Logic

Can a valid syllogism be fallacious? For example God can speak Mandarin. Charity is God. ∴ Charity can speak Mandarin. David can speak Tagalog. David's bones are David. ∴ David's bones can speak Tagalog. I'm pretty sure these are valid but unsound syllogisms, and I think they both commit the fallacy of division, but if the premises were true, would the conclusion also be true? I thought of an analogous syllogism that's sound, and I just can't figure this puzzler out. Basalt is rock. Rock is natural. ∴ Basalt is natural.

Comments

As logicians and contemporary philosophers use the word 'valid', a valid argument (or piece of reasoning) is one such that it is impossible for the premises to be true and the conclusion false. The primary task of symbolic logic is to determine which arguments are valid; logicians pursue this goal by providing rules and techniques for evaluating the validity of argument forms.

Any instance of a valid argument form -- that is, any particular piece of reasoning that has that form -- is valid. A valid syllogism -- or more generally any valid argument -- can exhibit no fallacy. (We may provisionally define 'fallacy' as a defect in an argument other than false premises.)

In the examples you are worried about, we have arguments that appear to possess a valid form, but really do not. Here is a valid form:

Thing A has property P.

Thing B is identical to Thing A.

Therefore, Thing B has property P.

Your first two examples seem to have this form, and it seems that their premises could be true while their conclusions are false, so they seem to show that the form is not valid after all. But when we reflect further on the second premise of each example, we can notice that they do not line up with the second premise of the above form. David's bones are part of David, but they are not identical to him. So your David example has the form:

Thing A has property P.

Thing B is part of Thing A.

Therefore, Thing B has property P.

This argument form is not valid, as your example itself shows.

Formal symbolic logic has given us algorithms for determining when an argument form is valid. But it still takes care and skill to figure out the logical form of a given piece of ordinary-language reasoning. An argument can masquerade as an instance of a valid form, when really it has a quite different form. Such arguments are fallacious, but the fallacy lies in whatever misleads us in ascribing a form to the argument. These fallacies do not impugn the validity of the good arguments they resemble.

Here's one more example to think about:

This chess piece is a king.

A king is, by definition, his nation's head of state.

Therefore, this chess piece is his nation's head of state.

What is the valid form this argument seems to have? Why does it not in fact have that form? That is, what fallacy does it commit?

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