An interesting question is raised here
about a priori beliefs. Recall that these
beliefs (logic, mathematics) are
supposed to be independent of
experience.

Aren't mathematical concepts aquired
through perception, since we learn to
count by counting physical objects or
looking at physical symbols?

Descartes would suggest that physical
input only brings out innate concepts of
mathematics already present in the mind.
One way to think about this is the
following: Once you learn mathematics,
could any new sensory experience
change your mind? It seems that it
couldn't. If you added four objects anda
fifth magically appeared, you wouldn't say
2 + 2 = 5, you'd say putting four objects
together magically creates a 5th.

As to the question of whether it's
legitimate to conceive of an orange as
one object because it's made of many
molecules, Descartes might say that this
shows that reason and not the senses
ought to be trusted when building a theory
of knowledge. The senses give us
fragmentary and arbitrarily arranged data,
and often mislead us. But the mind,
properly trained, can reason logically from
premises to conclusion. The answer to
the question "How many things are there
in this room" has no determinate answer.
But the question what is the square root
of 49 does (a purely mathematical
question as opposed to a question
involving the physical world).

Prof. Borrowdale
borrowdalej@lanecc.edu
541-463-5434