Search
Search
Second-order and Higher-order Logic
Second-order and Higher-order Logic

Date

source

share

[Revised entry by Jouko Väänänen on August 31, 2024.
Changes to: Main text, Bibliography]
Second-order logic has a subtle role in the philosophy of mathematics. It is stronger than first order logic in that it incorporates “for all properties” into the syntax, while first order logic can only say “for all elements”. At the same time it is arguably weaker than set theory in that its quantifiers range over one limited domain at a time, while set theory has the universalist approach in that its quantifiers range over all possible domains. This stronger-than-first-order-logic/weaker-than-set-theory duality is the…

Read the full article which is published on Stanford Encyclopedia of Philosophy (external link)

More
articles

More
news

What is Disagreement?

What is Disagreement?

This is Part 1 of a 4-part series on the academic, and specifically philosophical study of disagreement. In this series...

Recently Published Book Spotlight: Trans Philosophy

APA Member Interview, Peter Alward

Peter Alward is a Professor of Philosophy at the University of Saskatchewan. Originally from Halifax, Nova Scotia, he received his...

Recently Published Book Spotlight: Trans Philosophy

Science and the Public

I was awarded my Ph.D. in Philosophy in 2007. Early in my Ph.D. program, I mentioned to a more senior...