Induction and Laws of Form

I wrote before here about the book Laws of Form. I’ve written recently about conceptual induction here. This post connects the two.

In the book Laws of Form, Appendix 2, G. Spencer-Brown interprets the calculus of indication for logic and finds a problem when it is interpreted existentially. To avoid this problem he introduces “Interpretive theorem 2” which states (p. 132): “An existential inference is valid only in so far as its algebraic structure can be seen as a universal inference.”

That is, one should interpret an existential proposition in universal terms in order to make valid inferences. One way of doing this is to refine the terms and concepts of the existential proposition so that it expresses a universal proposition. That is what people such as Aristotle, Francis Bacon, and William Whewell meant by induction. John P. McCaskey offers several examples in the history of science in which a term was redefined to narrow its extension and ensure that inductive inferences were true by definition: cholera, electrical resistance, and tides.

This conceptual understanding of induction preceded the inferential understanding adopted by J.S. Mill and common today, in which induction is an inference from particular instances. Mill introduced the principle of the uniformity of nature as a necessary major premise of all inductive inferences. Others since De MorganĀ  have tried to base inductive inference on probability. The problem of induction, now traced back to David Hume, arose from the inferential version of induction. There is no such problem for the older conceptual induction.