Theoretical Mathematics vs Empirical Mathematics

In Intellectual Prudence: MetaIntellectual Analysis of Intellectual Subculture, I wrote that one of the problems of the intellectual tradition is:

Inattention to the cognitive problem posed by the difference between mathematics as an incorporeal conceptual order and mathematics as a predictor of the behavior of real physical systems (2 + 2 = 4 by the rules of the game mathematics, but 2 oranges + 2 oranges = 4 oranges is a falsifiable prediction about the future). Mathematics is not reality. It is a description of the possible relationships between real things.

Recently on the Scientific American website, Ted Grinthal wrote:

“Machines of the Infinite,” by John Pavlus, states that the “universe itself is beholden to the computational limits imposed by P versus NP,” the question of whether tough problems whose solutions can be quickly verified can also be quickly solved.
This is a common misunderstanding. Nothing in the real world (whatever that is) is constrained in any way by our mathematics, physical laws or anything else we invented. Mathematics is merely a useful tool created to describe the universe. When we find something that we can't calculate or describe with our math, it may be that we've found a limit or constraint on the universe; it could also be that we've found a limit or constraint to our mathematics. (Emphasis added)

The a priori concept of math—that math exists prior to the reality that we can see and touch—is first cousin to Plato's philosophical idealism, which was described in The Two Realms as follows:

To summarize, Plato taught that the [physical] table we think is real is an effect—in the parable of the cave a “shadow”—of a pre-existing immaterial template of the table. The template is usually referred to as a form (idea in Greek, producing the term philosophical idealism).

[Thomas] Cahill: In the Platonist model of knowledge, the real physical thing which you can see or touch is only an “appearance” generated by a hidden Form.

 Of philosophical idealism Aristotle said:
This form, which exists in the carpenter’s mind, is the formal cause of the table—but it can have no existence except in the carpenter’s mind and at length in his work. To speak otherwise—to say that there is an absolute Tableness floating somewhere that gives form to all particular tables—is “to speak abstractly and idly.” - Thomas Cahill, Sailing the Wine-Dark Sea: Why the Greeks Matter

Absent convincing evidence to the contrary, it is best to consider every deduction a concealed induction. The general principles of the theoretical approach (and of what was once called Theory) were arrived at by experience. They can in principle be falsified by a future experience.

The "problem of induction" is that what is demonstrated by experience can never provide metaphysical certitude. It can be certain for all practical purposes. We can even bet our lives on it (and we do, every day). But that perfect knowledge we would like to have is not attainable.

The error of Plato's abstract theory of reality is that it assumes that the real can start with deduction, escaping the provisional nature of the physical. This is an elemental intellectual error.

The First Six Months' Wrap

This might be subtitled "An Enlightenment Liberal Blog," and probably the most representative post would be The Liberal Founding, which said, among other things,

In this blog the term ‘liberalism’ means Enlightenment liberalism. Liberalism is substantially different from the outlook of the left, and from Marxism, progressivism, libertarianism, and conservatism (as Historian Fritz Stern writes, “Extremists of the right and the left have long attacked liberalism as their greatest enemy.”)

The knotty problem of the definition of liberalism is addressed by various posts which attempt to suggest the dimensions of a political philosophy which underlies the modern world, and which may represent humankind's best effort so far to address the problem of achieving liberty and justice for all: Defining Liberalism: Randall Kennedy's 'My Race Problem—And Ours'; Defining Liberalism: Hayek, Habakkuk and More; Defining Liberalism: Published Arguments for Liberalism; Defining Liberalism: An Overview; and Defining Liberalism: "Passing".

An unfriendly definition related by Charles K. Rowley:

Charles K. Rowley: In 1993, in his book, Post-Liberalism, [John] Gray poked around among the rubble of classical liberal philosophy to determine what, if anything was left. He concluded that none of the four constitutive elements of doctrinal liberalism — universalism, individualism, egalitarianism and meliorism (or human flourishing) — could survive the ordeal by value pluralism and that liberalism, as a political philosophy, therefore was dead. www.independent.org/pdf/tir/tir_01_1_rowley.pdf

There has also been an ongoing concern with our intellectual heritage, and the state of the academic humanities, as expressed in The Two Realms, Intellectual Prudence, and Intellectual Prudence: MetaIntellectual Analysis of Intellectual Subculture.

A perhaps related post was a retelling of "Oedipus Rex," This Is The Son of Kings, which attempted a reinterpretation of classical literary criticism on the topic of the most famous play of the ancient world.

A germane concern was Conscience and Language: Orwell, which noted, “Even a single taboo can have an all-round crippling effect upon the mind. … If one thinks fearlessly one cannot be politically orthodox.”

There were a number of posts on the presidential election of 2012: How Fares The Republic: The Liberal View of The Market; How Fares The Republic: The Post Truth Candidate; and How Fares The Republic: Movement Conservatism Cruelty. Related were: Mendacious Debater Disgraces Self: Media Call Him Victor; and The Third Debate: Mendacious Candidate Disgraces Self Redux.

And a post by an honorable Republican: Mitt's Father Articulates Republican Principles Before Goldwater.

There were various perhaps memorable quotes, including: Snippets 7/27/12:

I drink to our ruined house, to the dolor of my life, to our loneliness together, and to you I raise my glass, to lying lips that have betrayed us, to dead-cold, pitiless eyes, and to the hard realities: that the world is brutal and coarse, that God in fact has not saved us.

- Anna Akhmatova, in Red Square by Martin Cruz Smith

Molly Ball, who wrote:

“A smart [GOP] party strategist” ... wrote, “Bain was a critical part of the Romney image that just couldn't sell to enough voters in Ohio. He came off as the guy who got rich by buying your Dad's employer, firing your Dad, stripping down the business, and making hundreds of millions and buying jet-skis and houses with car elevators and dancing horses while your Dad visits the food bank and is forced onto unemployment. The Romney team should have known this was going to be a problem.” (Emphasis added.)

There were two articles addressing a little-known aspect of the civil rights revolution of the mid-twentieth century: In Retrospect: The Supreme Court and The Disabled; and Followup: Courts and the Civil Rights of the Disabled. In the latter a prosecutor noted:

There's case law out there regarding people commenting and gesturing against race and religion. But ... there's nothing out there regarding disabilities.

An early post wondered who now believes "that all men are created equal": The Condition of Equality Today, which cited, among others:

 [Conservatives] feel affection for the proliferating intricacy of long-established social institutions and modes of life, as distinguished from the narrowing uniformity and deadening egalitarianism of radical systems. For the preservation of a healthy diversity in any civilization, there must survive orders and classes, differences in material condition, and many sorts of inequality. The only true forms of equality are equality at the Last Judgment and equality before a just court of law; all other attempts at leveling must lead, at best, to social stagnation.
 - Russell Kirk,  “Ten Conservative Principles” (Emphasis added)

"Passing" Ctd.

With respect to the previous post, Defining Liberalism: "Passing", a reader of Andrew Sullivan's weblog wrote:

How would Foster being out of the closet have helped [gay people]? . . . This is extremely silly, collectivist, identity politics. Jodie Foster is an autonomous individual with her own ambitions, her own thoughts, and her own desires, as we all are. Just because she happens to share your and your friends’ sexual orientation does not make her part of your "community" in any meaningful way, and it certainly does not make her obligated to take up the cause of this [community] . . .

As the post on passing argues, "a liberal democracy . . . means complete freedom to live a private life so long as doing so does not infringe the rights and liberties of others."
 
[I elided the end of the reader's comment because I disagree with it. The reader concluded, "it certainly does not make her obligated to take up the cause of this community’s self-inflicted health problems" (my emphasis). "They asked for it?" No more than a multitude of voluntary activities which have downsides as well as upsides. The liberal spirit is a spirit of toleration, of being, as a version of the OED said, "generous in respect to the opinions, rights, or liberties of others." There is no place for what Frederick C. Crews called the "reckless dispensation of guilt."]

Defining Liberalism: "Passing"

Andrew Sullivan writes today, "Every gay person in the closet is an enabler of homophobia." Sullivan denies the right of the one who is different in some way to "pass" as part of the mainstream if he or she can.

This pains me, because for the last decade self-described conservative Sullivan's "Dish" blog has in many ways been a reliable guide to the liberal spirit in the public life of a democracy. But personal liberty in  a liberal democracy (see The Liberal Founding), while it encourages—and needs—public-spiritedness, means complete freedom to live a private life so long as doing so does not infringe the rights and liberties of others. (As Pericles' Funeral Oration notes, "And we live not only free in the administration of the state but also one with another void of jealousy touching each other’s daily course of life, not offended at any man for following his own humour, nor casting on any man censorious looks.")

It's a free country, and this means that Barry Goldwater gets to be an Episcopalian and Madeleine Albright gets to live as a gentile (when a media discussion arose concerning the fact that Albright is of Jewish descent, someone remarked, "She doesn't want to know from Jewish"). People of African-American descent who don't look black are free to just live as a person and need not deal every day with the identity issues which would arise if they did not pass as white. A gay actress (in this case Jodie Foster, the subject of Andrew Sullivan's article above) has no obligation to come out, and excellent reasons not to. The general roles Foster has played, and their conventional romantic scenes, probably wouldn't have been available to her if she had been out.

Privacy is a freedom of enormous value. Privacy means that one is free from being arbitrarily identified with some group, supposed to be in dire plight. It means that one is free from being saddled by others, or by what John Stuart Mill called "social tyranny," with an involuntary obligation to alleviate that plight. As Jim Sleeper observed in Liberal Racism, the assumption that each person of color is to be treated as a "racial delegate" is just wrong. Nor is Jodie Foster, or anyone else, to be involuntarily enlisted in the sexual orientation wars. It's a free country. We get to choose our battles, or no battles.

A signature difference between liberal and left is that liberal does not care about identity. As mentioned in these pages before, liberalism is public and civil. One's subculture, race, gender, religion or irreligion, esthetic taste, etc., may be freely enjoyed or ignored under the aegis of the liberal society, but are not otherwise of public concern. "We live . . . free," as Pericles said above.

In a liberal society the only identity that matters is that one is a citizen. A free citizen, not subservient to anyone or anything, unless in free and informed voluntary consent. As Immanuel Kant said in "What Is Enlightenment?" "Enlightenment is man's release from his self-incurred tutelage. Tutelage is man's inability to make use of his understanding without direction from another."

Intellectual Prudence: MetaIntellectual Analysis of Intellectual Subculture

Honest people just get out, leaving the field to those who don't mind deception or don't recognize it. - Linda Seebach, "Scientist Takes Academia for a Ride with Parody"

Last August's Intellectual Prudence discussed Literary Critic Frederick C. Crews' remark on the "Nietzschean scorn" often leveled by humanities intellectuals at what he called "intellectual prudence." Last week, in slate.com, Ron Rosenbaum warned "against the kind of grad school-nurtured exegesis of Shakespeare most egregiously represented by James Shapiro in the section of his book, 1599, wherein he purports to read Shakespeare’s mind and discover that Shakespeare would have wanted to cut, trash, delete, and disappear Hamlet’s final soliloquy; one of the high points of the play and of Shakespeare’s entire oeuvre." Rosenbaum concluded:

But grad school for literature, I can't advocate. I escaped Yale before it became the center of the frenzied fad for French literary theorists, as a result of which students read more about arcane metaphysics of language, semiotics and the like than the actual literature itself. But, even though many of the most sophisticated contemporary intellectuals who once bought into this sophistry (such as Terry Eagleton) have abandoned it, the tenured relics who imposed this intellectual regime are still there, still espousing their view that literature itself is only to be understood through their diminishing deconstructing lens. I can testify to it, having sat through enough seminars at the Shakespeare Association of America conferences to last a life time. Please don't waste your life this way.

Extreme as this may sound, it resonates with my own experience. I attended two humanities classes of a major state university the day after the historic presidential election of 2008, certain that there would be at least some reaction to the opening of the presidency to minorities. After all, isn't diversity a mantra of the academic left? But it was business as usual.
In Zen and The Art of Motorcycle Maintenance Robert Pirsig called the university the "church of reason," devoted to the disinterested search for truth. A church of reason would, as Socrates said, "follow the argument wherever it leads," without regard to the conventional wisdom or to social pressure. But the inhabitants of the faculty lounge are as much a subculture as any other, a vested interest which logically would be subject to sociological study in much the same fashion as an anthropologist studies the folkways of a stone age tribe. Such a meta-intellectual analysis of the intellectual would ask, as Crews once did, "Do Literary Studies Have an Ideology?"
But there is resistance to this. The Dissenter was once accused by a philosophy TA, in fact, of harboring the notion of a "meta-intellectual" examination of the way academic philosophy is taught. Anyone who did not realize that such a critique is self-evidently wrong, he implied, reveals intellectual inadequacy.
Much of what we consider the intellectual heritage violates the principles of the intellectual discipline. It is true that there are intellectuals who critique the intellectual tradition (Crews, Orwell, Popper—who spoke of "intellectualists"—and others) but the pressure not to break ranks is strong.
Here is a rough draft, written some time ago, critiquing Great Books-ism:

• Most of those who claim to participate in intellectual endeavors are metaphysically confused: 1. No clear concept of what the realm of the senses does and does not tell us; 2. Failure to distinguish between the kinds of knowledge afforded by nature, by the aesthetic, and by the mystical, and failure to distinguish between the knowledge methods applicable to each; 3. Using, impermissibly, metaphysical certitude as a standard of deductive proof; 4. Inattention to the cognitive problem posed by the difference between mathematics as an incorporeal conceptual order and mathematics as a predictor of the behavior of real physical systems (2 + 2 = 4 by the rules of the game mathematics, but 2 oranges + 2 oranges = 4 oranges is a falsifiable prediction about the future). Mathematics is not reality. It is a description of the possible relationships between real things.
• Iron age ontology and epistemology (i.e., Plato's philosophical idealism and such descendants as postmodernism)
• Inadequate definition of fact/truth
• Failure to examine the sociology of the great thinkers and of the intelligentsia
• Absence of meta-intellectual analysis
• Complacency about the reckless mind
• Inattention of the intellectual class to its own methodology. For example, are evidence and reason an indispensable starting point or simply one of many approaches which may be adopted?
• Treating propositions unworthy of critical inspection as if they were holy writ
• Reverse ad hominem; that is, treating the notions of canonical figures as indiscussable
• Failure to define the standards of the intellectual discipline
• Incoherence: Failure to recognize that two great, mutually inconsistent ideas cannot both be true
• Anti-intellectualism: Countenancing the notion that power can impose its own truth (cf. Nietzsche et al.)
• Anti-intellectualism: Failure to enforce a global prohibition on all argument by fallacy, including ad hominem
• Anti-intellectualism: Rejection of Kant's observation that a good will is the one indispensable intellectual quality, as all the others can be subverted to anti-intellectual and unethical ends
• Anti-intellectualism: Lack of comprehension that the intellectual realm defines an implied ethical order (cf. the cynicism of German idealism). As Benda cried, “humanity did evil for two thousand years, but honored good. This contradiction was an honor to the human species, and formed the rift whereby civilization slipped into the world.”
• The intellectual tendency to embrace esotericism and with it, elitism
• Crime against humanity: the Leo Strauss doctrine that intellectuals are the only humans that matter and therefore, as a kind of Herrenvolk, are entitled to treat the rest of the human instrumentally (as Kant said, as means only, and not also as ends).

Any one of these could in itself be the subject to one or more posts. However, "reverse ad hominem" may have a bearing on the lack of response to Obama's precedent-shattering election noted above. Where ad hominem purports to discredit a proposition by discrediting the person who propounds it, reverse ad hominem implies that a proposition is valid because of the greatness of its author.
For example, Plato, whom many humanities academics may consider the greatest thinker of all time, dismissed political democracy. It is quite possible that the historic election of 2008 was dismissed in the classes I witnessed because they were influenced by Plato's attitude toward democracy.
Does this seem preposterous? See "Scientist Takes Academia for a Ride with Parody", by Linda Seebach:

Physicist Alan Sokal of New York University meticulously observed all the rules of the academic game when he constructed his article on postmodern physics and submitted it to a prestigious journal of cultural studies called Social Text.
The people he cites as authorities in cultural studies are the superluminaries of the field, the quotations he uses to illustrate his argument are strictly accurate and the text is bristling with footnotes.
All the rules but one, that is: Sokal's article is a parody. Under the grandiloquent title "Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity," it appeared in the Spring/Summer 1996 special issue of the magazine, one entirely devoted to "the science wars," as the editors term the tension between people who actually do science and the critics who merely theorize about it. ...

Sokal's successful spoof calls into question the intellectual standards of the whole field.
If you're chuckling, but inclined to think it's just professors doing their usual angels-on-a-pinhead thing, please do think again. Tuition and fees at the priciest private universities run nearly $1,000 for each week of class. Taxpayers pick up a big chunk of the bill for public universities. Many of those classes are being taught, it appears, by professors who deny the distinction between truth and falsity and consequently can't distinguish double-talk from rational argument.
Maybe some of the junior professors and the graduate students do know what they're hearing is nonsense, but think it would be harmful to their careers to speak out. Living with such deception, possibly for a lifetime, is profoundly corrupting. Honest people just get out, leaving the field to those who don't mind deception or don't recognize it. ...
There is a political point to Sokal's demonstration, but it's not the right-wing one he's sure will be attributed to him. He's proud to call himself a leftist, and his resume includes a stint teaching mathematics at the National University of Nicaragua under the Sandinistas. "If you take up crazy philosophies you undermine your ability to tackle questions of public policy, like ecology," he said. "It really matters whether the world is warming up."
I don't remotely share Sokal's political views, but I agree with him that the corruption of clear thought and clear language is dangerous. And corruption has to be exposed before it can be cleaned up.

One might also note that Thomas Jefferson was horrified by what he found in Plato, noting that "Education is chiefly in the hands of persons who, from their profession, have an interest in the reputation and the dreams of Plato. They give the tone while at school . . . "

I amused myself [recently] with reading Plato's Republic. I am wrong, however, in calling it amusement, for it was the heaviest task-work I ever went through. I had occasionally before taken up some of his other works, but scarcely ever had patience to get through a whole dialogue. While wading through the whimsies, the puerilities, and unintelligible jargon of this work, I laid it down often to ask myself how it could have been that the world should have so long consented to give reputation to such nonsense as this? How the soi-disant Christian world, indeed, should have done it, is a piece of historical curiosity. But how could the Roman good sense do it? And particularly, how could Cicero bestow such eulogies on Plato? Although Cicero did not wield the dense logic of Demosthenes, yet he was able, learned, laborious, practiced in the business of the world, and honest. He could not be the dupe of mere style, of which he was himself the first master in the world. With the moderns. I think, it is rather a matter of fashion and authority. Education is chiefly in the hands of persons who, from their profession, have an interest in the reputation and the dreams of Plato. They give the tone while at school, and few in after years have occasion to revise their college opinions. But fashion and authority apart, and bringing Plato to the test of reason, take from him his sophisms, futilities and incomprehensibilities, and what remains?In truth, he is one of the race of genuine Sophists, who has escaped the oblivion of his brethren, first, by the eloquence of his diction, but chiefly, by the adoption and incorporation of his whimsies into the body of artificial Christianity. His foggv mind is forever presenting the semblances of objects which, half seen through a mist, can be defined neither in form nor dimensions. * * * Socrates had reason, indeed, to complain of the misrepresentations of Plato; for in truth, his dialogues are libels on Socrates. - Jefferson writing to John Adams