"The method of "postulating" what we want has many advantages; they are the same as the advantages of theft over honest toil."- Russell, Introduction to Mathematical Philosophy, New York and London, 1919, p 71.

"Almost everything that distinguishes the modern world from earlier centuries is attibutable to science, which achieved its most spectacular triumphs in the seventeenth century."Russell, History of Western Philosophy, (London, 1979) 512.

"The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it."- Russell


Mathematical Logic


Symbolic Logic

  1. Introduction
  2. Proposition Operators
  3. Equivalence
  4. Conditional
  5. Tautology
  6. Predicate Introduction
  7. Proposition Function
  8. Quantifiers
  9. Argument I
  10. Argument II


Proof Theory

  1. Definitions from Elementary Number Theory
  2. Direct Proof
  3. Proof by Contradiction
  4. Proof by Contraposition


Deduction Theory

  1. Formal Theory
  2. Formal Axiomatic Theory
  3. Examples
  4. The Deduction Theorem
  5. Examples of Proofs II
  6. Analysis of the Axiomatic Method


  History of Philosophy: As I see it 

In contradiction of mathematics and science, here I am more interested in people than in theories, in philosophers than in philosophy. Most people that I know of do not like this approach towards the subject but in my opinion, it is just a matter of preference for presenting their philosophies. The reason of this preference is to comprehend the difference between philosophy as it was understood in their period, and as it is most often understood today, at least in USA/Britain and in counties under their “control”. The other reason is that every philosophy is ultimately a way of life and every way of life implies some philosophy, for after all, philosophy is nothing more or less than the effort to think as clearly, as rigorously, as coherently and as effectively as we can about the matters most important to us. As an example of this second point consider the following. Pluto attributed the defeat of Athens in Peloponnesian War to Athens’ democracy. Furthermore, Socrates, for whom he had a profound respect, was executed by Athens’ democracy. Provided that these are historical facts, it is not hard to imagine that why pissed off Pluto’s commonwealth is the sketchy representation of Sparta instead of Athens. Even though the Sparta, at least for me, appears as a model of the state that the Nazis would establish if victorious in World War II. If one has no idea of his life or speaking a little more precisely, no idea of the sociopolitical conditions of his time, it would be very difficult, if not impossible, to answer such question like, why Athenian Pluto has chosen Sparta over Athens for his Utopia.


  Bertrand Arthur William Russell 

  Philosophy Departments Around The World 

  Philosophy of Mathematics/Science

Philosophy of Science

Philosophy of Mathematics

Turing Machines


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