The Nuts and Bolts of Arguments

This will be just a quick review of the structure and vocabulary of argumentation. Briefly, a philosophical argument is a series of premises logically leading to a conclusion. When considering an argument, we judge it based on the relationships the premises have to the sub-conclusions and, ultimately, the argument's final conclusion.

Arguments are neither true nor false. Instead, arguments are either valid or invalid. A valid argument is one for which there is no way that all the premises could be true and yet the conclusion be false. Put another way, in a valid argument the truth of the premises guarantees the truth of the conclusion. (Note: this latter definition of validity, while a bit easier to remember and understand, could be misconstrued to mean that valid arguments have true premises. This is not the case. It might be more precise to say that, in a valid argument, the truth of the premises would guarantee the truth of the conclusion-- if they were in fact true.)

The three most important valid argument forms are categorical syllogism, modus ponens, and modus tollens. Each can be illustrated with an example from class.

Argument Type	Argument Form	Example
Categorical Syllogism	All A's are B's x is an A x is a B	All men are mortal Socrates is a man. Socrates is mortal.
Modus Ponens	If p, then q. p q	If Nemo is a fish, then Nemo can swim. Nemo is a fish. Nemo can swim.
Modus Tollens	If p, then q. not q not p	If Nemo is a fish, then Nemo can swim. Nemo cannot swim. Nemo is not a fish.

Notice, for each example, that the sentences plugged into the scheme are irrelevant for evaluating the validity of the argument. In fact, we could plug in nonsensical words and it would not affect the validity:

All gleebs are sproos.
Arthur is a gleeb.
Arthur is a sproo.

Alternatively, we could plug in absurd premises:

If the aliens visited the Taj Mahal, then gas costs 50 cents a gallon.
The aliens visited the Taj Mahal.
Gas costs 50 cents a gallon.

When we evaluate an argument, we forget everything we know about the world. We take the premises as given. If the conclusion automatically follows, the argument is valid.

Any questions?