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 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.

Continue reading

The Alphabeticity of Nations

Dear Representative Pelosi:

My wife and I are stalwart Democrats seeking advice.  We are planning an elaborate summer tour of several nations, some of them transatlantic, and we would like to know the correct order in which we should visit those nations.  Here are some questions that we hope you can answer. –

Supposing that we planned a visit to London, should we list that on our itinerary as a trip to Britain or a trip to England?  In either case, if we wished also to visit Edinburgh, in Scotland, would we need to visit either Britain or England first?

If we listed our London and Edinburgh destinations as the United Kingdom rather than Britain, England, or Scotland, would we need to visit Serbia, Slovenia, or Ukraine first?  And does the Byelo in Byelorussia count, or is it the same, by your reckoning, as Russia?  Again, how should we count Abkhazia, were we to visit there?  Is it subsumed alphabetically by Georgia?

When visiting Finland, should we list it as Suomi, as Finns call their nation, and touch base Somalia first?

In what order might we correctly visit the different places called Georgia?

Finally, on a related topic, which bathrooms should we use when visiting the autonomous region of Trans-Dniester?

We are sincerely yours,

Mr. and Mrs. Qwerty

An Ogre Hates My Patch of Blue Sky

“Once religious imagination and yearning have departed from a culture, the lowest, grimmest, most tedious level of material existence becomes not just one of reality’s unpleasant aspects, but in some sense the limit that marks the ‘truth’ of things.” (David Bentley Hart, In the Aftermath (2009)

For years I have had a recurrent daydream.  It may have originated as a sleeping dream, but it is now a staple of my waking imagination.  This daydream steals over me whenever I feel myself slipping under the anesthetic of a committee meeting, or I am forced to wander through a wasteland of what Hart calls “epic drabness,” or I am closeted with a vampiric atheist who invites me to loosen my collar and close my eyes.  With this daydream, my imagination proposes that all of these experiences are, at bottom, one and the same experience.  I am of a romantic disposition, so I take the propositions of my imagination very seriously. Continue reading

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