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Home > Dictionary of Science Quotations > Scientist Names Index R > Bertrand Russell Quotes > Logic

 Bertrand Russell (18 May 1872 - 2 Feb 1970) Welsh mathematician, logician and philosopher known for his work in mathematical logic, but was also active in social and political campaigns, advocating pacifism and nuclear disarmament.

Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.
— Bertrand Russell
Our Knowledge of the External World (1914), 201.
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Mathematics is a study which, when we start from its most familiar portions, may be pursued in either of two opposite directions. The more familiar direction is constructive, towards gradually increasing complexity: from integers to fractions, real numbers, complex numbers; from addition and multiplication to differentiation and integration, and on to higher mathematics. The other direction, which is less familiar, proceeds, by analysing, to greater and greater abstractness and logical simplicity; instead of asking what can be defined and deduced from what is assumed to begin with, we ask instead what more general ideas and principles can be found, in terms of which what was our starting-point can be defined or deduced. It is the fact of pursuing this opposite direction that characterises mathematical philosophy as opposed to ordinary mathematics.
— Bertrand Russell
In Introduction to Mathematical Philosophy (1920), 1.
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Only mathematics and mathematical logic can say as little as the physicist means to say. (1931)
— Bertrand Russell
In The Scientific Outlook (1931, 2009), 57.
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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.
— Bertrand Russell
In The Scientific Outlook (1931, 2001), 61.
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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 Russell
In 'Definition of Pure Mathematics', Principles of Mathematics (1903), 3.
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Pure mathematics was discovered by Boole in a work which he called “The Laws of Thought” (1854).… His book was in fact concerned with formal logic, and this is the same thing as mathematics.
— Bertrand Russell
In 'Recent Work on the Principles of Mathematics', The International Monthly (Jul-Dec 1901), 4, 83. Relevant context appears in a footnote in William Bragg Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics (1996), Vol. 1, 442, which gives: “Russell’s essay was written for a popular audience, and (as he notes) for an editor who asked him to make the essay ‘as romantic as possible’. Russell’s considered appraisal of Boole was more sober. For instance, in Our Knowledge of the External World, Lecture II, he says of Boole: ‘But in him and his successors, before Peano and Frege, the only thing really achieved, apart from certain details, was the invention of a mathematical symbolism for deducing consequences from the premises which the newer methods shared with Aristotle.’”
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Science, in its ultimate ideal, consists of a set of propositions arranged in a hierarchy, the lowest level of the hierarchy being concerned with particular facts, and the highest with some general law, governing everything in the universe. The various levels in the hierarchy have a two-fold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.
— Bertrand Russell
In The Scientific Outlook (1931, 2009), 38.
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The distinctive Western character begins with the Greeks, who invented the habit of deductive reasoning and the science of geometry.
— Bertrand Russell
In 'Western Civilization', collected in In Praise of Idleness and Other Essays (1935), 161.
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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.
— Bertrand Russell
In Bertrand Russell, The Principles of Mathematics (1903), 5.
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The modern development of mathematical logic dates from Boole’s Laws of Thought (1854). But in him and his successors, before Peano and Frege, the only thing really achieved, apart from certain details, was the invention of a mathematical symbolism for deducing consequences from the premises which the newer methods shared with Aristotle.
— Bertrand Russell
From a Lowell Lecture delivered in Boston (Apr 1914), 'Logic as the Essence of Philosophy". Published in Our Knowledge of the External World: As A Field For Scientific Method in Philosophy (1914), Lecture II, 40. Also quoted in William Bragg Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics (1996), Vol. 1, footnote, 442. In the Footnote, Ewalt contrasts a more “romantic” view of Boole written by Russell for a popular audience. Refer to the latter quote elsewhere on this Bertrand Russell webpage, which begins “Pure mathematics was discovered by Boole….”
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The most obvious and easy things in mathematics are not those that come logically at the beginning; they are things that, from the point of view of logical deduction, come somewhere in the middle. Just as the easiest bodies to see are those that are neither very near nor very far…
— Bertrand Russell
In Introduction to Mathematical Philosophy (1920), 2.
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There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that "remembered" a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago.
— Bertrand Russell
In The Analysis of Mind (1921) 159–160.
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This method is, to define as the number of a class the class of all classes similar to the given class. Membership of this class of classes (considered as a predicate) is a common property of all the similar classes and of no others; moreover every class of the set of similar classes has to the set of a relation which it has to nothing else, and which every class has to its own set. Thus the conditions are completely fulfilled by this class of classes, and it has the merit of being determinate when a class is given, and of being different for two classes which are not similar. This, then, is an irreproachable definition of the number of a class in purely logical terms.
— Bertrand Russell
The Principles of Mathematics (1903), 115.
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What is this subject, which may be called indifferently either mathematics or logic? Is there any way in which we can define it? Certain characteristics of the subject are clear. To begin with, we do not, in this subject, deal with particular things or particular properties: we deal formally with what can be said about any thing or any property. We are prepared to say that one and one are two, but not that Socrates and Plato are two, because, in our capacity of logicians or pure mathematicians, we have never heard of Socrates or Plato. A world in which there were no such individuals would still be a world in which one and one are two. It is not open to us, as pure mathematicians or logicians, to mention anything at all, because, if we do so we introduce something irrelevant and not formal.
— Bertrand Russell
In Introduction to Mathematical Philosophy (1920), 196-197.
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When the intensity of emotional conviction subsides, a man who is in the habit of reasoning will search for logical grounds in favor of the belief which he finds in himself.
— Bertrand Russell
In Mysticism and Logic (2004), 15.
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• 18 May - short biography, births, deaths and events on date of Russell's birth.
• Bertrand Russell - context of quote “A process which led from the amoeba to man” - Medium image (500 x 350 px)
• Bertrand Russell - context of quote “A process which led from the amoeba to man” - Large image (800 x 600 px)

In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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