Philosophy Of Mathematics Quotes

The question as to which of these two theories applies to the actual world is, like all questions concerning the actual world, in itself irrelevant to pure mathematics.* But the argument against absolute position usually takes the form of maintaining that a space composed of points is logically inadmissible, and hence issues are raised which a philosophy of mathematics must discuss. In what follows, I am concerned only with the question: Is a space composed of points self-contradictory? It is true that, if this question be answered in the negative, the sole ground for denying that such a space exists in the actual world is removed; but this is a further point, which, being irrelevant to our subject, will be left entirely to the sagacity of the reader. ~ Bertrand Russell

When I was young, most teachers of philosophy in British and American universities were Hegelians, so that, until I read Hegel, I supposed there must be some truth to his system; I was cured, however, by discovering that everything he said on the philosophy of mathematics was plain nonsense. ~ Bertrand Russell

Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse. ~ John D. Barrow

The three main medieval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism. ~ Willard Van Orman Quine

The first method for estimating the intelligence of a ruler is to look at the men he has around him. ~ Niccolo Machiavelli

The greatest duty of life is to find the ultimate purpose of life. The second greatest duty is to put a laser focus on it and take action. ~ Debasish Mridha

Settle, for sure and universally, what conduct will promote the happiness of a rational being. ~ Immanuel Kant

Be curious! Curiosity is the mother of all knowledge. ~ Debasish Mridha

Oh, don't pull your hand away from me, I've promised myself that maybe by the end of this impossible narrative I shall understand, oh maybe it will be on Hell's road that I shall be able to find what we need - but don't pull your hand away, even though I now know that the finding has to come on the road of what we are, if I can succeed in not sinking completely into what we are. ~ Clarice Lispector

There is, I assure you, a medical art for the soul. It is philosophy, whose aid need not be sought, as in bodily diseases, from outside ourselves. We must endeavor with all our resources and all our strength to become capable of doctoring ourselves. ~ Marcus Tullius Cicero

Music, Schopenhauer wrote, is not unconscious arithmetic, as Leibniz had claimed, but unconscious philosophy, since in music the inner essence of the world, which is will, is made directly present to the mind. ~ Roger Scruton

In this case, a mother, noted for her beauty, might be reduced to a purple shadow ... (Tansley to Lily on her painting of the house & grounds) ~ Virginia Woolf

Faith is a question of eyesight; even the blind can see that. ~ Dejan Stojanovic

What never fails inside the mind of an intellectual never works outside the confines of his head. The world's stubborn refusal to vindicate the intellectual's theories serves as proof of humanity's irrationality, not his own. Thus, the true believer retrenches rather than rethinks; he launches a war on the world, denying reality because it fails to conform to his theories. If intellectuals are not prepared to reconcile theory and practice, then why do they bother to venture outside the ivory tower or the coffeehouse? Why not stay in the world of abstractions and fantasy? ~ Daniel J. Flynn

Education is important not because it helps you to get a job, but because it opens the window of the mind through which we can see the beauty of life. ~ Debasish Mridha

A formal education will give you knowledge; self-education will give you wisdom. ~ Debasish Mridha

It is equally important to learn from experience and from books. ~ Eraldo Banovac

A writer's voice emanates from their interest and compulsions that absorbs them completely. Only by fully committing himself or herself to a pet subject or issue can the writer develop a thematic tone that speaks to other people with authority and serenity. The quality of their literary voice is the crucial part of the writer's legitimacy, and their authenticity cannot come from mimicking other writers' style, but must evolve naturally from their inner sanctity and must flow effusively from an inner necessity. ~ Kilroy J. Oldster

Since the effects of your life that lead to pain and annoyance are always consequences of inner elements, what you commonly regard as "problems" are more accurately seen as outer symptoms of inner, causal problems. The practical approach is to begin looking at those specific aspects of your life that are not as you desire to find their source, rooted in your mindset. ~ Thomas Daniel Nehrer

I would not say that I was, these days, a 'student' of philosophy, although in my youth I was quite deeply involved with certain aspects of the British pragmatists. ~ Brian Ferneyhough

Inspiration may be a form of super-consciousness, or
perhaps of subconsciousness - I wouldn't know. But I am
sure it is the antithesis of self-consciousness. ~ Aaron Copland

Poets are being pursued by the philosophers today, out of the poverty of philosophy. God damn it, you might think a man had no business to be writing, to be a poet unless some philosophic stinker gave him permission. ~ William Carlos Williams

Life is sexy music, spicy-hot enchiladas and stacks of yellowed journals. It is the salsa and the gossip that floats on city breezes ~ Karl Wiggins

Aristotle's position on anger is that it is one of the most complex and distinctive of the human emotions, that it involves bodily, psychological, social, and moral dimensions, and that anger can and ought to be felt and acted upon in a number of right ways. ~ Gregory Sadler

We chose to do this work mathematically, which has the advantage of precision but is not always appreciated by readers. It is perhaps for this reason that anthropologists have not shown much interest in these models, unlike economists, for example, for whom the use of mathematics poses no problem. However, one could reach the same conclusions by using just a bit of common sense. ~ Luigi Luca Cavalli-Sforza

On January 27, 2001, the focus of my career and the process of changing the desires of my heart all began. It was no longer about me but rather how I could impact others for the Kingdom. I officially was in the people business. That philosophy, combined with a warrior mentality, I believe, has endeared me to being labeled a positive clubhouse influence. ~ Tony Clark

Trying to find answers to why and how my life got into such a dismal mess, I sought answers in the scriptures, in religion and philosophy, but it only confused me further. Stories, on the other hand, helped me cope, heal and recover. ~ Indu Muralidharan

Avoid judging others by trying to understand others and their concepts of love and care. ~ Debasish Mridha

[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are useful in testing the stability of a theory. ~ Gian-Carlo Rota

Intelligence is a tenant in the house of wisdom.
Knowledge is a tenant in the house of nature.
Insight is a tenant in the house of understanding.
Wealth is a tenant in the house of risk.
Mastery is a tenant in the house of discipline.
Patience is a tenant in the house of virtue.
Tolerance is a tenant in the house of freedom.
Awareness is a tenant in the house of experience.
Rest is a tenant in the house of sleep.
Laughter is a tenant in the house of joy.
Hope is a tenant in the house of faith.
Contentment is a tenant in the house of peace.
Kindness is a tenant in the house of love.
Harmony is a tenant in the house of order.
Humility is a tenant in the house of honor.
Caution is a tenant in the house of prudence.
Speech is a tenant in the house of silence.
Certainty is a tenant in the house of conviction.
Expectation is a tenant in the house of desire.
Need is a tenant in the house of want.
Truth is a tenant in the house of reality.
Chance is a tenant in the house of fate.
Time is a tenant in the house of eternity.
Life is a tenant in the house of death.
Nature is a tenant in the house of God. ~ Matshona Dhliwayo

The philosophy of the school was quite simple - the bright boys specialised in Latin, the not so bright in science and the rest managed with geography or the like. ~ Aaron Klug

In any genre it may happen that the first great example contains the whole potentiality of the genre. It has been said that all philosophy is a footnote to Plato. It can be said that all prose fiction is a variation on the theme of Don Quixote. ~ Lionel Trilling

No one can reach the pinnacle of success without crossing the treacherous valleys of failures. ~ Debasish Mridha

The beauty of a face is transient, but the beauty of a heart is everlasting and magnificent. ~ Debasish Mridha

Mathematics, natural science, laws, arts, even morality, etc. do not completely fill the soul; there is always a space left over reserved for pure and speculative reason, the emptiness of which prompts us to seek in vagaries, buffooneries, and mysticism for what seems to be employment and entertainment, but what actually is mere pastime undertaken in order to deaden the troublesome voice of reason, which, in accordance with its nature, requires something that can satisfy it and does not merely subserve other ends or the interests of our inclinations. ~ Immanuel Kant

Tuesdays are full of popcorn & smiles. ~ Anthony T. Hincks

This Self is never born, nor does It die. It did not spring from anything, nor did anything spring from It. This Ancient One is unborn, eternal, everlasting. It is not slain even though the body is slain. ~ The Upanishads

Tolerating organized crime promotes the cheap philosophy that everything is a racket. It promotes cynicism among adults. It contributes to the confusion of the young and to the increase of juvenile delinquency. ~ Robert Kennedy

In my reading of philosophy, I saw that there were innumerable problems that nobody was giving answers for. the Bible, it struck me, dealt with man's problems in a sweeping, all-encompassing thrust. ~ Francis Schaeffer