do with ravens? The claim is "if something is not black then it is not a raven". Therefore, to be relevant, surely it must have something to do with not being a raven? Which it does; apples aren't ravens.