Alexander Pruss's Blog

A simplified version of Goedel’s first incompleteness theorem (it’s really just a special case of Tarski’s indefinability of truth) goes lik...

The most common argument that mathematical truth is not provability uses Tarski’s indefinability of truth theorem or Goedel’s first incomple...

For years in my logic classes I’ve been giving a rough but fairly accessible sketch of the fact that there are unprovable arithmetical truth...

Famously, Goedel’s incompleteness theorems refuted (naive) logicism, the view that mathematical truth is just provability. But one doesn’t ...

Let # s be the Goedel number of s . The following fact is useful for thinking about the foundations of mathematics: Proposition. There is...

The relativity of FOL-validity is the fact that whether a sentence ϕ of First Order Logic is valid (equivalently, provable from no axioms b...

Once one absorbs the lessons of the Goedel incompleteness theorems, a formalist view of mathematics as just about logical relationships such...

The more I think about the foundations of mathematics, the more wisdom I see in Kronecker’s famous saying: “God made the natural numbers; al...

A sentence ϕ of a dialect of First Order Logic is FOL-valid if and only if ϕ is true in every non-empty model under every interpretation. ...

A family of views of necessity (e.g., Peacocke, Sider, Swinburne, and maybe Chalmers) identifies a family F of special true statements that...

A plausible account of necessity is that p is necessary provided that p can be proved in the correct logical system K and p is possi...