Purple asked:

I was wondering if you could help me find information on substitute instances for the hypothetical
syllogism and substitution instances for conjunctions.

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Substitution is a test for truth functionality of a connective in modern logic. The conjunction in formal
language is true just as long as both components are true. You can substitute any true sentence for A
or B in the conjunction 'A and B' and the truth value of the whole remains the same. So whereas 'and'
is truth functional, 'knew that' is not because you can know that Aristotle was a philosopher
(proposition A) but not that Xenophanes (proposition B) was. If you use the substitution test replacing
proposition A by proposition B then if 'knew that' was truth functional substitution would preserve the
truth of the whole. But it doesn't.

Propositional logic has replaced the syllogistic study of logic, however the propositional form is:

If A then B

If B then C

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So, if A then C

According to the truth tables of logic a conditional is true as long as the consequent is true. By
contrast, for a syllogism to make sense the content has to make sense to us in a transitive way
because the antecedent and consequents are conceptually related. You cannot substitute different
content. A dictionary example of a hypothetical syllogism is:

If the sun shines it will be warm

If it is the warm the plants will grow

_______________________________

So if the sun shines the plants will grow.

There is a conceptual connection between the sun shining and warmth. In ordinary language we need
a connection between the antecedent and consequent and it is not the case that for a conditional to
be true all that is needed is for the truth of the consequent.

Propositional logic is formal so substitution is possible, but in thought or argument in ordinary
language we need to know what each component means and how they are related. As Aristotle says
at the beginning of Posterior Analytics,'argument proceeds from pre-existent knowledge'. Aristotle
refers to semantic argument such as the syllogism above where we know or understand the
conceptual content. Formal logic and substitution are syntactical rules.

You might look at L S Stebbing's A Modern Introduction to Logicand J Lukasiewicz Aristotle's
Syllogistic.Or go back to Aristotle's Analytics.

Rachel Browne