Dear Ben - Good posting. We should not attempt too hardhandedly, armchair-wise to legislate the dependency relations between sciences. We should rather look at which connections are, in fact, out there. And as to neurology and mathematics, I think it is safe to say that the dependence until now has been unambiguously unilateral. Mathematical does not depend upon neurology at all - I know of no mathematical result which depends upon neurology, neurological methods or theories, brain scannings etc. In the opposite direction, neurology increasingly depends upon complicated applied mathematics (I touch a bit upon this towards the end of the Antipsychologism chapter). The construction of brain imaging machinery depends upon physical results expressed mathematically, and the analysis of brain images requires sophisticated mathematical statistics, often by mathematical experts hired as special members of scanning teams at the hospitals. So the results of recent neurology, many of them exciting, are dependent upon mathematics. I think it follows from these observations that it is a preposterous claim to say that mathematics is the study of neurological structures - or that mathematics could, in any way, be reduced to neuropsychology. Given the recent successes of neuroscience, it is natural that this science is in a growth phase, sort of testing the limits of what it can explain. This leads to overblown reduction ideas like the ones mentioned. Probably such ideas may be fruitful to present in your grant applications - if neurology could really explain mathematics, then it would be a surprise result worth funding. But nothing points in the direction of that being possible. Rather, the neurology-as-explanation-of-everything seems to me to form a science bubble - such bubbles now being studied by my colleague Vincent Hendricks - taking its departure in valuable assets whose worth is overestimated in an echo-chamber effect amont grant-seeking scientists. Such echo-chambers are an effect of science being a social construction. But the bursting of bubbles also shows that science, in a self-correcting development, is able to overcome such social side-effects and reach results which are not only social.
Best F Den 15/09/2014 kl. 18.36 skrev Benjamin Udell <[email protected]<mailto:[email protected]>> : Stan, Gary F., list, When mathematicians start basing their findings on those of neurology, I'll start to think that maybe there's something to the idea that mathematics is a neural phenomenon. Instead, mathematics is applied in neurology, not vice versa, and there seem good reasons in practice for it. Now, the process of discovery is influenced, promoted, limited, etc., by pscyhological (and social) factors. But to say that math is the study of certain neural phenomena is like saying that astronomy is the study of telescopes (and of certain neural phenomena), as if stars were only secondarily real. The question is not whether numbers exist like stars, hardly anybody thinks that. The question is whether they can be objectively investigated as numbers. We commonly think that a broadcast of the first 20 prime numbers what indicate an extra-terrestrial intelligence, although that E.T. might differ psychologically and socially so much from us as to be generally bewildering to us. We don't think that they'll find different properties of prime numbers than we do. To be consistent with the view that math is a neural phenomenon, one should also say that biology is a neural phenomenon, chemistry is a biological and neural phenomenon, and physics a chemical, biological, and neural phenomenon. It actually starts to make some sense, albeit with some sort of shift in the sense of the word 'phenomenon'. Areas of research can be ordered according to their bases in principles of how we know things (ordo cognoscendi, the order of learning or familiarity) and, in pretty much reverse order, in principles (entities, laws, etc.) whereby we explain things (ordo essendi, the order of being). The order of being is often preferred in the special sciences (physics first, etc.), while the order of learning and of the verificatory bases on which we know things is sometimes preferred in maths (where such preference tends to put mathematical logic and theory of structures of order first). "Basic" versus "low", profundus versus bathos: Too much feeling of prestige or status sometimes rides on these discussions. One may characterize phenomena as "more basic" and "less basic", which tends to be taken to make physics, for example, seem better than psychology, for example; or as "lower" and "higher," which tends to be taken to make psychology seem better. This issue has turned up in one form on a US sitcom:http://www.youtube.com/watch?v=FitG_PLO9Rg (scene 2 min., 22 secs long; pardon the ad). Maybe those researches which I call "sequenced in the order of being" you would call "sequenced in the order of abstractness." Still could well be the same ordering. I'm not saying that the ontological questions are unimportant, to the intellectual climate, the human spirit, and the ultimate bearings which people take in their decisions. But when an ontological view conflicts with the structures of dependences among sciences and math, to me it signifies that one's classification is either deficient in firm and fertile constraints or just plain nebulous. And, if people argue over whether some sciences should be ordered by increasing concreteness or increasing abstractness, and if it's essentially the same ordering forwards versus backwards, ♂♀✳†∞$ versus $∞†✳♀♂ , then they're arguing over a shiny gewgaw, the right of some science to be called "1st" rather than "last"; the real classificational choices have already been made, and the two orderings just need to be distinctly named, so that people can specify the sense of the ordering. Various orderings can be quite compatible when distinguished by an articulated sense or standard of the ordering. Questions of ontology and questions of research-classificatory preference are often best separated. Same is true for the topic of logical quantity and any connected research-classificatory preference issues. Best, Ben
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
