Studia humana (SH) is a multi-disciplinary peer reviewed journal publishing valuable

contributions on any aspect of human sciences such as...

read more...

Studia humana (SH) is a multi-disciplinary peer reviewed journal publishing valuable

contributions on any aspect of human sciences such as...

read more...

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.

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.

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.