Tom Wolfe

 

Tom Wolfe, who died May of last year at age 88 quipped:

‘I think every living moment of a human being’s life, unless the person is starving or in immediate danger of death in some other way, is controlled by a concern for status.’

 


Perhaps Aretha Franklin prefers ‘Respect’.

Wolfe got my attention with his ‘The Painted Word’ way back in the ’90’s, an incisive take on the New York Art Scene. You couldn’t miss him walking down Madison Avenue in his bespoke white suits [‘Neo-Pretentious’, he called it].

‘A  Satirist is just a highbrow Populist-hence his attacks on Modernist Art’-snarled the literary crowd.

Contemporary urban Indians have a more finely calibrated radar for hierarchy and status than almost any other culture I know. Wolfe would have been in tune.

The Turing Machine

 

Alan Mathison Turing [1912-1954]A Turing Machine is a device that uses a set of rules to work a list of symbols on a length of tape.

And it was the progenitor of the idea that became the modern computer. Or more accurately, what we call ‘Software’.

Kurt Godel’s paper was published in 1930. Within a decade, Alan Turing applied Godel’s work using the Self-Eating Expression to solve issues fundamental in the birthing of Modern Software [‘Undecidability’; The’Halting Problem’, 1937]. And Academic Departments went about marveling at the quirkiness of ‘Strange Loops’.

Both Godel and Turing reach for variants of the Self-Eating Expression to seal their respective proofs [I have not read Turing’s paper but have been told that this is accurate]. So why not just start with the opening Self-Eating Expression: ‘I don’t exist!’ It’s a lot more fun to work with than the cryptic symbols of these two pioneers.

What is it with brilliant Logicians who see too far? Why are the deities of Consistency and Rule so indifferent to their first-born? Godel died from self-imposed starvation, according to the coroner; Turing, from cyanide poisoning.

‘The Mathematical Truth of the Century’

 

As noted earlier, the Self-Eating Expression comes alive from the shadows anytime something is used on itself, anytime we are wading, knowingly or otherwise, into the swamp of the Self-Loop.

If the early philosophical links with the West were Greek, the first mathematical links were Italian. The development of the Concept of Zero, its Western intellectual foundations, begin with Guiseppe Peano [1858-1932] and Fibonacci [1170 1240; ‘The Greatest Western Mathematician of the Middle Period’].

Now, Bertrand Russell and Alfred Whitehead wanted to produce a founding Bible that built up the rules of Mathematics from the ground-up. So they began with Peano’s work and titled their opus Principia Mathematica. [Latin titles are always dangerous, vide Wittgenstein and his Tractatus Logico Philosophicus.]

The wreck of this Titanic, the Principia Mathematica, on the Godel iceberg is common knowledge among pop. mathematicians and I’ll limit myself to the outlines.

Everything went along fine until they entered the zone of Set Theory [again founded by Peano]. Its most prolific user was the celebrated Professor Georg Cantor in his construction of various types of ‘Infinities’. And in Set Theory they hit head-on into the Self-Loop. [I chuckle, when I think how Cantor mocked Immanuel Kant, one remarkably alert to the Self-Loop, as a mathematical ignoramus.]

In 1952, Harvard University awarded the pioneering Logician Kurt Godel an Honorary Doctorate for: ‘ The discovery of the most significant mathematical truth of the century’ for his paper: ‘ On formally undecidable propositions of Principia Mathematica and related systems.’

Godel proved that the consistency of any Formal System cannot be proven using the methods of that System without simultaneously violating the basis of consistency of that System itself. [ Where have we seen that before?]

Godel discreetly states in a footnote to his paper: ‘Any Epistemological Antinomy, such as the ‘Liar’s Paradox’ could be used for a similar proof’. ‘The Liar’s Paradox’ is the famously confusing declaration by Epimenides the Cretan who pronounced: ‘All Cretans are liars!’

The proof of ‘The most significant mathematical truth of the century’-lay in a Self-Eating Expression. But Kurt Godel was shaking things up at a deeper level. What was the flower of Peano’s seed?

Following his discovery a professor of mathematics summarizing Godel’s work solemnly intoned: ‘[Godel’s Theorem] ‘requires that the ultimate foundations of Mathematics and all its derivative truths remain a mystery’. [In other words: ‘We don’t really know what we are doing, but we are doing it anyway’.]

Less kindly, it suggests that all Mathematical Modeling cannot be differentiated in any provable way from a manufactured reality in indeterminate Self-Loop.

Are Logico-Mathematical truths intrinsic, hard-wired into Nature? Or are they a man-made convenience, a modeled-understanding of Self and World?

Get to True Nothing and find out for yourself.

 


The ‘Liar’s Paradox’, venerated but winked away in Logician’s circles, is a paradox only because we don’t know if Epimenides is a liar or not. He is neither, for the phrase is a Self-Eating Expression. This might be more transparent if: ‘All Cretans are liars’ is replaced with: ‘All Words are false’ which denies you the ability to extract yourself out of the loop and pronounce on its truth or falsity.

The Limits of Legitimate Expression

 

Tautology and Contradiction are the Logico-linguistic limits of the legitimate expression. They mark the boundary of the sensible. Go past that boundary and you are in absurdist territory.

Respectable folks largely live in the zone between Tautology and Contradiction, the mapped terrain of ‘Conventional Understanding’ [vyavharasatya].

Worthwhile Teaching however [and there is not much of it around], begins at this border and moves outward into zones of ever-increasing Absurdity.

To search within the limits of the familiar and the sensible is to look for your lost keys under the lamp-post, ‘because that’s where the light shines’.

 


The metaphor of the light under the lamp-post goes back to early Sufi literature but has been appropriated as the ‘Streetlight Effect’ by modern Academia.

None of what follows is dependent on you agreeing to this particular marking of boundary. We can define it in other ways, but I have found this boundary most reliable. But we need to define a boundary because the mystics and the obscurantists have had a field-day in the literature by keeping it undefined.

Russell: ‘The Foundations of Mathematics’

 

This subject called Mathematics, in fact it’s larger family, the complex of Analytics that fall under the banner of Logico-Mathematical Method, is erected on multiple pillars. If they shake an inch the entire structure will swing by a mile. So it’s a good idea to step down with a flashlight and take a look at these foundations every now and then.

The first and most important is the pillar labeled with the little word ‘ Is’ [we will get to it in the Posts, by-and-by]. The second of the pillars is the Principle of Contradiction.  And the third, often ignored, is the concept of the Tautology.

Here is Professor Bertrand Russell:

It is clear that the definition of ‘Logic’ or ‘Mathematics’ must be [newly] sought..[we must] no longer be satisfied [defining] logical propositions as those that follow from the Law of Contradiction..[but] must admit a wholly different class of propositions..[that] all have the characteristic which we
agree..to call Tautology.

For the moment, I do not know how to define ‘Tautology’..I know of none that I feel to be satisfactory, in spite of feeling thoroughly familiar with the characteristic of which a definition is wanted.

At this point, therefore, for the moment, we reach the frontier of knowledge on our backward journey into the logical foundations of Mathematics.’

Honest and finely crafted lines from the co-author of Principia Mathematica. In English: ‘The  ‘[Foundational] Principles of Mathematics’.

 


In the early part of the last century, Cambridge Analytic Philosophers, lead by Bertrand Russell [Wittgenstein wrote his Doctoral Dissertation under him, if I recall] and bewitched by the Rational, had tried hard to anoint it as the only true God. And they had thought long and hard about the meaning of words like ‘Tautology’. Kurt Godel’s work, among others, ended their ambitions for good.

As a teenager growing up in Madras [now, Chennai], I spent my free afternoons at the British Council Library mainly because it was free, air-conditioned and always had pretty girls visiting from the neighboring college.

And the library carried all his books [he won a Nobel for Literature]. And I must have read everything the good professor ever wrote. [I admired his courage: ‘Traitor to Class and Country’]. He was a hero to my youth.

Wittgenstein: ‘The Dissolution of Symbols’

 

The Wittgenstein family in Vienna, summer 1917. From left, siblings Kurt, Paul, and Hermine Wittgenstein; their brother-in-law, Max Salzer; their mother, Leopoldine Wittgenstein; Helene Wittgenstein Salzer; and Ludwig Wittgenstein.

Here is Ludwig Wittgenstein from his Tractatus Logico Philosophicus, a seminal text on the Philosophy of Logic:

The Tautology is unconditionally true; the Contradiction is in no condition true…the Truth of Tautology is certain, of Proposition possible, of Contradiction impossible.

Tautology and Contradiction are without sense..Tautology leaves to Reality the whole infinite logical space; Contradiction fills the whole logical space and leaves no point to Reality.

Neither one of them therefore can in any way determine Reality..(They) are the limiting case of the combination of symbols, namely their dissolution.

[The latter Wittgenstein, older, wiser, and burdened with a remarkable intellectual integrity, walked away from his youthful fire; but that is another long story.]

 


O.K. So what in heaven’s name is a ‘Tautology’? I’m glad you asked. For strictly speaking, we don’t know.

What is a Contradiction? We are not too sure either.

But here are examples of what we think they mean:

‘It is raining’ is a proposition. You can verify its truth by looking out the window. ‘It is raining or not raining’ is a Tautology: it’s truth, a Logician would say, is certain. ‘It is both raining and not raining’ is a Contradiction: it’s truth, a Logician would say, is impossible.

‘It is neither raining nor not-raining’ however is Sweet Nonsense. The Logician does not see the need to dignify it with a comment [we’ll meet up with it again on the way to Śūnyam.]

Never-Never Land

 

The Principle of Contradiction, the criterion for Logico-Mathematical ‘Proof’, itself has no proof, cannot be proven in a rational framework.

If ‘All things are False’-so is the claim: ‘All things are False!’ If ‘Nothing is True’- so is the declaration: ‘Nothing is True!

But hold on just a second. To say; ‘Nothing is True!’ is not a lie. In fact, I have no idea what it is. For I am firmly in the grip of the Self-Loop.

The principal defense of the Principal Principle, Aristotle’s ‘Self-Destroying Argument’ is contained in a Self-Eating Expression.

In Aristotle’s words: ‘The beginning of demonstration cannot [itself] be demonstrated..those who insist on being refuted by argument seek the impossible; for in insisting that they be proven to be self-contradictory, they already contradict themselves..’.

So why should you not violate the Principle of Contradiction?

You should not violate the Principle of Contradiction because if you violate the Principle of Contradiction you thereby contradict yourself and thereby violate the Principle of Contradiction.

Never-Never Land.

 


The Contradiction Principle becomes the ‘First Principle of Analytic Cognition’ when, and only when, the cognition begins on the presumption of an Independent and Separate ‘Self’. Question that, and as the anxious Physicist warned: ‘you question everything’.

The Self-Destroying Argument includes ‘positive terms’ such as ‘All Things are True’. This will ultimately get you to True Nothing, but it is the longer and more confusing route.