Full Idea
A 'theory' is any logically closed set of propositions, ..and since any proposition has infinitely many consequences, including all the logical truths, so that theories have infinitely many premisses.
Gist of Idea
A theory is logically closed, which means infinite premisses
Source
Stephen Read (Thinking About Logic [1995], Ch.2)
Book Reference
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.43
A Reaction
Read is introducing this as the essential preliminary to an account of the Compactness Theorem, which relates these infinite premisses to the finite.