Robert Anthony

Some people seem to think that when dealing with mathematical relations, we are participating in some sort of finer ideal realm, in which the nasty empiricities of life on planet Earth are beautifully transcended. These people often bring up the a priori nature of mathematical operations in a gushing emotional overflow of mystical yearning. That is where the cliche, "God is a mathematician", comes from.

But is the a priority of mathematics so really a priori? It seems to me that all its relations and facts, even the sum total of its inherent formal possibilities, are solidly grounded in the empirical universe and its impingings upon the human nervous system. Where is the cognition that does not ultimately derive from sensorial conditions? Without the fact that as a species we exist in a three-dimensional world of manipulable objects, the development of the science of mathematics would never have been possible. I grant that mathematical knowledge is less immediately related to sensorial conditions. But in no way is the present world magically eliminated when we cognize mathematically. It is merely recycled according to a deeply complex, human-made schema.

Maybe what I'm trying to say is that the concept of "a priority" shouldn't be taken so absolutely and transcendently (perhaps supernaturalistically), and that different levels or gradations of "a priority" exist.

Now I'm beginning to wonder if I made sense. The sleep-deprivation sometimes disables my thoughts.

Any comments?

tensorproduct

But mathematics is not based on the world around us (well some branches are, but that would be physics rather than maths), it is based on logic. The fundamental theorem of algebra is going to be true on Earth, or on Jupiter or at the moment of creation. Mathematical theorems are not limited by the surrounding environment, since logic is constant. The only way that maths would not be valid id that if logic were somehow to be switched off.