Geoff Goddu, U. Richmond

"How Many Premises Can an Argument Have?"

Opening question: Is it possible for an argument to have either zero premises or an infinite number of premises?

Goddu's answer is that regardless of how you conceive of arguments  (as sets of propositions, sentences or speech acts), you should accept that an argument could have an infinite number of premises. Goddu's case: arguments that prove that there is a one-to-one relation between all numbers and even numbers (they can have an infinite number of premises).

The zero premise case is more complicated. On certain conceptions there are good reasons to accept the possibility of zero premise arguments, but on other conceptions there are good reasons to reject this possibility.  Goddu's case: Sorensen arguments of the form:

Is there an argument that there are no-premise arguments? Yes: here's one.

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C Therefore, there are arguments with zero premises.

Cute!

Q1: Can there be arguments with non-denumerably infinite premises?

Q2: Doesn't this misrepresent what arguments are about, namely, making  a transition in thought?

Q3: Aren't demonstrations of tautologies (e.g., with CP or IP) arguments with no premises?

Q4: "Why p?  Just because!"  Can' that be a zero-premise argument?