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.
Bertrand RussellRelated topics
above constituent containing following form general implication mathematics nor pure truth usesRelated quotes
In one point I fully agree with the gentlemen to whose general views I am opposed. I feel with them, that it is impossible for us, with our limited means, to attempt to educate the body of the people. We must at present do our best to form a class who may be interpreters between us and the millions whom we govern; a class of persons, Indian in blood and colour, but English in taste, in opinions, in morals, and in intellect. To that class we may leave it to refine the vernacular dialects of the country, to enrich those dialects with terms of science borrowed from the Western nomenclature, and to render them by degrees fit vehicles for conveying knowledge to the great mass of the population.
Thomas Babington Macaulay
I've lived, Sir, a long time, and the longer I live, the more convincing Proofs I see of this Truth - That God governs in the Affairs of Men. And if a sparrow cannot fall to the ground without his Notice, is it probable that an Empire can rise without his Aid? We have been assured, Sir, in the Sacred Writings, that except the Lord build the House they labor in vain who build it. I firmly believe this, - and I also believe that without his concurring Aid, we shall succeed in this political Building no better than the Builders of Babel: We shall be divided by our little partial local interests; our Projects will be confounded, and we ourselves shall become a Reproach and Bye word down to future Ages.
Benjamin Franklin
The object of this paper is to give a satisfactory account of the Foundations of Mathematics in accordance with the general method of Frege, Whitehead and Russell. Following these authorities, I hold that mathematics is part of logic, and so belong to what may be called the logical school as opposed to the formalist and intuitionist schools. I have therefore taken Principia Mathematica as a basis for discussion and ammendment; and believe myself to have discovered how, by using the work of Mr Ludwig Wittgenstein, it can be rendered free from the serious objections which have caused its rejection by the majority of German authorities, who have deserted altogether its line of approach.
Frank P. Ramsey
By asserting the objectivity of the physical world, naturalism identifies the existence and the conditions of existence of the physical world with existence and the conditions of existence in general. It forgets that the world of the physicist necessarily refers back, through its intrinsic meaning, through the subjective world which one tries to exclude from reality as being pure appearance, conditioned by the empirical nature of man, which is incapable of reaching directly to a world of things in themselves. But while the world of the physicist claims to go beyond naive experience, his world really exists only in relation to naive experience.
Emmanuel Levinas
Do not let us imagine that discoveries in the world of the higher mathematics, of physics or biology are going to remove or even reduce our difficulties on the moral plane...The realm of morals is a world neither of quantity nor of chemical action. It is a world of values. It is precisely these values of right and wrong, of good and evil, of honesty and courage, which matter supremely for religion and national life...I am not despising science. I am only suggesting that moral values, eternal in their quality, transient in their form and application, are the foundation of a country's greatness. If moral values flourish in our common life all will be well with the nation.
Stanley Baldwin