Ben: I really don't see why you think that, say, mathematical theorem-proving needs to be sensorially grounded... Of course sensorimotor reality is a potent source of analogies to guide mathematical theorem-proving, but, surely there can be purely abstract reasoning without a direct or useful sensorimotor connection!!
Ben, No. Everything is grounded. This is a huge subject. Perhaps you should read: Where Mathematics Comes From, written by George Lakoff and Rafael Nunez, You really do need to know about Lakoff/Fauconnier/Mark Johnson/Mark Turner. Especially: The Body in the Mind. Mark Johnson The Way We Think - Fauconnier/Turner. There is now a very large and ever growing body of scientific evidence for their ideas, (and for "grounded cognition")which are very influential in cognitive linguistics & cognitive semantics (although my ideas are an extreme version). I recommend reading the v. latest cognitive linguistics textbook. (Email me). Even the very forms of mathematics, which to you, a top mathematician, may seem totally abstract, actually have a great deal of concreteness. The symbols are arranged in a grounded way! And often themselves have a grounded nature! For example: "Schoolchildren everywhere have little trouble learning to manipulate simple equations like x+7 = 15 or x+15-7 or x=8, but developing this notation took the efforts of many mathematicians over centuries in many different cultures - Greek, Roman, Hindu, Arabic and many others. In the twelfth century the Hindu mathematician Bhaskara said, "The root of the root of the quotient of the greater irrational divided by the lesser one being increased by one; the sum being squared and multiplied by the smaller irrationalk quantity is the sum of the two surd roots" This we wou;ld now express in the form of an equation.. Similarly, Cardan... wrote x2 = 4x + 32, as qdratu aeqtur 4 rebus p:32." from Fauconnier, The Way We Think + - = and many other crucial maths signs are of course, GRAPHICS, indicating the underlying graphic/imaginative grounding of all mathematical thought. But see Lakoff & co for much, much more. As I said, I believe you are making the most expensive professional mistake of your life. (Not your fault - it's a near universal illusion - but still a mistake). P.S. Why on earth do you think that maths only came about at such a belated evolutionary stage? Obviously it only became necessary when grounded in a complex society where extensive addition, subtraction, etc of objects had become a routine matter. And note your own words... "I really don't SEE why..." ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=52855386-4499a4
