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Matematiske fundament
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Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the …
A sentence of first-order logic is satisfiable if it is true in some structure, and finitely satisfiable if it is true in some finite structure. The question arises as to whether …
Many of the most famous results in mathematics are impossibility theorems stating that something cannot be done. Good examples include the quadrature of the circle by ruler and …
Very Short Introductions: Brilliant, Sharp, Inspiring Kurt Gödel first published his celebrated theorem, showing that no axiomatization can determine the whole truth and nothing …
The publication of Rasiowa and Sikorski's The Mathematics of Metamathematics (1970), Rasiowa's An Algebraic Approach to Non-Classical Logics (1974), and Wójcicki's Theory of …
Logical monism is the claim that there is a single correct logic, the 'one true logic' of our title. The view has evident appeal, as it reflects assumptions made in ordinary …
An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's …
Frege is widely regarded as having set much of the agenda of contemporary analytic philosophy. As standardly read, he meant to introduce--and make crucial contributions to--the …
Customarily, much of traditional mathematics curricula was predicated on 'by hand' calculation. However, ubiquitous computing requires us to refresh what we teach and how it is …
As the famous Pythagorean statement reads, 'Number rules the universe', and its veracity is proven in the many mathematical discoveries that have accelerated the development of …