Syllogism problem

What is the basis for reason? And mathematics?

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Re: Syllogism problem

Post by duszek » Wed May 18, 2016 11:44 am

I agree with Greta and add two remarks:

1. his syllogism is that of exposition, called darii, which is a valid one

a (universal positive)
i (particular positive)
i (particular positive)


A swim suit is a runner in a metaphorical sense of the word.
A swim suit is an athlete in a metaphorical sense of the word.

Do metaphores meet the requirements of acting as a term in a premise in a syllogism ?
Only if the conclusion is metaphorical too.

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Re: Syllogism problem

Post by GWLovan » Thu Jun 22, 2017 6:52 am

What bothers me about logic is the consequence of the vagueness of terms for deductive validity. Most important concepts in philosophy and the humanities are vague in the way 'tall' is vague, or perhaps even 'a good figure skating performance.' Be the necessary and sufficient conditions ever so precise, you are always confronted with borderline cases because that is the nature of what you are referring to. When does somebody start being tall? When does a figure skating performance cross the imaginary line and because 'good'? And all the interesting discussions are over these borderline cases; theories are adjusted to try to accommodate them. etc.

Defining terms with necessary and sufficient conditions, either for all possible worlds or in the natural world, seems like a Google search engine logic: the hit or miss, the hits going into the extension and the misses being excluded. But, to take the example of ‘poetry translation,’ most are neither 'translations of the original' pure and simple or 'transformations or new poems,' but to some extent translations and to some extent transformations - they are mixtures, compound elements. And interpretation or judgment - just as in an Olympic sport like figure skating - cannot be avoided. This means the extension of 'poetry translation' is open. Like who is tall and who is not, as applied to human beings. Like ‘sentimental’ as applied to novels or movies. etc.

And doesn't that mean that inferences cannot be made from a proposition using that term, unless we have some kind of relative logic appropriate to things that exist on a continuum: not 'if and only if' but 'to the extent that'? That Socrates is mortal only follows from ‘all men are mortal’ if the set of ‘men’ is closed, determinate; otherwise, we would not logically be able to know whether ‘Socrates’ was a part of this set, not a part of this set, or arguably a part (borderline case). The inference would not seem to be ‘truth-preserving’ without the closed set (clear concept). And isn’t this the point of technical, stipulated terms in the sciences: to make extension or set membership determinate? Could logic still apply to arguments using inherently open or vague terms?

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Re: Syllogism problem

Post by Londoner » Wed Jun 28, 2017 1:13 pm

GWLovan wrote:
Thu Jun 22, 2017 6:52 am
And isn’t this the point of technical, stipulated terms in the sciences: to make extension or set membership determinate? Could logic still apply to arguments using inherently open or vague terms?
I would say; 'No'. I don't think logic applies to ordinary language; as you say, ordinary language just doesn't work like that.

I don't think it is a matter of definition; if you are working within an absolutely strict definition then you can only produce tautologies, the equivalent to A=A. For example, we can say 'work' means the same thing as a relationship of force and displacement (and vice-versa). (Once if we move outside that tautology, i.e. try to measure an instance of 'work', then we cannot do that through logic. It will depend on empirical observation.)

I would say that when we use ordinary language examples we are not really using logic. It is more that these examples demonstrate why we think logic as a system is valid. It is because we (humans) find those 'Socrates is a man...' type arguments compelling that we have formulated abstract rules of logic around them...rather than humans having started off with the rule and then applied it.

But it is a one-way process. We can create abstract - general - rules from particular instances, but we cannot apply them. Since any given example of a syllogism is different to any other, i.e. it is particular, then we cannot apply a general rule - not unless we change its meaning to remove the ways it is particular. Which we usually do by replacing the terms by symbols; 'if P then Q' etc.

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