Alien math

Continuing the theme from the last two post, in the same referenced IPS thread infimatas said:

"I recall an interview with Daniel Dennet where he argued that mathematics has a sort of Platonic quality.  Not in the metaphysical sense, but in the way that basic mathematical principles will constantly be rediscovered because they are so useful.  So if we discovered an alien culture, it seems likely that it would have some knowledge of mathematics -- perhaps not a base-10 system, but something at least. Do you buy that argument?  What implications does it have for an embodied philosophy of mathematics?"

I replied:

In the Preface to WMCF Nunez discusses the “romance of mathematics,” one such notion being that to learn it is “to learn the language of nature, a mode of thought that would have to be shared by any highly intelligent beings anywhere in the universe” (xv.) He lists other aspects of the romance but he asserts that all of them appear to be false. My guess is that he might argue that given math is based on empirical observation of nature, and that our sensori-motor facilities and basic metaphors are quite close to nature, that is indeed why it “works” so well. But given an alien sensori-motor system from a planet where they breath not oxygen but something else, where the environment has different challenges, etc. my guess is that their math would be just as accurate but look entirely different. That is, math is enacted and not discovered as a fully formed a prori (i.e. Platonic form) inherent to the structure of the universe. But being a “realist” of sorts Nunez still accepts that there is a “there” there.* (I like the reiteration of the word “there” in that sentence, having three different meanings in the space of five words.)

And of course implicit to the above is that both the human an alien are residents of the same uni-verse. This does not take into account possible other and co-existing universes where their physics might be of an entirely different order, thus their “there” is still there but not in the same sense as ours. Such multi-verses are not merely the work of science fiction either, for as I referenced elsewhere it is a viable option among some quantum theorists.

* Which gives me an idea for a postmetaphysical bumper sticker: There is a there there, but...

And now I'm hearing it sung to the tune of Ole McDonald Had a Farm: "Here a there, there a there, everywhere a there there..."