01. Notes on the System's Construction

 

 Notes in Learning the “Language”

 of the Construction of

Alfred North Whitehead’s and Bertrand Russell’s

Principia Mathematica to *56

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Denoting Variables and Constants:

Small letters of ordinary alphabet are all used as variables

(except “p” and “s” after *40 when p and s are assigned as constants.)

Capital letters used as constants:

       B, C, D, E, F, I and J.

 Small Greek letters used as constants: є epsilon, ί iota, and later  η eta, θ theta, ω omega.

 Certain Greek capitals will be introduced as constants, but not as variables.

p, q, r : propositional letters that will stand for variable propositions to *40: onwards “p” must not be used as a variable.

f, g, φ phi, ψ psi, χ chi, θ theta, and (until *33) F : Functional letters that will not be used for variable functions.

 The small Greek letters not named above will be used for variables whose values are classes, and will be referred to as ‘Greek letters.’

 The small common letters other than p, q, r, s, f and g will be used for variables whose values are not known to be functions, classes or relationships. These will be referred to as ‘small Latin letters.’

 Later:    variable classes: small Greek letters

              variable relationships: Capitals

              variables not given as necessarily classes or relations: small Latin letters

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These early posts are more abbreviated in relation to Whitehead and Russell’s original text than later posts will be. I hear Bertrand Russell’s voice so clearly in this introduction that I would judge that he actually wrote this, but expressing, I suppose both men’s thought discussed at length between them. I stress this is only my feeling, and the point is of no importance, but the text delights me to a great degree, as has every other Russell work I have read, and in the same fashion.

Beginning here to define terms that will express the work, these are largely familiar from the study of mathematics. However the authors are persistent in saying within the work, and I am reinforcing here with my own voice, that the title Principia Mathematica is a sort of joke. The work is one of metaphysics, in which the introduction constructs a wondrous web of means of thought and expression of fine distinction. Then the Body of the work expresses this new metaphysical construct in discussing mathematics.

In every discussion or analysis of Whitehead and Russell’s Principia Mathematica soon they want to change, modernize and simplify the work to conform to other agendas they have, usually in making the present work into one of mathematics. This is a mistake, for the goal of this work is to develop a condition of the mind in the reader that did not exist before beginning it. If one feels that it is necessary to change or simplify this work, you are playing in the wrong sandbox.

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