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
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].