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What accounts for humans’ math ability?

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Various foolish explanations are on offer: the adaptationist hypothesis, the byproduct hypothesis, and the sexual selection hypothesis.

From Bill Dembski and Jonathan Wells at Evolution News & Views:

Leaving aside whether mathematical ability really is a form of sexual display (most mathematicians would be surprised to learn as much), there is a fundamental problem with these hypotheses. To be sure, they presuppose that the traits in question evolved, which in itself is problematic. The main problem, however, is that none of them provides a detailed, testable model for assessing its validity. If spectacular mathematical ability is adaptive, as the adaptationist hypothesis claims, how do we determine that? What precise evolutionary steps would be needed to achieve that ability? If it is a byproduct of other abilities, as the byproduct hypothesis claims, of which abilities exactly is it a byproduct and how do these other abilities facilitate it? If it is a form of sexual display, as the sexual selection hypothesis claims, how exactly did the ability become a criterion for mate selection?More.

O’Leary for News: My cats might be better hunters if they could do math and engineering. But come back in a million years and cats just like them will still be crouching in the long grass listening for rodents.

Meanwhile, some brilliant young nerd is fooling around with transcendental numbers, unable to make a living or find a girl.

Only a society wholly committed to naturalism would find much use in the kind of theories naturalism offers to explain these phenomena: The explanation need not account for the facts. It need only be naturalist.

See also: What great physicists have said about immateriality and consciousness

Comments
Mathematics is precisely not a discipline in which theoretical constructs are empirically tested and are taken as a sort of weak form, provisional knowledge due to empirical reliability.
Eh? The four colour map theorem was a theoretical construct that was empirically tested: they narrow down the possible maps, and then used a computer to literally try every combination. Other postulates are certainly "a sort of weak form, provisional knowledge due to empirical reliability", because not every combination can be tested, and no other proofs are available (e.g. Golbach's conjecture).Bob O'H
July 10, 2017
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Folks, the fundamental problem with an evolutionary materialist account of Mathematical ability is that Mathematics requires responsible, rational freedom to identify and follow chains of highly abstract reasoning. All that stuff about jumped up apes with excess neurons in a world driven and controlled by blind chance and/or mechanical necessity simply cannot account for such freedom. Indeed, notoriously, it leads to self-referential incoherence, undermining the very theory itself, as say Haldane pointed out so long ago now:
"It seems to me immensely unlikely that mind is a mere by-product of matter. For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true. They may be sound chemically, but that does not make them sound logically. And hence I have no reason for supposing my brain to be composed of atoms. In order to escape from this necessity of sawing away the branch on which I am sitting, so to speak, I am compelled to believe that mind is not wholly conditioned by matter.” ["When I am dead," in Possible Worlds: And Other Essays [1927], Chatto and Windus: London, 1932, reprint, p.209. (NB: DI Fellow, Nancy Pearcey brings this right up to date (HT: ENV) in a current book, Finding Truth.)]
Of course, Pearcey and many others have kept this issue in circulation down to today. We need to recognise that a self-undermining, self-falsifying frame of thought destabilises reasoning beyond that point. Through, the challenge that implications following on falsity at best may be empirically testable and shown reliable in a domain of thought, but are inherently prone to error, due to ex falso quodlibet. Indeed, this is a root of the Mathematical proof technique of reducing what one wishes to eliminate, to absurdity. KF PS: I have also recently seen someone describing Mathematics as a "Science" -- a sign of Scientism's attempt to monopolise all serious knowledge. Of course Scientism is itself self-referentially incoherent. However, more importantly, Mathematics is precisely not a discipline in which theoretical constructs are empirically tested and are taken as a sort of weak form, provisional knowledge due to empirical reliability. We need sterner stuff, rooted in logic and coherence, driven in the end by self-evident first principles of right reason. For example, number itself pivots on distinct identity, e.g. A vs ~A leads to 1 and 2 etc. Indeed, this pattern of being rooted in logic is part of why Mathematics plays the role of a plumbline in considerations on scientific endeavours. We need the logic of structure and quantity (including space etc) to be a standard of reference. That we can do Mathematics is a sign.kairosfocus
July 10, 2017
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BTW, Denyse, how do insulting stereotypes of mathematicians help ID? Do you think Dr. Dembski & Prof Marks will appreciate the your insinuations about them ("some brilliant young nerd is fooling around with transcendental numbers, unable to make a living or find a girl")? Actually, will their wives appreciate it? FWIW I'm not a mathematician. But don't tell my department head.Bob O'H
July 10, 2017
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Dembski & Wells write:
The main problem, however, is that none of [the Evolutionary Hypotheses] provides a detailed, testable model for assessing its validity.
Which, by and large, is a fair criticism. (I think work could be done on this, e.g. looking at the genetic basis of mathematical ability, and seeing what other aspects of intelligence it correlates with. Or looking at whether people find mathematicians of the opposite gender attractive). But then the authors write:
On the other hand, from an intelligent design perspective, mathematics is readily viewed as an inherent feature of intelligence and rationality. Moreover, the fact that the mathematical theorems we prove mirror the deep structure of physical reality suggests that intelligence is fundamental to nature and not merely an accidental or historical byproduct of blind material forces.
Which raises the obvious question - what is the detailed, testable model for assessing its validity? My prediction (based on a sufficiently detailed testable model of ID): rather than provide one, Dembski & Wells will take a leisurely boat ride down the Isis.Bob O'H
July 10, 2017
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Well, the math thing is an interesting specific developed talent, but what playing the violin? It ain't got no frets. You either know EXACTLY where your fingers go, or you're wrong. One or the other of the primitive tribes had developed, prior to flood of Western culture, a system of counts by body parts (including elbows and knees) whose last "number" was "many". And for a REALLY big herd of antelope, you could double down with "MANY many". So the Sun is many many yards from Earth. A mile is also many many yards. But then who counts distance in miles? I was told once that in modern California the distance "just down the road" means "you don't have to stop to EAT during the drive". I imagine "just down the savanna" is still a popular yardstick for explaining distances. I have to feel sorry for the math whizz sitting around a campfire and trying to invent names for, oh, "many antelopes distributed among 'elbow' hunters". And there wasn't much chance that he would EVER meet another human who also had an interest in the IDEA of numbers. But I also believe that the numeric coprocessor was always there. It just took 900,000 years to come up with methods for coding the query so the coprocessor could kick in.vmahuna
July 9, 2017
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