[FOM] Perception of mathematical truth
mark_bridger at yahoo.com
Sat Feb 18 13:45:26 EST 2006
Nik Weaver writes:
"I imagine the same is true in all instances of mathematical
intuition. Some brain structures used for sensory processing
will always be involved, and that is why we have the feeling of
direct perception of mathematical truth that is so like sensory
I don't know whether the second sentence is true or not, but isn't this
exactly the kind of question that researchers in cognitive neuroscience
are examining with real-time PET (and other) scans? The idea, as I
understand it, is to map which regions of the brain are active during
different kinds of mental tasks. Perhaps some day we will get an answer
to the question of whether mathematical intuition and sensory
processing always take place in the same areas of the brain. This will
not definitively resolve the issue, but it will have more weight than
the statement "I imagine that."
Nik Weaver also writes: "This is no evidence for the actual existence
of non-physical abstract mathematical objects."
I'm not sure what sort of evidence is considered acceptible for showing
the "actual" existence of non-physical objects? I mean, even for
physical objects, we take a lot on faith or on analogy. What evidence
do we have of the "actual" existence of a certain 20th magnitude star
in the constellation of Taurus? Only analogy: it produces a blip -- or
better, a blip is produced -- on a CCD chip inside Hubble that is
similar to a blip produced by another star for which we have (slightly)
better reasons to believe exists.
In other words, I agree with Weaver's statement, but I'm not sure of
Associate Professor, Mathematics
Northeastern University, Boston MA
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