Help with Logical Proof

Nimbooku

I hope it's okay to post this here. I thought you guys might be the people to ask.

I'm having trouble constructing a truth tree for the following syllogism

P1No animals are immortal
P2All men are animals
.'.
CTherefore, some men are immortal.

Now, looking at it I know it's valid. There's a suppressed premise in the argument which makes it so. If P1 and P2 are true, then we get to the conclusion 'All men are immortal' which contains within it C.

But undoubtedly through my own stupidity, I can't get the truth tree to close. Looksee:

@x (Ax -> ~Ix) [P1]
@x (Mx -> Ax) [P2]
@x (Mx -> Ix) [The negation of C which was Ex(Mx . ~Ix)


Can anyone help?

solice

*head hurts*

ok, no animal is imortal.
all men are animals.

no man is imortal!

I realise i dont even know what a truth tree is but to be honest, why are u wasting your time? Everyone dies!

DadaKopf

Zzzzz, it's LOGIC.

I honestly don't understand how, logically, you can get from "all animals are mortal" to "some men are immortal", which is another way of putting what you said.

So maybe something like: "all animals are mortal", "men are animals", "therefore all men are mortal". Basic Socratic syllogism.

If it said "not all animals are mortal", then I could see where the difficulty arises, but I don't understand the ontological assumptions made in the premises, and it seems to be an incorrect assumption. But I'm sure it's as simple as things exist/don't exist and animals/men are mortal/imortal. Perhaps your only option is to go for a reductio ad absurdum.

But your logical deduction seems absurd enough to me as it is.

Fysh

Looking at it from a basic set-theory angle (because I was never very good at syllogistic logic to begin with), you're basically saying:

1) there is a group called "men" which is a subset of the group "animals"
2) there is an absolute property of the group "animals" which determines that none of its members are immortal

Without at least one more premise, you cannot reach the conclusion that some men are immortal, because to reach this conclusion would require either 1) or 2) to be false (ie. either not all men are animals, or that some animals are immortal). The only get-out clause that might get you anywhere near there is defining "some" as meaning "zero or more men", although this is arguable since the implication of the "or more" would require that the conclusion have a finite non-zero probability of occuring, and an absolute binary state such as "no animals are immortal" is not compatible with such a case.

(Oh, dear god, the jargon abuse going on in that paragraph....still, it makes sense. I think.)

Frankly, I'd be more worried if you could close the truth tree, because it would be formally proving something ridiculous.

GUBU

I have to admit I've never heard of a "truth tree" either, but logically, you're conclusion makes no sense. I don't see how you can draw the self-evidently false conclusion "some men are immortal" from two obviously true and logical statements. It's just common sense.