Soundness in Logic
Soundness ensures that a logical system's derived theorems are always true under…
Objectual Quantifiers in Formal Logic
Objectual quantifiers are a type of quantifier in formal logic that specifically…
The Indispensability Argument in Philosophy of Mathematics
This argument posits that if mathematical entities are essential for our most…
Hilbert’s Program
An ambitious project by David Hilbert to formalize all mathematics and prove…
Frege’s Theorem
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how…
Free Choice Sequence
A sequence of numbers where each element is chosen without any predetermined…
Constructive Mathematics
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It…
Bad Company Objection
The bad company objection challenges mathematical abstractionism by highlighting the difficulty in…
Aristotelian Comprehension Schema
The Aristotelian comprehension schema, represented as (∃x)Φ → (∃Y)(∀x)(Yx ↔ Φ) in…
Abstraction Principle
An abstraction principle is a formula stating that two abstract objects are…