"All men are mortal" A critique off Aristotle' well know example off deductive logic.

Hunter.S

I have discovered what I believe to be a problem with a widely used example for deductive reasoning (logic).

As you know deductive logic is the more “true” of the two main forms off reasoning it uses premises to support a conclusion were as inductive logic only provides a probable conclusion by sowing that something is true most off the time well being unable to prove that it will be or is always true. For example “all plums have stones inside them” is an inductive statement because we cannot know that all plumes have stones because we cannot look inside every plum that is and will be but as we have seen many plums with stones inside them and otters before us have all seen a lot of plums with stones inside them we can say with high probability that all plums have stones even do we cannot prove it for sure.

The example off deductive logic I have a problem with is Aristotle’s well known example of what has become known as syllogism:

Premise 1: All men are mortal.

Premise 2: Socrates is a man.

Conclusion: Socrates is mortal

The conclusion is sound but the first premise is what I have a problem with. It is in a fact a statement basset on inductive logic and therefore only probable (extremely probable but probable none the less) and therefore invalid as a premise in deductive logic.

Netter Aristotle or myself can know for sure that every man is mortal because we have not meet every man that has been and will ever be it is possible however unlikely that an immortal man or women lives among us right now. It is also possible that due to improving medical science that one day we may have the ability to prevent death I doubt that very much but cannot rule it out as impossible.

I think a correct example to use for deductive reasoning would be this:

P1: All mortals die.

P2 : Socrates is mortal.

C: Socrates will die.

We know all mortals die because that is the definition off the word and we know Socrates was mortal because he is dead so the conclusion is sound.

An alternative example could read like this:

P1: All mortals age and die.

P2: I am ageing and will die.

C: I am mortal.

We know I am ageing because both you and I have first hand experience with that and we know that I will die because ageing is dyeing so the conclusion here is also sound.

So that’s it I’m sure I’m not the first to see this problem but I myself have not yet read or hear it anywhere.

Would love to hear peoples thought on this hopefully like a most good philosophy it will lead to some fun questions and debate.

18AD

If you look at it purely formally if the premises are true then the conclusion must be true.

I don't think it makes the argument inductive because the premise is arrived at inductively.

I guess you could argue that the form of the syllogism is what makes it deductive as it's moving from a universal statement to a particular to a particular conclusion. In this sense the form of the arguement is deductive. Along these lines you could argue anything and it would be a deuctive argument.

All cats are dogs.
Bob is a cat.
Therefore Bob is a dog.

This is still a deductive argument, albeit a false one.

You have to distinguish between truth and validity. So the mortal socrates arguement is valid and true. The truth of it is what you have a problem with, not the validity.

Morbert

To echo 18AD: Deduction is about what to infer from premises. It is not about what is necessarily true.

Peregrinus

I agree with 18AD and Morbert. And I would add:

Your second argument (starting with “all mortals die”) is trivial. Your conclusion is that Socrates dies, but your premise P2 is established by the fact that Socrates is dead. Consequently the argument doesn’t establish anything other than, because Socrates is dead, Socrates dies.

Your third argument (starting with “all mortals age and die”) is formally invalid. Your P1 is that all mortals age and die, not that only mortals age and die. Your P1 leaves open the possibility that there is a class of things which are not mortal, but which nevertheless age and die. Consequently your conclusion does not flow from your premises.