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[1] 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?”[2] In German this is called Entscheidungsproblem – the decision problem.[3]

Turing found that he could answer this question by framing it in terms of a Turing machine[4] – 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.”[5]

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Apparitions of the Gods

Gods 01 Muses by Andreas Mantegna (1496)

The Muses (1496) by Andreas Mantegna (1431 – 1503)

“The dove – the rood – the loaf – the wine.”

Men know the gods because they have seen or intuited them, but not all men have seen or intuited the gods, and some men are incapable of seeing or intuiting them.  The gods, moreover, sometimes disguise themselves so as to test men, or they appear in and as omens and auguries, which the dull of mind and the wicked of heart invariably either miss entirely through their mental obtuseness or, through self-serving prejudice, blatantly misread.

I. The gods appear in and as their attributes, which again only those who have vested themselves in the proper lore and the requisite discipline can correctly interpret. Who would see the gods must enjoy a gift of pre-attunement, even before he bows under the discipline and engraves the lore in his heart that will let him see them. Such a man is called a poet.  The ancient Boeotian teller of the gods, Hesiod, whom scholars assign to the late Eighth Century or early Seventh Century BC, bears a name that means simply “The” (he or hos) “Poet” (aiodos), suggesting that the Boeotians, or at least those of them in the vicinity of Mt. Helicon, recognized his special talent and accorded him the status owing thereto.  That status may claim itself paramount because the community must communicate with the gods, just as the gods must communicate with the community, and an efficient go-between nicely serves the requirement both ways.  One misthinking modern school argues through Hesiod’s name that any particular poet is a non-existence, as though no one could write a poem, as though poems constituted themselves, authorless, and as though therefore no one really ever saw Hesiod’s gods or heard them speak.  This thesis of a literary fantasy amounts, however, merely to another kind of noetic obtuseness.  Someone wrote Hesiod’s poems, obviously, and if Hesiod were the invention of that someone then that someone nevertheless would have seen Hesiod’s gods – through his invention, as it were, and taking Hesiod’s name, but equally in a vision such that the seeing must guarantee its own authenticity and such that He remains The Poet.

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Our Dreams of the Implicate Order

On the walk from my office to the train a week ago last Monday, I reflected on the fact that I had all day been curiously alive to moments from my past. In part this was due to the fact that it was my birthday, and people from every era of my life were reaching out to wish my happiness. But other factors were at work, too. I ran into a blog post that linked to a recording of Allegri’s Miserere Mei – one of the most sublime works ever written – and vividly remembered singing it as a boy, and so enacting Heaven. A story I had told my little granddaughter the day before, about the time when I was only four, and went camping with my Dad, and woke up unable to find my way out of the mummy sleeping bag, so that I tried to stand up and get his help, in the process falling down the steps out of the open forest shelter (and almost into the fire he had started), made me chuckle again. So did the memory of her reaction: “Silly Poppy!” I began to remember lots and lots of things from long and not so long ago – some of them tagged (oops!) for later use in the confessional – and suddenly as I walked the moments all crowded in upon me at once. Not in a chaos or a hurry, but as it were quietly, softly.

It was no stampede. Rather, it was a stately pavane.

Suddenly I staggered, thunderstruck by a completely unexpected notion: what if those moments *really were* immediately present to this one? What if I could feel that moment of suffocated terror in the mummy bag as if it were still happening? Clearly, I could: all that I had to do, in order to make that happen, was simply attend to it carefully enough, and without distraction. It might take a few moments of concentration, but if I wanted to I could, I knew, bring back any moment I wanted with as much clarity and intensity as I wished.

Then – this was the strike of the thunder – I thought: “That’s what dreams are like; and it is the way things really are; for, in Eternity, and to Eternity, everything (whether actual or not) is all at once together.”

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Upstate Consolation University Celebrates First Graduating Class in New Degree Program


College Graduate in Educationally Mismatched Job

“Higher education is not about knowledge or skills,” says Upstate Consolation University Executive Deputy Chancellor of the Committee on Investor Communications Marl Flaybiter from behind the large mahogany desk in his office overlooking West Campus’s scenic Green Parking Lot; “no – higher education is about respect.”  A few years ago, on being appointed to his incumbency, Flaybiter began noticing how little respect graduating degree-holders from UCU were receiving when they entered the job market and presented their credentials to prospective employers.  While escorting potential investors around Uppchoock-on-the-Lake, the small, northerly city where his institution is located, Flaybiter observed that many of the service personnel in the local coffee bars and chain restaurants were recent UCU graduates.

Flaybiter counts off the many types of prestigious UCU-granted degrees held by these disrespectfully under-employed new alumni: “At least three of those kids – bright kids – had come out of our Social Justice and Sustainability Programs; five or six had bachelor’s or bachelorette’s degrees in Women’s Studies, and others came from Adventure Education, Puppet Arts, Safe Space Organizing, Slut-March Planning, and Critical White-Privilege Sciences.”  Flaybiter pauses to shake his head sorrowfully.  “I just couldn’t bear to see those kids – I mean, those young people – so shamefully disrespected by having to work as baristas, cashiers, waiters, and waitresses while living in their parents’ basements and going to work in their pajamas.”  As Flaybiter sees it, “The mismatch between the education and the job is, well, a tragedy, not just for the kids, and not just for the pajamas, but for the community.”

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When God is Dead, Rationalists Accept Contradictions to Fill the Void

Goedel’s Theorem is an application to mathematics of Aristotle’s thesis that thinking relies on first principles and that first principles are unprovable assumptions. This means that faith and hope are ineradicable features of human existence even in the exact sciences. The briefest summary of the implications of Goedel’s Theorem and the necessity for first principles is the notion that not everything that is true can be proven to be true.

Goedel’s Theorem states that an axiomatic system can be consistent and incomplete, inconsistent and complete, but never consistent and complete. Eternal verities can only be proven in relation to other eternal verities. Axiomatic systems exist on the rational plane of thought. Their rationally approximate and unprovable nature is due to their ultimate reliance on transcendent truths described in Plato’s realm of Forms. For instance, people contrast earthly justice with perfect justice, though the latter has never been instantiated in the physical realm. This implies some intuition of perfect justice, though no one has ever experienced such a thing.

Positivists and post-modern relativists are likely to regard each other as opposites. More than likely both will be liberals and in most cases share a contempt for religion and any notion of transcendence. As rationalists, they will also most likely reject emotional attachment to and especial preference for family, tradition, community, culture and the local physical landscape. The modern liberal instead is committed to being a citizen of the world and welcoming to all comers, no matter their basic hostility to the ethos of the host culture.

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The Illogicality of Determinism – Further Considerations

This article is now available at the Sydney Traditionalist Forum. Among other things, I argue that if physical determinism were true, then the appearance of intelligent behavior and the fact that car accidents, for instance, are the exception, not the rule, would be a mystery. Determinists typically want to banish God and consciousness – that is, our ordinary subjective experience of freely thinking, evaluating, deciding and having purposes – yet end up imbuing The Big Bang, by logical implication, with many of the properties of both God and consciousness, including omniscience, omnipotence, benevolence, purpose, intention and desire.

The link is The Illogicality of Determinism – Further Considerations.

It is a follow up to The Illogicality of Determinism.

And it is related to The Reflexive Problem in Analytic Philosophy – Illogical Logicians.

The Reflexive Problem in Analytic Philosophy: Illogical Logicians


Analytic philosophers either accept or regard as perfectly reasonable two philosophical contentions that violate logic and common sense: determinism and the denial of consciousness. Arguing for determinism implies free will and in denying the existence of consciousness the philosopher is using the very thing he says does not exist. In this article published by the Sydney Traditionalist Forum, I argue that this is a result of certain interesting psychological and emotional deficits, a commitment to materialism and atheism, the “philosophy as the handmaiden of science” notion and the very methods and approach used by analytic philosophers. These methods include conceptual analysis and arguments considered as words on a page or monitor – looking at internal coherence and validity – but overlooking the reflexive implications for the person doing the analysis.

This results in risible performative contradictions; a notion absent from the logical toolbox of analytic philosophers as far as I know.

The Reflexive Problem In Analytic Philosophy: Illogical Logicians