E-mail addresses: apat1erson@gmail.com, m1p1t@yahoo.com
Research areas: Noncommutative Geometry, Hegelian Philosophy, Mathematical Philosophy
Contents
1. My Books 2. Recent Conference talks 3. Research interests 4. Recent mathematical research papers (with files) 5. Recent mathematical/Hegelian philosophy research papers (with files) 6. Some Quotations
1. My Books
Amenability, by Alan L. T. Paterson, was published in 1988 by the American Mathematical Society in their Mathematical Surveys and Monographs Series, Number 29, 452pp.. ISBN: 0-8218-1529-6. Second edition, paperback, came out in December, 2000.
Groupoids, inverse semigroups and their operator algebras, by Alan L. T. Paterson, was published in 1999 by Birkhäuser and is Volume 170 of their Series: Progress in Mathematics, 290 pp. ISBN: 0817640517.
2. Recent talks
Analysis Seminar, Iowa State Mathematics Department, 03/27/2008, Talk Title: Asymptotic morphisms and the families index theorem.
Iowa State University Mathematics Colloquium, 03/25/2008, Talk Title: The index theorem from an analysis perspective.
Southeastern Analysis Meeting, Vanderbilt University, 03/06/2008, Talk Title: The families index theorem without embedding.
Groupoidfest 07, University of Iowa, 11/03/2007, Talk title: The E-theoretic descent functor for groupoids.
Great Plains Operator Theory Seminar, University of Nebraska, 5/16/2007, Talk title: Exactness for the groupoid functor.
Workshop on ``Groupoids in operator algebras and noncommutative geometry'', Institut Henri Poincare, Centre Emile Borel, University of Paris, France 02/26/2007-03/02/2007. Talk title: The E-theoretic descent functor for groupoids.
Groupoidfest 06, Arizona State University, 11/11/2006, Talk title: A definition of ``groupoid action'' on a C*-algebra.
3. Research interests
My main mathematical research interest is in the area of Noncommutative Geometry. Central in all of this is the concept of a C*-algebra, which can be thought of as an infinite dimensional generalization of the matrix algebras: while matrices act on finite dimensional inner product spaces, C*-algebras act as algebras of bounded operators on complete, infinite dimensional inner product spaces (Hilbert spaces). The main motivation for C*-algebras arose in quantum mechanics out of the Heisenberg uncertainty principle, which is an expression of the fact that the position and momentum observables do not commute. Here the observables are no longer conceived in terms of functions (for these commute) but in terms of non-commuting operators on a Hilbert space. Noncommutative Geometry is largely the creation of the great French mathematician and Fields medallist, ALAIN CONNES, and it extends to the noncommutative context an astonishing range of ``commutative'' mathematics, not just in the study of C*-algebras and von Neumann algebras, but also in ``noncommutative'' algebraic topology (KK-theory, E-theory and cyclic cohomology), noncommutative differential geometry (such as the quantized calculus), noncommutative index theory (involving, for example, the C*-algebras of foliated spaces and groupoids) and the noncommutative geometry of particle physics and string theory. The classical vehicle for symmetry - the group - is no longer adequate to deal with the symmetry structures that arise in noncommutative geometry. Instead, one has to use a generalization of the group concept called a groupoid. My particular field of interest is in groupoid theory and its associated index theorems. The reader is referred to Alain Connes's web page http://www.alainconnes.org/ , from which his famous book Noncommutative geometry (1994), his recent book with Matilde Marcolli, and many of his papers, can be downloaded. I am currently working on developing an approach to the families (more generally, to the groupoid) Atiyah-Singer index theorem using the Connes-Higson asymptotic morphism of E-Theory. Two elegant proofs of the index theorem have been given, using this asymptotic morphism. The first is by Alain Connes in his book, and it involves the tangent groupoid. Another approach is given by Nigel Higson (http://www.math.psu.edu/higson/) and the immediate objective is to extend his approach to the families context. (The original families index theorem was proved by Atiyah and Singer in their 4th paper: one uses a continuous family of elliptic operators rather than just a single one, and the index lies in the K-theory of the parameter space.)
My main philosophical interest lies in developing a new philosophy of mathematics based on self-referential logic. The thought of such a logic initially appears rather strange, but in fact, close inspection of the ``paradoxes'' of modern mathematical logic - in particular, in model theory and the Gödel incompleteness theorems - show, I believe, that underlying normal mathematics and its logic is such a self-referential logic. Indeed, this inescapable self-referentiality in mathematical logic was pointed out by Gödel himself in one of his papers (see infra). The most profound, well-developed classical logic of this kind is that of the Wissenschaft der Logik written in the early 1800's by the great German philosopher, G. W. F. HEGEL, and this is studied and developed in my papers. Unfortunately, the mathematics discussed by Hegel is pre-Cantorian (for he lived well before the time of Cantor), and much work is still required to develop a self-referential philosophy of mathematics in a manner that will give a satisfactory philosophical basis for present day mathematics. There are many traces of a self-referential logic operating in human culture and science, and this indicates for me that such a logic is fundamental to human thought and experience in general rather than just to mathematics. It is my long term plan to develop this logic beyond mathematics and develop a philosophical basis for other fields, notably for science, religion, ethics and aesthetics.
Recent Research Papers (many with WORD/PDF files)
4. Mathematical papers
The E-theoretic descent functor for groupoids, preprint, April 2007, 21 pages. descenthom6.pdf
(with A. T. Lau) Amenability properties for group actions on von Neumann algebras, Indiana University Mathematics Journal 55(2006), 1363-1388. 2787.pdf
(with Amy E. Welch) Tychonoff's theorem for locally compact space and an elementary approach to the topology of path spaces, Proceedings of the American Mathematical Society 133(2005), 2761-2770. tychonoff3.pdf
The equivariant analytic index for proper groupoid actions K-theory, 32(2004), 198-230. Index10.pdf
The Fourier algebra for locally compact groupoids, Canadian Journal of Mathematics 56(2004), 1259-1289. falg6.pdf
The Fourier-Stieltjes and Fourier algebras for locally compact groupoids, Contemporary Mathematics 321(2003), 233-237. memfour.pdf
Graph inverse semigroups, groupoids and their C*-algebras, Journal of Operator Theory, 48(2002), 645-662. graph.pdf
The analytic index for proper, Lie groupoid actions, Contemporary Mathematics 282(2001), 115-135. jsrc.pdf
Continuous Family groupoids, Homology, Homotopy and Applications, 2(2000), 89-104. families.pdf
(with Roger Smith) Higher dimensional amenability for operator algebras, Transactions of the American Mathematical Society, 349(1997), 1919-1943. Highamen.pdf
Virtual diagonals and n-amenability for Banach algebras, Pacific Journal of Mathematics, 175(1996), 161-185. cohom3.pdf
Invariant Mean Charaterizations of von Neumann Algebras, Indiana University Mathematics Journal, 41(1992), 233-252. invarvN.pdf
(with A. T. Lau) Inner amenable locally compact groups, Transactions of the American Mathematical Society, 325(1991), 155-169. inneramen.pdf
Invariant mean characterizations of amenable C*-algebras, Houston Journal of Mathematics, 17(1991), 551-565. invarcs.pdf
5. Mathematical/Hegelian Philosophy papers
The Hegelian Concept and set theory, 15 pages, 2007.
A modern Hegelian Philosophy of Special Relativity, 32 pages, 2006.
Hegel's Early Geometry, Hegel Studien 39/40, 2004/2005, 61-124. Heggeom7.doc , Heggeom7.pdf
G. W. F. Hegel: Geometrical Studies - translated with Introduction and Notes, preprint, 2007, 33 pages.
Does Hegel have anything to say to modern mathematical philosophy?, Idealistic Studies 32:2, 2002, 143-158. sjp6.doc , sjp6.pdf
The Successor Function and Induction Principle in a Hegelian Philosophy of Number, Idealistic Studies 30 (1) 2000, 25-61. inductio.doc , inductio.pdf
Frege and Hegel on concepts and number, 22 pages. nnfregh.doc , nnfregh.pdf
Self-reference and the natural numbers as the logic of Dasein, Hegel Studien 32(1997), 93-121. HEGSTUFR.pdf
Towards a Hegelian philosophy of mathematics, Idealistic Studies, 27(1997), 1-10. TOHEGFF.doc , TOHEGFF.pdf
6. Some Quotations
That in the end
I may find
Something not sold for a penny
In the slums of Mind.
That I may break
With these hands
The bread of wisdom that grows
In the other lands.
For this, for this
Do I wear
The rags of hunger and climb
The unending stair.
[Ascetic, Patrick Kavanagh]
Few live for the sake of eternity.
But if the passing moment makes you anxious
Your lot is terror and your house precarious!
[Osip Mandelshtam, 1912, in: Osip Mandelshtam: Selected Poems, trans. James Greene]
Small doubt, small enlightenment; big doubt, big enlightenment. [Zen koan]
A very popular error: having the courage of one's convictions; rather it is a matter of having the courage for an attack on one's convictions!!! [Friedrich Nietzsche]
Our first question about the value of a book, of a human being, or a musical composition are: Can they walk? Even more, can they dance? ... Almost always, the books of scholars are somehow oppressive, oppressed; the ``specialist'' emerges somewhere - his zeal, his seriousness, his fury, his overestimation of the nook in which he sits and spins, his hunched back. ... No, my scholarly friends, I bless you for your hunched backs. And for despising, as I do, the ``men of letters'' and culture parasites. And for not knowing how to make a business of spirit. And for having opinions that cannot be translated into financial values. And because your sole aim is to become masters of your craft ... with uncompromising opposition to everything that is semblance, half-genuine, dressed up, virtuoso-like, demagogical ... [Friedrich Nietzsche, The Gay Science, 366]
[On prophets and poets]
[On prophets and moral hypocrisy - Joseph Brodsky’s comment on the furious reaction of the Moscow intelligentsia to the publication of the memoirs of Nadezhda Mandelshtam (which, among other things, charged them with virtual complicity with the Stalinist regime).]
There is something in the consciousness of literati that cannot stand the notion of someone’s moral authority. They resign themselves to the existence of a First Party Secretary or a Führer, as to a necessary evil, but they would eagerly question a prophet. This is so, presumably, because being told that you are a slave is less disheartening news than being told that morally you are a zero. After all, a fallen dog shouldn't be kicked. However, a prophet kicks the fallen dog not to finish it off but to get it back on its feet. The resistance to those kicks, the questioning of a writer’s assertions and charges, come not from the desire for truth but from the intellectual smugness of slavery...
[Excerpts from: Nadezhda Mandelshtam (1899-1980) – an obituary, by Joseph Brodsky]
Once there were the prophets whom we couldn’t shut up, lacerating us with their relentless ``Thus saith the Lord’’; then there were the poets, whose pitiless probings exposed our hollowness, and who didn’t seem to care in the least about hurting our feelings in the process; but now there are the public relations experts, seemingly affirming, in their ``mission statements’’, a saintly ``dedication’’ to our welfare, soothing our worries with cliché’s, sensitive about our ``comfort level’’, assuring us that we are like ``family’’ (pronounced with a long ``ah’’) and easing themselves into the parent role, smilingly trading their placebos for money, and tenderly ``nurturing'', for the next time, the growth of our emptiness as if it were a young plant.
Come, my friend, let us turn aside from our agitated grazing in this future-driven world of trickery, material plenty and spiritual vacuity, and feed instead on the astringent, genuine sustenance of the ignored poets.
*****
Poetry may make us from time to time a little more aware of the deeper, unnamed feelings which form the substratum of our being, to which we rarely penetrate; for our lives are mostly a constant evasion of ourselves. [T. S. Eliot]
It is difficult to get the news from poems
yet men die miserably every day
for lack of what is found there. [William Carlos Williams]
Look around — there’s only one thing of danger for you here — poetry. [comment made by the 20th century Chilean poet, Pablo Neruda, terminally ill with cancer, while his house and grounds were being searched by the armed forces of the Chilean general and dictator, Augusto Pinochet]
[Abuse of Power]
I have often heard it said that cowardice is the mother of cruelty. [Montaigne]
[Osip Mandelshtam (1891-1938) was a Russian poet who protested against Stalin. He died on the way to a labor camp in Eastern Siberia. His brave wife Nadezhda managed to evade capture by the NKVD, and preserved her husband’s work by memorizing it, the written word being dangerous. Here is Osip’s bitter poem on Stalin which caused his first arrest. The ``mountaineer’’ metaphor evokes the image of Stalin’s climbing to power over piled up bodies, and, rather than caring for the welfare of the people, the terrifying, thrilling, enjoyment that the tyrant, his ``leaders'', and their equivalents further down the chain of command, always get from crushing people.]
We live, deaf to the land beneath us,
Ten steps away no one hears our speeches,
But where there's so much as half a conversation
Then the Kremlin's mountaineer will get his mention.
His fingers are fat as grubs
And the words, final as lead weights, fall from his lips,
His cockroach whiskers leer,
And his boot tops gleam.
And around him a rabble of thin-necked leaders – fawning half-men for him to play with.
They whinny, purr or whine
As he prates and points a finger,
One by one forging his laws, to be flung Like horseshoes at the head, the eye or the groin.
And every killing is a treat
For the broad-chested Ossete.
[Osip Mandelshtam, Ode to Stalin, trans. Max Hayward.]
[Warning about uncritical, passionate embracing of (apparently) attractive causes: when, in 1951, the Mexican poet and diplomat, Octavio Paz, published in an Argentinian magazine an article on the horrors of the Soviet labor camps. it was greeted by his fellow Latin-American ``radicals'' with public silence and private abuse.] When I consider Aragon, Eluard, Neruda, and other famous Stalinist writers and poets, I feel the gooseflesh that I get from reading certain passages in the Inferno. No doubt they began in good faith. How could they have shut their eyes to the horrors of capitalism and the disaster of imperialism in Asia, Africa and our part of America? They experienced a generous surge of indignation and of solidarity with the victims. But insensibly, commitment by commitment, they saw themselves become tangled in a mesh of lies, falsehoods, deceits and perjuries, until they lost their souls. They became, literally, soulless. This may seem exaggerated: Dante and his punishments for some wrongheaded political views? Who nowadays, anyway, believes in the soul? I will add that our opinions on this subject have not been mere errors or flaws in our faculty of judgment. They have been a sin in the old religious sense of that word: something that affects the whole being. Very few of us could look a Solzhenitsyn, or a Nadejda Mandelshtam, in the eye. That sin has stained us and, fatally, has stained our writings as well. I say this with sadness, and with humility. [Considering Solzhenitsyn: Dust after Mud, Octavio Paz (essay in: On Poets and Others, 1986)]
[The ``peak of fame'' as the peak of shame. (The climbing metaphor evokes the ``Kremlin mountaineer'' above, but to varying degrees, has, I believe, a much wider significance.)]
``Well, step aside, old man!
We are young, which means, right ...’’
``Where are you going, youngsters?’’
``To the peak of fame ...’’
``Hold on! I too clambered up there,
gouging out steps with an ice ax,
till I became a sculpture of ice,
glorified, but unloved. And is this my peak? No smoke, no flame, neither a kind word, nor a sprig of green,...
It's not true, that upward means ahead. Even when palaced with gold,
to hell with the top,
where tin cans and condoms freeze in the ice.
On the peak of fame
there’s a faint smell of murder ....
When, half hidden in clouds,
murderers ascend to power,
dismembered corpses
are concealed in their rucksacks...’’
``Trying to spoil our mood, old man?!’’
``For your general enlightenment.
The peak of fame easily changes to a peak of shame....
There are colossuses on the peak of shame,
so icy, only made of clay –
plasticine kings wretchedly disintegrating.
There, like frozen spittle,
decorations and medals,
those sordid throwaways,
are given to cowards with contempt.
In its graveyard of rusted crowns –
both of Ancient Rome and Russian empires,
there are piles of names and banners,
eaten by the moth of infamy.
It’s dangerous when fog deceives the eyes
to confuse labels foolishly,
shamefully calling a peak of decay a peak of blossoms.
When will we rid ourselves of all this clambering and sweating of our infamous degradations, and squalid false summits?''
``Old man, are there really no true summits?’’
``There are. Young people, they’re ahead of you.
But together we’ll accomplish more.
I’m going with you, with the young.’’
[From The Peak of Shame, by Yevgeny Yevtushenko, The Collected Poems, 1952-1990]
The lesson we learn from history is that we cannot keep our liberty secure by relying alone on the good faith of men with great power. [Walter Mondale]
Thou shalt not follow a multitude to do evil; neither shalt thou speak in a cause to decline after many to wrest judgment ... Thou shalt not wrest the judgment of thy poor in his cause ... Keep thee far from a false matter ... And thou shalt take no gift: for the gift blindeth the wise, and perverteth the words of the righteous. [Exodus, Chapter 23]
. . . for she [nature] can so inform
The mind that is within us, so impress
With quietness and beauty, and so feed
With lofty thoughts, that neither evil tongues,
Rash judgments, nor the sneers of selfish men,
Nor greetings where no kindness is, nor all
The dreary intercourse of daily life,
Shall e'er prevail against us, or disturb
Our cheerful faith, that all which we behold
Is full of blessings. [William Wordsworth, Lines composed a few miles above Tintern Abbey]
What is hateful to you, don’t do to your fellow man – that’s the whole Torah and the rest is just commentary. Go then and learn it. [Response of Rabbi Hillel when asked if he could summarize the whole Torah while standing on one foot]
The darksome statesman, hung with weights and woe,
Like a thick midnight-fog, mov'd there so slow,
He did nor stay, nor go;
Condemning thoughts — like sad eclipses — scowl
Upon his soul,
And clouds of crying witnesses without
Pursued him with one shout.
Yet digg'd the mole, and lest his ways be found,
Work'd under ground,
Where he did clutch his prey; ....
[Excerpt from: The World, Thomas Vaughan, 1622-1695]
[Aristotle on friendship and the bad man] And wicked men seek for people with whom to spend their days, and shun themselves; for they remember many a grievous deed, and anticipate others like them, when they are by themselves, but when they are with others they forget. And having nothing lovable in them they have no feeling of love to themselves. Therefore also such men do not rejoice or grieve with themselves; for their soul is rent by faction, and one element in it by reason of its wickedness grieves when it abstains from certain acts, while the other part is pleased, and one draws them this way and the other that, as if they were pulling them in pieces. If a man cannot at the same time be pained and pleased, at all events after a short time he is pained because he was pleased, and he could have wished that these things had not been pleasant to him; for bad men are laden with regrets.
Therefore, the bad man does not seem to be amicably disposed even to himself, because there is nothing in him to love; so that if to be thus is the height of wretchedness, we should strain every nerve to avoid wickedness and should endeavor to be good; for so one may be both friendly to oneself and a friend to another. [Nicomachean Ethics, Book 9, 1166b, The Complete Works of Aristotle, ed. Jonathan Barnes] How the people will cry out against me! I hear from afar the shouts of that false wisdom which is ever dragging us onwards, counting the present as nothing, and pursuing without a pause a future which flies as we pursue, that false wisdom which removes us from our place and never brings us to any other. [Jean-Jacques Rousseau, Émile.]
[Silence and Speaking]
I was dumb with silence, I held my peace, having no good things to say, and my sorrow was stirred. [Psalm 39]
[Silence before royalty! – earlier (in the First World War), Bertrand Russell had been jailed because of his pacifist sympathies.] When he [Russell] was given the Order of Merit, King George VI was affable but slightly embarrassed at decorating a former jailbird, saying that "You have sometimes behaved in a manner that would not do if otherwise adopted." Russell merely smiled, but afterwards claimed that the reply "That's right, just like your brother" immediately came to mind, but he did not say it.
[A deeper kind of silence]
The radiant one inside me has never said a word.
[Response of the great 13th century Sufi poet Rumi (Jalal ad-Din Muhammad Balkhi-Rumi), when asked why, since he valued silence so much, he produced such a volume of language.]
[Wrong silence]
Als die Nazis die Kommunisten holten, When the Nazis came for the communists
habe ich geschwiegen; I remained silent;
ich war ja kein Kommunist. I was, after all, no communist.
Als sie die Sozialdemokraten einsperrten, When they locked up the social democrats,
habe ich geschwiegen; I remained silent;
ich war ja kein Sozialdemokrat. I was, after all, no social democrat.
Als sie die Gewerkschafter holten, When they came for the trade unionists,
habe ich nicht protestiert; I did not protest;
ich war ja kein Gewerkschafter. I was, after all, no trade unionist.
Als sie die Juden holten, When they came for the Jews,
habe ich geschwiegen; I remained silent;
ich war ja kein Jude. I was, after all, no Jew.
Als sie mich holten, When they came for me,
gab es keinen mehr, der protestieren konnte. there was no one left who could protest.
[The 1976 version of Niemöller’s famous poem]
[A Mathematical Theorem]
A figure and a stepping stone, not a figure and three obols. [Pythagorean proverb - mathematics is not primarily about money]
[Comments on the Atiyah-Singer index theorem] The Atiyah-Singer index theorem is one of the truly great theorems of all time. It was proved by the English mathematician, Sir Michael Atiyah, and the United States mathematician, Isadore Singer, in the 1960’s. (One should also mention the pioneering work of Friedrich Hirzebruch and Raoul Bott.) There are, I think, three criteria for judging the greatness of a mathematical theorem. The first is the range of ideas that are involved: it should not be concerned with just one area of mathematics but arise out of the interplay of a number of important fields of mathematics, showing that it is genuinely fundamental to mathematics as a whole. The Atiyah-Singer theorem in this respect is remarkable: it involves areas such as algebraic topology, algebraic geometry, functional analysis, operator algebras, partial differential equations, differential geometry, the representation theory of Lie groups and number theory. A second criterion is that, in some way, the great mathematics arises out of the real world which provides its rationale and expresses itself in the mathematics, stops it from relapsing into mere subjective preference, ``fun stuff’’, for the practitioner. The Atiyah-Singer theorem is impressive in this respect as well: part of its background (ref. 1) lies in Hodge theory which was strongly motivated by Maxwell’s equations in Physics. Further, one of the most remarkable of the achievements of Atiyah and Singer (ref. 3) – their construction of the Dirac operator in the context of Riemannian geometry and spin manifolds – first arose in Minkowski space in Dirac’s relativistic theory of the electron (in particular, in his discovery of a square root of the relativistic Laplacian). The Dirac operator of Atiyah and Singer has surprisingly continued to prove fundamental in modern particle physics and cosmology - ``The theorem has had innumerable applications, first within mathematics and then, beginning in the late 70s, in theoretical physics: gauge theory, instantons, monopoles, string theory, the theory of anomalies’’ (Norwegian Academy of Science and Letters on the occasion of the award of the Abel prize to Atiyah and Singer. In this respect, the theorem also satisfies a third criterion for mathematical greatness, that it should be not an end but rather the beginning of a flood of new insights and results, through the developing and extending of the deep insights that it embodies. Reinforcing this are the new developments in noncommutative geometry (Alain Connes), including (among many other things) the development of K-theoretic techniques in C*-algebra theory, in particular, the bivariant Kasparov KK-theory and E-theory.
[Statement of the theorem - not its most general form]
Let M be a smooth compact manifold of dimension n, E and F be smooth complex vector bundles over M, and D be an elliptic partial differential operator from the space of smooth sections of E to the space of smooth sections of F. Since D is elliptic, the kernel ker(D) and the cokernel coker(D) of D are finite-dimensional vector spaces. The index ind(D) is defined by:
ind(D)=dim(ker(D)) – dim(coker(D))
Next, the symbol σ(D) of D determines an element [σ(D)] of the K-theory group K(T*M) (K-theory with compact supports) where T*M is the cotangent bundle of M. The index theorem gives a formula that calculates the index of D using the topological and differential geometric data present, and integrating over the orientable manifold T*M; the formula is:
ind(D)= (nth power of -1) x integral{ch([σ(D)])Td}
where ch is the Chern character (that takes you from K-theory to cohomology) and Td is the Todd class of the complexified cotangent bundle.
[Some references: (1) Michael Atiyah, ``Collected Works’’, (2) Patrick
Shanahan, ``The Atiyah-Singer Index Theorem’’, (3) H. B. Lawson and M.
Michelsohn, ``Spin Geometry’’, (4) N. Higson and J. Roe, ``Analytic
K-Homology’’, (5) B. Boos and D. D. Bleecker, ``The Atiyah-Singer index
formula and Gauge-Theoretic Physics’’, (5) J. Rognes, ``On the
Atiyah-Singer index theorem’’, written on the occasion of the award of
the Abel prize to M. Atiyah and I. M Singer, 2004.]
[On Children]
[Popular poem by the children’s poet, Walter Wingate, about the kindly Scottish dominie [school master] removing a skelf (``needling a splinter’’) from the sair [sore] finger of a little school-boy, John, and wrapping it (``rowing it’’) in a little hankie as a bandage. The hankie does not go unnoticed (greet=``sob'', rin=``run'', ana'=``as well’’, saw=``ointment'' (I think!)).] THE SAIR FINGER You've hurt your finger? Puir wee man!
Your pinkie? Deary me!
Noo, juist you haud it that wey till
I get my specs and see!
My, so it is - and there's the skelf!
Noo, dinna greet nae mair.
See there - my needle's gotten't out!
I'm sure that wasna sair?
And noo, to make it hale the morn,
Put on a wee bit saw,
And tie a Bonnie hankie roun't
Noo, there na - rin awa'!
Your finger sair ana'? Ye rogue,
You're only lettin' on.
Weel, weel, then - see noo, there ye are,
Row'd up the same as John!
[Walter Wingate]
*****
Art is never finished, only abandoned. [Lenardo da Vinci]
Only one man has understood me, and he did not understand me either. [attributed to J. G. Fichte]
You are as likely to find a real philosopher in a philosophy department as you are to discover a Picasso in the department of fine arts. [Leo Strauss]
[On resisting the ``mob'', and the price it exacts]
[Advice from Zarathustra to the ``great souls’’ concerning ``the new idol’’ (the state and political power) , ``the market place'' (the ``rat race'') and shooing flies.] Somewhere there are still peoples and herds, but not with us, my brothers: here there are states. .... State is the name of the coldest of all cold monsters. Coldly it tells lies also; and this lie crawls out of its mouth: "I, the state, am the people." That is a lie! Creators were they who created peoples, and hung a faith and a love over them: thus they served life. ... "On earth there is nothing greater than I: it is I who am the regulating finger of God" - thus roars the monster. And not only the long-eared and short-sighted fall upon their knees! Ah! even in your ears, you great souls, it whispers its gloomy lies! .....
Just look at these superfluous ones! Wealth they acquire and become poorer thereby. Power they seek for, and above all, the lever of power, much money - these impotent ones! See them clamber, these nimble apes! They clamber over one another, and thus scuffle into the mud and the abyss. Towards the throne they all strive: that is their madness - as if happiness sat on the throne! Often sits filth on the throne - and often also the throne on filth. Badly smells their idol, the cold monster: badly they all smell to me, these idolaters. Escape from the bad smell!
Full of solemn jesters is the market place ... and from you they want a Yes or No ... Flee into your solitude! ... Far from the market place and from fame happens all that is great ... You have lived too close to the small and the miserable. Flee their invisible revenge! Against you they are nothing but revenge. ... Numberless are these small and miserable creatures; and many a proud building has perished of raindrops and weeds. ... I see you wearied by poisonous flies, bloody in a hundred places; and your pride refuses even to be angry. ... Their bloodless souls crave blood, and so they sting in all innocence. ... They hum around you in their praise too: obtrusiveness is their praise. They want the proximity of your skin and your blood. ... Often they affect charm. But that has always been the cleverness of cowards ... They think a lot about you with their petty souls – you always seem problematic to them. ... Even when you are gentle to them they still feel despised by you: and they return your benefaction with hidden malefactions. Your silent pride always runs counter to their taste ... Before you they feel small, and their baseness glimmers and glows in invisible revenge. Have you not noticed how often they became mute when you stepped among them ...? Indeed, my friend, you are the bad conscience of your neighbors ... They hate you, therefore ...
A free life is still free for great souls. Verily, whoever possesses little is possessed that much less: praised be a little poverty! Empty are still many seats for the lonesome ... fanned by the fragrance of tranquil seas. Flee, my friend, into your solitude and where the air is raw and strong. It is not your job to shoo flies.
Thus spoke Zarathustra.
[Friedrich Nietzsche, Also sprach Zarathustra, Part 1, translated by Walter Kaufman]
[A more positive view of the state] The state in and by itself is the ethical whole, the actualization of freedom; and it is an absolute end of reason that freedom should be actual. ... The basis of the state is the power of reason actualizing itself as will. ... But since it is easier to find defects than to understand the affirmative, we may readily fall into the mistake of looking at isolated aspects of the state and so forgetting its inward organic life. The state is no ideal work of art; it stands on earth and so in the sphere of caprice, chance, and error, and bad behaviour may disfigure it in many respects. But the ugliest of men, or a criminal ... is still always a living man. The affirmative, life, subsists despite his defects ... We are confident that the state must subsist and that in it alone can particular interests be secured. But habit blinds us to that on which our whole existence depends. When we walk the streets at night in safety, it does not strike us that this might be otherwise. This habit of feeling safe has become second nature, and we do not reflect on just how this is due solely to the working of special institutions. Commonplace thinking often has the impression that force holds the state together, but in fact its only bond is the fundamental sense of order which everybody possesses.
[G. W. F. Hegel, Grundlinien der Philosophie des Rechts, Zusätze, translated by T. M. Knox]
It is a notorious fact that the morality of a society as a whole is in inverse ratio to its size; for the greater the aggregation of individuals, the more the individual factors are blotted out, and with them morality, which rests entirely on the moral sense of the individual and the freedom necessary for this. Hence every man is, in a certain sense, unconsciously a worse man when he is in society than when acting alone; for he is carried by society and to that extent relieved of his individual responsibility. ...... The bigger the organization, the more unavoidable is its immorality and blind stupidity (Senatus bestia, senatores boni viri). Society, by automatically stressing all the collective qualities in its individual representatives, puts a premium on mediocrity, on everything that settles down to vegetate in an easy, irresponsible way. ...... The man of today, who resembles more or less the collective ideal, has made his heart into a den of murderers, as can easily be proved by an analysis of his unconscious, even though he himself is not in the least disturbed by it. ..... So obvious does it seem to us that a man should drown in his own dignity, so utterly incomprehensible that he should seek anything other than what the mob wants, and that he should vanish permanently from view in this other. [Carl G. Jung, Relations Between the Ego and the Unconscious]
... but with the advance of age, when they are no longer fit for political or military service, then at last they should be given `free range of the pasture' and do nothing but philosophize, except incidentally, if they are to live happily ...the philosopher remains quiet, minds his own business, and, as it were, standing aside under the shelter of a wall in a storm and blast of dust and hail, and seeing others full of lawlessness, is content if in any way he may keep himself free from wickedness and wrong in this life and take his departure with good hope, serene and cheerful when the end comes. [Plato, The Republic, 7.498c, 7.496d]
[Piotr Franzevich Lesgaft, Professor of Physiological Anatomy at the Kazan University, was fired in 1871 for a statement made against arbitrariness on the part of the professorate and authorities of the university.]
... A person who has allowed himself to act in such a manner ... should not be tolerated in Education Service ... [A note in the St. Petersburg Gazette by the Minister for Enlightenment, D. A. Tolstoy, in connection with an earlier article written by P. F. Lesgaft]
Every arbitrary act is very sad, but it is still sadder, and more distressing, when there is no defense against arbitrary administration and unlawful action, when people refuse, not only to understand, but even to listen to what is going on ... [P. F. Lesgaft - the following is an excerpt from the poem Lesgaft by Yevgeny Yevtushenko, where the poet ``discusses’’ the matter with Lesgaft.]
``Why have you, dearest Piotr Franzevich,
got involved in seditious affairs?
Your love for liberal phrases
has led you into foolishness....
When you have such talent for anatomy,
to spoil a career in one moment!
Why, explain to me?’’ ``Is that necessary?
After all, your conscience is only rudimentary.’’
``That means I am a scoundrel?’’ ``Not completely,
That you are a complete coward is true, ...’’
``But subtle strategy also exists.
Sometimes it is wiser to retreat.
Posterity glorifies only the one who knows how to retreat.
Stubborn rashness is senseless...’’
``But often when we rationalize,
the beautiful word strategy
is only a pseudonym for cowardice ... ’’
``Aren’t you tired of writing protests?’’ ``A bit ...’’
``The wall will not crumble, because you shout ...’’
``If it only totters, that is enough.
Social protest is the discovery of oneself for oneself...
... What is all this rotten regime?
A malignant growth!...
Only surgical intervention
can possibly save Russia!’’
``To slash living tissue? Can’t you see the danger?’’
``Of course I can, I’m sober.
But one should make a decisive cut
with the scalpel of publicity ..’’
``But where are you living, poor Piotr Franzevich? ...
To talk in Russia about equality and fraternity?!
That’s asking for the whip!
Should censorship soften even slightly
what will be printed? ...
All shops will be looted in a second.
and your downtrodden brother, barking at you furiously –
because your spectacles aren’t the right kind –
will knock you down with an axle,
as a symbol of `fraternity’....
But tell me, Piotr Franzevich,
how do you see our future?’’
``I see a different Russia:
a Russia ruled neither by the whip
nor by axles used as clubs,
both are alien to me.
She will be ruled ... by the best people of the nation.’’
``You are naïve ... Neither now nor in the future,
can power be in the hands of the people.
The people are beasts of burden, Piotr Franzevich,
and if, at times, the people,
disgruntled shake their yoke,
it’s not at all because they thirst for freedom.
It’s better fodder they would like
It’s cleaner sties they’re after ...
The educated need freedom,
but the illiterate: fodder.
What need has he of your call to protest?’’
``The struggle for freedom is a great education in itself ...’’
``Or perhaps only a change of yoke?’’...
``I side with the optimists.
Wide vistas will yet be flung open,
and the real Truth, as queen, will yet ascend
the Russian throne....
We are the seed. We will yet bear fruit. ....’’
``Would you permit me an indiscreet question?
It seems you have been expelled from the faculty,
but are still carrying on regardless?
Forgive this ticklish question,
But I am curious, it’s one of my faults.’’
``I am a citizen.
From this faculty one can never be expelled.’’ [Excerpts from: Lesgaft, by Yevgeny Yevtushenko, The Collected Poems, 1952-1990]
[De Profundis]
So long as the world moves along accustomed paths, so long as there are no wild catastrophes, man can find sufficient substance for his life by contemplating surface events, theories, and movements of society. He can acquire his inner richnesses from this external kind of ``property’’. But this is not the case when life encounters fiery forces of evil and chaos. Then the ``revealed’’ world begins to totter. Then the man who tries to sustain himself only from the surface aspects of existence will suffer terrible impoverishment, begin to stagger ... then he will feel welling up within himself a burning thirst for that inner substance and vision which transcends the obvious surfaces of existence and remains unaffected by the world’s catastrophes. From such inner sources he will seek the waters of joy which can quicken the dry outer skeleton of existence. [Rabbi Abraham Isaac Kook]
[Truth and classical political philosophy] The central theme of classical political philosophy is virtue, or human excellence. The questions that typically preoccupy Socrates and his followers are: What is virtue? Can it be taught, and if so, how? What is the education that makes a full citizen and human being? What is a virtuous statesman and citizen? What political regime best promotes virtue or excellence? What is a true friend? Who or what is worthy of passionate love?
Now this kind of questioning and preoccupation immediately appears to characterize Socrates and his rationalism as far removed from, not to say alien to, the sophistication which tends to predominate in our contemporary culture. To know, as we are sure we do, that morals and principles of justice are values, is to know that Socrates’ questions are deeply misconceived ... Values are individual preferences, or subjective commitments, or cultural creations, or historical dispensations. Once this truth – this absolute and unquestionable truth – is recognized, the sophisticated response is one that turns its back on sustained argument over the ``truth’’ of values and instead proceeds to ``self-expression’’ and search for ``community’’ ... This quest is to be regulated only by the absolute moral principle that we ought to express ourselves and seek community and values-clarification only in such ways as respect the equal right of all others to express themselves...
It is not very difficult to unmask the incoherence in this pseudo-sophistication: the denial of the possibility of absolute or universal truth rests on the assertion of an absolute or universal truth and is said to entail the assertion of universally valid moral imperatives or prohibitions – of human rights that transcend race, color, creed or ethnic and historical background. It is more important to observe that no human being can actually live according to this pseudo-sophistication. This basis for loyalty to democracy and equality contradicts and thus undermines itself at every moment, in action as well as logic. For as soon as one turns from the silly abstractions about values and relativism back to real life – back to elections, jury duty, hiring decisions, the forming of friendships, the choice of a spouse, the raising of children, the communion with one’s own conscience – one sees the inescapable need and obligation to evaluate and judge the characters of other people at every turn. So long as we live, we cannot help but feel the urgency of our need to know what Socrates sought to know ... Just beneath the sophisticated veneer that distorts our moral experience there is to be found, then, overwhelming evidence of the primordial and permanent power of the concerns or questions that are the Socratic starting point.
[Thomas L. Pangle, Introduction to: The Rebirth of Classical Political Rationalism, by Leo Strauss]
In the coming of the Messiah,
And even if he delays, nevertheless, I believe.
In your lifetime, and in your days,
And in the life of the household of all Israel,
Speedily, Soon.
And say you - ``Amen’’.
[sung by the Hasidic Jews at Auschwitz, based on words by Moses Maimonides]
[The Bardo Thodol (by Padma Sambhava, 8th or 9th century, AD), often called The Tibetan Book of the Dead, gives detailed guidance for the deceased concerning liberation from the cycle of death and rebirth (samsara) and how to choose a ``good womb'' for the next incarnation if liberation is not achieved. (I am using the translation by Robert Thurman.) Four and one half days after her death, the deceased becomes aware of her loved ones left behind; she sees them weeping and wailing, her place at the table is no longer there, her bed is broken, her clothes stripped, she hears them speak but they cannot hear her. She must depart distraught, faint with fear and terror. On the following days, the Buddhist mild deities, images of her own awareness, appear from their different worlds to guide her towards liberation. On the second day after this:]
from the blue eastern pure land of Abhirati, ... the blue Lord Vajrasattva Akshobhya arises before you seated on an elephant, in union with his consort Buddhalochana, attended by the male Boddhisattvas Kshitigarbha and Maitreya and the female Bodhisattvas Lasya and Pushpa - a group of six Archetype Deities. The white light of the Mirror wisdom ... white and piercing, bright and clear, shines from the heart of the Vajrasattva couple before you, penetrating, unbearable to your eyes. At the same time, the soft smoky light of the hells shines before you in parallel with the wisdom light. At that time, under the influence of hate you panic, terrified by that brilliant white light, and you flee from it. You feel a liking for that soft smoky light of the hells and you approach it. But now you must fearlessly recognize that brilliant white, piercing, dazzling, clear light as wisdom. ... Pray and increase your love for it, thinking, ``It is the light of the compassion of Lord Vajrasattva! I take refuge in it!'' It is Lord Vajrasattva's shining upon you to escort you through the terrors of the between. It is the tractor-beam of the light of the compassion of Vajrasattva - have faith in it! Don't be enticed by that soft smoky light of hell! ... That is the path of destruction from the sins you have accumulated by your strong hatred! ... Don't look upon it! Abandon all hate! Don't cling to it! Don't long for it! Have faith in that dazzlingly bright white light! .....
Know what is in front of your face and what is hidden from you will be disclosed. [Gospel of Thomas]
It is difficult to speak the truth, for although there is only one truth, it is alive and therefore has a live and changing face. [Franz Kafka]
The Feminine Spirit
... Surely my God is feminine, for Heaven
Is the generous impulse, is contented
With feeding praise to the good. And all
Of these that I have known have come from women.
While men the poet’s tragic light resented,
The spirit that is Woman caressed his soul.
[God is Woman, Patrick Kavanagh]
[The role of the feminine was much stronger in gnostic Christianity than it was in the orthodox Christianity that eventually overwhelmed it. Of particular importance was the divine female figure of Sophia (Wisdom) (or Barbelo) who, in Gnosticism, is the ``first power’’ or forethought of the Father (who ``himself’’ is thought of as a kind of NeoPlatonic One). She is (ultimately) the source of the creation of the world (through her ``gloomy’’, ``misshapen’’ son Yaldabaoth), the ``divine spark’’ within us and the salvation of the world. The amazing, paradoxical, gnostic poem Thunder, a small part of which is given below, asserts the ``eternal feminine’’ in its universality, revelling in the contradictions and antitheses of the real world through which it triumphs.]
I am the first and the last.
I am the honored and the scorned....
I am the wife and the virgin.
I am the mother and the daughter....
I am the midwife and do not give birth.
I am the solace of my labor pains.
I am the bride and the groom ...
I am a silence incomprehensible
and an idea remembered often....
Why do you who hate me love me
and hate those who love me?...
You who tell the truth about me lie about me,
and you who lie tell the truth....
I am knowledge and ignorance.
I am shame and fearlessness.
I am shameless and ashamed.
I am strength and fear.
I am war and peace....
Consider my poverty and wealth.
Don’t be arrogant when I am cast down on the earth,
and you will find me in those who are to come.
Don’t stare at me lying on a dung heap.
Don’t run off and cast me away.
Don’t stare when I am cast with the disgraced
in the most sordid places
or laugh at me....
I am compassionate and cruel....
Be careful....
I am a woman existing in every fear
and in my strength when I tremble....
I am senseless and wise....
I am hated everywhere and loved everywhere.
I am called life [ζωή, Eve] and you have called me death....
I am unlettered and you learn from me....
I am perfect mind and rest ...
I am the knowledge of my search,
the finding of those who look for me,
the command of those who ask about me,
the power of powers...
and of spirits of all who exist with me
and of women who live in me.
[Thunder, from The Gnostic Bible, edited by W. Barnstone and M. Meyer]
kindness
[A number of remarkable songs and hymns have been preserved in the Coptic Manichaean Songbook. This is part of one of those songs, in which the humble ox cries out against his abuse by the human race.]
CRY OF PAMOUN THE OX
Hear an ox. The cry of Pamoun, an ox. Mercy.
I make the worlds weep.
What have the children of the earth given me?
They grabbed two-edged axes
And stuck me in marshes. They felled fat trees
and even thin ones.
They didn’t leave alone. With the fat tree
they cut out a plow.
From the thin one they made a sharp goad.
Then took it to a craftsman who in his own hand fashioned a yoke,
stuck it on my neck,
and hooked the plow hanging behind me.
They used the goad
to pierce my ribs. Then they carried me
to the butcher’s son,
the fattener of oxen; it was the butcher’s
son who chopped me up,
scattered me to foreign tents, hung me
in far markets, ... tossed my bones to stray beasts...
They burn what is inside me, even that.
Don’t beat Pamoun, the ox....
[Cry of Pamoun the Ox, Gnostic Bible, edited by W. Barnstone and M. Meyer]
***** [Lily Tomlin] The best mind-altering drug is truth.
Television is a medium of entertainment which permits millions of people to listen to the same joke at the same time, and yet remain lonesome. [T. S. Eliot]
[For College athletics] Mens sana in corpore sano.
[Against ``big’’ College athletics] Nine out of 10 teams are cheating, the other is in last place. [Jerry Tarkanian]
Tongue-in-cheek (?)
BAD MORNING
Here I sit
With my shoes mismated.
Lawdy-mercy!
I's frustrated!
[Langston Hughes]
[Doric was (and is) the dialect of the North East of Scotland. Traditionally, it was the language of the large body of migrant farm workers in the area, the creators of the ``Bothy Ballads’’. The name ``Doric’’ seems to have been given to the dialect by analogy with the Doric of ancient Greece, the language of Sparta, the relation between Spartan Doric and the Attic of Athens corresponding to that between the North East dialect and the ``posher’’, more ``educated’’, speech of Edinburgh (the ``Athens of the North’’). The dialect has a driving, direct, down-to-earth nature combined with ironic humor. Here are two Doric poems. The first, Gin I was God (If I was God), is by Charles Murray (1864-1941) of Alford, Aberdeenshire, a veteran of the second Boer and the first world wars, and gives God some advice on how to deal with this sorry world. The second, more homiletic, I once saw on a public bus in Aberdeen.]
Gin I was God
Gin I was God, sittin' up there abeen,
Weariet nae doot noo a' my darg was deen,
Deaved wi' the harps an' hymns oonendin' ringin',
Tired o' the flockin' angels hairse wi' singin',
To some clood-edge I'd daunder furth an', feth,
Look ower an' watch hoo things were gyaun aneth.
Syne, gin I saw hoo men I'd made mysel'
Had startit in to pooshan, sheet an' fell,
To reive an' rape, an' fairly mak' a hell
O' my braw birlin' Earth, - a hale week's wark - I'd cast my coat again, rowe up my sark,
An' or they'd time to lench a second ark,
Tak' back my word an' sen' anither spate,
Droon oot the hale hypothec, dicht the sklate,
Own my mistak', an, aince I cleared the brod,
Start a'thing ower again, gin I was God.
*****
So dinna fash or greet aboot oorsels.
God’s licht disnae dee! – the lampie is aye foo.
Oor laird if in oor herts gies muckle joy.
His kist gies us meat and ale, we nivver wint.
His werdies, cam fit mae, they will aye wyes ding,
Fit e’er a warld o’ doot or fear dirls in oor lugs.
[In Goethe’s masterpiece, Faust, Dr. Faust, profoundly disillusioned by 10 years of academic life - the ``emptiness'' of what he teaches, and leading his pupils ``by the nose'' - takes up ``the abyss'' of necromancy. This leads to him agreeing to sell his soul to the devil (``the Prince of Lies’’) in exchange for an (apparently) thrilling life of pleasure to be provided by the devil's ``servant’’ Mephistopheles, and which will eventually lead to Faust’s heartbreak and ruin. Mephistopheles points out that ``all theory, my friend, is gray, but green is life's glad golden tree''. Faust is concerned that ``bearded and gray'' he lacks the ``sprightliness'' needed for the attack on the thrills that lie ahead, and that he gets embarrassed sometimes in front of people. Mephistopheles assures him that he will soon ``learn the art of living''. While Faust is absent from his office preparing for the new life, a student knocks on the door looking for academic advice, which Mephistopheles, dressed in Faust’s cap and gown, gives, with devilish wit. The student first asks Mephistopheles on how to choose a faculty.]
MEPHISTOPHELES.
.... I counsel first the depths you plumb
Of our Collegium Logicum.
Its rigor will confine your mind
Like Inquisition boots, you’ll find,
And teach it hence to walk with reason,
Smoothly trained to thoughts in season,
... The web of thought, I’d have you know,
Is like a weaver’s masterpiece:
The restless shuttles never cease
... And so philosophers step in
To weave a proof that things begin,
Past question, with an origin.
...The method scholars praise, and keenly clutch;
As weavers, though, they don’t amount to much. ....
STUDENT
O Sir, I feel so dazed at what you’ve said;
It goes round like a mill-wheel in my head.
MEPHISTOPHELES
Next, most important thing of all,
To metaphysics you must fall,
And see with deep discernment plain,
What things won’t fit the human brain;
But, fit or not, why vex your head? -
You use a sounding phrase instead. ...
Five lectures are your daily plan –
And show yourself a punctual man.
For your professor, pray, prepare;
No paragraph, Sir, overlook!
And then you soon will be aware
He never deviates from the book.
But write it down, Sir, every bit,
As if the Holy Ghost dictated it. ...
STUDENT
I doubt if I’d be happy taking Laws.
MEPHISTOPHELES
A hesitation that I comprehend.
Knowing the subject, I myself would pause.
They’ve statues, clauses, rights in such a smother
As spreads from place to place the legal taint,
And ties one generation to another
Worse than a slow inherited complaint.
And grandsons learn to curse the lawyers’ usance. ...
STUDENT
... Perhaps theology has claims more strong?
MEPHISTOPHELES
Sir, I should grieve to see you going wrong.
The aspirants who choose that learned field
May fail to see the pitfalls, oversure;
And zealotry has virus so concealed
It’s hard to tell the poison from the cure!
So stick to one professor all your days,
And swear by every word the Master says.
In short, you pin your faith on words, my friend,
Make words your safeguard, so that you ascend
To certainty’s high temple in the end.
STUDENT
But, Sir, concede
That words must have some meaning underlying.
MEPHISTOPHELES
Why yes, agreed,
But never fear to find that mortifying,
For if your meaning’s threatened with stagnation,
Then words come in, to save the situation:
They’ll fight your battles well if you enlist them
Or furnish you a universal system.
Thus words will serve us grandly for a creed,
Where every syllable is guaranteed.
[J. W. von Goethe, Faust, Part 1, translated by Phillip Wayne (for a comment of Goethe's concerning Faust, see the following)]
[Goethe talking to a young Englishman who found reading Faust rather difficult] Really ... I would not have advised you to undertake Faust. It is mad stuff, and goes quite beyond all ordinary feeling. ... Faust is so strange an individual, that only few can sympathize with his internal condition. Then the character of Mephistopheles is, on account of his irony, and also because he is a living result of an extensive acquaintance with the world, also very difficult. ...
[from: Conversations with Goethe (Gespräche mit Goethe), J. P. Eckermann, 1836, trans. J. Oxenford, p.79]
[Gödel's realism]
[Russell's vicious circle principle rules out set theoretic
paradoxes by excluding totalities with members definable only in terms
of the totality, resulting in a constructivistic, type theoretic
approach to set theory, in which sets are built from the bottom up,
starting with individuals, the more complicated in terms of the
simpler. (So, for example, it is illegitimate to refer to ``the set of
all sets'' since that set has itself as a member which is defined in
terms of the whole totality.) Also impredicative propositions
(a proposition involving arguments that are defined in terms of the
proposition) are excluded. Unfortunately, among other problems with
the principle, it also ruled out the construction of the reals from the
rationals (to prove the existence of least upper bounds requires an
impredicative proposition) and much of modern Mathematics. Gödel
argues that the principle is false, and that concepts can legitimately
refer to themselves, i.e. be self-reflexive.] Since concepts are
supposed to exist objectively, there seems to be objection neither to
speaking of all of them ... nor to describing some of them by reference
to all .... But, one may ask, isn't this view refutable also for
concepts because it leads to the ``absurdity'' that there will exist
properties φ such that φ(a) consists in a certain state of affairs
involving all properties (including φ itself and properties defined in
terms of φ), which would mean that the vicious circle principle does
not hold . . . . for concepts or propositions? There is no doubt that
the totality of all properties . . . . does lead to situations of this
kind, but I don't think they contain any absurdity. It is true that
such properties φ . . . . will have to contain themselves as
constituents of their content . . . . but this only makes it impossible
to construct their meaning . . . . which is no objection for one
who takes the realistic standpoint. Nor is it self-contradictory that
a proper part should be identical (not merely equal) to the whole, as
is seen in the case of structures in the abstract sense. The structure
of the series of integers , e.g., contains itself as a proper part and
it is easily seen that there exist also structures containing
infinitely many different parts, each containing the whole structure as
a part. In addition, there exist, even within the domain of
constructivistic logic, certain approximations to this self-reflexivity
of impredicative properties, namely propositions which contain as parts
of their meaning not themselves but their own formal demonstrability. [Kurt Gödel, Russell's Mathematical Logic]
[Gödel and philosophy] He [Gödel] attended seriously, as well, to the history of philosophy, devoting endless hours to the study of Leibniz and acquiring a profound understanding of Kant. His grasp of Hegel astonished the logician and philosopher Georg Kreisel, a man not easy to impress. Looking over the set of quotations from Hegel that Gödel had assembled, Kreisel remarked that ``the publication of such an anthology is likely to produce a minor revolution in philosophy.'' He also studied Plato and Aristotle .... he put his grasp of the history of philosophy to creative use, enlisting his knowledge of Kant to help him comprehend the philosophical significance of the theory of relativity, and turning to Husserl's phenomenology for assistance in developing an epistemology adequate to the Platonist ontology he espoused for mathematics. He believed that the history of philosophy could help free us from prejudice. ``Even science,'' he said, ``is very heavily prejudiced in one direction. Knowledge in everyday life is also prejudiced. Two methods to transcend such prejudices are: (1) phenomenology; (2) going back to other ages.'' [p.182 of: Palle Yourgrau, A World Without Time - The Forgotten Legacy of Gödel and Einstein.]
Not he who rejects the gods of the crowd is impious, but he who embraces the crowd’s opinion of the gods. [Epicurus]
What cannot be satisfied is not a man's stomach, as most men think, but rather the false opinion that the stomach requires unlimited filling. [Epicurus]
[On the United States]
The Citizens of the United States of America have a right to applaud themselves for having given to mankind examples of an enlarged and liberal policy: a policy worthy of imitation. All possess alike liberty of conscience and immunities of citizenship. It is now no more that toleration is spoken of, as if it was by the indulgence of one class of people, that another enjoyed the exercise of their inherent natural rights. For happily the Government of the United States, which gives to bigotry no sanction, to persecution no assistance requires only that they who live under its protection should demean themselves as good citizens, in giving it on all occasions their effectual support.
[George Washington, letter to the congregation of Touro Synagogue, Newport, Rhode Island, August, 1790.]
[George Washington and communion] With respect to the inquiry you make, I can only state the following facts: that as pastor of the Episcopal Church, observing that, on sacramental Sundays George Washington, immediately after the desk and pulpit services, went out with the greater part of the congregation - always leaving Mrs. Washington with the other communicants, she invariably being one - I considered it my duty, in a sermon on public worship, to state the unhappy tendency of example, particularly of those in elevated stations, who uniformly turned their backs on the Lord's Supper. I acknowledge the remark was intended for the President; and as such he received it. A few days after, in conversation, I believe, with a Senator of the United States, he told me he had dined the day before with the President, who, in the course of conversation at the table, said that, on the previous Sunday, he had received a very just rebuke from the pulpit for always leaving the church before the administration of the sacrament; that he honored the preacher for his integrity and candor; that he had never sufficiently considered the influence of his example, and that he would not again give cause for the repetition of the reproof; and that, as he had never been a communicant, were he to become one then, it would be imputed to an ostentatious display of religious zeal, arising altogether from his elevated station. Accordingly, he never afterwards came on the morning of sacrament Sunday, though at other times he was a constant attendant in the morning. [The Reverend Doctor James Abercrombie in a letter to a friend in 1833]
[Aside: Rumi on the merits of fasting and its own peculiar kind of communion]
There’s a hidden sweetness in the stomach’s emptiness.
We are lutes, no more, no less. If the soundbox
Is stuffed full of anything, no music....
When you fast,
good habits gather like friends who want to help.
Fasting is Soloman’s ring. Don’t give it
to some illusion and lose your power, but even if you have, if you've lost all will and control, they come back when you fast ... A table descends to your tents,
Jesus’s table.
Expect to see it, when you fast, this table
spread with other food, better than the broth of cabbages. [The Essential Rumi, trans. Coleman Barks with John Moyne, p.69]
[The bitter political party polemics between the Federalists and the Republicans in the early 1800’s in the United States led to a split between John and Abigail Adams on the one hand and Thomas Jefferson on the other. Correspondence between Abigail and Jefferson (who was then president) restarted in May, 1804 when Abigail sent a sympathy letter to Jefferson on the death of his daughter, Martha Randolph, whom Abigail had cared for when Martha Randolph was a child in France, and to whom she was deeply attached. In a later letter (August 18) to Jefferson, Abigail laments ``the rageing fury of party animosity''. (The ``late instance'' that she refers to is no doubt the duel on July 11 between Hamilton and Burr in which Hamilton was killed.)] In no Country has calumny falshood, and revileing stalked abroad more licentiously, than in this. No political Character has been secure from its attacks, no reputation so fair, as not to be wounded by it, untill truth and falshood lie in one undistinguished heap. If there are no checks to be resorted to in the Laws of the Land, and no reparation to be made to the injured, will not Man become the judge and avenger of his own wrongs, and as in a late instance, the sword and pistol decide the contest? All the Christian and social virtues will be banished from the Land. All that makes Life desirable, and softens the ferocious passions of Man will assume a savage deportment, and like Cain of old, every Mans hand will be against his Neighbour. Party spirit is blind malevolent uncandid, ungenerous, unjust and unforgiving. It is equally so under federal as under democratic Banners, yet upon both sides are Characters, who possess honest views, and act from honorable motives, who disdain to be led blindfold, and who tho entertaining different opinions, have for their object the public welfare and happiness. .... Party hatred by its deadly poison blinds the Eyes and envenoms the heart. It is fatal to the integrity of the moral Character. It sees not that wisdom dwells with moderation, and that firmness of conduct is seldom united with outrageous voilence of sentiment. Thus blame is too often liberally bestowed upon actions, which if fully understood, and candidly judged would merit praise instead of censure. [From The Adams-Jefferson Letters, edited by Lester J. Cappon]
[Thoughts on Mathematics]
[A research mathematician's life can be discouraging] A colleague of mine once said ``We work for the grudging approbation of a few friends''. It is true that since the research work is of a rather solitary nature we need badly that approbation in one way or another, but quite frankly don't expect much .... In fact there is no way to fool around with the only real judge which is oneself, and caring too much about the opinion of others is a waste of time: so far no theorem has been proved as a result of a vote. As Feynman put it ``why do you care what other people think''! [Alain Connes, Advice to the beginner]
[That the great mathematics comes from physics:] Not this short lived novelty which can too often influence the mathematician left to his own devices, but this infinitely fecund novelty which springs from the nature of things. [Hadamard]
Quantum field theory is a very rich subject for mathematics as well as for physics. But its development in the last seventy years has been mainly by physicists, and it is still largely out of reach as a rigorous mathematical theory . . . So most of its impact on mathematics has not yet been felt. Yet in many active areas of mathematics, problems are studied that actually have their most natural setting in quantum field theory . . . their natural home in quantum field theory is not now part of the mathematical theory. To make a rough analogy, one has here a vast mountain range, most of which is still covered with fog. Only the loftiest peaks, which reach above the clouds, are seen in the mathematical theories of today and these splendid peaks are studied in isolation . . . Still lost in the mist is the body of the range, with its quantum field theory bedrock and the great bulk of the mathematical treasures. [Edward Witten, Magic, Mystery and Matrix, Josiah Willard Gibbs Lecture, 1998.]
A milestone for mathematics. Connes has created a theory that embraces most aspects of `classical' mathematics and sets us out on a long and exciting voyage into the world of noncommutative mathematics. [Vaughan F. R. Jones commenting on Alain Connes's book: Noncommutative Geometry.]
[Hegelian ideas]
[Hegel’s disapproval of overemphasizing arithmetic calculation practice in education] Number is a non-sensuous object, and occupation with it and its combinations is a non-sensuous business; in it, mind is held to communing with itself and to an inner abstract labor, a matter of great though one-sided importance .... such occupation is an unthinking, mechanical one. The effort consists mainly in holding fast what is devoid of the Concept and in combining it purely mechanically
.... the substantial content of moral and spiritual life in its various forms .... is to be supplanted by the blank one or unit .... the only possible outcome must be to dull the mind and to empty it of both form and substance .... it has been possible to construct machines which perform arithmetical operations with complete accuracy. A knowledge of just this one fact about the nature of calculation is sufficient for an appraisal of the idea of making calculation the principal means for educating the mind and stretching it on a rack in order to perfect it as a machine. [G. W. F. Hegel, Wissenschaft der Logik (The Science of Logic), translated by A. V. Miller]
One word more about giving instruction as to what the world ought to be. Philosophy in any case always comes on the scene too late to give it. As the thought of the world, it appears only when actuality is already there cut and dried after its process of formation has been completed. The teaching of the Concept, which is also history's inescapable lesson, is that it is only when actuality is mature that the ideal first appears over against the real and that the ideal apprehends this same real world in its substance and builds it up for itself into the shape of an intellectual realm. When philosophy paints its grey in grey, then has a shape of life grown old. By philosophy's grey in grey it cannot be rejuvenated but only understood. The owl of Minerva first starts its flight with the setting in of twilight. [G. W. F. Hegel, Grundlinien der Philosophie des Rechts (Philosophy of Right, Preface), translated by T. M. Knox (slight changes)]
To speak of the absolute idea may suggest the conception that we are at length reaching the right thing and the sum of the whole matter. .... But its true content is only the whole system of which we have been hitherto studying the development.... The absolute idea may in this respect be compared to the old man who utters the same creed as the child, but for whom it is pregnant with the significance of a lifetime. Even if the child understands the truths of religion, he cannot but imagine them to be something outside of which lies the whole of life and the whole of the world. The same may be said to be the case with human life as a whole ... All work is directed only to the aim or end; and when it is attained, people are surprised to find nothing else but just the very thing which they wished for. The interest lies in the whole development... So, too, the content of the absolute idea is the whole breadth of ground which has passed under our view up to this point. Last of all comes the discovery that the whole evolution is what constitutes the content and interest. [G. W. F. Hegel, Enzyklopädie (Encyclopedia Logic, section 237, Zusatz, translated by William Wallace.)]
[From an account of a visit by Christoph Theodor Schwab to the great
German poet Hölderlin shortly before the latter's death in 1843.
Hölderlin had been insane since 1806, and was a close friend of
Hegel's in their early years.] He
[Schwab] asked him [Hölderlin] whether he had thought of Hegel.
Hölderlin answered that of course he had, muttered something
incomprehensible, and then noted simply, ``The Absolute.'' [Taken from p.665 of ``Hegel - A Biography'', by Terry Pinkard.]