As a person who has studied logic quite a bit, I can say I don't actually think like that. What VanishedOne did was essentially proving what is called modus tollens. I would have phrase the problem as to prove "not for all X, man(x) -> tall(x)", and by moving the negation across the universal quantifier, you get "exists x such that not man(x) -> tall(x)", and by expanding the implication, "exists x such that not(not man(x) or tall(x))" and by distributing the not, you get "exists x such that man(x) and not tall(x)", which means if you find a 7 foot tall man, you have disproved the original statement that all man are below that height. Again, this is proved for you already in modus tollens, you never actually have to perform this proof. Larger logic proofs do however take this kind of form.

Do most logical people think in terms of those kinds of structured rules? I consider myself extremely logical but spelling it all out in a step-by-step tautology is a terrific bore. In my mind, either something makes sense or it doesn't; I don't need to run through a checklist of conditions to evaluate it. I had assumed I was normal in that regard...

Not impeccable working out, but I don't like formal logic much. Anyway, the point is that if your rule says 'always' then a single exception case shows it to be false. 'Often' is safer.

I had an economics professor who coined this phrase and used it to keep us honest. A man-who story is any line of logic that begins along the lines of "I know a man who..." as a way of refuting a hypothesis or rule. In other words, it refers to anecdotal evidence. A man-who story can be considered unsubstantial and of no consequence to anyone except the man.

seanahan commented on the word man-who story

As a person who has studied logic quite a bit, I can say I don't actually think like that. What VanishedOne did was essentially proving what is called modus tollens. I would have phrase the problem as to prove "not for all X, man(x) -> tall(x)", and by moving the negation across the universal quantifier, you get "exists x such that not man(x) -> tall(x)", and by expanding the implication, "exists x such that not(not man(x) or tall(x))" and by distributing the not, you get "exists x such that man(x) and not tall(x)", which means if you find a 7 foot tall man, you have disproved the original statement that all man are below that height. Again, this is proved for you already in modus tollens, you never actually have to perform this proof. Larger logic proofs do however take this kind of form.

Lewis Carroll actually wrote a book about logic.

December 11, 2007

sionnach commented on the word man-who story

I know a (reliable) man who travelled to Australia, where he saw a black swan. Ergo, not all swans are white.

December 11, 2007

uselessness commented on the word man-who story

Do most logical people think in terms of those kinds of structured rules? I consider myself extremely logical but spelling it all out in a step-by-step tautology is a terrific bore. In my mind, either something makes sense or it doesn't; I don't need to run through a checklist of conditions to evaluate it. I had assumed I was normal in that regard...

December 11, 2007

vanishedone commented on the word man-who story

Maybe it's insubstantial in ecomomics. In logic single cases can be perfectly substantial by way of refutation:

1) Hypothetical rule: 'all men are under seven feet tall'

2) Anecdote (which we can assume here is true): 'I know a man who is over seven feet tall'

3) From (2): there exists at least one man (A) who is not under seven feet tall

4) From (3): (A) is a man

5) From(3): (A) is over seven feet tall

6) Implication of hypothetical rule: If (A) is a man, then (A) is under seven feet tall

7) From (4) and (6): (A) is under seven feet tall

8) Reductio ad absurdum from (5) and (7)

9) Hypothetical rule is false

Not impeccable working out, but I don't like formal logic much. Anyway, the point is that if your rule says 'always' then a single exception case shows it to be false. 'Often' is safer.

December 11, 2007

pomegranate commented on the word man-who story

I had an economics professor who coined this phrase and used it to keep us honest. A man-who story is any line of logic that begins along the lines of "I know a man who..." as a way of refuting a hypothesis or rule. In other words, it refers to anecdotal evidence. A man-who story can be considered unsubstantial and of no consequence to anyone except the man.

December 11, 2007