"An inquiry into Meaning and Truth" by Bertrand Russell,1940

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Empirical knowledge has its basis in percepts -sense experiences- ;
from basic propositions about percepts empirical knowledge is constructed.
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Although basic propositions are not indubitably true,
as propositions of the utmost particularity,
referring to percepts,
they are the most dependable propositions of empirical inquiry.
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Empirical knowledge requires provision for general statements,
for stating logical relationships,and for modes of inference.
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Propositions are both objective and subjective ;
they are objective in that they indicate factually,
and they are subjective in that they express the state of mind of the speaker
-belief,denial,or doubt-.
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Sentences are true if what they indicate is the case ;
to know a sentence to be true one must perceive its verifier
-the event the sentence indicates-.
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"Introduction to Mathematical Philosophy" by Bertrand Russell,1919

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Mathematics can be shown to be a logical development of certain basic ideas ;
mathematics can be reduced to logic.
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The number of a class is the class of all those classes which are similar to it,.
(Classes are similar when their members can be put into a one-to-one relation with each other.)
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A relation is symmetrical when if one thing has the relation to another,
the other has the same relation to it ;
a relation is transitive when if one thing has the relation to a second,
and the second has the same relation to a third,
the first has the relation to the third.
(Other relations are defined.)
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An infinite cardinal number satisfies the equation,n equals n plus l.
(An infinite collection has parts which have as many terms as the infinite collection itself.)
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By distinguishing between types of entities it is possible to avoid paradoxes which have perplexed philosophers for centuries.
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Mathematical truths are a priori and have nothing to do with facts about the world ;
they are logical tautologies.
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"Our knowledge of external World" by Bertrand Russell,1914

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The method of logical analysis makes the resolution of philosophical problems possible by defining the limits of scientific philosophy so as to exclude speculative metaphysics.
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We can account for our knowledge of the external world by realizing,through logical analysis,that the world as we know it is a construction from the data given in sense experience ; an individual's "private world" is the class of all data within his perspective,and a perceived object is the class of all aspects to be found in all the perspectives which include the object.
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The conception of permanent things can be constructed by reference to appearances if points are defined by reference to enclosure series of spaces,and if time is defined by reference to classes of events simultaneous with each other.
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Zeno's paradoxes of motion can be resolved by use of the mathematical theory of continuity.
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