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...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!
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...
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!