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Mar
4
awarded  Citizen Patrol
Mar
4
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
What is off-putting is that numerous other people, including Simon Klaver in his answer, and DanielV, in his comment above, noted that your "if your original conditional statement holds, another one holds as well" is completely baseless, and yet you simply ignored this ... which I suppose is consistent with inventing the baseless claim in the first place. Also baseless is "There's an understood but unstated ...". Making random unsupported assumptions is no way to go about determining what are the logical implications of a statement, and it's quite off-putting to not first seek concurrence.
Feb
26
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
@CarlMummert The comments sections on YouTube videos about .(9) = 1 or the Collatz conjecture are full of mathematical illiterates who are absolutely certain that they know better than all the world's mathematicians, but it's sad to see that such folk are now posting at math.stackexchange
Feb
26
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
@BenjaminLindqvist Yes, it's bizarre that someone would whine about comments pointing out errors in their answer -- that's a large part of why there are comments. But I suppose it is to be expected of someone who thinks that people who are competent at logic are "total jerks". And this drivel about "context" is funny; the context is a question in a math/logic forum about the formal implications of a statement. The context is also about being bald, not "bold".
Feb
26
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
" But the original statement was framed in English, not formal logic." -- This is silly sophistry. The question, asked in a math/logic forum, is about the formal implications of the statement. If the statement is to be taken to have vague indeterminate meaning, then it is pointless to ask the question and any answer is acceptable.
Feb
26
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
"Only through the vacuous truth" -- in other words, "only" through truth. "they don't have enough information to say who's bald or not" -- indeed, but that has nothing to do with the problem at hand. But if they take off the blindfold and see that they are at the front of the line, then they do -- if they are competent at logic and take your statement to be factually correct. Of course it is quite possible that the person making the statement is incompetent and doesn't understand logic themselves, but that's assumed otherwise in problems like this.
Feb
26
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
" if your original conditional statement holds, another one holds as well: ∀p∈Pn−1,¬b(p)→¬b(pn)" -- No, this is completely, utterly wrong, reminiscent of the Bellman in The Hunting of the Snark. Not only doesn't your inference follow from the title statement, it is contradicted by it ... that is the source of the contradiction you find -- you invented it. See Simon Klaver's answer, where he correctly states that "there is no rule about property 2, so it plays no role".
Feb
26
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
+1 Good answer. Unfortunately, a lot of people responding, including the OP and especially jpmc26, are inept and are unable to appreciate or understand it.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
'what you mean by "incoherent."' -- If simply asserting the statement in the title "can lead to contradictions", then logic is broken. "This suggests we either have an ill formed problem statement or vacuous truths pose a problem." -- but neither of those is true; thus, it's your analysis that is wrong. The premise, given in the title, is ∀p∈Pn−1,b(p)→b(pn), from which it follows that ∀p∈{},b(p) →b(p1). It's also (vacuously) true that ∀p∈{},¬b(p) but nothing follows from that; certainly not that ¬b(p1).
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
@emory " I do not see the contradiction" -- how odd. "If [vacuously true] then X" and "If [vacuously true] then not X" are clearly contradictory.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
@aroth Ironically, you did not answer my question. Anyway, a) 31 people upvoted the "non-answer" and the OP accepted it, and b) this answer is flat out wrong (no one in front of the first person is equivalent to everyone in front of them being bald), so I don't think your O is worth much.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
@aroth So being explicitly wrong is better than giving a correct argument that implies the correct answer?
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
"You are too caught up by the notion of "the first person" when the position is not important at all." -- This is nonsense. The question is specifically about the first person. "says nothing about" -- of course it does. (Everyone is X) implies (not (someone is not X)).
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
'"There's an understood but unstated "for the second person on" in your conditional statement' -- wrong. 'Interpreting the statement as holding true for the first person can lead to contradictions.' -- wrong and incoherent.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
@emory "If you are at the head of the line, both are vacuously true" -- No, the antecedents are vacuously true, making the statements contradictory.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
"it simply doesn't have a truth value, I'd say" -- you would say wrong. It's bizarre, or tragic, that this got 6 upvotes.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
"But what does a logical statement suggest beyond itself? " -- suggestion is a psychological, not logical, property. There are no intrinsic suggestions.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
"if the subject doesn't exist, then does the statement have a truth value?" -- it depends on the statement. "I think there's a convention in math that if the subject doesn't exist, then the statement is right." -- you are quite confused. If the antecedent of a material implication is false, then the implication is true. Your more general statement is nonsensical.
Feb
25
comment “If everyone in front of you is bald, then you're bald.” Does this logically mean that the first person is bald?
"In my opinion, it means" -- If that is your opinion of what it means, then it doesn't imply that the first person is bald, because the antecedent is false. And there is no objective matter of fact as to what it does mean, because it is an ambiguous sentence of the English language, not a formal statement in logic.
Jul
2
awarded  Autobiographer