Categorization is not a matter to be taken lightly. There is nothing more basic than categorization to our thought, perception, action, and speech [Lakoff, 1990].
Concepts are the glue that holds are mental world together [...] They tie our past experiences to our present interactions with the world [Murphy, 2002].
Without concepts, mental life would be chaotic [Smith & Medin, 1981].
Concepts are the building blocks of thoughts. Consequently, they are crucial to such psychological processes as
categorization, inference, memory, learning, and decision-making.
This much is relatively uncontroversial.
But the nature of concepts—the kind of things concepts are—and the constraints that govern a theory of concepts
have been the subject of much debate (Margolis & Laurence 1999, Margolis & Laurence 2015).
https://plato.stanford.edu/entries/concepts/
Representations of
numerosity (how many) are found in the dorsal stream, particularly in the intraparietal sulcus, in both humans and monkeys. Current models
propose that advanced mathematical capabilities in humans are built upon an
evolutionarily older “number sense” that is localized in parietal cortex [Banich & Compton, 2018].
It is my conviction that
pure mathematical construction enables us to
discover the concepts and the laws connecting them which give us the
key to the
understanding of the phenomena of Nature [Einstein, 1933].
[…] in my own opinion,
mathematics is interesting as an instrument for condensing concepts which, by their own right, without mathematics, would still be what they are [de Finetti, 1979].
[the]
aim of philosophy,
abstractly formulated,
is to understand how things
in the broadest possible sense of the term
hang together in the broadest possible sense of the term [Sellars, 1962].
