I believe that one has taken the most important step in philosophy if one has gained a perfect understanding of the nature of logic and its relation to reality or experience. In the first lecture I spoke of that particular misunderstanding of logic which has been called psychologism and consists in the belief that the logical principles are psychological laws of the working of human minds. The same error may take a more general form. Often the logical rules are treated as if they were laws of nature or of "Being".
This error is committed by many "rationalistic" schools of philosophy from the time of the Eleatic Thinkers down to Hegel and some recent writers. It is committed by those who assert an "identity of thought and reality" as well as by those who believe that the "correspondence of thought and reality" which is exhibited in knowledge is due to some special property of reality, commonly expressed by the phrase that "reality is rational". It is even committed by those who like to speak of an "irrational element" in reality, because this phrase implies that reality could partly lend itself, partly oppose itself to the rule of logic.
Just as psychologism must lead to the meaningless questions: "May not other beings have a logic which is different from our human logic? May not even human minds differ in their logic? Should we not try to construct some non-Aristotelian logic?" — in the same way the general error concerning the relation of logic to experience must lead to senseless questions like these: "May there not be some region in the world where the Law of Contradiction does not hold ? Might not (say) some astronomical observation, by being contrary to the predictions of our mathematicians, show, that our calculations, and consequently our logic, were not valid for the behaviour of our heavenly bodies?" But no fact can prove or disprove the validity of logical principles, simply because they do not assert any fact, and are, therefore, compatible with any observation.
Usually our astronomical predictions are very accurately confirmed by observations, and we may justly be proud of this mastery of the human mind over nature — but we shall be speaking nonsense if we try to express our joy and our wonder by saying : "how marvellously logical is the universe! how astonishing is the corresspondence between our reasoning and the ways of nature! There must be a preëstablished harmony between them!" And yet a great many philosophers have indulged in thoughts of this kind. They
