Sentence examples for mathematical objects as from inspiring English sources

According to platonism, mathematical objects (as well as mathematical relations and structures) exist and are abstract; that is, they are not located in space and time and have no causal connection with us.

The situation with the endogenous interpretation (mathematical objects as global equivalence classes) is potentially more satisfactory.

Commentators on Aristotle from the 2nd century on tended to interpret Aristotle's mathematical objects as mental objects, which made Aristotle more compatible with neo-Platonism.

A slightly different way to make sense of the situation is to think of mathematical objects as types for which there are tokens given in different contexts.

Aristotle occasionally refers to mathematical objects as things by, in, from, or through removal (in different works Aristotle uses different expressions: ta aphairesei, ta en aphairesei, ta ex aphaireseôs, ta di' aphaireseôs).

Secondly, naturalist-platonists run a standard Quinean line by construing any challenge to the reliability of our beliefs about platonic mathematical objects as a general challenge to the scientific method's reliability.

It is only if one takes as a starting point the primacy of the mathematical object as the truth-maker of theories, that one has to worry about how their objects manage to co-exist.

Mathematical objects and concepts are as objective as physical objects and properties.

After all, the platonist is then in a position to examine mathematical theories as they are actually formulated in mathematical practice, rather than discuss a parallel discourse offered by various reconstructions of mathematics given by those who avoid the commitment to mathematical objects (such as the nominalists).

To many mathematicians, mathematical objects such as the number pi seem to exist in an external, objective reality.

The essential ideas here are that the real objects of study in mathematics are structures, or patterns things such as infinite series, geometric spaces, and set-theoretic hierarchies and that individual mathematical objects (such as the number 4) are not really objects at all in the ordinary sense of the term.