THE PLATONIST FILE: You might be a Platonist if...!

TUESDAY, SEPTEMBER 11, 2018

Timeless lack of clarity:
Friend, are you a Platonist? You might be a Platonist if you adhere to certain "beliefs."

Maybe you've found yourself thinking that "numbers and circles have a perfect, timeless existence independent of the human mind."

Perhaps you've come to believe that "the truths of mathematics are determined by the reality of mathematics"—more specifically, "by the nature of the entities that make up that reality."

Granted, those are fuzzy claims, at least as presented. But such fleeting thoughts may serve as signs of incipient Platonism.

Borrowing from Professor Foxworthy, You might be a Platonist if...—if you believe such puzzling and/or apparently vapid claims. Beyond that, you may be part of a slightly embarrassing, mildly endearing human story—a story which has been unfolding for several millennia now.

We mention Professor Foxworthy, a resident scholar at Humorist U., because this is, in large part, an ongoing comical story. Indeed, if it weren't for all the warfare and killing which accompany the intellectual dysfunction of our upper-end intellectual elites, we could call it a comical story and leave the matter right there.

Who is Professor Foxworthy? This professor, searching for fun, has often employed this formulation: "You might be a redneck if..."

After presenting that formulation, the professor has told a series of jokes. Like his forerunner, Professor Irwin Corey, the professor has done this for fun.

That's what one resident scholar has done, though only in search of amusement. Concerning the loftier question—the question of whether you might be a Platonist—well, that largely ridiculous question emerges from a more consequential tale.

Friend, are you a Platonist? Depending on how you want to score it, it's possible that no one is—but some of our leading intellectual lights apparently say they are. We base that claim upon this passage from Jim Holt's well-reviewed new collection of essays, When Einstein Walked With Godel: Excursions to the Edge of Thought:
HOLT (page 8): Gödel entered the University of Vienna in 1924. He had intended to study physics, but he was soon seduced by the beauties of mathematics, and especially by the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind. This doctrine, which is called Platonism, because it descends from Plato’s theory of ideas, has always been popular among mathematicians...
It's Holt who was willing to define Platonism as "the notion that abstractions like numbers and circles had a perfect, timeless existence independent of the human mind." To us, that formulation seems to exhibit a perfect, timeless lack of clarity. But there it sits, right near the start of Holt's robotically-praised new book!

Friend, you might be a Platonist if you find yourself advancing that fuzzy claim or quite a few others much like it. And if you are, it seems that you'll never walk alone!

According to Holt, this supposed doctrine "has always been popular among mathematicians." This claim also appears in Goldstein's earlier book, the book Holt was reviewing back in 2005, when he penned this version of the title essay from his current book.

Warning! "Philosophy" done by mathematicians may be a bit like shortstop play as done by 350-pound left tackles. That is to say, even the most brilliant mathematician may not be especially skilled at the types of rumination which fall under the traditional rubric of "philosophy"—and judgments about this fuzzy "doctrine" would certainly land on that pile.

Alas! Each Thanksgiving, your Uncle Charlie, who you otherwise love, may prove to you, at the dinner table, that he may not be the most expert political analyst in the land. That doesn't necessarily mean that he isn't a wonderful uncle.

A similar type of situation may imaginably obtain when those perfervid mathematicians succumb to a bout of philosophizin', however brilliant they may be in their principal field.

As we saw last week, Holt is the fellow who offered that first, remarkably fuzzy account of Platonism. The second account we've cited above comes from Goldstein, a highly-regarded philosophy professor who wrote the 2005 general interest book, Incompleteness: The Proof and Paradox of Kurt Godel.

That second, tautological-sounding definiton seems to be lurking here::
GOLDSTEIN (page 44): Godel's commitment to the objective existence of mathematical reality is the view known as conceptual, or mathematical realism. It is also known as mathematical Platonism, in honor of the ancient Greek philosopher...

Platonism is the view that the truths of mathematics are independent of any human activities, such as the construction of formal systems—with their axioms, definitions, rules of inference and proofs. The truths of mathematics are determined, according to Platonism, by the reality of mathematics, by the nature of the real, though abstract entities (numbers, sets, etc.) that make up that reality...
Friend, do you believe in "the objective existence of mathematical reality," whatever that perfect, timeless bowl of salad is supposed to mean? You might be a Platonist if you adhere to such murky ideas!

Now that we've had our transient fun, let's get down to brass tacks. Let's go where the rubber meets the road, where the reader will surely think this:

The reader may be inclined to assume that we're being unfair to Goldstein and Holt, each of whom is praised as a highly skilled authority figure by members of our lightly-skilled upper-end mainstream press corps.

The reader may be inclined to assume that Holt and Goldstein went on, in their respective works, to offer fuller, clearer accounts of this "doctrine. A decent, fair-minded reader may be inclined to make that assumption. We'll explore that assumption all week.

Above, we've offered shards of explication by Goldstein and Holt. Sadly, you might be an Aristotelian if—if you assume that these widely praised writers went on to explain "Platonism" in a capable manner.

More precisely, you may be another victim of the misconception we'll describe as Aristotle's error—of the self-admiring supposition that "man [sic] is the rational animal."

Stating the obvious, no rational person would leave those fuzzy accounts of Platonism laying there all by their lonesome, with no further attempt at clarification. You may assume that star writers like Goldstein and Holt, proceeding onward from there, produced explications of this alleged doctrine which are amazingly clear.

It would be natural to assume such a thing. It would also be wrong.

To what extent are we humans really "the rational animal?" To what extent do our rational abilities, such as they are, really define our essence?

In our own studied view, that timeless doctrine from Aristotle "surrounds the actual working of [human nature] with a haze which makes clear vision impossible." It may disperse the fog to spend a few days studying the efforts made by Goldstein and Holt to make the Platonist doctrine more clear, with mathematician G. H. Hardy thrown in.

Aristotle is said to have said that we humans are "the rational animal." At least over here in the western world, this doctrine lies at the heart of the way we've tended to define ourselves, rather plainly seeing ourselves from afar.

By way of contrast, Professor Harari has said that we came to rule the world through our chance acquisition of a less lofty set of skills. Friend, you may be seeing things Harari's way by the end of our current file.

Tomorrow: As cited by Holt, 2 + 2 = 4!

39 comments:

  1. "The reader may be inclined to assume that we're being unfair to Goldstein and Holt, each of whom is praised as a highly skilled authority figure by members of our lightly-skilled upper-end mainstream press corps."

    These authors are not "authority figures". They are accomplished professors in their field of expertise. They have years of training following by years of research. That makes them experts, not "authority figures." People believe them because of their expertise, not because they are anointed leaders.

    Somerby claims that their description of Platonism is fuzzy. He never explains what he means by that. I find their description of Platonism clear. So, the burden is on Somerby to make his case that we are following blindly and not simply agreeing with and understanding these authors.

    Presumably, Somerby's case that we are failed apes depends on the lack of clarity of these authors too. I don't see that either. We have come very far from hunter-gatherer societies. We did that using some faculties beyond the other apes. Their existence is manifest in our current lives. Somerby needs to say a lot more if he is going to convince anyone that we don't think.

    ReplyDelete
    Replies
    1. A "good" philosopher though is able to kick up a whole bunch of dust and then complain that he cannot see.

      That is the question though, is the explanation unclear or is the particular reader just a nidiot?

      Once upon a time I was in a microeconomics class and the TA explained a shifting demand curve. Seemed as simple as Simon to me in the back row, but some girl in the second row raised her hand and said "I don't get it".

      So the TA took another ten minutes trying to explain it in even more excruciating detail. At which point the girl said "I still don't get it" and he started to explain it again, but at that point I exited stage right.

      On the other hand, I was trying to help my roommate with physics and he said "I don't understand that." and I was thinking "understand? What is to understand? There's the formula. You commit that formula to memory and then when you take a test you plug numbers into the formula and get the answer. Who understands? Certainly not me."

      Later on though, when I was ten years out of school and taking the GRE I could no longer remember the formula for the angle on a standard polygon. So I had to derive it from what I knew about triangles and squares.

      Seems to me that in the academic world, often we just pretend to understand, and they also pretend to teach. If they fail at their task, they give you a bad grade.

      Delete
    2. Here is what you do as a TA or teacher when a student says "I don't get it." You identify the point where they are stuck ("Which part don't you get?"). You explain just that part in a different way. If that doesn't work, you tell the student to come see you during office hours (or after class) and you move on, so the rest of the class doesn't get bored.

      Not everyone pretends to understand and just memorizes things. That approach isn't actually learning. If you pretend to teach where I worked, you lose your job. This is more true now when most faculty are adjunct and there is always someone to replace you.

      If you don't understand something at the college level, you keep at it until you get it. Because your ability to do the rest of the course work frequently demands it. You should fail if you don't do this.

      The bad grade is for achievement, not effort. The teacher is a resource, someone to ask questions of, not someone to drum learning into your head if you have no interest in the subject. If you are willing to simply memorize, you are showing no interest. It is the student's responsibility to learn, not the teacher's.

      The academic world does not reward pretending to understand. It rewards persistence until understanding is achieved. Better that you did not go on in academia. Those who become teachers are self-motivated people who pursue ideas for interest. Blaming them for your disinterest isn't fair or the right explanation for your failure to learn.

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  2. Mathematical Platonism seems to me like much of the rest of math - true but trivial.

    Examples of the truths of mathematics would be
    1. 2 + 2 = 4 (yes)
    2. the area of a circle is pi r squared
    3. the circumference of a circle is 2 pi r
    4. the 31st digit of pi is 5

    Is it not also true that those truths are objective and timeless and independent of human activity?

    Humans can discover those truths, but they cannot change them. Also, they were true 1,000 years ago and 1,000,000 ago and will seemingly be true a billion years from now. They were true before, during and after the big bang.

    The Platonist looks at that and believes that, because they are so timeless that they are MORE real than the actual physical reality which is in a constant state of flux, so much so that you cannot even step into the same river once.

    2 + 2 = 4 is more real than the dagger I see before me. First, because the dagger may not even exist. I might be imagining it all in my fevered, pressured, guilty mind. Or I could be hypnotized to believe there is a dagger before me, or I could be in the matrix with a computer program firing my neurons such that I believe there is a dagger before me.

    Even beyond all that, if the dagger is really there, it is in a constant state of flux. Given enough time it will rust or its molecules will otherwise merge with its surroundings. As such, the bare dagger, although it currently exists and has the power to seemingly end the heartache and thousand natural shocks that flesh is heir to...It has a mere transitory existence. As such, it is not, they would say, as real as the number two which has no such limitations.

    Even numbers, in this vale of tears, do not have the perfect existence as they do in math. In math I can have 12 and that is what it is, dammit. Here in the real world though, twelve is not so perfect. If I get the damned Indian out of the way, I can count that there are 12 pringles cans in my cupboard.

    But how can I be sure, in a world that's constantly changing? Do they weigh the same? If a Platonic ideal can of Pringles is 158 grams (although I do not see how that is more ideal than a 400 gram can which is far less likely to be emptied in an afternoon.) A precise measurement might show then that I really have 12.1 cans of Pringles or that I sadly have a mere 11.9999998 cans (dammit! No wonder I ran out!)

    To an idealist, this is a mere approximation, a mere shadow of the underlying ideal reality from which it is derived. To fans of Madonna though, this is ridiculous since we happen to be living in a material world where real daggers can accomplish a lot more than imaginary ideal numbers can (and pay no attention to all the math that is used in the modern process of manufacturing daggers.)

    Doubtless that clears everything up and now there are tweets we could be discussing or op-eds or maybe Serena Williams or Colon Cancernik or something. Something real.

    ReplyDelete
  3. Many scientists are realists and materialists. That doesn't change anything at all about what they discover, are able to prove about the world. It changes only their personal views, which are separate from scientific findings, data, theories.

    ReplyDelete
  4. Aristotle believed many ridiculous things. He thought women had fewer teeth than men (couldn't he just count them?). He thought that some people deserved to be enslaved. He thought that eels, flies, lice spontaneously generated from inanimate materials (didn't reproduce). He didn't believe in evolution any more than Plato did. He put the earth at the center of the cosmos. He supported many of the current superstitions of his society.

    Somerby needs to weep for Aristotle, not use him as a surrogate critic of the rest of humanity.

    ReplyDelete
  5. Bob, a Philosophy major, says, even the most brilliant mathematician may not be especially skilled at philosophy

    I would turn this around and say, even the most brilliant philosopher may not be especially skilled at mathematics

    IMHO Godel's Incompleteness Theorem is part of mathematics. Analyzing it from a philosopher's POV is not the best way to understand it.

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    Replies
    1. Somerby isn't analyzing it from any point of view. He is criticizing it because Godel became mentally ill. He is criticizing the authors who wrote about Godel too. He hasn't grappled with the theorems at all. I don't believe he is capable of it.

      Anyone can be a critic. But here, Somerby has only succeeded in making himself look stupid.

      For giggles, imagine Trump trying to join this conversation.

      Delete
    2. It's not just Trump. For some reason, the Presidents and Presidential candidates who we choose seldom know much about math and science. I would love to see a President who had studied these subjects, but that doesn't seem to be what the voting public wants.

      Delete
    3. Well, Gore knew something about climate science.

      Hillary supported science and science funding more than any candidate before her and more than Obama.

      We have some economists and engineers who have been presidents. That comes close.

      Delete
    4. A bunch were soldiers, the rest mostly lawyers:

      https://www.infoplease.com/history-and-government/us-presidents/presidents-occupations

      Delete
    5. Gore took almost no math or science in college. As a grad student he studied Theology.

      Delete
    6. And yet he won a Nobel prize for his film on global warming.

      Delete
    7. The Nobel Peace Prize has been notoriously political. E.g., Barack Obama won that prize for being elected President while having black skin. Gore's movie was excellent propaganda, but it had a number of scientific flaws. Gore did not win a Nobel Prize for any field of science.

      Delete
    8. I don't think Obama won the Nobel Prize just for being elected President while having black skin. I think he won the Nobel Prize because he was elected President of the United States of America while having black skin. Big difference.

      Delete
  6. Jeff Foxworthy was never a professor.

    Yes, Somerby is creating a literary conceit, but he demonstrates his contempt for professors in general when he places Foxworthy in that category.

    Somerby says: "Indeed, if it weren't for all the warfare and killing which accompany the intellectual dysfunction of our upper-end intellectual elites, we could call it a comical story and leave the matter right there."

    Warfare and killing are not instigated by professors, except perhaps the teachers at Westpoint and Annapolis. The so-called intellectual elite don't start wars -- they try to end them. Politicians engage in wars after diplomacy fails. Neither of those jobs are filled by professors. They are mostly filled by lawyers, another profession that tends to negotiate conflict.

    Somerby might as well be blaming architects for starting wars, or engineers, or poets, or comedians.

    I am really disliking Somerby these days.

    ReplyDelete
    Replies
    1. A former professor of law at the University of Chicago expanded a war in Afghanistan and instigated a war in Libya.

      Delete
    2. 1;11,
      Despite that, the GOP hated him because he was (part) black.

      Delete
  7. Somerby asserts that Goldstein's description of mathematical Platonism is a "bowl of salad" without offering any reason why. There are two underlying questions: 1) what is mathematical Platonism, and 2) is Goldstein's description accurate? Somerby not only doesn't answer those questions; he doesn't even pose them.

    But there is a third question: is Goldstein's description an accurate reflection of what Gödel believed? Of course, Gödel's thoughts on the subject are available to anyone who is interested. But instead of being interested, Somerby apparently wants to emphasize Gödel's mental illness to show that even our greatest logician was, contra Aristotle, not rational. Again, Somerby does this without the slightest reference to what Gödel himself said on the matter of his Platonism.

    If even our greatest logician was irrational and ill, what hope is there for the rest of us schlubs? That seems to be Somerby's argument, such as it is, in a nutshell.

    What kind of grades did Somerby get in his philosophy classes? One wonders. If you turn in a paper on Plato's idea of Forms that simply says "Plato is saying nothing but word salad", you would get an "F." The professor might even accuse you of handing in utterly unserious drivel.

    ReplyDelete
  8. Somerby likes to revel in his anti-intellectualism, the kind that says "Your explanation doesn't make sense to me, therefore your explanation doesn't make sense."

    ReplyDelete
  9. For a different take on Homo Sapiens vs Neanderthals debate:

    Climate Change Likely Iced Neanderthals Out Of Existence

    https://www.smithsonianmag.com/smart-news/modern-humans-didnt-kill-neanderthals-weather-did-180970167/#u1RTxRA887v7CdJe.99

    ReplyDelete
  10. I think Somerby's revulsion at fuzzy accounts of Platonism are a form of racism.

    ReplyDelete
    Replies
    1. This has basically turned into a hate site.

      Delete
  11. You might a mathematician, if you understand math...

    ReplyDelete
  12. Take five.

    https://www.youtube.com/watch?v=vmDDOFXSgAs

    ReplyDelete
  13. I'd take into consideration the intended audience. What Plato called the divided line, or the duality of material vs intelligible reality, might be a bit of overload for a general audience.

    Numbers and mathematics, exist without mass, dimension, or location, yet seemingly have their own laws. So they are the best arguments for the existence of the intelligible. I can easily imagine that inspiring a mathematician.

    ReplyDelete
  14. Oh, Mr. Somerby, by your argument Kurt Gödel’s good friend Albert Einstein must also have been a “Platonist”, in that he likewise asserted the ‘reality’ of his mathematical constructions... which to many lay complainers back then and even today likewise “exhibit a perfect, timeless lack of clarity.”

    Of course, as paralleled by comments above, that represents a limitation of those complainers’ understanding, not a flaw in Einstein’s work.

    ReplyDelete
  15. Numbers might be said to have an independent existence, but it's actually a matter of dispute. Consider the example given above, C = pi*r^2. Well, pi is pi within base 10. It's a different number in any other base. Each base is a human creation. It's all calculable and consistent within the domain of human reasoning. That doesn't mean that it exists as an independent entity outside the human mind.

    You can talk about truths as being timeless--fine. However, if you want to consider mathematical objects, such as circles, numbers, limits, derivatives, variables, and so on, these have value especially as objects that model the world in which we live. To say that they exist independently of the human mind is a dubious proposition. They are the best model we have, and we certainly couldn't do physics and engineering without them. But their value, again, comes in their very precise capability to model and describe the world in which we live.

    Also, mathematics doesn't have any laws apart from those assigned to it by the human mind. When you get much more deeply into mathematics, you find that many problems exist at the fundamental level of basic assumptions. Mathematicians commonly define these problems away. A simple example is zero to the zero power, defined as 1. There are many good arguments that zero to the zero equals zero, but this leads to inconsistencies with other accepted facts, so mathematicians define away the problem by simply saying that zero to the zero = 1.

    For example, see:

    http://www.askamathematician.com/2010/12/q-what-does-00-zero-raised-to-the-zeroth-power-equal-why-do-mathematicians-and-high-school-teachers-disagree/

    Is that some sort of eternal truth? Hardly. But it works and that's what counts.

    ReplyDelete
    Replies
    1. I'm not arguing that numbers prove the existence of the intelligible; I said they are the strongest argument in favor (that I know of). Plato himself considered the existence of the One no more than a working assumption, yet it was the basis for his entire system.

      Delete
    2. Emerson Marlowe > “... C = pi*r^2. Well, pi is pi within base 10. It's a different number in any other base.”

      Er, no, pi is pi, the same number (numeric value), whether within base 10, base 12, base 16, base 8, base 2, or any other base you care to use.

      It will of course be represented as a different endless string of non-repeating digits in each of those bases....

      You do understand that binary (base 2) “10” is the same number (numeric value) as decimal “2”, not decimal “10”, right?

      So likewise, all those different bases’ representations of pi, despite using different digits, are still the same number, not “a different number” in each base.

      Delete
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