During his lifetime Ludwig Wittgenstein published one book review, one book 75 page book, one article and one so called children’s dictionary. Below is the book review which was written by Wittgenstein when he was an undergrad student at Cambridge.

The Science of Logic: an inquiry into the principles of accuratethought and scientific method. By P. Coffey, Ph.D. (Louvain),Professor of Logic and Metaphysics, Maynooth College. Longmans,Green & Co 1912.In no branch of learning can an author disregard the results of honest research with so much impunity as he can in Philosophy and Logic. To this circumstance we owe the publication of such a book as Mr Coffey’s Science of Logic: and only as a typical example of the work of many logicians of today does this book deserve consideration. The author’s Logic is that of the scholastic philosophers, and he makes all their mistakes-of course with the usual references to Aristotle. (Aristotle, whose name is taken so much in vain by our logicians, would turn in his grave if he knew that so many Logicians know no more about Logic to-day than he did 2,000 years ago). The author has not taken the slightest notice of the great work of the modern mathematical logicians – work which has brought about an advance in Logic comparable only to that which made Astronomy out of Astrology, and Chemistry out of Alchemy.

Mr Coffey, like many logicians, draws great advantage from an unclear way of expressing himself; for if you cannot tell whether he means to say Yes or No, it is difficult to argue against him. However, even through his foggy expression, many grave mistakes can be recognised clearly enough; and I propose to give a list of some of the most

striking ones, and would advise the student of Logic to trace these mistakes and their consequences in other books on Logic also. (The numbers in brackets indicate the pages of Mr Coffey’s book – volume I. – where a mistake occurs for the first time; the illustrative examples are my own).[36] The author believes that all propositions are of the subject-predicate form.

[31] He believes that reality is changed by becoming an object of our thoughts.

[6] He confounds the copula is with the word is expressing identity. (The word is has obviously different meanings in the propositions— Twice two is four and Socrates is mortal.)

[46] He confounds things with the classes to which they belong. (A man is obviously something quite different from mankind.)

[48] He confounds classes and complexes. (Mankind is a class whose elements are men; but a library is not a class whose elements are books, because books become parts of a library only by standing in certain spatial relations to one another – while classes are independent of the relations between their members.)

[47] He confounds complexes and sums. (Two plus two is four, but four is not a complex of two and itself.)

This list of mistakes could be extended a good deal.

The worst of such books is that they prejudice sensible people against the study of Logic.

Clearly Wittgenstein is not your average undergrad. And indeed, he wasn’t considered an average student even during his tenure as a student at Cambridge. For me this book review is indicative of things that followed. For me, Wittgenstein is the gatekeeper who stands between the classical logic of the last 2 millennia and the mathematical logic that developed in the last century. Classical philosophical logic, in a sense, stops with Wittgenstein leaving formal mathematical logic free to develop — like Chemistry out of Alchemy.

In the Tractatus, Wittgenstein somewhat rightfully points out that by chasing tautologies we are not really learning anything about the world, but only about the logic of our language. Somewhat sadly he didn’t think much of learning the logic of out language. He held that it was the world that was more interesting. I wonder what Wittgenstein would have thought of our formal languages of today, of operational and denotational semantics and the formalization of metatheory of languages. I wonder what he would have thought of the ado we make of studying the logic of our languages today.