Quotes About Logic

And where a solution appears possible, the new logic provides a method which enables us to obtain results that do not merely embody personal idiosyncrasies, but must command the assent of all who are competent to form an opinion.

When there are rational grounds for an opinion, people are content to set them forth and wait for them to operate. In such cases, people do not hold their opinions with passion; they hold them calmly, and set forth their reasons quietly. The opinions that are held with passion are always those for which no good ground exists; indeed the passion is the measure of the holder's lack of rational conviction.

But between theology and science there is a No Man's Land, exposed to attack from both sides; this No Man's Land is philosophy.

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe – because, like Spinoza's God, it won't love us in return.

1) 0 is a number. (2) The successor of any number is a number. (3) No two numbers have the same successor. (page 6) (4) 0 is not the successor of any number. (5) Any property which belongs to 0, and also to the successor of every number which has the property, belongs to all numbers.

If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument.

It must be admitted, for the reasons already stated, that logical principles are known to us, and cannot be themselves proved by experience, since all proof presupposes them. In this, therefore, which was the most important point of the controversy, the rationalists were in the right. On the other hand, even that part of our knowledge which is logically independent of experience (in the sense that experience cannot prove it) is yet elicited and caused by experience.

Plato is perpetually getting into trouble through not understanding relative terms. He thinks that if A is greater than B and less than C, then A is at once great and small, which seems to him a contradiction. Such troubles are among the infantile diseases of philosophy.

I do not agree with Plato, but if anything could make me do so, it would be Aristotle's arguments against him.

Frege's work it followed that arithmetic, and pure mathematics generally, is nothing but a prolongation of deductive logic. This disproved Kant's theory that arithmetical propositions are 'synthetic' and involve a reference to time. The development of pure mathematics from logic was set forth in detail in Principia Mathematica, by Whitehead and myself.

a priori knowledge such as mathematics or logic is general, whereas all experience is particular.

These two sentences suffice to show, as I shall try to prove, that Bergson does not know what number is, and has himself no clear idea of it.

To begin with rationality in opinion: I should define it merely as the habit of taking account of all relevant evidence in arriving at a belief. Where certainty is unattainable, a rational man will give most weight to the most probable opinion, while retaining others, which have an appreciable probability, in his mind as hypotheses which subsequent evidence may show to be preferable.

all our reasonings concerning causes and effects are derived from nothing but custom; and that belief is more properly an act of the sensitive, than of the cogitative part of our natures.

most holders of authority were bigoted, illogical and not to be taken seriously. I

If our logic is to find the common world intelligible, it must not be hostile, but must be inspired by a genuine acceptance such as is not usually to be found among metaphysicians.

The degree of one's emotion varies inversely with one's knowledge of the facts. The less you know the hotter you get.

one should not regard anything that one accepts as quite certain, but only as probable in a greater or a less degree. Not to be absolutely certain is, I think, one of the essential things in rationality.

The number 0 is the number of terms in a class which has no members, i.e. in the class which is called the null-class.

0 is the class whose only member is the null-class.

To begin with the logical objection: 'When we have found a resemblance among several objects,' Hume says, 'we apply the same name to all of them.' Every nominalist would agree. But in fact a common name, such as 'cat,' is just as unreal as the universal CAT is. The nominalist solution of the problem of universals thus fails through being insufficiently drastic in the application of its own principles; it mistakenly applies these principles only to 'things,' and not also to words.

It remains to define successor. Given any number n, let ? be a class which has n members, and let x be a term which is not a member of ?. Then the class consisting of ? with x added on will have n+1 members.

The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it.

If any one asks: 'Why should I accept the results of valid arguments based on true premisses?' we can only answer by appealing to our principle. In fact, the truth of the principle is impossible to doubt, and its obviousness is so great that at first sight it seems almost trivial. Such principles, however, are not trivial to the philosopher, for they show that we may have indubitable knowledge which is in no way derived from objects of sense. The