It is! You know how I know? Because I know that Hitler wasn’t a woman, and I know that Hitler didn’t persecute the blacks (not in any overwhelming scale comparable to the Jews anyway), and according to the rules of Logical Implication, if the antecedent proposition of a conditional expression and the consequent proposition are both false, the expression as a whole is true.

So we know that if Hitler was a woman, he would have persecuted black people.

Well, it’s not logically false. Just need logic squares that have a third, ‘indeterminate’ option maybe.

Also, if you forget about the common-sense meaning of ‘if’, and just treat it as a purely logical operator that is the equivalent of “Either not-a or b” then it works fine.

I’m glad you mentioned this, because that’s where I wanted to go with this. Whatever medieval scholar it was who decided the truth values of conditionals had to have been one of those thinkers who didn’t believe in indeterminate truth values. I say, if you just allow for indeterminates, a lot more in the philosophy of logic and language would make sense.

As in either Hitler wasn’t a woman, or he persecuted the blacks?

Yes, that does sound more realistic, but there still is a trace of that same absurdity. If you said that to someone–“either Hitler wasn’t a woman, or he persecuted the blacks”–someone might say “uh… why would Hitler have persecuted blacks if he was a woman?”

Well, these operators ‘if’ and ‘or’ aren’t intended to make predictions about future or possible states of affairs. That’s another confusion between the logical operators and their common usage as words.
All we’re really saying is that given
1.)Hitler isn’t a woman, and given that
2.) he didn’t persecute blacks,
the conditions of “Either Hitler wasn’t a woman, or he didn’t persecute blacks” are satisfied. If you wanted to, you could replace the second part of that statement with some completely unrelated clause and it would still work. “Either Hitler wasn’t a woman, or Mississippi is spelled with 5 s’s” is satisfied just as well by 1 and 2.

Yeah, it’s satisfied, but that still leaves us with the statement “If Hitler was a woman, he would have persecuted the blacks,” as being true. I mean, you could say that it’s only true as an outcome of the rules of logic and not as an outcome of anything to do with meaning or reality, but then logic loses it’s connection to language. I always thought the rules of logic are supposed to be our guide to determining the truth of statements, and the truth of statements a guide to determining the state of reality. But if the rules of logic don’t help us determine the state of reality, then they’re meaningless.

I see what you’re saying, but I don’t think so. The statement is actually “If Hitler is a woman, he persecutes Blacks”. Your statement above is making a prediction about the future or a possible state of affairs not covered by the rules of implication at all.

“If hitler is a woman, he persecutes blacks” is true because Hitler is not a woman, so the statement clearly isn’t false by the one obvious way an ‘if’ statement can be false- A being true, and B being false. It seems dubious at first that we can say an if/then is true if the first parameter is false, but we see that it’s true (instead of undetermined) because of the proof that shows that “either not A or B” is the same thing.

You have to be careful not to use ‘If’ as a modal statement, because that’s not covered by simple logic. Your statement above is the equivalent of “In any possible world in which Hitler is a woman, he persecutes blacks”, which is certainly not the kind of thing said by “If A then B” in simple sentential logic.

The problem is using two implicit hypotheticals together, “if” and “would have”.

If Hitler was a woman (false)
Then he “would have” persecuted black (true/false).

The second hypothetical is irrelevant. It implies that there is a necessary relationship between “women persecuting blacks”. So this is the underlying premise of both hypothetical conditions.

If women necessarily persecute blacks then the entire statement is true.

If women sometimes do not persecute blacks then the entire statement can be falsified.

Hitler is just irrelevant to the entire statement. What does Hitler have to do with “women persecuting blacks”? Probably nothing. It is a distraction.

I don’t think what the statemet is doing plays any part in the rules of logic. From what I understand (which isn’t much), the only constraints on what the rules of logic apply to is that the statements have to count as propositions. Unless I’m seriously mistaken, I’m sure these are propositions:

“Hitler was a woman.”
“Hitler would have persecuted the blacks.”

If the first sentence can be denoted by P and the second by Q, it seems you should be able to fit them into the form of a conditional (P → Q) and the rules of logic would apply.

But then there’s the “would have” part, which makes me think of “not.” If we say “Hitler was not a woman,” is this a proper proposition, or would logicians insist that we take out the “not” to make: not “Hitler was a woman.” In that case “Hitler was a woman” would be the proper proposition and “not” would be a negating operator working on the proposition. In the present case, instead of saying “It is not the case that Hitler was a woman,” we would say “It would be the case that Hitler persecuted black people.” How does this “would have” affect the rules of conditional statements?

Well, whatever rules apply to conditionals–whether the statements make future predictions or what would be the case in some possible world–I would think the same should apply to either/or statements.

I don’t think it’s a modal statement if I understand your meaning.

“Necessary” as in modal?

The problem is, even if it’s falsified, logicians would still insist the statement is true.

We can replace Hitler with Bozo the Clown and we’d still have the same problem.

You are misunderstanding what a “Logical Implication” means.

Your statement is a valid logical implication if and only if the statement satisfies the logical implication truth table. Since your statement doesn’t satisfy that table, your statement is not a valid logical implication.

You may have something with the second point (see my reply to Uccisore), but your first point is an evasion. If empirical evidence had the power to trump the rules of logic, we could dismiss any logical argument by saying “Well, that’s just true according to logic.” As I said to Uccisore, logic is supposed to be a guide to truth, to reality, and if absurd statements can be made because “that’s just according to the rules of logic,” then logic isn’t doing it’s job.

In what way does it not satisfy the table?

Yes, I think “would” is the culprit. It seems it could be counted as a qualifier or logical operator (like not, like possibly, like all or at least one, etc.). So “Hitler would have persecuted the blacks” becomes “It would be the case that Hitler persecuted the blacks,” and that could be denoted wH (where H = “Hitler persecuted the blacks” and w = “It would be the case that”).

Then, we could tie this into the point I wanted to bring in from the beginning–that logical truth values need not be binary–it can be trinary with the “indeterminate” value being a third option. I would say that the rule for a “would” proposition is that it is indeterminate. If you want to talk about something that would be the case in some alternative hypothetical world, how are you going to figure out if it’s true or not? If you can’t–if it makes no sense to talk about its truth or falsity–then perhaps we should be allowed to say it has an indeterminate truth value. So the rule for conditionals in the case where the antecedent is false and the consequent is indeterminate is that the whole expression is indeterminate. That would make much more sense to me than saying “If Hitler were female, he’d be a God damn racist bastard,” is unequivocally true.

Read the below baring in mind that I only got a B in formal logic, and it was a hard-earned B.

The propositions above would be properly expressed in sentential logic as

“If it IS the case that Hitler was a woman, then it IS the case that Hitler would have persecuted the blacks.”

Baring in mind that sentential logic isn’t examining what Hitler would or would not have done, but merely how certain sentences hang together. The “if it is the case that” can usually be omitted, but here a proper understanding of what’s going on requires it.

And see what I said above- the above is true because it’s not the case that Hitler was a woman, and what we know about ‘either not A or B’. However you want to parse it, you can’t put the labor of discerning what might be the case in the future or another possible world on basic sentential logic- we have other operators for that. The above is not logically equivalent to “If Hitler was a woman, he would have persecuted the blacks”, because this second sentence is not attached to what is in fact the case in the way the above one is. You need that attachment to what is in fact the case for your logic square to work the way you want it to.

So, all sentential logic can say is that the above sentence is true- by virtue of the fact that that’s what you get when the first premise in an ‘if then’ is false. The question of what Hitler would have done in some other circumstance isn’t a subject for sentential logic.

I think you can stick the ‘not’ wherever works for you, because ‘not’ is a basic operator of sentential logic.

Yeah…you might be right about that, on second thought. Still, I don’t think ‘would have’ is what sentential logic 'if’s are about. The truth value of those kind of ifs are a very controversial thing.

But it’s not the way sentences hang together, not in the way we ordinarily use sentences anyway. What the above statement is saying is that there are two cases: 1) that Hitler was a woman, and 2) that Hitler would have persecuted the blacks, and that the latter depends, for its being true, on the former being true. Now you take the rules of conditional statements into account, and they say that if both cases are not true, then the whole statement is true–that is, the second case does depend, for being true, on the first case being true.

But as insightfoul so untacitly stated, there is no correlation between Hitler’s sex and his being a racist (he was a racist, but not because of his sex). That is to say, in reality, the second case does not depend on the first case for its truth. In other words, the rules of logic fail us here. They tell us that it’s true that if Hitler was a woman, he would have persecuted the blacks, but we simply cannot intuitively take that seriously. In reality, one would think, Hitler’s sex had nothing to do with his racist orientations. My point in this thread is that this particular logical rule–that a false antecedent and a false consequent makes for a true conditional statement–is misguided at best.

I’m saying that if logic is to serve a purpose at all, it ought to tell what actually follows in reality, or at least semantically, given certain true assumptions. I’m saying that if all logic is is a system according to which we apply meaningless and arbitrary rules to symbols (i.e. propositions) given certain meaningless and arbitrary operators (i.e. and, or, if/then), then we can make up whatever the hell rules we want. We could say that if the antecedent is true and the consequent is true, then the whole compound proposition is false. Why not? We just have to agree that that’ll be the rule and that we’ll all follow it. That way, we can say statements like “If you drink the poison, you will die,” are unequivocally false. How so? Well, that’s just the rules of logic–and we all know that those rules are just arbitrary and meaningless–we just made them up and agreed to follow them–so don’t worry if it doesn’t make sense in reality, it’s just a logical rule.

Of course, I’m not saying I’m smarter than centuries worth of professional logicians, but that this assignment of binary truth values to propositions is not the only option: we could have a trinary system in which we are allowed to assign an “indeterminate” truth value to some propositions, including compound ones.

Yeah, that one I’m still struggling with. It certainly does seem pretty cut and dry that “Either not A or B” is true given that not-A is true and B is false. Which of course, implies that “If A then B” is also true. Not sure how that will play out, but I’ll think about it some more (maybe).

I’m not exactly sure what you’re saying here, but if I understand you correctly, I think that’s what I’m saying. I’m saying that “Hitler would have persecuted the blacks” depends on “Hitler was a woman” being the case in actuality just to have any truth value at all (let alone true or false). Since “Hitler was a woman” is in fact false, “Hitler would have persecuted the blacks,” has no truth value (in a binary system), and therefore warrants (in a trinary system) the value “indeterminate”.

But you see why that entails a failure on the part of logic–at least in binary systems–that is, if all that sentential logic can say is that the above sentence is true, when in fact there is no truth or falsity to the sentence in reality, then it’s options are rather limited, and it falls short of informing us of actual states of affairs. But if we introduce a trinary system, we get the leverage of re-connecting logic with reality.

But in any case, I thought of this instead:

If my name is Sam, then I’m a Marsian. ← It’s true!

A logical implication is a statement that forms only one particular truth table.
You have to look at your statement and decide if it fits that truth table.
Yours doesn’t.

p = Hitler was a woman
q = persecuted blacks
p → q = Hitler would have persecuted blacks

Truth table for a Logical Implication:
p _ q _ p → q
F _ F _ T
F _ T _ T
T _ F _ F
T _ T _ T

For your statement to be a valid implication, all four lines have to be valid.

Hitler was woman : not persecuted blacks :: T/F Unknown
Hitler was woman : persecuted blacks :: T/F Unknown
Hitler not woman : not persecuted blacks :: F Known
Hitler not woman : persecuted blacks :: T Known

Your statement met only two of the four requirements.
You would have had to have included some assertion connecting being a woman and persecuting blacks.

Not exactly clear on what you’re saying, but it sounds like this: given that my statement is the second one above (which it is), then it has an unknown truth value. “Hitler was woman” is definitely known to be false, but “Hitler would have persecuted the blacks” is unknown. Now, you realize that in order for that to make sense, we would have to be saying that such a statement (with “would” in it) can’t be assigned a truth value, not just that we don’t know in fact. And this may be the case: how does the truth of a statement with “would” in it get decided?

But of course, this is what I’ve been arguing all along–that we allow “unknown” as a third truth value. In a binary system, you’d be right–my statement wouldn’t fit the truth table. But in a trinary system, it could fit the table seeing as how an “unknown” truth value would be perfectly valid.

What about a little box turned sideways so it’s like a 4 sided diamond sitting on one of it’s corners, with an arrow coming out the side of it pointing to the right? It could mean “possibly”.