"Suppose that the colour struck you as brighter on one day than on another; would you sometimes say: "I must be wrong, that colour is certainly the same as yesterday"? This shews that we do not always resort to what memory tells us as the verdict of the highest court of appeal."

Christianity is not a doctrine, I mean, a theory about what has happened and will happen to the human soul, but a description of something that actually takes place in human life. For 'consciousness of sin' is a real event an so are despair and salvation through faith. Those who speak of such things (Bunyan for instance) are simply describing what has happened to them, whatever gloss anyone may want to put on it.

Brouwer is right when he says that the properties of his Pendelzahl [pendulum number] are incompatible with the law of the excluded middle. But, saying this doesn’t reveal a peculiarity of propositions about infinite aggregates. Rather, it is based on the fact that logic presupposes that it cannot be a priori — i.e. logically — impossible to tell whether a proposition is true or false. For, if the question of the truth or falsity of a proposition is a priori undecidable, the consequence is that the proposition loses its sense, and the consequence of this is precisely that the propositions of logic lose their validity for it.

This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. The spirit expresses itself in an onwards movement, building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery — in its variety; the second at its center — in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same.

There are problems I never tackle, which do not lie in my path or belong to my world. Problems of the intellectual world of the West which Beethoven (& perhaps Goethe to a certain extent) tackled & wrestled with but which no philosopher has ever confronted (perhaps Nietzsche passed close to them). And perhaps they are lost to western philosophy, that is there will be no one there who experiences and so can describe the development of this culture as an epic. Or more precisely it just is no longer an epic, or is one only for someone who observes it from outside & perhaps Beethoven did this with prevision (as Spengler hints in one place).

The essential business of language is to assert or deny facts. Given the syntax of a language, the meaning of a sentence is determinate as soon as the meaning of the component words is known. In order that a certain sentence should assert a certain fact there must, however the language may be constructed, be something in common between the structure of the sentence and the structure of the fact.

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Giving grounds, however, justifying the evidence, comes to an end; but the end is not certain propositions striking us immediately as true i.e. It is not a kind of seeing on our part; it is our acting which lies at the bottom of the language game.

[T]he enigma of the continuum arises because language misleads us into applying to it a picture that doesn’t fit. Set theory preserves the inappropriate picture of something discontinuous, but makes statements about it that contradict the picture, under the impression that it is breaking with prejudices; whereas what should really have been done is to point out that the picture just doesn’t fit…