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### Single Idea 10976

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 6. Compactness]

Full Idea

Compactness is a virtue - it makes the consequence relation more manageable; but it is also a limitation - it limits the expressive power of the logic.

Gist of Idea

Compactness makes consequence manageable, but restricts expressive power

Source

Stephen Read (Thinking About Logic [1995], Ch.2)

Book Reference

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.44

A Reaction

The major limitation is that wholly infinite proofs are not permitted, as in Idea 10977.

Related Idea

Idea 10977
Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite) **[Read]**