Soundness ensures that a logical system's derived theorems are always true under any interpretation. It's a fundamental property for reliable…
Objectual quantifiers are a type of quantifier in formal logic that specifically refer to objects within the domain of discourse,…
This argument posits that if mathematical entities are essential for our most successful scientific theories, we should accept their existence.…
An ambitious project by David Hilbert to formalize all mathematics and prove its consistency using finitary methods. It aimed to…
Frege's theorem establishes that arithmetic is reducible to logic. It demonstrates how basic arithmetic principles can be derived from logical…
A sequence of numbers where each element is chosen without any predetermined rule or algorithm. It's a concept central to…
Constructive mathematics emphasizes mathematical objects that are provably constructible and computable. It avoids non-constructive proofs, like those relying on the…
The bad company objection challenges mathematical abstractionism by highlighting the difficulty in separating valid from invalid abstractions, especially concerning Frege's…
The Aristotelian comprehension schema, represented as (∃x)Φ → (∃Y)(∀x)(Yx ↔ Φ) in second-order logic, defines the existence of a property…
An abstraction principle is a formula stating that two abstract objects are identical if and only if the objects they…