But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortois
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.
All traditional logic habitually assumes that precise symbols are being employed. It is therefore not applicable to this terrestial life but only to an imagined celestial existence... logic takes us nearer to heaven than other studies.
The rules of logic are to mathematics what those of structure are to architecture.
The question of "unreality"is a very important one. Misled by grammar, the great majority of those logicians who have dealt with this question have dealt with it on mistaken lines. They have regarded grammatical form as a surer guide in analysis than, in fact, it is. And they have not known what dif
Inferences of Science and Common Sense differ from those of deductive logic and mathematics in a very important respect, namely, when the premises are true and the reasoning correct, the conclusion is only probable.
Logic must no more admit a unicorn than zoology can.
I am allowed to use plain English because everybody knows that I could use mathematical logic if I chose.
This illustrates an important truth, namely, that the worse your logic, the more interesting the consequences to which it gives rise.
The true function of logic ... as applied to matters of experience ... is analytic rather than constructive; taken a priori, it shows the possibility of hitherto unsuspected alternatives more often than the impossibility of alternatives which seemed prima facie possible. Thus, while it liberates ima
Only mathematics and mathematical logic can say as little as the physicist means to say.
The fact that all Mathematics is Symbolic Logic is one of the greatest discoveries of our age; and when this fact has been established, the remainder of the principles of mathematics consists of the analysis of Symbolic Logic itself.
The conception of the necessary unit of all that is resolves itself into the poverty of the imagination, and a freer logic emancipates us from the straitwaistcoated benevolent institution, which idealism palms off as the totality of being.
Ordinary language is totally unsuited for expressing what physics really asserts, since the words of everyday life are not sufficiently abstract. Only mathematics and mathematical logic can say as little as the physicist means to say.
Analytic It is clear that the definition of "logic" or "mathematics" must be sought by trying to give a new definition of the old notion of "analytic" propositions.
Formality Thus the absence of all mention of particular things or properties in logic or pure mathematics is a necessary result of the fact that this study is, as we say, "purely formal".
I am delighted to know that Principia Mathematica can now be done by machinery. . . I am quite willing to believe that anything in deductive logic can be done by machinery.
In the first place a philosophical proposition must be general. It must not deal specially with things on the surface of the earth, or within the solar system, or with any other portion of space and time. . . . This brings us to a second characteristic of philosophical propositions, namely that they
Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.
I know how hard it is for you to put food on your family.
He has certainly earned a reputation as a fantastic mayor, because the results speak for themselves. I mean, New York's a safer place for him to be.
Too many of our children cannot read. Reading is the building block, and it must be the foundation for education reform.
If there's any comparison between the compassion and decency of the American people and the terrorist tactics of extremists, it's flawed logic. It's just I simply can't accept that. It's unacceptable to think that there's any kind of comparison between the behavior of the United States of America an
Sometimes when I sleep at night I think of (Dr. Seuss's) 'Hop on Pop.'
We come before God to pray for the missing and the dead, and for those who loved them... Our purpose as a nation is firm, yet our wounds as a people are recent and unhealed and lead us to pray... This world he created is of moral design. Grief and tragedy and hatred are only for a time. Goodness, re
I've thought a lot about what it means to be the President. I also understand an administration is not one person but an administration is dedicated citizens who are called by the President to serve the country, to serve a cause greater than self. And so I've thought about an administration of peopl
Iran aggressively pursues these weapons and exports terror, while an unelected few repress the Iranian people's hope for freedom. The Iraqi regime has plotted to develop anthrax, and nerve gas, and nuclear weapons for over a decade. This is a regime that has already used poison gas to murder thousan
America will never seek a permission slip to defend the security of our people.
I don't know, maybe I made it up. Anyway, it's an arbo-tree-ist, somebody who knows about trees.
I think the fundamentals of the economy are finally in the electronic economy and they are strong are we have reason for great optimism.
Americans are a free people, who know that freedom is the right of every person and the future of every nation. The liberty we prize is not America's gift to the world; it is God's gift to humanity.
America is a Nation with a mission - and that mission comes from our most basic beliefs. We have no desire to dominate, no ambitions of empire. Our aim is a democratic peace - a peace founded upon the dignity and rights of every man and woman.
Good stewardship of the environment is not just a personal responsibility, it is a public value... Our duty is to use the land well, and sometimes not to use it at all. This is our responsibility as citizens, but more than that, it is our calling as stewards of the earth.
Today the Iraqi and Afghan people are on the path to democracy and freedom. The governments that are rising will pose no threat to others. Instead of harboring terrorists, they're fighting terrorist groups. And this progress is good for the long-term security of all of us.
I do not like abortions. I will do everything in my power to restrict abortion.
We can have confidence in the long-term foundation of our economy ... I think the system basically is sound. I truly do.
A good run adds a little bounce to my step. I get a certain amount of self-esteem from it.
Â”I favor leaving up to a woman and her doctor the abortion question.Â”
I support the death penalty because I believe, if administered swiftly and justly, capital punishment is a deterrent against future violence and will save other innocent lives.