Mirqāt The Ascent of Logic

Foundation · a field of logic

Predicate Logic

Quantifiers and first-order logic: the language that reaches inside propositions, to objects, properties, and relations.

The problem
Propositional logic cannot express “every” and “some.” How do we reason about objects, properties, and relations?
The turning point
Quantification over a domain (∀, ∃) with bound variables, and the completeness and compactness of first-order logic.
An open question
When is second-order strength worth losing completeness, and where does first-order logic stop being enough?

To study it

  • Enderton A Mathematical Introduction to Logic
  • Mendelson Introduction to Mathematical Logic
  • Hamilton Logic for Mathematicians
  • van Dalen Logic and Structure
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