Mathematical Entities

Some articles on entities, mathematical entities, mathematical:

Hilary Putnam - Criticism
... assumption that languages are static and immutable entities ... that the Quine–Putnam indispensability thesis does not demonstrate that mathematical entities are truly indispensable ... the argument for indispensability described above and replace all references to existent entities with references to entities assumed to exist as follows ...
Hilary Putnam - Philosophy of Mathematics
... of mathematics in the Quine–Putnam "indispensability argument" for mathematical realism ... challenging arguments in favor of the acceptance of the existence of abstract mathematical entities, such as numbers and sets ... One must have ontological commitments to all entities that are indispensable to the best scientific theories, and to those entities only (commonly referred to as "all and only") ...
Philosophers Of Mathematics - Arguments - Indispensability Argument For Realism
... most challenging arguments in favor of the acceptance of the existence of abstract mathematical entities, such as numbers and sets ... One must have ontological commitments to all entities that are indispensable to the best scientific theories, and to those entities only (commonly referred to as "all and only") ... Mathematical entities are indispensable to the best scientific theories ...

Famous quotes containing the words entities and/or mathematical:

    Experimental work provides the strongest evidence for scientific realism. This is not because we test hypotheses about entities. It is because entities that in principle cannot be ‘observed’ are manipulated to produce a new phenomena
    [sic] and to investigate other aspects of nature.
    Ian Hacking (b. 1936)

    The circumstances of human society are too complicated to be submitted to the rigour of mathematical calculation.
    Marquis De Custine (1790–1857)