(source) 
Bertrand Russell
(18 May 1872  2 Feb 1970)

Bertrand Russell Quotes on Logic (10 quotes)
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Frege has the merit of ... finding a third assertion by recognising the world of logic which is neither mental nor physical.
— Bertrand Russell
Only mathematics and mathematical logic can say as little as the physicist means to say. (1931)
— Bertrand Russell
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
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 twofold logical connection, travelling one up, one down; the upward connection proceeds by induction, the downward by deduction.
— Bertrand Russell
The distinctive Western character begins with the Greeks, who invented the habit of deductive reasoning and the science of geometry.
— Bertrand Russell
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
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
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
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
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
See also:
 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)