A Quote by Georg Cantor

The old and oft-repeated proposition "Totum est majus sua parte" [the whole is larger than the part] may be applied without proof only in the case of entities that are based upon whole and part; then and only then is it an undeniable consequence of the concepts "totum" and "pars". Unfortunately, however, this "axiom" is used innumerably often without any basis and in neglect of the necessary distinction between "reality" and "quantity", on the one hand, and "number" and "set", on the other, precisely in the sense in which it is generally false.

Georg Cantor

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Any Applied Axiom Based Basis Between Case Concepts Consequence Distinction Entities False Generally Hand However Larger May Necessary Neglect Number Oft Often Old Only Other Part Precisely Proof Proposition Quantity Reality Repeated Sense Set Than Then Undeniable Unfortunately Used Which Whole Without

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Georg Cantor
German - Mathematician
March 3, 1845 - January 6, 1918

That the world is not the embodiment of an eternal rationality can be conclusively proved by the fact that the piece of the worldthat we know--I mean our human reason--is not so very rational. And if it is not eternally and completely wise and rational, then the rest of the world will not be either; here the conclusion a minori ad majus, a parte ad totum applies, and does so with decisive force.

Friedrich Nietzsche

To make our position clearer, we may formulate it in another way. Let us call a proposition which records an actual or possible observation an experiential proposition. Then we may say that it is the mark of a genuine factual proposition, not that it should be equivalent to an experiential proposition, or any finite number of experiential propositions, but simply that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from those other premises alone.

A.J. Ayer

To swear, except when necessary, is becoming to an honorable man. [Lat., In totum jurare, nisi ubi necesse est, gravi viro parum convenit.]

Quintilian

Then there is the further question of what is the relationship of thinking to reality. As careful attention shows, thought itself is in an actual process of movement. That is to say, one can feel a sense of flow in the stream of consciousness not dissimilar to the sense of flow in the movement of matter in general. May not thought itself thus be a part of reality as a whole? But then, what could it mean for one part of reality to 'know' another, and to what extent would this be possible?

David Bohm

All our thoughts and concepts are called up by sense-experiences and have a meaning only in reference to these sense-experiences. On the other hand, however, they are products of the spontaneous activity of our minds; they are thus in no wise logical consequences of the contents of these sense-experiences. If, therefore, we wish to grasp the essence of a complex of abstract notions we must for the one part investigate the mutual relationships between the concepts and the assertions made about them; for the other, we must investigate how they are related to the experiences.

Albert Einstein

We assert then that nothing has been accomplished without interest on the part of the actors; and — if interest be called passion, inasmuch as the whole individuality, to the neglect of all other actual or possible interests and claims, is devoted to an object with every fibre of volition, concentrating all its desires and powers upon it — we may affirm absolutely that nothing great in the World has been accomplished without passion.

Georg Wilhelm Friedrich Hegel

For the sacrificed, in the hour of sacrifice, only one thing counts: faith-alone among enemies and skeptics. Faith, in spite of the humiliation which is both the necessary precondition and the consequence of faith, faith without any hope of compensation other than he can find in a faith which reality seems so thoroughly to refute.

Dag Hammarskjold

And do you know, do you know that mankind can live without the Englishman, it can live without Germany, it can live only too well without the Russian man, it can live without science, without bread, and it only cannot live without beauty, for then there would be nothing at all to do in the world! The whole secret is here, the whole of history is here. Science itself would not stand for a minute without beauty

Fyodor Dostoevsky

I considered the case and realized that if something can exist in opinion without existing in reality, or exist in reality without existing in opinion, the conclusion is that of the two parallel lives, only opinion is necessary – not reality, which is only a secondary consideration.

Machado de Assis

First, then, I say, that the mind, which we often call the intellect, in which is placed the conduct and government of life, is not less an integral part of man himself, than the hand, and foot, and eyes, are portions of the whole animal.

Lucretius

Man is not only part of a field, but a part and member of his group. When people are together, as when they are at work, then the most unnatural behavior, which only appears in late stages or abnormal cases, would be to behave as separate Egos. Under normal circumstances they work in common, each a meaningfully functioning part of the whole.

Max Wertheimer

Horsemanship is the one art for which it seems one needs only practice. However, practice without true principles is nothing other than routine, the fruit of which is a strained and unsure execution, a false diamond which dazzles semi-connoisseurs often more impressed by the accomplishments of the horse than the merit of the horseman.

Francois Robichon de La Gueriniere

All writing seems to me worse in the state of proof than in any other form. In manuscript one's own wisdom is rather remarkable to one, but in proof it has the effect of one's private furniture repeated in the shop windows. And then there is the sense that the worst errors will go to press unnoticed!

George Eliot

Number, in consequence, includes all things that are capable of comparison. It is not then in quantity only that number produces proportion; it produces it in all things that are capable of agreement and differences in any way at all, whether substantially or accidentally.

Nicholas of Cusa

We may lay it down as an incontestible axiom, that, in all the operations of art and nature, nothing is created; an equal quantity of matter exists both before and after the experiment; the quality and quantity of the elements remain precisely the same; and nothing takes place beyond changes and modifications in the combination of these elements. Upon this principle the whole art of performing chemical experiments depends: We must always suppose an exact equality between the elements of the body examined and those of the products of its analysis.

Antoine Lavoisier

An Individual, whatever species it might be, is nothing in the Universe. A hundred, a thousand individuals are still nothing. The species are the only creatures of Nature, perpetual creatures, as old and as permanent as it. In order to judge it better, we no longer consider the species as a collection or as a series of similar individuals, but as a whole independent of number, independent of time, a whole always living, always the same, a whole which has been counted as one in the works of creation, and which, as a consequence, makes only a unity in Nature.

Georges-Louis Leclerc, Comte de Buffon

A Quote by Georg Cantor

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