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”.
I had to read this a few times to figure out what was going on, I’ve been revising my position as I go, because these are matters I haven’t thought about for a while. Going back to your very first post is what clued me in, in the end. Let me know what you think about this:
You began this by telling us what we know: we know that Hitler wasn’t a woman, and that he didn’t persecute blacks.
1.) Hitler wasn’t a woman,
2.) Hitler didn’t persecute blacks.
From that we can conclude that
3.) If Hitler wasn’t a woman, then he didn’t persecute blacks.
That should tell you something right there- that the “IF” relation in formal logic is saying nothing at all about causation. It is certainly not saying that Hitler’s not being a woman caused him to not persecute blacks, because that’s not implied in your two premises, and an analytic operator, by definition, contributes no new information.
“Hitler’ WOULD HAVE” persecuted blacks thus comes from no where- no where but an incorrect reading of ‘if’ that assumes causation where, I hope you agree with me based on the above, it does not exist.
“If Hitler was a woman, he would have persecuted Blacks” thus does not follow from the information you gave us. the ‘would have’ clause has different content than what we started with, it is not a simple negation of 2, and it’s not a proper interpretation of what ‘if’ means in formal logic. What the rules of implication actually give us is this
“If Hitler was a woman, then Hitler persecuted blacks”. Not ‘would have’.
I think seeing that 4 is true is a little odd, but it’s not a full break from reality- it’s no harm to our understanding of the universe or logic’s place in it to see that a conditional with a false antecedent and consequent is true. Is 4 true or false on a common-sense understanding? Meh. Hitler was NOT a woman, so common-sense has no horse in this race. If implication tells us it’s true because of the ‘either not a or b’ thing, then that’s fine now that we’re no longer actually making a claim about womanhood or it’s causative influence on racism or whatever, right?
It’s taking me a long time to get to an answer here, because I know intuitively that the problem is with ‘would have’, but I’m so cussed bad at formal logic that sussing it takes a lot of finagling; I apologize for changing my approach with every fresh reply.
A trinary system produces a different truth table (3x3).
Your statement has to fit ALL rows in the truth table for it to be of that type.
An implied statement leaves out one of the presumed premises, which in your case is an unknown.
If Hitler was a woman [and women abuse blacks] then Hitler would have abused blacks.
If Hitler was a woman [and don’t know shit bout women] then Don’t know shit bout Hitler.
I’m glad you think real logic is trinary, but I think you’re confusing conditional statements for syllogisms in the above.
Syllogism are of the form:
P → Q
P
Q
Whereas a condition statement is just the “P → Q” above.
There need not be an “implied” or “hidden” clause in “If Hitler was a woman [and women abuse blacks] then Hitler would have abused blacks.” ← This is just the P → Q part. If you want to pull out “and women abuse blacks” then you’re just making a syllogism of the form:
[X is a woman] → [X abuses blacks]
[Hitler is a woman]
[Hitler abuses blacks]
Any syllogism can be converted into a complex conditional statement. For example, the above syllogism (with the P’s and the Q’s) can be rewritten as “[(P → Q) & P] → Q”. I think that’s what you’ve done here: “If Hitler was a woman [and women abuse blacks] then Hitler would have abused blacks.”
What I was saying is that an “implied statement” leaves out one of the conditionals that would normally be required for a deductive statement. In your case, the statement left out involved the connection between being a woman and abusing blacks. If you had put that one in, the statement would have been a “deduction”, not an “implication”. But as it was, it was neither.
Yeah, you got that right. Except I do want to point out that even though logical conditionals have nothing to do with causation per se, they do seem to insinuate a dependence relation–in that the consequent depends on the antecedent.
Technically, you’re right, but I think we can do better. If we could just say that the truth value of the conditional is unknown, that (to me) would fit with the way we think of reality much more squarely.
Yeah, still struggling with this.
No need to apologize, Uccisore, changing one’s approach can be a sign of rationality.
My thoughts so far on the “would” qualifier are as follows: In itself, it seems almost to demand that the truth value of the proposition it’s a part of be determined as part of a conditional. What I mean is, you take the statement “Hitler would have persecuted the blacks,” and even though it is a grammatically well-formed sentence, semantically it seems to hint that it cannot stand by itself, that it requires being the consequent of a conditional just to make any sense. I mean, you say that to someone, and they’ll likely respond “If what?” So the reason we have trouble with it is that we can’t determine its truth value unless we can determine the truth value of some antecedent proposition it is connected to as its consequent. And in some case (such as this one), that the truth value of the antecedent be “true” specifically.
That’s unlike the following conditional:
If my name is Sam, then I’m a Martian.
which again, brings up the same absurdity I tried to exemplify in my OP (although, in some way, not as much), but this time, without the “would” involved, it’s quite easy to see that the antecedent and consequent are both false. You can take either out and treat them as stand-alone propositions, and not only will they be well-formed sentences grammatically, but there won’t be any question as to their truth/falsity.
