What do you say in response to a theory of things that is simplified to the point of absurdity: that asserts that existence is an illusion, or physical objects do not exist, or language is all a rhetorical power-game, or mathematical objects are only physiological states of someone’s brain? Some possibilities:
- Argument. It’s illuminating to argue such points a couple of times, but it gets old because the issues are so overarching that everything becomes grist for the mill. Also, odd theories energize people. It’s the same problem as with global conspiracy theories.
- The Doctor Johnson approach. If Bishop Berkeley claims material objects don’t exist, kick a rock as a refutation. From Bishop B.’s standpoint the refutation misses the point, but from Doctor J.’s it reinforces his sense that the point is well worth missing.
- The go-along-with-the-gag approach. Almost anything can be reformulated in almost any terms. You don’t see why you should do something because life is all an illusion anyway? Well just have an illusion of doing it.
The reformulation game grows tiresome. Also, it really does matter to us what’s real, so the reformulations won’t be altogether satisfying. It might be possible to reformulate ethics on the assumption that minds other than my own don’t exist, but there would be something missing.
- The take-him-at-his-word-approach. You say all language is a move in a rhetorical power game or purely the outcome of a physiological process? I don’t care what you’re trying to pull off or what the state of your brain chemistry is, I got my own issues, so I’ll ignore you. Similarly, Doctor Johnson suggested that if someone really believes that morality is simply a flatus vocis, when he’s been visiting us we should count our spoons.
- The just-a-stage-he’s-going-through approach, a.k.a. the indulgent-mom approach. Say “yes dear” and assume the guy will grow out of it.
That often works. The common-sense language that people fall into when they speak about the events of daily life corresponds to a common-sense view of what’s real. It saves effort to assume common-sense ontology as true, so most people eventually give up the struggle to maintain metaphysical purity.
One problem with that approach is the willed artificiality of the way people speak today. Bureaucrats and experts speak in a sort of mechanized way that can increase the power and exactitude of what they say, but at the cost of limiting what it can deal with. If a way of speaking has power people try to extend it beyond its proper domain. Depending on circumstances, they may try to substitute rhetoric for mathematics or the reverse. And depending on how we are ruled they may carry their point. The view that gender is a social construction, because gender roles don’t have the universality and exactitude of particle physics, may actually become official doctrine.
- The ignore-it-so-it-goes-away approach. In the end that’s usually the practical answer, since life must go on, but often it doesn’t go away, at least not soon enough. You can’t reform the world, though.
There’s no sure-fire cure for the problem. Intelligence can’t refute stupidity from the standpoint of stupidity, and in any case stupidity is a universal human condition. None of us escapes completely. The best you can do is aspire to reason in your own case, discuss things reasonably with reasonable people, hold to what’s good, present the occasional argument when the mood strikes you, and hope better ways of thinking catch on. It’s not a perfect world, there aren’t always adults in charge, and people do what they want, so we’re not always going to get things as we would like them to be.
Intellectual impostures:
I guess the most comprehensive response to at least one of these theories (that language is all a rhetorical power-game), is to write a thesis that exposes postmodernism as an intellectual imposture.
Alan Sokal and Jean Bricmont have already produced a refutation of postmodern ‘arguments’ that abuse science.
Hermetic hermeneutics defy criticism
The problem with such a refutation of course is that it doesn’t work for someone who views language as a rhetorical power game. He will simply take it as another move in such a game. And there will always be some support for his position. For example, Sokal and Bricmont probably think that pomo hyperrelativists shouldn’t get grants and tenure, that they shouldn’t decide the curriculum, and so on. So the whole thing can be presented as a battle over money and position.
Facts as a cure for stupidity
“or mathematical objects are only physiological states of someone’s brain?”
While it is hardly simple, 100% of the evidence supports that proposition. What makes you think that mathematics is anything else?
You say, “100% of the
You say, “100% of the evidence…” Show us the evidence.
Neuroscience
There is a large and growing amount of literature by neuroscientists and cognitive psychologists on the mental origins of mathematics. You might start here:
The Mathematical Brain
I won’t be holding my breath waiting for evidence that it is something else.
That’s pretty thin gruel.
That’s pretty thin gruel.
Don’t choke on it then
“That’s pretty thin gruel.”
Yeah, right. Numerous books and dozens of papers documenting his repeatable experiments and that is just from one author alone.
Where is the evidence that mathematics is anything other than a function of the brain?
Kalb suggested: The
Kalb suggested: The ignore-it-so-it-goes-away approach. In the end that’s usually the practical answer, since life must go on, but often it doesn’t go away, at least not soon enough. You can’t reform the world, though.
Good advice. I’ll take it.
more brains
If you deny that mathematics is anything other than a function of the brain, then presumably you believe that in the absence of brains there is no mathematics.
To answer your question directly: the body of knowledge studying the universe and discovering it behaves in mathematical ways—“science”, in short—casts doubt on the idea mathematics is nothing more than a function of the brain.
Do you believe that the Pythagorean theorem was neither true nor false before the development of the brain? Did the emergence of the first brains in the universe impose a retroactive mathematical order on Creation? If all brains in the universe were to die, would questions involving number and quantity simply stop making sense?
Do you simply redefine mathematics to exclude this?
Or, if you agree the PT was still true before there were brains to admire it, then isn’t it obvious that mathematics has some ontological status—whatever that may be—which doesn’t involve the presence or absence of brains?
(I seem to recall an argument for the existence of God which proceeded from the fact that mathematical truth was eternal and immutable and infinite but could only exist in a mind. It was cute but I never understood the “could only exist” part.)
More logic
“If you deny that mathematics is anything other than a function of the brain, then presumably you believe that in the absence of brains there is no mathematics.”
That’s right, mathematics is a human invention. At least higher math is anyway since some animals also have the rudimentary ability to count small numbers of things.
And of course the Pythagorean theorem was neither true nor false before it existed. Just as it would cease being true or false should brains cease to conceive it.
As far as brains imposing mathematical order on creation, why yes they do, although the theories are only an approximation of a seemingly underlying order. I can only say that the fact that certain elements or compounds for instance, can be found in mathematically regular lattices when in crystalline form is a long, long way from being a justification for belief in Moses getting stone tablets from the mountaintop, or the resurrection of Jesus Christ, or whatever other Iron Age myth you prefer to offer.
You are in fact exactly wrong. The increasing body of scientific knowledge has discovered absolutely nothing that would imply that mathematics is anything other than a function of the brain.
more words, at least
Wow! I’ve never spoken with anyone who supports such a strong form of creative antirealism before.
(To get my biases on the table: my day job is as an astrophysicist, so I have a professional interest in the subject.)
I don’t recall mentioning Moses, so let’s stick to the issue of mathematics; although ISTM your views are so profoundly anthropocentric (making even the truths of mathematics dependent on human minds) that Western theism seems pleasantly austere and universal by comparison. Yours is an anthropic argument on crack.
“And of course the Pythagorean theorem was neither true nor false before it existed. Just as it would cease being true or false should brains cease to conceive it.”
To my mind this is so manifestly wrong that it’s not obvious where to begin. I now understand in a way I didn’t before Jim’s points about the subject.
So prior to the emergence of the first brain, if two straight objects lined up at right angles to each other, the distance between the far endpoints was simply arbitrary? Since Keplerian orbital motion depends (among other things) on the truth of the PT, prior to the “invention” of the PT by a brain, stars and planets did what, exactly?
How strong does a brain have to be before it succeeds in having the power to make a theorem true?
Because the laws of physics depend intimately on mathematics, I can build a device [a computer, say] which sets off a bomb if and only if [to within some failure probability] the PT is true. If I destroy all life but mine in the universe, turn the machine on, and then commit suicide, is the future simply undefined?
Since our views are so different, I’d like to be clear I understand yours to the degree possible: “[t]he increasing body of scientific knowledge has discovered absolutely nothing that would imply that mathematics is anything other than a function of the brain.”
You genuinely believe that the fact that physics shows incredibly complex mathematical structure on all scales, including when there were no brains at all, is irrelevant to the question of whether mathematics is a merely a function of the brain?
Let Platonism die
Not only is your misapplication of the Schrodinger’s Cat thought experiment specious, you’re argument from authority is fallacious too. I don’t care if you are King Farouk, you spout nonsense.
Kepler’s description of orbits do not explain them, and Newton’s explanations are not perfectly accurate in regards to time and distances where relatavistic effects come in to play.
Let me repeat again, the mathematical models of the universe are approximate explanations of phenomena not phenomena (other than psychological) themselves. The seeming fact that constants exist does not imply that they exist as logical constructs in the absence of a brain. Please refer to the article on page 24 of a recent Newsletter of the European Mathematical Society for a dismissal of even more outrageous claims by certain Platonists.
http://www.ems-ph.org/journals/newsletter/pdf/2007-06-64.pdf
unanswered
Truly, we don’t have a meeting of the minds at all. I suspect we have similar theories about why that is, differing only in direction.
You claim I misapply a Schroedinger’s cat analogy— I don’t even raise one. (Rather like I didn’t mention Moses.) And nothing I said depends upon anything related to quantum physics, merely upon your belief that mathematical truth is dependent on minds conceiving it. I did ask a question about how your belief that mathematical theorems stop being true or false when there are no minds to conceive them interacts with the laws of purely classical physics, which you do not answer.
You claim I make an argument from authority: I don’t see how. The closest I come is mentioning in a parenthetical aside that I have a professional interest in the idea that science probes a real world which is independent of our minds. If such a statement strikes you as an argument from authority, I can’t imagine what wouldn’t.
Kepler’s description of orbits works perfectly well to a certain order; Newton’s laws are better yet, in the non-Kepler limit; SR better yet in the high-velocity limit; and GR is better still in the high stress-energy tensor limit. Like most physicists (excepting some communist ones) I believe there is a capital-T theory beyond GR/QFT which has all successful theories as limits.
But I don’t understand what any of this has to do with my question about the orbital behaviour of planets and stars before there were minds. I claim they behaved just like they do now, and couldn’t care less about minds.
Choose whatever accuracy of representation you like: the model will be a mathematical one. According you to you, the truth of mathematical statements depends on minds conceiving them. So is it your claim that even with no minds around, the natural world will still behave (to ten-digit accuracy) as if various theorems were true even though they’re neither true nor false?
True, a model of X is a different thing than X. (Duh.) But if our model of X—which gives ten-plus digits of accuracy when compared to X—shows deep mathematical connections (consider loop corrections in field theories), I think it’s unreasonable to say the small-scale physics of the universe wasn’t aware of fixed mathematics long before minds showed up in the universe.
Criticisms of Platonism are interesting, but since everything I’ve said is compatible with a pure formalist approach to mathematics, they seem beside the point. The problem I have with your worldview isn’t the ontological status of the Pythagorean theorem (we both agree you can’t buy it a drink), but the objectivity and mind-independence of its truth value.
Since the last time you directly answered a question the answer was fascinating (and frankly hilarious), would you mind doing it again? Choose whichever you find the standard realist view most obviously fallacious on.
You’ve said that the Pythagorean theorem is neither true nor false when minds aren’t conceiving it. Could a mind have conceived it so that it was false?
When the first mind did conceive it, and turned it from neither true nor false to true, did it start being true everywhere in the universe “simultaneously” or did news of the discovery/invention propagate outward at lightspeed?
How complex does a theorem need to be before its truth is dependent on minds? You mentioned counting as an example that may have subhuman requirements. In the absence of plant or animal life of any kind, would one star and one star still make two stars?
No mind, no physics
“Choose whatever accuracy of representation you like: the model will be a mathematical one.”
Yes, and as you point out an approximation to an arbitrary accuracy, and I dispute your claim that all physicists believe in a capital T theory. There indeed exist physicists who are skeptical even of our ability to conceive such a theory. And, as I said before, the mathematics is an invention created to explain physical phenomena not the phenomena itself.
“I think it’s unreasonable to say the small-scale physics of the universe wasn’t aware of fixed mathematics long before minds showed up in the universe.”
An absurd statement on its face. Since only minds are aware (it’s sort of part of the definition) it is false. “small-scale physics” is not aware. Conscious minds are aware of physics. With no mind, no physics; just matter and energy.
“You’ve said that the Pythagorean theorem is neither true nor false when minds aren’t conceiving it. Could a mind have conceived it so that it was false?”
Well in some arbitrary non-Euclidian geometry I suppose it could be. At any rate, formal systems can exist wherein something that is true in one is not in another.
“In the absence of plant or animal life of any kind, would one star and one star still make two stars?”
In the absence of a mind to observe them I am almost certain that the ineffable matter and energy would exist, there would not however be “two” “stars” because both two and stars are human invented concepts to enumerate distinct things and luminous balls of plasma respectively. The “star” doesn’t know it’s luminous, it just is.
The human capacity for language and logic arose as human adaptations to their environment and mathematical formulas are no more or less invented than the Iliad or Gruyere cheese.
Stupid is as stupid does
“The common-sense language that people fall into when they speak about the events of daily life corresponds to a common-sense view of what’s real. It saves effort to assume common-sense ontology as true, so most people eventually give up the struggle to maintain metaphysical purity.”
Some common sense conclusions are truer than others but there is no reason to think that common sense ontology is not congruent with reality. There is no need for metaphysical purity or metaphysical anything else when you are dealing with a single reality.
Irrefutable Nonsense:
The problem with such a refutation of course is that it doesn’t work for someone who views language as a rhetorical power game. He will simply take it as another move in such a game.
On this basis the postmodern view of language is impervious to reasoned contradiction. So probably the best strategy is the take-him-at-his-word-approach, and to retire from the company of people who disseminate irrefutable nonsense.
Retirement can have disadvantages
For example when power is an issue.
Suppose pomo hypermodernists came to dominate (say) academia. In that case saving academia would involve getting rid of them. That could only be done by superior power, since discussion would get nowhere. Retirement might be irresponsible in such a case. But then the pomo hypermodernists would in a sense be right: at bottom, all the complaints were a front for a will to get rid of them, with words if possible but otherwise with whatever more forceful methods are available.
The moral of the story: determined and irrational men often find it easy to reduce discussions and other social arrangements that rely on freedom and rationality to their level.
Tenured Radicals
The moral of the story: determined and irrational men often find it easy to reduce discussions and other social arrangements that rely on freedom and rationality to their level.
There is no way of getting rid of the tenured radicals – short of expelling them by invidious subterfuge. So they are left in situ and will inculcate another generation of students with postmodern “principles”.
Fading to irrelevance
The extreme relativists in literature and various ethnic/cultural “studies” programs are considered a laughingstock by everyone in the sciences and in the real world people with degrees in these subjects are considered, at best, fit for entry level careers in the restaurant business. That is, slightly less useful than those with degrees in theology.
They will slowly fade away as an ever smaller share of the higher education dollar is allocated to them.