Anoop Verma's Diary: Itihasa & Darshana: Gödel’s Incompleteness Theorems And Philosophy

Friday, 13 March 2020

Gödel’s Incompleteness Theorems And Philosophy

One of the philosophical implications of Kurt Gödel’s two incompleteness theorems is that an all-inclusive definition of philosophical truth is not possible. The human brain has built-in limitations of its own, and there are several problems that it is incapable of solving. The obvious truths for which cogent proof is not possible are generally accepted by the philosophers as being prior to philosophy or axiomatic. But there can be a number of true statements which cannot be formally deduced from a given set of axioms and are neither provable nor refutable. It follows that philosophy is not possible without intuitions, creativity, and rationalization, and that the nature of the philosophical truth cannot be fully formalized, since new perspectives on this truth will forever await invention and discovery. Therefore, no limits can be placed on the inventiveness of the philosophers in their development of new methods of finding the truth.

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Nirad C. Chaudhuri

“In the south the temples have survived, and in the north they have not. Over seven centuries from the eleventh to the end of the seventeenth all the great cities of northern India dating from Hindu times were sacked by the Muslim invaders and conquerors of India. All the temples there and in all other centres of Hinduism were systematically destroyed. None were left standing at Ujjain, Ajmere, Delhi, Mathura, Brindaban, Kanauj, Prayag, or Benares—which were the centres of the political, cultural, and religious life of the Hindus. In most of these places mosques were built on the sites of the temples, and in some with pillars taken from them. This religious vandalism also worked its fury on the Buddhist centres. Moreover, it was not simply that the great temples in the cities were destroyed; so were the village temples. For most of the period of Muslim rule, there was a ban on building new temples and rebuilding the old in the regions the Muslims controlled.” ~ Nirad C. Chaudhuri

“The moral ideal, that when slapped on one cheek you should offer the other for a slap, has no place in politics. Here the maxim is just the reverse. If you are slapped, give proper return, and you would at once find a desire by the other side to make friends. The method of offering the other cheek for being slapped has now been tried for over 20 years. There has been enough of coaxing and fawning, which by giving undue importance to the other community has begotten only insolence and impudence. May we not now try the counter method and see its result?” ~ Rai Bahadur Lalchand

“Aristotle died in the autumn of 322 BC. He was sixty-two and at the height of his powers; a scholar whose scientific explorations were as wide-ranging as his philosophical speculations were profound; a teacher who enchanted and inspired the brightest youth of Greece; a public figure who lived a turbulent life in a turbulent world. He bestrode antiquity like an intellectual colossus. No man before him had contributed so much to learning. No man after him might aspire to rival his achievements.” ~ Jonathan Barnes

"Within twelve months Greece had lost her greatest ruler [Alexander], her greatest orator [Demosthenes], and her greatest philosopher [Aristotle]. The glory that had been Greece faded now in the dawn of the Roman sun; and the grandeur that was Rome was the pomp of power rather than the light of thought. Then that grandeur too decayed, that little light went almost out. For a thousand years darkness brooded over the face of Europe. All the world awaited the resurrection of philosophy." ~ Will Durant

“The age at which we obtain the complete use of reason may be determined as follows: [i] as far as the facility (to use it competently to achieve any goal) is concerned it is approximately the twentieth year, [ii] as far as calculation (to use other human beings for one's own purposes) is concerned, it is the fortieth year, and [iii] the age of wisdom be¬ gins around sixty. The latter age is entirely negative. We are finally able to recognize all the foolish mistakes we made in the first two.” ~ Immanuel Kant

“Where Plato is whimsical and ironic, and proceeds by suggestion and indirection, Aristotle is matter-of-fact, almost pedestrian. Where Plato’s writing is filled with his sense of better and more beautiful world behind, above, beyond the world of ordinary experience, illuminating that experience but transcending it, Aristotle keeps his feet firm on the ground of ordinary experience. This is Aristotle's reality, and the business of philosophy in his view is to make sense of the here and now.” ~ W. T. Jones

“The existence of man in political society is historical existence; and a theory of politics, if it penetrates to principles, must at the same time be a theory of history.” ~ Eric Voegelin

“Social evils cannot be reformed by legislation; defects of government machinery cannot be repaired by changes in the constitution; differences of opinion cannot be settled by compromise.” ~ Eric Voegelin

"There is no such thing as a right to be stupid; there is no such thing as a right to be illiterate; there is no such thing as a right to be incompetent.” ~ Eric Voegelin

"Fanaticism consists in redoubling your efforts when you have forgotten your aim." ~ George Santayana

"One can easily imagine how indignant a humanistic liberal will be when he is told that his particular type of immanentism is one step on the road to Marxism.” ~ Eric Voegelin

"In National Socialist and related documents we are still further below the level on which rational argument is possible than in the case of Hegel and Marx. In order to deal with rhetoric of this type, one must first develop a philosophy of language, going into the problems of symbolization on the basis of the philosophers’ experience of humanity and of the perversion of such symbols on the vulgarian level by people who are utterly unable to read a philosopher’s work.” ~ Eric Voegelin

“The fallacy in the ethics of evolution is the equation of the “struggle for existence” with the “survival of the fittest,” and the assumption that “the fittest” is identical with “the best.” But that struggle may favor the worst rather than the best.” ~ Gertrude Himmelfarb

“The quest for the origin must take into account that the world of our experience is not a static structure but a process; and the speculation on the origin must project (in one symbolism or another) this experience into a process in the origin itself.” ~ Eric Voegelin

“The world can only be grasped by action, not by contemplation. The hand is more important than the eye.” ~ Jacob Bronowski

“You can run agriculture for centuries by manual labor and oxcarts. But destroy the last of this country's industrial plant—and centuries of effort won't be able to rebuild it or to gather the economic strength to make a start.” ~ Ayn Rand

“Can you be a conservative and believe in God? Obviously. Can you be a conservative and not believe in God? This is an empirical essay, and so the answer is, as obviously, yes. Can you be a conservative and despise God and feel contempt for those who believe in him? I would say no.” ~ William F. Buckley Jr.

“The most radical change in the human condition we can imagine would be an emigration of men from the earth to some other planet. Such an event, no longer totally impossible, would imply that man would have to live under man-made conditions, radically different from those the earth offers him. Neither labor nor work nor action nor, indeed, thought as we know it would then make sense any longer. Yet even these hypothetical wanderers from the earth would still be human; but the only statement we could make regarding their "nature" is that they still are conditioned beings, even though their condition is now self-made to a considerable extent.” ~ Hannah Arendt

“Carefree, mocking, violent–this is how wisdom wants us: she is a woman, all she ever loves is a warrior.” ~ Nietzsche

“Which great philosopher, so far, has been married? Heraclitus, Plato, Descartes, Spinoza, Leibniz, Kant, Schopenhauer – were not; indeed it is impossible to even think about them as married. A married philosopher belongs to comedy, that is my proposition: and that exception, Socrates, the mischievous Socrates, appears to have married ironice, simply in order to demonstrate this proposition.” ~ Nietzsche

“Hubris characterizes our attitude towards ourselves,–for we experiment on ourselves in a way we would never allow on animals, we merrily vivisect our souls out of curiosity: that is how much we care about the ‘salvation’ of the soul!” ~ Nietzsche

“Think you're escaping and run into yourself. Longest way round is the shortest way home.” ~ James Joyce