I like to read axiomatized versions of books

First, what does it mean to “axiomatize” an argumentative book? It is to divide the propositions of the book into two parts, called “axioms” and “theorems.” The axioms will be statements which are asserted, but which cannot be derived deductively or inductively from other statements; the theorems will be those statements which can be derived from the axioms by deduction and induction. When philosophers treat a book in the above manner, they normally do not use the word “axiom”; instead they talk about “foundations,” “premises,” “assumptions,” “presuppositions,” and such.

The paradigm of this “axiomatic” approach as applied to argumentative books is Bertrand Russell’s book A Critical Exposition of the Philosophy of Leibniz (1900) in which Russell claims that Leibniz’s metaphysics is based on five premises. Here are Russell’s words:

The principal premisses of Leibniz’s philosophy appear to me to be five. Of these some were by him definitely laid down, while others were so fundamental that he was scarcely conscious of them. I shall now enumerate these premisses, and shall endeavour to show, in subsequent chapters, how the rest of Leibniz follows from them. The premisses in question are as follows:

  1. Every proposition has a subject and a predicate.
  2. A subject may have predicates which are qualities existing at various times. (Such a subject is called a substance.)
  3. True propositions not asserting existence at particular times are necessary and analytic, but such as assert existence at particular times are contingent and synthetic. The latter depend upon final causes.
  4. The Ego is a substance.
  5. Perception yields knowledge of an external world, i.e. of existents other than myself and my states.

The fundamental objection to Leibniz’s philosophy will be found to be the inconsistency of the first premiss with the fourth and fifth; and in this inconsistency we shall find a general objection to Monadism.

What am I driving at with this? Let us take as an example John Rawl’s book A Theory of Justice (1971). It is a massive book of over 600 pages. It is very difficult to keep track of everything which is being asserted and argued for. But a reader has to have an understanding of the book before making an assessment. What is needed is some kind of skeletal structure of the book — a digest, divided into, what I am calling “axioms” and “theorems.” Such an analysis is provided by R. M. Hare in two articles, consisting of 22 pages: “Rawl’s Theory of Justice.”

Other such “axiomatizations” are provided by C. D. Broad in his Five Types of Ethical Theory (1930), especially of Sidgwick’s monumental Methods of Ethics.

What is the merit of such axiomatizations? It makes understanding and critical assessment easier.

The philosopher who was most conscious of this approach was James W. Cornman, who presented his arguments in the form of explicit premises and conclusions.

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