more from Stephen Read

### Single Idea 10973

#### [catalogued under 5. Theory of Logic / E. Structures of Logic / 8. Theories in Logic]

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.