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itinerant1
Guest
I think you are making some logical leaps here. Post # 236 explains matters clearly.Actually, the cerebral underpinnings of mathematics are being closely zeroed in on; (pun intended) see the recent issue of DISCOVER magazine. Not only do infants and even some apes seem to have an innate sense of number and the ability to learn number symbols, but 2 brain regions have been identified via MRI as being involved in these operations (at the front and the top of the cerebral cortex; sorry, haven’t committed the names to my mind).
No doubt the cerebral activity in mental arithmetic is now or will soon be studied in the same manner. As to making mistakes, well, that will probably take longer. It will be hard to experimentally control the making of mathematical errors
ICXC NIKA.
In regard to what you call “the innate sense of number”, I find that to be a rather vague expression. What precisely is a “sense of number” and what about it makes it supposedly innate? This needs to be articulated.
What is the ability to “learn number symbols?” Humans create language, which is symbol manipulation. We attach meanings to symbols. Apes can learn to visually recognize the symbol “2” and be taught to associate that symbol with two things. However, this associative learning which takes place on the perceptual level, and which I will call here perceptual thinking, is radically different than conceptual thinking.
Conceptual thinking involves the abstract notion of “twoness”, which is the meaning we attach to the symbol “2”. No non-human animal possess this conceptual ability and awareness, either innately or in a rudimentary way. Hence, your statement does not show any recognition of the radical difference between human and non-human thinking. In fact, they appear conflated in your post.
Brain regions may be involved as a necessary condition for conceptual thinking, but the brain and its functions do not constitute a sufficient condition. Another one of your logical leaps is to conflate necessary and sufficient conditions. This does not make for good science.