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November 23, 2009

Comments

nato

Nathan claims to offer an example of something a computer can't do: representing 2/3 as a fraction as opposed to a decimal. Of course, there are many ways for computers to represent 2/3 perfectly, some of which are trivial, and some of which are not. One way would be to implement a base three register where 2/3 would be a simple and infinitely exact "0.2". Another one that occurs in extant computer algebra systems would be to represent the fraction explicitly as a numerator and denominator. Still, I encourage Nathan's impulse to offer empirical challenge; perhaps continued responses will serve to inform intuition.

"I repeat that to say it *does* apply leads to radical skepticism since if we once abandon the innate conviction that our logeto-mathematical faculty apprehends truth we can't get back to it"

I will repeat that this is a non-sequitur. It does not follow that because we cannot prove all true propositions that we cannot prove anything or be certain of anything. I hope Nathan will restate why it is that he thinks this follows.

"to the extent that I was simply offering a *definition* the charge of "triviality" is neither here nor there"

But the very crux of my position was that this was not a *useful* definition because it does not identify anything very interesting. Hurricanes are interesting weather patterns and are most usefully approached as discrete systems despite the fact that they never are truly separate from the rest of the atmosphere. We can choose to define "weather pattern" as only the sum of all atmospheric thermodynamics, but this wouldn't be a useful definition. In fact, it would put us in the very odd position of saying that the weather is static and only its flow changes.

That said, Nathan is right that there are philosophical consequences of the technical truth of consciousness being an algorithm. Many of the consequences he and Penrose offer are quite empirical in flavor, however. Penrose cannot see how we could approach the ideal of 'perfect understanders' with a deterministic algorithm that directly manipulates semantic objects* and harnesses that intuition to Godelian incompleteness. Of course, the original empirical objection can be answered with an alternate model for why we can approach the ideal of the perfect understander, starting with abandoning the contemplation of algorithms manipulating semantic objects**. At that point it becomes necessary for the objector to explain exactly why the ability to logeto-mathematically prove all true propositions is a qualification for consciousness.

This doesn't remotely dispose of all objections; it merely responds to Penrose's.

*He's right, it's probably impossible.

**For one thing, if we stick to that model then the available dispositions toward any semantic object become as fixed and limited as the available positions of a bead on an abacus. I believe it is this image that leads hard realists to reject functionalism, and they're right as far it goes. If that's really what the mind did, it wouldn't be much of a mind.

Nathan Smith

re: "Nathan claims to offer an example of something a computer can't do: representing 2/3 as a fraction as opposed to a decimal."

Not exactly. What I said was that a computer can't grasp the decimal representation of "zero point six repeating." If it were really important to use 2/3 with perfect accuracy, algorithms could be designed that would do that, of course. But your home computer won't. It will use an approximation. And that's a striking and curious fact, considering that for many purposes your home computer's arithmetical skills are vastly superior to yours. As a programming book I once read put it: "Computers are very fast but very stupid."

re: "It does not follow that because we cannot prove all true propositions that we cannot prove anything or be certain of anything."

This *negative* claim is all right as far as it goes. It's *logically* possible that we cannot prove all true propositions even of a class that is in some ways narrow, such as those of arithmetic, yet we can prove or be certain of some things. But do we have any reason to believe the anti-skeptical proposition that we can prove or know at least some things is true? I think the normal answer, the answer that everyone believes even if for some purposes the entertain contrary ideas, the answer that is implicit in all mathematics and even all systematic thought, is that we have a logeto-mathematical faculty, so to speak, which is reliable. Not probabilistically reliable-- probability and statistics are a separate field from mathematics and logic-- but certainly reliable. How do we know this? Well, what can you say to that? We just know it. Yes, we make mistakes, but the mistakes are not *of* the logeto-mathematical faculty, but *lapses from* it, *interruptions* of its operations by laziness or distractions or mental shortcuts, and the logeto-mathematical faculty itself is the appropriate and capable tool with which to correct errors made in our efforts to apply the logeto-mathematical faculty.

In short, the reason we have for accepting that we can prove/know some mathematical truths is, by its nature, a reason to accept that we can prove/know *all* mathematical truths-- not in practice perhaps due to limitations of time or powers of concentration, but we possess the faculty. If we dismiss this, so to speak, introspective evidence, we have nothing else to substitute for it. If you concede that there may be some arithmetical facts which are beyond our power to understand-- a strange, absurd, scandalous notion if you think about-- then where do you draw the line? We might be mistaken about all sorts of things we think every day.

Evolutionary arguments about how natural selection would have favored bright thinkers are next to useless to vindicate the mathematical faculty. Nothing beyond the very simplest arithmetic would have been of any obvious use to our caveman ancestors, and even a few centuries ago the capacity to understand calculus would have been a white elephant; indeed even today it's far from obvious that anyone's reproductive success is enhanced by a capacity to master topology or combinatorial optimization. We're maladapted in all sorts of ways thanks to the rapid changes in our environment: we want to eat all sorts of things that are not good for us at the margin amidst the bounty of a modern economy, to cite just one example. Our minds also have aspects that seem to be explainable in terms of evolutionary biology: we enjoy gossiping, we have notions of fairness, men can't help thinking about sex much more than is good for them. If we have to turn to evolutionary biology stories to explain our logeto-mathematical faculty, nothing is more probable than that this faculty is as maladapted to discern truth as our dietary instinct is to keep us healthy or our sexual instinct is to lead us to fertile, healthy family life under modern conditions. Of course, we wouldn't know: we'd be mistaking truth for falsehood all the time. But then, since the logeto-mathematical faculty undergirds virtually all our thoughts and beliefs, doubt is cast on all of them too, leaving us with nothing.

It's the woodcutter cutting off the tree that he himself is sitting on.

Nato

"If you concede that there may be some arithmetical facts which are beyond our power to understand-- a strange, absurd, scandalous notion if you think about-- then where do you draw the line?"

First off, they would be beyond our power to prove. This leaves open the possibility of something seeming correct, but our being unable to show that it necessarily so from our base set of axioms. Further, nothing about the incompleteness theorem implies that an algorithmic/arithmetical system would be *wrong* about anything, merely incomplete. Thus there is nothing here that calls into doubt any a priori reasoning. It challenges only Penrose's poorly-motivated assumption that conscious beings can in principle achieve certainty equivalent to mathematical proof for all true propositions.

Dennett's statement regarding the trickster knowing things about your brain could do so, but this merely locates our familiar fallibility. One could use Nathanic language to describe the situation: if Rumpelstiltskin knows enough about anyone's brain, he'll be able to predict when they will lapse from their logeto-mathematical faculty, or what sort of conundrum will result in an interruption*. That's nothing more than taking advantage of the fallibility that Nathan would deny no more than anyone else. True, it still leaves us with the question of how to draw the line, but I deny that whether the mind is an algorithm or not has any effect at the theoretical level.

*Nathan could, of course, say that this would only be a statistical truth at best and that if the mind is focused enough it will be able to overcome any weaknesses in the algorithmic brain, but that's a separate issue.

Nathan Smith

re: "if Rumpelstiltskin knows enough about anyone's brain, he'll be able to predict when they will lapse from their logeto-mathematical faculty, or what sort of conundrum will result in an interruption*."

Nato seems to have anticipated my response to this, but I'll put it in my own way: No, Rumpelstiltskin could not predict this (with certainty), because of free will. Without going out on a limb to say we could achieve perfect concentration by trying hard enough, we can still say that no one could predict with certainty where we would lapse.

re: "nothing about the incompleteness theorem implies that an algorithmic/arithmetical system would be *wrong* about anything, merely incomplete. Thus there is nothing here that calls into doubt any a priori reasoning... True, it still leaves us with the question of how to draw the line, but I deny that whether the mind is an algorithm or not has any effect at the theoretical level."

Yes, we might not be wrong about anything: we might just be unable to figure out certain arithmetical facts. And they might be rather remote. But do we have any reason to believe that that is the case. To clarify, consider:

Hypothesis A: Our logeto-mathematical faculty, when applied with sufficient diligence and concentration and when not interrupted and distracted, can prove/know with certainty any arithmetical proposition.

Hypothesis B: Our logeto-mathematical faculty is incomplete, i.e., there are some arithmetical propositions it cannot know with certainty. (Nato suggests, too, that the truth may "seem right" even if we can't prove it/know it with certainty. I don't really understand this suggestion but I won't absolutely rule it out.)

Hypothesis C: Our logeto-mathematical faculty is severely maladapted to discern truth and often leads us astray, leading us to think arithmetical truths false and falsehoods true.

Now, what Nato is saying is that if we accept that Godel's incompleteness theorem proves that Hypothesis A can't be true (provided that we are algorithms), then Hypothesis B might still be true. What I am saying is that Hypothesis A is true, and that we have reliable introspective evidence that it is true-- I might even go so far as to say that it's inconceivable, properly speaking, that it's false-- but *if we reject* our introspective evidence in favor of Hypothesis A, as we are compelled to do if we accept that the brain is algorithmic, then we haven't the slightest bit of evidence for Hypothesis B, and what evidence we have points, if anything, to Hypothesis C.

re: "Penrose's poorly-motivated assumption that conscious beings can in principle achieve certainty equivalent to mathematical proof for all true propositions."

Correction: All true propositions *of arithmetic.* Surely Penrose wasn't say that, say, an 8th-century Viking could have proved the existence of the Egyptian Pyramids by pure reason. If so, I agree that he went too far.

Nato

I don't understand how it is that Nathan thinks we have no evidence for B. So far as we can tell, everything we've proven logeto-mathematically to be true is in fact true. Essentially, almost any evidence that supports A also supports B. C is generally inconceivable. The only phenomenon that might have any bearing is if there are non-axiomatic facts nearly everyone considers certain but for which no one can give a proof. Conversely if we merely suspect these things are true but they resist proof through the centuries, that could potentially point to B. Of course, Fermat's last theorem would have been an example of this yet it was eventually proven, so it's obviously a very inferior kind of 'evidence'. There just doesn't appear to be any dispositive case to decide between A and B. C would seem to rule out ever increasing knowledge and power over the outside world, which conflicts strongly with subjective experience and should be rejectable on those grounds. Of course if C is true in the strongest sense then reason could tell us nothing certain, even about itself. Hence its ultimate inconceivability.

So, we'll have to choose between A and B on different grounds than 'evidence'. Nathan offers intuition, but is his basement intuition really that the mind can achieve mathematical certainty of all true propositions? Or is that the formalization he superposes over a rather less detailed intuition. I'm not sure but what I might harbor an intuition (really more of a strong hunch) that, given enough time and resources, humans can find a way to discover all discoverable answers. I cannot, however find any trace of intuition in the form Nathan gives. Perhaps C is true only for unlucky souls such as myself.

Nato

Also, no correction necessary: the Vikings need only to be able *in principle* to arrive at certainty regarding the pyramids.

Nathan Smith

"So far as we can tell, everything we've proven logeto-mathematically to be true is in fact true."

But that is precisely what we would expect to observe if Hypothesis C were true, isn't it? Presented with the same question, our hopelessly maladapted brains would tend to give the same wrong answers, and "so far as we could tell, everything we've proven logeto-mathematically to be true would be in fact true." It wouldn't *really* be true, but it would be, as far as *we* could tell.

Nato brings up the conceivability criterion. Or I guess I did. Anyway, I would assert that the falsity of Hypothesis A is what is inconceivable. Now that might sound odd because the falsity Hypothesis A doesn't superficially *seem* inconceivable. For that matter, the truth of Hypothesis C doesn't seem inconceivable: we can easily say "Human brains are maladapted to discern truth," and if we don't think too hard about that-- and especially, if we don't think about how to apply it to ourselves personally-- the claim seems not absurd or even odd or improbable. But when you actually try to think that even what you find most logically compelling might be false, without hope of correction by more careful logical thinking, you realize that that just can't be right. And it's the same if you assert that there are some arithmetical propositions we just can't solve. We believe-- we know-- that we can solve any arithmetical proposition; we even know that "two over three is zero point six repeating." That's the implicit assumption every time we set out to do mathematics.

The above paragraph is, as I like to put it, perhaps with willful obscurity although I don't know a better way, operating in "the domain of reason" but not "the domain of intersubjectivity," so there are inherent limits to the extent to which I can make the argument compelling. I can really only argue rather than demonstrate. But if you ask what my evidence for Hypothesis A is, that's my answer. If we *reject* that evidence, the evidence that points to Hypothesis C rather than Hypothesis B is that the only other argument we seem to have to fall back on is the natural selection argument that better arithmetical skills will have guaranteed past reproductive success, and that argument does not remotely point to us being perfect arithmeticians. Advanced mathematical skills would be essentially useless in nature. And we're maladapted in so many other ways, e.g., with respect to food and sex, that it seems more than likely we'd be equally maladapted for doing math. If you want to say this argument is a little tenuous, fine, but you're still left without any grounds for credence in our logeto-mathematical faculty, sitting on your amputated tree branch as it plunges into the abyss of skepticism.

P.S. If Penrose thought the Vikings could prove the existence of the Pyramids by mere thinking, he did overreach. But that overreaching seems irrelevant to the argument here.

nato

First I will admit that there are senses in which C is conceivable. I just want to say that the strong form of C (which I believe to be in play here) negates the validity of imagining implications. Or perhaps it could be better said to negate the validity of validity judgments themselves. I don't think 'conceiving' can work in such an uprooted fashion.

"f we *reject* that evidence [that !A is inconceivable], the evidence that points to Hypothesis C rather than Hypothesis B is that the only other argument we seem to have to fall back on is the natural selection argument that better arithmetical skills will have guaranteed past reproductive success, and that argument does not remotely point to us being perfect arithmeticians"

I think this line of reasoning is a bit of a red herring, but I'll respond to it anyway. If the world follows rules, then even a moderate form of C would seem to (insofar as such a thing can be imagined, of course) doom a species such as ours to extinction because we'd be forever poisoning ourselves, being eaten by predators, falling off cliffs and so on. A very attenuated C in which our logeto-mathematical incompetence is mostly confined to formalized mathematics seems much more evolutionarily plausible, but this doesn't result in the overthrow of all certainty, but rather in something like an ape. In fact, one could even take an evolutionary argument as explaining why it is that we're so good at reliable manipulation of symbols (very useful in a culture!) and so miserable at brute calculation (floating point math isn't so helpful), but we still end up being able to prove things with well-justified certainty (i.e. !C).

But returning from that digression, I think we can dismiss any strong form of C a priori because either 1)It's not true or 2)It is true, but that means I have no valid grounds to believe its truth has any particular implications. That leaves us with either A or B, both of which imply that anything we can actually prove (in the formal sense of the word) is incontrovertibly true.

"And it's the same if you assert that there are some arithmetical propositions we just can't solve. We believe-- we know-- that we can solve any arithmetical proposition; we even know that "two over three is zero point six repeating." That's the implicit assumption every time we set out to do mathematics."

There are certainly insoluble problems in mathematics, the most famous being the analytical trisection of an arbitrary angle and the construction of triangles from three sides of arbitrary length. In the first case it's obvious that *some* set of angles would be the correct trisection, and in the second it's easy to see that some sets of sides would yield no euclidean triangle whatsoever. In other cases it's possible to prove that there is no system for determining whether there is a solution. I'm not sure which side Nathan would take these examples to support, but it's worth noting that in many of these cases human mathematicians are as universally stumped as their systems of equations. Perhaps Nathan can explain what he means when he says "we can solve any arithmetical proposition" in light of these apparent counter-examples so that a reader can essay an evaluation of the intuition that is supposedly informing him.

P.S. The Viking item was sort of a joke because there were two levels of difficulty: 1) a priori proofs aren't supposed to say anything on contingent realities for which we must rely on empiricism, even if it's about whether or not I'm holding a toothbrush or not and 2) the Vikings had no empirical access to the pyramids either.

nato

Or whether or not I'm repeating a phrase or not.

Or not.

Nathan Smith

re: "even a moderate form of C would seem to (insofar as such a thing can be imagined, of course) doom a species such as ours to extinction because we'd be forever poisoning ourselves, being eaten by predators, falling off cliffs and so on"

To avoid such dangers would, of course, not require any of the lofty functions which the human mind exhibits in figures like Plato, Newton, Bach, etc.; it is only a slight exaggeration that everything really interesting that the human mind does is completely orthogonal to the Darwinian criterion of reproductive success. Hypothesis C is quite consistent with our species having whatever rudimentary reasoning skills might be necessary for survival.

And those may not be large. For it is interesting to note, too, that even in avoiding getting poisoned or eaten by predators or falling off cliffs, nature seems not to rely on reason but to equip us with *instinct.* Human children tend to have a keen fascination with predatory animals like tigers, lions, wolves, bears, sharks, etc. From the modern point of view this fascination is an example of how maladapted we are, for none of those predators pose any real danger in modern life; it would be far more useful for children to be fascinated by food crops. We fear predators from instinct, not reason. Again, humans have a natural fear of heights, which is I think more or less universal though some of us overcome it in varying degrees. It is sometimes inconvenient, for nowadays there are many occasions-- having an office in a skyscraper, flying in an airplane, looking down over a waterfall from above from behind a railing-- when our instinctive fear of heights gets in the way of utility or enjoyment when our reason tells us we are perfectly safe. Again, in the case of poison, our natural aversion to spiders and snakes, sometimes amounting to panic, seems to reflect an awareness not gained by reason but coded into our instincts, that these animals are (sometimes) poisonous.

And when you think about it, you can see why nature equips us with instinct in such cases, for it's not clear that reason would be all that useful in avoiding dangers like these. We can learn by induction; but if one falls off a cliff, or gets eaten by a bear, or bitten by a black widow, one is unlikely to have the opportunity to reason, "Hmm, that didn't work out very well; I'd better avoid that in future."

Nato

"...it is only a slight exaggeration that everything really interesting that the human mind does is completely orthogonal to the Darwinian criterion of reproductive success."

I think Nathan is flatly mistaken about this. As a point of fact, it is our ability to formalize, communicate and manipulate semantic objects that has allowed us to outcompete any comparable organism in history. From before we were a species we resided atop the food chain and made clothes of our most dangerous fellow predators. Nathan's general points about instinct can account for us not falling off cliffs, but it doesn't explain how stone-age humans learn to process otherwise poisonous plants into staples or to defeat a tiger's claw with a spear. We have been a technological and cultural species for at least 100k years, and during that time any humans who couldn't keep up would certainly not have a lot of reproductive success. Technology and culture moves faster today than it ever has in some respects, but not by as much as would appear at first blush. Over and over again entire cultures and races have be entirely or nearly entirely extinguished when overrun by foreigners with alien weaponry and customs. Survivors would have been those who could quickly adapt. A flexible general intellect is a gigantic evolutionary advantage.

Nathan Smith

I certainly agree that reason has enhanced the reproductive success of mankind in general, but that's not the issue. The question is: Does excellence in reason enhance the reproductive success of individuals vis-a-vis their fellows? And here I am skeptical.

The pre-eminent 20th-century example of a person's reason enhancing human reproductive success is Norman Borlaug, "the man who fed the world," the father of the Green Revolution, who pioneered the development of new high-yield crop varieties that expanded food production in Mexico, India, and elsewhere, and made possible a major retreat in world hunger. Wikipedia says of Borlaug that he "had three children, Norma Jean 'Jeanie' Laube, Scotty (who died soon after birth due to spina bifida), and William Borlaug, five grandchildren, and six great-grandchildren." Borlaug enhanced the reproductive success of *others*, not his own, and hardly indeed that of his countrymen, for America was already well-fed before Borlaug came along. This seems to be the typical case. Nato mentions the domestication of crops as an example of an advance that enhanced human reproductive success. Yes, but crops, once domesticated, spread far and wide: most of Afro-Eurasia has been eating the same crops, many of them domesticated in the Near East, for thousands of years. Today, the nations which have the lowest birthrates are precisely those which are the best-educated and the most scientifically advanced. That girls' education reduces birthrates is such a well-established regularity that population control is actually one of the reasons development economists cite when advocating more education for girls. Within Western populations, too, I think birthrates are negatively correlated with education... and I think most Americans have noticed in their personal experience that the people in their high school who married young and had a lot of kids were a different set from the "nerds" who went on to pursue advanced degrees. Was it different in the past? In the Middle Ages the tendency is arguably even stronger, since it was primarily in the monasteries that the life of the mind was pursued, and celibacy was a condition of entry there. (The universities were important in the later Middle Ages; celibacy was not, I think, a general requirement there, though many scholars were clericals with celibacy obligations, e.g. Thomas Aquinas.)

If I had to name an example of reason contributing to reproductive success the best I could do is Genghis Khan. (J.S. Bach did have a large family but I don't think his musical genius had anything to do with that.) Genghis Khan is not exactly one of the heroes of the life of the mind, but he did show a good deal of political sagacity in the way he unified the Mongol tribes, and a ruthless rationality in the way he imposed military best practice on them. And I read somewhere that his success gave him access to nubile females on a scale unsurpassed before or after his career, and that he may have the most offspring of any human being who has ever lived (to pass over some complexities about multiple ancestries...). But first, note that the case of Genghis Khan not only does not confirm that (reason=>reproductive success) at the individual level has anything to do with (reason=>reproductive success) at the level of the species, but contradicts it, for the Mongol incursions were a major setback to all the cultures affected. Also, it's not clear that the selfish genes of the conquered did so badly from the result: if I get massacred by the Mongol hordes but my sisters get appropriated by Genghis Khan, my selfish genes might do just fine by the exchange. In any case, rationality is far from Genghis Khan's most salient characteristic: what stands out more is his reckless courage.

Genghis Khan is a sort of bridge to prehistory since he was a leader of preliterate tribes, and maybe human prehistory was dominated by Genghis Khan-type figures. So the idea that evolutionary forces can explain increasing rationality depends on the plausible but necessarily scantily-supported notion that human history prior to the invention of writing, which we don't know much about, looked a lot different than human history after the invention of writing, which we do, but which doesn't seem to support a link between excellence in reason and reproductive success. Possibly the case for evolutionary forces improving intelligence during recorded history is stronger than I've made out: economist Greg Clark made this case, I believe, in a book (mis)titled *A Farewell to Alms.* Anyway, all this may, as Nato suggested, be a bit of a detour, since a huge question mark is whether the practical cunning and the knack for sizing up people and situations which seem to be the determinants of success for a medieval Mongol khan or a modern businessman have much or anything to do with the loftier faculties of abstract thought. The "everything really interesting that the human mind does" to which I alluded includes things like the theory of gravity and Plato's *Republic* and I'm not aware of a single historical example of such things being linked to reproductive success and would be surprised if more than a few examples could be produced. Maybe these are extensions of more basic and general faculties that... Did the scribes in ancient Egypt have large families? In the end, though, my Hypothesis C is pretty flexible: it's hard to put an upper bound on the amount of practical mental skills we might have while being preprogrammed to err when, say, trying to prove the First Welfare Theorem in Arrow-Debreu general equilibrium economics. At best, the evolutionary argument leaves us undecided between Hypothesis C and Hypothesis B; and from that it basically follows that all our thought is unreliable.

Ultimately the epistemic question is: are logic and math *foundational*? I answer: Yes. A materialist has to answer No, since his reductionist ontology doesn't have room for minds with supernatural access to truth, and then try to give some deeper account of why they are nonetheless reliable; and this he cannot (even come close to) do(ing).

nato

First, an aside about agrigulture: the example I actually had in find were the Maidu processing the tannins out of acorns. Because they discovered how to process tree products that were otherwise impossible to eat, they could flourish in areas uncontested by tribes that didn't have the necessary technology.

In any case, Nathan is looking far too late to locate the dynamics that most strongly shaped our genetic makeup. As he points out, 2k years doesn't allow very many human generations over which to work. Instead, it is in human* societies of the stone age that the gene set that defines distinctly human cognition arose. In that context, inventions certainly advantaged those with similar genes more than they did those with dissimilar genes as a side-effect of the fact that those near the inventor were much more likely to have the same genes than those far away. Further, people were not very mobile, so opportunities for peaceful cultural exchange were curtailed. If the exchange was more violent, then those sub-groups with the best technology would have been most able to resist or negotiate favorable settlements that would allow their lines to continue. Even when there *was* peaceful exchange through trade expeditions or the like, it would be more ephemeral and those groups along the route with more intellectually-flexible populations would be more likely to be able to quickly learn and adopt helpful techniques.

It is only very recently that reproductive success came unmoored from intellectual capability. In fact, this is probably only really true in the last 100 years or less. Even in the case of Bach, his immediate reproductive success probably had nothing to do with his musical ability, but his music almost certainly had something to do with being able to, for example, reduce the likelihood that his children would die of starvation.

Nathan could go a little beyond the original scope of the argument to say that there's no evolutionary advantage of musical ability in stone-age societies. This certainly does touch on some interesting issues, and the evolutionary history of our aesthetic sense is and has remained a hot topic for the last several decades. I don't think there's a consensus on the question, but there are certainly a number of possible explanations still in play and a number of others for which evidence has been less kind. One regarding aural aethetics that I believe remains in good standing is that a fine and exploratory sense of rhythm is a big advantage for those who hunt and fight with projectiles. Marksmanship tends to vary with subconscious awareness of one's own heartbeat (a common explanation for why women tend to be better shooters is because they are on average more aware of their heartbeat). Rhythm and the ability to manipulate it is also very important in martial arts, which I imagine to be true for similar reasons when trying to lead a target. Human arm joints are also notably different from those of our forbears in their suitability for throwing things. Does this "just so" story explain it? I don't really know, but I'm just sketching an outline here. Other hypotheses focus on sexual selection. The point is that I'm aware of nothing about our cognitive abilities and proclivities that is obviously orthogonal to reproductive success. I'm not saying that evolution has actually selected all our basal capabilities - I'm sure that at least some of them are nothing more than side-effects - but I just think the line of argument that there's no evolutionary reason for us to be so smart in so many ways is extremely weak.

Finally, I would argue that a materialist adhering to A (Penrose) or B (Dennett) would not have to abandon the foundational nature of logic. In fact, I can't even see how that could be a consistent position for anyone. Rather, materialists have to reconcile other apparent data points with the necessary assumption that our logic is correct. Chief amongst those is the construction of our own logic-consideration apparatus. Any hypothetical construction of consciousness that has no reliable access to logic must be rejected on first principles, so we accept or reject materialist accounts of mind based at least partly on whether they allow for reliable logic. There are problem cases such as the insane (who are clearly conscious!), but I think one can correct for those apparent paradoxes if one adjusts for their altered perceptions, then applied the ordinary epistemic procedures for dealing with how we can know anything in the world if we cannot trust our perceptions.

This leads us back to our long-running arguments about the epistemic underpinnings of empiricism, but that's a further conversation.

*Actually most of the genes would have arisen in our predecessor species, but there's plenty of evidence that significant changes to the "universal" human continued up through at least 40k years ago.

nato

Upon reflection that's really a poor account of reconciliation of problem cases. Hopefully I can wave my hands a bit here and hope the reader will see that they could easily come up with some good accounts without me writing them.

Nathan Smith

Nato uses the phrase "just so stories"... exactly. One could imagine experiments that would test the proposed theory of the origins of music. (a) Create a population of organisms with a variety of proto aural aesthetic sensibilities. (b) Place them in an environment where hunting supplies a large part of their food. (c) Let evolution play out for 100,000 years and see if they evolve a sense of rhythm and harmony. Of course this experiment is not feasible to implement. One can imagine, too, computer simulations which would start with genomes and map them into sim-persons and track the interactions of the sim-persons... if such simulations could be run they would leave a lot of questions but they might at least demonstrate certain possibilities. They can't be run. We don't know whether the proposed evolution of musical tastes makes any sense at the level of logic, or whether it is possible, let alone whether it actually happened. Scientifically it is on a level with the Viking theory that thunder and lightning come from Thor riding around the heavens in his chariot. That goes for just about everything at the intersection of sociobiology and natural history. Evolution is helpless even to explain why we wear clothes. I dare anyone to prove me wrong on that. I'm not sure whether to laugh or weep at the efforts of evolutionists to explain aesthetic sensibilities: they are often amusing, like pagan myths, but that anyone might be gullible enough to take them for "science" is depressing.

Nato's suggestions about the evolution of reason are also "just so stories." He writes that "opportunities for peaceful cultural exchange were curtailed," but we know nothing of the sort. He writes that "people were not very mobile," which is an odd claim since it is agriculture that pins people to particular places; hunter-gatherers typically have to move when the supplies available in a particular locality are exhausted. He writes: "If the exchange was more violent, then those sub-groups with the best technology would have been most able to resist or negotiate favorable settlements that would allow their lines to continue," but as I pointed out, you don't have to win the battle for your selfish genes to do well: Genghis Khan's concubines' lines continued, too. We just don't know most of the facts we would need to know to confirm or falsify the account.

nato

Before I digress into disputing Nathan's criticism of the just-so stories I've offered I should reiterate what they are supposed to illustrate: there are plenty of good *potential* justifications for why evolutionary pressures would favor those with reliable access to logic. Nathan first claimed "everything really interesting that the human mind does is completely orthogonal to the Darwinian criterion of reproductive success" but I pointed out ways in which reliable access to logic gives us huge evolutionary advantages. Nathan clarified (or retrenched?) to say that he just meant skepticism as to whether excellence in reason gave humans advantages relative to their fellows. This is, I think, a rather amazing statement is coming from a person versed in game theory and economics, but he did give some examples in recent times that supposedly showed how reproductive success due to excellence in reason could be decoupled from the differential reproductive success of the genes creating the excellence in reason. Not all of these examples carried (it *is* pretty clear that selfish genes of the conquered had reduced differential reproductive success) but I thought it would be more useful to make the more substantial point that most reproductive pressures were made in a different time and in the presence of different dynamics than in the last 2k years, so his case for decoupling was not made. Evidently my offers of just-so stories may have confused things, giving the impression that unless I could prove them that the case for differential reproductive success collapsed, but the prima-fascie evidence goes quite the other direction. Rather, if I can't prove my just-so stories, I am in the place of a scientist unable to give an account of the evolution of the eye: clearly a good eye confers an advantage on its owners' genes, but we don't know how it all started. Likewise, mastery of reason clearly gives an organism's genes a leg up in differential reproductive success, but we may not be able to correctly account for the dynamics of its rise.

Moving on from there, I should address this mistake: "Hypothesis C is pretty flexible: it's hard to put an upper bound on the amount of practical mental skills we might have while being preprogrammed to err when, say, trying to prove the First Welfare Theorem in Arrow-Debreu general equilibrium economics. At best, the evolutionary argument leaves us undecided between Hypothesis C and Hypothesis B; and from that it basically follows that all our thought is unreliable"

No, it is not actually quite that flexible. Though I'll entertain the possibility of being constitutionally unable to grasp domains of mathematics and call that an attenuated Hypothesis C, that is different in type (rather than scale) from being programmed to always take as true something that contravenes our own axioms. That would indeed render all thought unreliable, including the thought that Hypothesis C has any particular implications. It is, I submit, Nathan who saws off the limb on which he stands with respect to C.

Note that this is not the same thing as saying we have a tendency - even a strong one - to misapprehend the truth of some proposition. That would still mean we could eventually work our way around to correcting our misapprehension, e.g. dropping two stones of unequal weight to show they accelerate at the same rate contra intuitive physics, or using geometrical proofs to correct the intuition I had when I was about seven years old that the hypotenuse of a right triangle is shorter than the sum of its two sides by a length equal to the line running perpendicularly from the hypotenuse to the 90 degree corner*. As long as our axiomatic logic is valid, there must always be a path back to consistency. Not completeness, but consistency. Even if we want to posit some supervisor process watching as we start our way down a path of thought and then disrupting it to something false every time, we're back to casting doubt on all thoughts, including those that would purport to tell us what the implications of that are. We are all in the same epistemic boat when it comes to logic itself.

Finally a quick response to Nathan's criticisms of my just-so stories. I think I was clear when I first offered them that I do not take them to be anything like proven, but I do want to defend the possibility of there being evidence for or against them.

For example, Nathan seems to doubt that we can assume people weren't very mobile, but measurement of genetic travel would support this, as would the habits of neolithic cultures that survived into more modern eras. So would study of technological and cultural artifacts of neolithic populations. If we started finding in one place 50k year-old items made of animals or vegetables from another place far away, that would support the idea of extensive cultural and technological exchange. So would finding that techniques for making tools appeared almost simultaneously in all contiguous populations. But we haven't found that. In the 19th century some Native Americans in North America were far more advanced than others, sometimes even of near neighbors. Finally, the evidence that we have that people were hunter-gatherers is from the same corpus that tells us that they nevertheless rarely moved very far very quickly. I don't think there are reasonable grounds for skepticism on the differential advantages of reason.

The just-so stories about aural aesthetics are trickier, of course, and the evidence pretty fragmentary. That said, the fact that Neanderthals made flutes would tend to militate against the projectile story as their joints and tools are much less projectile-centric. A related one regarding personal combat might make sense, but one would expect to see some music affinity in all the animals with lots of social combat if that were the primary driver. Though I wouldn't say these stories are necessarily disproved by just these considerations, with enough countervailing evidence they would be considered disconfirmed. I can't say with perfect confidence that we'll ever have more than a "best-supported guess" in some matters, but that doesn't mean that we can say nothing meaningful on the matter.

Of course we can get back to Nathan's rejection of artifacts as evidence in the absence of a written record and argue about that again, but I think most people would be content to note that no archaeologist shares his fastidiousness and dismiss that source of skepticism.

*I think I was mislead because I could "see" my intuition approaching the truth as one side approached zero length.

Nathan Smith

Well, we could debate this forever I suppose. Evolution drives me crazy; I can't stand the way evidentiary standards are debased whenever the subject comes up. I don't "reject artifacts as evidence" but one must bear in mind their very severe limitations. They are vastly inferior to experimental evidence. The term "science" really should be restricted to things that (a) we can demonstrate by experiment, or for which (b) we have to rely on observation but we have well-grounded knowledge of what is possible with which to interpret the evidence of observation. When Nato writes, "I don't think there are reasonable grounds for skepticism on the differential advantages of reason"... well, fine, that's his opinion. He doesn't have anything close to a complete theory of *how* reason contributed in the past, as it does not in the late 20th century, to reproductive success. For that matter we haven't adequately defined what "reason" is. It's clear *ex ante* that if some theory were defined so as to be in principle testable the evidence actually to test it would not be remotely adequate. In modern times there is a science of demography, and it would be possible to conduct surveys of psychological traits and mental performance and then use regression analysis, with data sets of thousands or tens of thousands of observations derived from a scientific sample of a population, to see whether and how these traits might be correlated with family size. Even then there would be plenty of room for debate about econometric methodology etc., and it's doubtful whether sober researchers would feel sufficiently emboldened to say "I don't feel there are reasonable grounds for skepticism..." but at least such explorations would deserve the name of science. That's what I mean by evidentiary standards. Proper evidence for the kind of claims Nato is making would require such surveys to be conducted for thousands of generations and analyzed with proper statistical techniques.

To sum up, on the evolution/reason question, my position is still that the ability to understand the differential calculus would have been of absolutely no use to our ancestors, so natural selection can't explain our having it. I believe we know that Hypothesis A is true on introspective evidence; and that if we reject that, the pattern of our maladaptation in other respects and the fact that the higher mathematics is of no use to hunter-gatherers would point us weakly to Hypothesis C rather than Hypothesis B. Of course I think Hypothesis B is also rejected on introspective evidence. It might be valid to defend Daniel Dennett against the charge of radical skepticism by saying that he accepts Hypothesis B rather than Hypothesis C, even if he has inadequate grounds for doing so. So being a materialist requires one to accept that one of these days we could stumble onto a fact of arithmetic, something along the lines of, say, 7047+7011=14058, that we are permanently unable to prove. No concern to me since I'm not one. Free will is an independent and sufficient ground for rejecting materialism. More fundamentally, there is no ground for *accepting* materialism; there are all sorts of things it can't account for. Indeed the mocking question "What is the chemical composition of the number two?" is enough to show that the world can't be accounted for in merely material terms, i.e., that materialism is false. I pity the poor materialists, trying to cram math and music and morality and so many other good and mysterious and wonderful things into their impoverished ontological framework. But I suppose I should leave them to their own devices.

Nato

"Proper evidence for the kind of claims Nato is making would require such surveys to be conducted for thousands of generations and analyzed with proper statistical techniques."

Does Nathan really mean to say that in order to conclude that mastery of reason confers a differential reproductive advantage, this is the level of detailed data one would need? Seriously? That's ridiculous on its face and I can't believe that Nathan can possibly mean what that appears to mean.

Perhaps Nathan is thinking that I am claiming to have demonstrated Truth beyond contravention. In that case he would have a point, but I'm merely talking about the ordinary standards applicable in any empirical science for considering a matter settled until further notice.

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