Chaos and Order; the right and left hemispheres

Chaos and Order; the right and left hemispheres

In The Master and His Emissary, Iain McGilchrist writes that a creature like a bird needs two types of consciousness simultaneously. It needs to be able to focus on something specific, such as pecking at food, while it also needs to keep an eye out for predators which requires a more general awareness of environment.

These are quite different activities. The Left Hemisphere (LH) is adapted for a narrow focus. The Right Hemisphere (RH) for the broad. The brains of human beings have the same division of function.

The LH governs the right side of the body, the RH, the left side. With birds, the left eye (RH) looks for predators, the right eye (LH) focuses on food and specifics. Since danger can take many forms and is unpredictable, the RH has to be very open-minded. Continue reading

Gödel’s Theorem (revised)

Kurt Gödel[1] was a Platonist,[2] logician and mathematician who developed the intention of making a profound and lasting impact on philosophical mathematics. His next task was to think of something! Amazingly, at the age of twenty five, he achieved his goal, publishing his incompleteness theorem.

Godel and Einstein

Kurt Gödel and Einstein

A good friend of Albert Einstein’s, Einstein once said that late in life when his own work was not amounting to much, the only reason he bothered going to his office at the Institute for Advanced Study at Princeton was for the pleasure of walking home with Gödel.

John von Neumann wrote: “Kurt Gödel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel’s achievement.”[3]

While at university, Gödel attended a seminar run by David Hilbert who posed the problem of completeness: Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system? Continue reading

The Halting Problem – there is, definitively, more to thinking than computation

Alan Turing

Alan Turing

Kurt Gödel’s Incompleteness Theorem was inspired by David Hilbert’s question “Are the axioms of a formal system sufficient to derive every statement that is true in all models of the system?” Hilbert played the same role regarding Alan Turing’s proof of the halting problem. Hilbert had asked: “Is there some mechanical procedure [an algorithm] for answering all mathematical problems, belonging to some broad, but well-defined class?”[1] In German this is called Entscheidungsproblem – the decision problem.[2]

Turing found that he could answer this question by framing it in terms of a Turing machine[3] – could there be a program that could determine whether any other arbitrary computer program and input would eventually stop or just loop forever? This was called the halting problem.

“Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist.”[4]

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Writing about Literature Revisited (Coleridge)


“In Xanadu did Kubla Khan…”

I wrote previously about student responses in my “Writing about Literature” course to Percy Shelley’s famous sonnet “Ozymandias,” which I set them to interpret on the basis of workshops in identifying the formal and meaningful  elements of poems.  Last week I set the same students to write up in class an interpretation of Coleridge’s “Kubla Khan” (1797), a rather more challenging poem than “Ozymandias,” although Shelley proved challenge enough, but at the same time possibly easier to interpret because its phantasmagoria allows for considerable play on the part of the reader.  Coleridge’s poem has its origin in a bizarre and unrepeatable incident.  In September 1797 while a house guest of his friend William Wordsworth, who had taken him in because he found himself in a phase of indigence, Coleridge one morning took a dose of opium, as was his wont, and fell into a visionary trance.  A major ode of some two hundred lines manifested itself to Coleridge, complete, during the psychedelic phase, and as he returned to ordinary consciousness he began to transcribe it.  At that moment, one of Coleridge’s creditors came knocking loudly at Wordsworth’s door, and in the shock of hearing it, the majority of those two hundred finished lines slipped away from the poet’s grasp into oblivion.  Coleridge could rescue only thirty-six lines, which constitute Part I of the poem as it was published, finally, in 1816.

The poem appears in its paradoxical truncated entirety below. –

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Look on my works, ye mighty, and despair!


“Half sunk, a shattered visage lies.”

My department pays me fairly handsomely to teach a particularly futile course – one among no few others – that styles itself as “Writing about Literature.”  The course is futile at both ends: Public education produces nowadays only an uneducated public, many individuals of whom, including those who are invited to college or university to matriculate, write only at the level of functional illiteracy; and none of whom has ever read anything that might qualify as literature.  I approach the course as a fully remedial one because that, in effect, is what it must be.  Dedicating the first half of the semester to “writing about poetry,” I offer up as fare for mental nourishment short poems, mostly sonnets, by writers of the Romantic generations of the late Eighteenth and early Nineteenth Centuries.  I run the class-sessions as workshops in careful reading, or close reading, for which a sonnet by William Wordsworth or Samuel Taylor Coleridge or John Keats or Percy Bysshe Shelley is meet.  I ask the students to begin by noticing the periods or full stops that divide the poem into its sentences and to notice, for example, that, in verse, lines and sentences do not necessarily correspond, so that their interaction must be carefully worked out.  I ask them to notice the grammatical features of each poem.  In what person is the poem couched?  Whom does the speaker address?  What setting is implied? What argument does the speaker make in his sequence of figures and images?  I want students to see that language can function at a higher level than it does in a campus newspaper article or in the instructions for the latest cell phone.  Readers of poems must slow down their thought processes so as to notice everything and they must let the poem provoke them into thinking word by word and line by line.

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Plato’s Cave

Plato’s Cave

Plato’s allegory of the cave appears in Book VII of Plato’s most famous and longest dialog, The Republic. Plato’s dialogs frequently star Plato’s teacher Socrates as a character. The dialogs involved discussions and philosophical arguments between various characters, some of whom were based on real people. Plato particularly disliked the sophists who were professional rhetoricians and who seemed to care more about money and social success than truth. In fact, Plato accused them of teaching their students how to make the worse argument appear better – enabling their students to convict the innocent and set free the guilty.

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Linguistic Subscendence

Dunce - Let's Play Dunce

No Caption Necessary

It is the end of the term, so my life consists of tall stacks of student papers, which I must read and evaluate.  A number of patterns – or maybe a better term would be grammatical de-patternings – have forced themselves on my attention.  There is, for example, the almost invariable “they” employed as the subsequent of a singular subject in a sentence.  A half-dozen of these, at least, appear in every four-page theme, even in papers written by English majors.  Twenty years ago, in a journal article, I referred to this as gemination – the one and only child miraculously becomes a set of twins.  Many among the English professoriate no longer bother to correct this, but I do, insistently.  While English is a latitudinous language in terms of its regularity, the logic of its pronominal system is rigorous.  Someone is, precisely, one, not two people or more.  Ditto anyone, everyone, and no one or none, the last being the contraction of its syntactic precursor in the sentence.  In the real world, neither a person nor the man can suddenly become they or them.  To write so, however, is surely to think so; and to think so is bad arithmetic even in the first grade.  It is perhaps not an unrelated fact that when I give my students the instruction to subtract the number of questions they answered wrongly on the quiz from the total number of questions and to post the result as their score – they reach that result with glacial slowness through grimacing, dull effort.

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Philosophical Skeleton Keys: The Ontological Priority of Wholes to Parts

I struggled for several decades to understand composite wholes (organisms, organs, ecologies, societies, and so forth (not to mention molecules, atoms (in the Rutherfordian sense rather than the Democritean), cells, organelles, hadrons, etc.)) as deriving from and completely explained by the interactions of their constituent parts, until I finally realized that it simply can’t be done. Such “explanations” inevitably invoke the whole they are trying to explain as an obscure feature of their parts. They are, i.e., somehow or other circular. This is why honest and careful materialism *just is* eliminative.

The derivation must run the other way, if we are to understand either wholes or their parts. And once we run the derivation in the proper direction, taking the whole as itself an ontological real independent of its parts, and prior thereto, and furthermore definitive thereof, why then all sorts of vexing problems that simply cannot be solved under the terms of materialist modernism – the mind/body problem, in particular – simply vanish. There are to such ontological holism furthermore all sorts of interesting consequences, that tend to validate both our quotidian experience and the deliverances of traditional supernaturalism.

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The Narcissism Test: Reality. Who Needs It?

Some people exhibit an amazing lack of interest in reality, content to imagine living in a wholly invented world. The notion that much of subjective experience is illusory is strongly connected with the beginnings of “modern” philosophy.



Galileo and Locke claimed that only things which are physical and measurable really exist. Galileo argued that primary qualities; solidity, motion, figure, extension and number were really real – being the objective properties of objects and that secondary qualities; color, sight, sound, small, taste and touch did not actually exist per se. They are merely artifacts; products of the sense organs that really have nothing to do with the objects being perceived. They are merely what our brains do when confronted with sensory input and primary qualities.

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Materialist Reduction *Just Is* Elimination

To say that the organism is nothing but its atomic constituents – taking “atom” in its original Democritean sense, as the most basic and indisintegrable component of all corporeal objects – is to say that in itself it is nothing. It is to say that there is in fact no organism at all, but rather only atoms.

For anyone trying to understand anything more complex than atoms, this is obviously an unsatisfactory result. It eliminates all such complexities ontologically. If everything is nothing but atoms, then there are no such things as organisms, or societies, or ecologies, or watersheds, or even vortices, winds, currents, crystals – or, indeed, atoms in the modern, Rutherfordian sense, or for that matter protons on the one hand, or molecules on the other. What’s worse, there are then no such things as the minds and thoughts of organisms such as we. In that case, there is no such thing as the system of thoughts that constitutes materialist reduction. Having devoured all science, the doctrine devours itself.

Like all evil ideas, materialist reduction reduces in the end, and logically, to the ultimate absurdity: nothingness.

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