Stanisław Krajewski

Stanislaw Krajewski is a professor at the Faculty of Philosophy of the University of Warsaw. He has been involved in research in the field of logic and philosophy of mathematics as well as philosophy of dialogue, philosophy of religion and interfaith dialogue. He also co-authored the post-World War II section of the core exhibition in Polin, the Museum of the History of Polish Jews.

Issue: 9:3/4 (the thirty fifth/sixth issue)

The Euclidean ideal of mathematics as well as all the foundational schools in
the philosophy of mathematics have been contested by the new approach,
called the “maverick” trend in the philosophy of mathematics. Several points
made by its main representatives are mentioned – from the revisability of
actual proofs to the stress on real mathematical practice as opposed to its
idealized reconstruction. Main features of real proofs are then mentioned; for
example, whether they are convincing, understandable, and/or explanatory.
Therefore, the new approach questions Hilbert’s Thesis, according to which a
correct mathematical proof is in principle reducible to a formal proof, based on
explicit axioms and logic.

Issue: 13:2 (The forty ninth issue)

Context is essential in virtually all human activities. Yet some logical notions
seem to be context-free. For example, the nature of the universal quantifier, the
very meaning of “all”, seems to be independent of the context. At the same
time, there are many quantifier expressions, and some are context-independent,
while others are not. Similarly, purely logical consequence seems to be
context-independent. Yet often we encounter strong inferences, good enough
for practical purposes, but not valid. The two types of examples suggest a
general problem: how to characterise the context-free logical concepts in their
natural environment, that is, in the field of their context-dependent associates.
A general Thesis on Quantifiers is formulated: among all quantifiers, the
context-free ones are just those definable by the universal quantifier. The issue
of inferences is treated following the approach introduced by Richard L.
Epstein: valid ones are an extreme case, the result of the disappearance of
context-dependence. This idea can be applied to an analysis of a form of
abduction, called “reductive inference” in Polish literature on logic. A tentative
Thesis on Inferences identifies the validity of a strong inference that is context-independent.