I should like to believe my people's religion, which was just what I could wish, but alas, it is impossible. I have really no religion, for my God, being a spirit shown merely by reason to exist, his properties utterly unknown, is no help to my life. I have nor the parson's comfortable doctrine that every good action has its reward, and every sin is forgiven. My whole religion is this: do every duty, and expect no reward for it, either here or hereafter. .
I am looking forward very much to getting back to Cambridge, and being able to say what I think and not to mean what I say: two things which at home are impossible. Cambridge is one of the few places where one can talk unlimited nonsense and generalities without anyone pulling one up or confronting one with them when one says just the opposite the next day. .
Thee might observe incidentally that if the state paid for child-bearing it might and ought to require a medical certificate that the parents were such as to give a reasonable result of a healthy child – this would afford a very good inducement to some sort of care for the race, and gradually as public opinion became educated by the law, it might react on the law and make that more stringent, until one got to some state of things in which there would be a little genuine care for the race, instead of the present haphazard higgledy-piggledy ways. .
Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true ... If our hypothesis is about anything, and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate. .
It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect and yet true. .
Pure Mathematics is the class of all propositions of the form “p implies q,” where p and q are propositions containing one or more variables, the same in the two propositions, and neither p nor q contains any constants except logical constants. And logical constants are all notions definable in terms of the following: Implication, the relation of a term to a class of which it is a member, the notion of such that, the notion of relation, and such further notions as may be involved in the general notion of propositions of the above form. In addition to these, mathematics uses a notion which is not a constituent of the propositions which it considers, namely the notion of truth. .
I have been merely oppressed by the weariness and tedium and vanity of things lately: nothing stirs me, nothing seems worth doing or worth having done: the only thing that I strongly feel worth while would be to murder as many people as possible so as to diminish the amount of consciousness in the world. These times have to be lived through: there is nothing to be done with them. .
A logical theory may be tested by its capacity for dealing with puzzles, and it is a wholesome plan, in thinking about logic, to stock the mind with as many puzzles as possible, since these serve much the same purpose as is served by experiments in physical science. .
Take the question whether other people exist. ...It is plain that it makes for happiness to believe that they exist – for even the greatest misanthropist would not wish to be deprived of the objects of his hate. Hence the belief that other people exist is, pragmatically, a true belief. But if I am troubled by solipsism, the discovery that a belief in the existence of others is 'true' in the pragmatist's sense is not enough to allay my sense of loneliness: the perception that I should profit by rejecting solipsism is not alone sufficient to make me reject it. For what I desire is not that the belief in solipsism should be false in the pragmatic sense, but that other people should in fact exist. And with the pragmatist's meaning of truth, these two do not necessarily go together. The belief in solipsism might be false even if I were the only person or thing in the universe. .
The number of syllables in the English names of finite integers tends to increase as the integers grow larger, and must gradually increase indefinitely, since only a finite number of names can be made with a given finite number of syllables. Hence the names of some integers must consist of at least nineteen syllables, and among these there must be a least. Hence "the least integer not nameable in fewer than nineteen syllables" must denote a definite integer; in fact, it denotes 111, 777. But "the least integer not nameable in fewer than nineteen syllables" is itself a name consisting of eighteen syllables; hence the least integer not nameable in fewer than nineteen syllables can be named in eighteen syllables, which is a contradiction. This contradiction was suggested to us by Mr. G. G. Berry of the Bodleian Library. .
People are said to believe in God, or to disbelieve in Adam and Eve. But in such cases what is believed or disbelieved is that there is an entity answering a certain description. This, which can be believed or disbelieved is quite different from the actual entity (if any) which does answer the description. Thus the matter of belief is, in all cases, different in kind from the matter of sensation or presentation, and error is in no way analogous to hallucination. A hallucination is a fact, not an error; what is erroneous is a judgment based upon it. .
In the revolt against idealism, the ambiguities of the word “experience” have been perceived, with the result that realists have more and more avoided the word. It is to be feared, however, that if the word is avoided the confusions of thought with which it has been associated may persist. .
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