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". — Michael

The point you are missing is that if I don't exist, there can be no evidence as to my gender or my place of habitation. None at all. Not green apples, and not my genitals. Evidence can only be brought for or against existential claims.

"All dragons are Welsh." Look around and you will not find a non-Welsh dragon, though there may be stories. And of course there are those green apples in England. But this is nonsense. There are no dragons, and so no evidence is forthcoming about their nationality. "all dragons are Welsh" says nothing about the world, and therefore there is no evidence for or against it.

Why must it have something to do with ravens? — Michael

Why most people have that requirement for evidence is a good question maybe. It's not so easy to answer that. But whether we can answer that question or not, it's a fact that for most people, purported evidence needs to have something to do with what it's evidence for--so if it's purported evidence for something about ravens and the color they are, it needs to have something to do with the creature in question and their color.

The point you are missing is that if I don't exist, there can be no evidence as to my gender or my place of habitation. None at all. Not green apples, and not my genitals. Evidence can only be brought for or against existential claims.

"All dragons are Welsh." Look around and you will not find a non-Welsh dragon, though there may be stories. And of course there are those green apples in England. But this is nonsense. There are no dragons, and so no evidence is forthcoming about their nationality. "all dragons are Welsh" says nothing about the world, and therefore there is no evidence for or against it. — unenlightened

Again, we're considering the claim "if something is a raven then it is black". You admitted that your existence as a Welsh man is evidence against the claim "if someone is Welsh then they are a woman". Presumably there is also possible evidence for it. And so by the same token, there is possible evidence for the claim "if something is not black then it is not a raven". According to Hempel, the existence of green apples is evidence for the claim "if something is not black then it is not a raven". Therefore it is also evidence for the claim "if something is a raven then it is black".

Why most people have that requirement for evidence is a good question maybe. It's not so easy to answer that. But whether we can answer that question or not, it's a fact that for most people, purported evidence needs to have something to do with what it's evidence for--so if it's purported evidence for something about ravens and the color they are, it needs to have something to do with the creature in question and their color. — Terrapin Station

Terrapin, address the entirety of my comment. Your response doesn't make sense in context.

...if it's purported evidence for something about ravens and the color they are

See, this shows that you're not reading what I'm writing. The claim isn't about the colour of ravens but about the colour of things that aren't ravens.

The claim "All ravens are black"

Evidence for that, for the vast majority of people, has to have something to do with ravens, the creatures, and their color, supposedly black.

"Everything that is not black is not a raven"

This doesn't have anything to do with the creatures in question--ravens, and their supposed color. It rather has to do with things that aren't black and things that aren't ravens.

"green apples support the claim that all ravens are black."

No they dont, because green apples have nothing to do with the creatures in question or their supposed color.

The logic game you're referencing has nothing to do with how most people think about this or what they count as evidence. Which is good evidence that the logic game in this instance doesn't very well capture how people actually think. It's not at all a "law of thought," at least not without further qualification/modification.

The existence of green apples is relevant to the proposition that if something is not black then it is not a raven.
The proposition that if something is not black then it is not a raven is logically equivalent to the proposition that if something is a raven then it is black.
Therefore, the existence of green apples is relevant to the proposition that if something is a raven then it is black.

The claim "if something is not black then it is a raven" is logically equivalent to the claim "if something is a raven then it is black". — Michael

No in terms of evidence it isn't, for most people. You can just ignore that, but philosophizing while ignoring something so clear and simple is going to result in philosophy that sucks because all it's going to capture is a very limited way to play a certain sort of game, where that has nothing to do with the actual world.

What do you mean by saying that one claim isn't logically equivalent to another in terms of evidence?

You just clearly don't understand what logical equivalence means, despite my many attempts to explain it to you. This really is a futile discussion.

You just clearly don't understand what logical equivalence means, — Michael

You can't go outside of your computer program (which is what makes every discussion with you futile). That's not logically equivalent to most people in a "what-counts-as-evidence-for" context.

You admit that your existence as a Welsh man is evidence against the claim "if someone is Welsh then they are a woman". — Michael

I'd say it's a knock down disproof. Unless you wish to make it definitional in some way, such that being Welsh means being a woman, and men cannot be Welsh. At which point the claim is definitional and says nothing about the world. And at that point evidence does not exist.

"Those particles are not electrons, because all electrons have a negative charge."
"Those white birds are not ravens, because all ravens are black."

It is a choice whether the statement is about the world or about the way we are going to talk. If it is about the world, then there will be evidence. But if it is about the world, it is not the same as the contrapositive, for reasons I've already gone into ad nauseam. The paradox relies on the ambiguity, and the refusal to choose whether the statement is actually making a claim about the world or not, but still applying rules of evidence as though it were.

Just to confuse you further, 'Welsh' is a contested term. Since I was born and brought up in England of English and Scottish parents, I do not consider myself 'Welsh', though in quasi-legal terms I am Welsh, by virtue of living here. On the other hand, Mrs un was born in England of Welsh and Caribbean parents but brought up mainly in Wales, and does consider herself Welsh, though many people consider her 'foreign' by virtue of the colour of her skin. And then there is the language issue... My existence as a Welsh man is highly contestable. :-O

It is a choice whether the statement is about the world or about the way we are going to talk. If it is about the world, then there will be evidence. But if it is about the world, it is not the same as the contrapositive, for reasons I've already gone into ad nauseam. The paradox relies on the ambiguity, and the refusal to choose whether the statement is actually making a claim about the world or not, but still applying rules of evidence as though it were. — unenlightened

I still don't understand this. So perhaps to keep it simple you could clarify which of these you disagree with:

1. The proposition that if something is a raven then it is black is logically equivalent to the proposition that if something is not black then it is not a raven.

2. The existence of green apples is evidence (even if weak) that the proposition that if something is not black then it is not a raven is true.

As I see it, 1 is confirmed by the law of contraposition and 2 is confirmed by the maths provided here (coupled with the seemingly reasonable definition of "evidence" given in that same post¹). I certainly don't see anything that can be construed as ambiguous.

The conclusion that the existence of green apples is evidence (even if weak) that the proposition that if something is a raven then it is black is true then follows.

¹ Although saying that, the paradox holds even if we don't use the term "evidence". If the observation of a single white egg increases the probability that the proposition that if something is not black then it is not a raven is true then it increases the probability that the proposition that if something is a raven then it is black is true.

1. The proposition that if something is a raven then it is black is logically equivalent to the proposition that if something is not black then it is not a raven.

2. The existence of green apples is evidence (even if weak) that the proposition that if something is not black then it is not a raven is true. — Michael

2. Is false. There is no such thing as evidence for a universal statement. What's more, you can't apply probabilities to universal statements.

In the case where the universal statement is an hypothesis - i..e a tentative explanation for some aspect of reality, you can't use probabilities either. The negation of an explanation is not an explanation, so the two are in different classes of objects. In such circumstances attributing (p) to an explanation and (1-p) to its negation is meaningless.

1. The proposition that (a) if something is a raven then it is black is logically equivalent to the proposition that (b) if something is not black then it is not a raven. — Michael

This is false for most people in the context of considering what counts as evidence for each statement. Unenlightened also makes a good point in that (b) isn't something that anyone would consider there to be evidence for really unless we've already stipulated that black things are necessarily not ravens. But that's a definitional issue, and not an evidential issue.

2. The existence of green apples is evidence (even if weak) that the proposition that if something is not black then it is not a raven is true. — Michael

That's false for most people, too. There are a number of problems with it, including what I just said above (that (b) isn't something we'd have evidence for, as it's stipulative).

Also, green apples certainly wouldn't be considered evidence for (a) by the vast majority of people.

As I see it, 1 is confirmed by the law of contraposition and 2 is confirmed by the maths provided here (coupled with the seemingly reasonable definition of "evidence" given in that same post1). I certainly don't see anything that can be construed as ambiguous. — Michael

The law of contraposition has little to do with what people count as evidence or not, and the definition of evidence you gave ignores the relevance element as I described it, which most people require.

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

OK, I wasn't clear on your definition of "logical equivalence". If this is your definition of logical equivalence:

Two statements have the same truth value in every model — Michael

Then (1) and (2) of the op are not logically equivalent. That is the problem, you are assuming that they are logically equivalent, without adhering to your definition of "logically equivalent".

Re "if something is not black then it is not a raven"

Let's assume that's something we're not stipulating, but it's instead a hypothesis that we feel we need to gather evidence for.

Well, first off, if we're checking it, we very well could be wrong. Maybe it's going to turn out to be that ravens are red and purple and all sorts of other colors, too.

So we check a green thing and see that it's an apple. That doesn't tell us anything about whether there are any non-black things that are ravens, it just tells us that one non-black thing isn't a raven. It only increases the probability that no non-black things are ravens if we assume that we're dealing with a finite set of colored items, and we don't at all know this.

(2) Everything that is not black is not a raven. — Michael

The problem is that this (2) also allows that "Everything that is black is not a raven" is true as well. So it is impossible that (1) and (2) are logically equivalent, under that definition of logically equivalent.

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). — Michael

I think that there is an equivocation here on what we mean by "probability." You are really talking about our (subjective) confidence in the truth of a proposition, rather than its (objective) likelihood. "All ravens are black" is either true (p=1) or false (p=0), regardless of what we think.

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

I agree. In this case, the relevance requirement is tied primarily to the subject (ravens), rather than the predicate (black). The fact that green apples are not black things is not nearly as relevant as the fact that green apples are not ravens.

Said another way, there is a relation between the perceived strength of evidence and the number of items in a collection to which we are attributing a universal property. There are vastly fewer ravens than non-black things, so each black raven that we encounter increases our confidence that "all ravens are black" by a much larger degree than each green apple that we encounter increases our confidence that "all non-black things are non-ravens." This may be the asymmetry of the two logically equivalent formulations that others have been trying to articulate. For most people, something counts as (even weak) evidence for the truth of a proposition only if it significantly increases our confidence.

2. Is false. There is no such thing as evidence for a universal statement. What's more, you can't apply probabilities to universal statements. — tom

That. If 1. then not 2.



"All ravens are black" declares the blue area to be empty. This is refuted by evidence that there is something in the blue area, but not confirmed or made more likely by anything appearing anywhere else. The contrapositive says exactly the same thing, and the same evidence rule applies.

"There are ravens, and they are all black" on the other hand, declares that there is nothing in the blue area and something in the turquoise. In this case, the contrapositive is not the same, and every black raven found in the absence of any non-black ravens can be said to support the compound statement. But again stuff appearing elsewhere in the diagram is irrelevant.

I think that there is an equivocation here on what we mean by "probability." You are really talking about our (subjective) confidence in the truth of a proposition, rather than its (objective) likelihood. "All ravens are black" is either true (p=1) or false (p=0), regardless of what we think. — aletheist

Given a shuffled deck of cards, what's the probability that the first card we turn over is the Ace of Spades? 1 in 52. Even though either it's the Ace of Spades or it isn't. And if the first card we turn over isn't the Ace of Spades then what's the probability that the next card is? 1 in 51.

So I don't understand what you mean by "probability".

The problem is that this (2) also allows that "Everything that is black is not a raven" is true as well. So it is impossible that (1) and (2) are logically equivalent, under that definition of logically equivalent. — Metaphysician Undercover

No it doesn't. How have you derived that? Certainly not with the law of contraposition.

Then (1) and (2) of the op are not logically equivalent. — Metaphysician Undercover

Yes they are. It's guaranteed by contraposition.

2. Is false. There is no such thing as evidence for a universal statement. What's more, you can't apply probabilities to universal statements. — tom

I would count as evidence anything that increases the probability that the statement is true. As shown here, each successful observation increases the probability that the statement "if something is an egg then it is white" is true.

This is refuted by evidence that there is something in the blue area, but not confirmed or made more likely by anything appearing anywhere else. — unenlightened

Then where does my math fail here? Each successful observation does increase the probability that the statement is true.

Well you start with a compound statement from the beginning. "there are eggs and they are all white." Then you also stipulate how many eggs there are - 12. And finally you put a completely arbitrary value on the probability of an egg being white.

But given that original probability, why should each white egg found make it more likely that the next one is white rather than less likely?I looks like a reverse gambler's fallacy to me.

Edit. No, that last bit's wrong. It's the limited number of eggs that raises the probability, If there were only 12 ravens and eleven had been found to be black, your probabilities would work. It's knowing how many there are before you start looking at them that is problematic, along with making the existential claim that I have been pointing out all along.

For most people, something counts as (even weak) evidence for the truth of a proposition only if it significantly increases our confidence — aletheist

As I said here, we don't even need to think about it in terms of evidence. The paradox arises even if we just think about it in terms of the probability that the statement is true. Given that the existence of green apples increases the probability that "if something isn't black then it isn't a raven" is true then it increases the probability that "if something is a raven then it is black", despite the fact that the existence of green apples is prima facie irrelevant.

So I don't understand what you mean by "probability". — Michael

Strictly speaking, probability only applies to the long run of experience, not to an individual case. In general, the probability is 1/52 that the top card of any randomly shuffled deck is the ace of spades; i.e., that is the value to which the proportion of cases where that happens will converge as the number of trials increases to infinity. However, in each individual case, the probability is either 1 (if it is the ace of spades) or 0 (if it is any other card). Again, you are confusing this (objective) fact of the matter with the (subjective) confidence that someone has before looking at the card.

I would count as evidence anything that increases the probability that the statement is true. — Michael

But nothing that you think, say, or do can increase the (objective) probability that the statement is true; it is either true (p=1) or false (p=0) all along.

As shown here, each successful observation increases the probability that the statement "if something is an egg then it is white" is true. — Michael

No, it increases your (subjective) confidence that the statement is true; and when you only have 12 things in a collection, each "successful" observation significantly increases that confidence. However, notice that it has no effect whatsoever on whether the 12th egg (or even the billionth) actually turns out to be white.

Given that the existence of green apples increases the probability that "if something isn't black then it isn't a raven" is true ... — Michael

Saying this over and over does not make it accurate. The existence of green apples has no effect whatsoever on the probability that "if something isn't black then it isn't a raven" is true. The observation of a green apple might have a very small effect on one's confidence that "if something isn't black then it isn't a raven" is true; but since such confidence is subjective, the (lack of) relevance of the observation will in most cases prevent it from being counted as genuine evidence.

As explained here, the actual numbers don't matter. You can increase the number of eggs to any arbitrarily high number and decrease the probability to any arbitrarily low number and it is still the case that each successful observation increases the probability that the statement is true.

Decrease the number to zero, and see how that affects things. You have already declared that there are eggs. That is confirmed by every egg, but that they are all white is only confirmed by looking at them all. The whole problem is that you are translating the symmetry of the logic without existential claims to a real world of existential claims and ignoring the existential claims you are actually making. Look again at the diagram, and tell me what's wrong with that.

But I am right out of breath now, someone else have a go.

Strictly speaking, probability only applies to the long run of experience, not to an individual case. In general, the probability is 1/52 that the top card of any randomly shuffled deck is the ace of spades; i.e., that is the value to which the proportion of cases where that happens will converge as the number of trials increases to infinity. However, in each individual case, the probability is either 1 (if it is the ace of spades) or 0 (if it is any other card). Again, you are confusing this (objective) fact of the matter with the (subjective) confidence that someone has before looking at the card. — aletheist

Again, I don't know what you mean by probability. Probability isn't simply limited to either there being a probability of 1 or a probability of 0. We can talk about the probability that I won the lottery yesterday being 1/x million (whatever it is) and we can talk about the probability that nobody won yesterday being (1 - 1/x million)^{the number of players}.

Decrease the number to zero, and see how that affects things. You have already declared that there are eggs. That is confirmed by every egg, but that they are all white is only confirmed by looking at them all. — unenlightened

I'm not talking about confirmation, i.e. proof. I'm talking about evidence. Evidence is just whatever increases the probability that the statement is true. Given that observing a white egg proves that the number of eggs isn't zero and that the probability that an egg is white isn't zero, each successful observation increases the probability that every egg is white (as the maths shows).

And to continue with my example of the pack of cards, imagine that we tear one of the cards. What's the probability that none of the intact cards is the Ace of Spades? It's certainly not correct to just say "either 1 or 0". It'll be 1/52. And each time you turn over a card and find it not to be the Ace of Spades the likelihood that none of them is the Ace of Spades increases (with the probability being 1/2 when you get to the last intact card). Because there are fewer opportunities for the hypothesis to be refuted.