Whitehead on Deduction

[Ted Winslow <winslow@xxxxxxxx>]

Title: Whitehead on Deduction

Here is another passage from Whitehead (this time from Modes of Thought) relevant to the discussion of Keynes's view of the logic of the social sciences.  In it, Whitehead explains not only why "deduction" cannot be the main method of "philosophy" but also why one must be very careful in using it in a "special science" such a economics.  At the end he also explains what is meant by the claim that certain forms of deductive reasoning presuppose that interdependence is "atomic".  In particular, this is true of any form of deductive reasoning, e.g. algebra, that makes use of the idea of the "variable".  It follows that such forms cannot be validly (i.e. "rigorously") employed where relations are internal in a way relevant to the argument.  

The discussion employs the distinction I earlier pointed to in Ramsey between "human logic or the logic of truth" and "formal logic" and makes claims about human logic similar though not identical to Ramsey's.  In particular, Whitehead identifies "human logic" with a notion of "pragmatism" wider than the notion (taken from Charles Peirce) with which Ramsey identifies it.  

In his review of Ramsey's Foundations of Mathematics (X, pp. 338-9), Keynes embraces Ramsey's distinction between human and formal logic (and in doing so abandons key foundational aspects of the argument he had made in A Treatise on Probability).  The distinction, Keynes notes, was Ramsey's response to the fact that "the gradual perfection of the formal treatment [of logic] at the hands of himself [Russell], of Wittgenstein and of Ramsey had been ... gradually to empty it of content and to reduce it more and more to mere dry bones, until finally it seemed to exclude not only all experience, but most of the principles, usually reckoned logical, of reasonable thought."  Though embracing Ramsey's idea of "human logic" as the answer to how to deal with "everything" that could not be handled with formal logic,  Keynes dissented from Ramsey's attempt to elaborate the idea in terms of Peirce's pragmatism.  

Though not much attention is paid to the fact in interpretive writing on Keynes, Keynes was a student of Whitehead.  Whatever the nature of this relation, however, the following passage and much else (including the chapter in Adventures of Ideas to which I recently pointed) demonstrate, in my judgement,  that Keynes's ideas on these matters are very like Whitehead's.

I should also say, by way of introduction, that Whitehead, in sharp contrast to much contemporary writing on epistemology and the philosophy of science, took Hume's radical skepticism to be a reductio ad absurdum of the premises about experience from which it had been deduced.  In fact, he claims, Hume himself did not carry his skepticism far enough.   The final reductio ad absurdum of Hume's starting point is "solipsism of the present moment" (Symbolism, p. 38).   Whitehead's answer to Hume is to take issue with his premises about experience and to argue that direct experience shows that Hume's conception of experience as a flux of atomically conceived "sense data" is mistaken.  (A summary of the argument can be found in Whitehead's book Symbolism.)


"In this lecture we seek the evidence for that conception of the universe which is the justification for the ideals characterizing the civilized phases of human society.
   "We have been assuming as self-evident the many actualities, their forms of coordination in the historic process, their separate importance, and their joint importance for the universe in its unity.  It must be clearly understood, as stated in earlier lectures, that we are not arguing from well-defined premises.  Philosophy is the search for premises.  It is not deduction.  Such deductions as occur are for the purpose of testing the starting points by the evidence of the conclusions.
 "A special science takes the philosophic assumptions and transforms them into comparative clarity by narrowing them to the forms of the special topic in question.  Also even in reasoning thus limited to special topics, there is no absolute conclusiveness in the deductive logic.  The premises have assumed their limited clarity by reason of presuming the irrelevance of considerations extraneous to the assigned topic.  The premises are conceived in the simplicity of their individual isolation.  But there can be no logical test for the possibility that deductive procedure, leading to the elaboration of compositions, may introduce into relevance considerations from which the primitive notions of the topic have been abstracted.  The mutual conformity of the various perspectives can never be adequately determined.
 "The history of science is full of such examples of sciences bursting through the bounds of their original assumptions.  Even in pure abstract logic as applied to arithmetic, it has within the last half century been found necessary to introduce the doctrine of types to correct the omissions of the original premises.
 "Thus deductive logic has not the coercive supremacy which is conventionally conceded to it.  When applied to concrete instances, it is a tentative procedure, finally to be judged by the self-evidence of its issues.  This doctrine places philosophy on a pragmatic basis.  But the meaning of 'pragmatism' must be given its widest extension.  In much modern thought, it has been limited by arbitrary specialist assumptions.  There should be no pragmatic exclusion of self-evidence by dogmatic denial.  Pragmatism is simply an appeal to that self-evidence which sustains itself in civilized experience.  Thus pragmatism ultimately appeals to the wide self-evidence of civilization, and to the self-evidence of what we mean by 'civilization.'
 "Before we finally dismiss deductive logic, it is well to note the function of the 'variable' in logical reason.  In this connection the term variable is applied to a symbol, occurring in a propositional form which merely indicates any entity to which the propositional form can be validly applied, so as to constitute a determinate proposition.  Also the variable, though undetermined, sustains its identity throughout the arguments.  The notion originally assumed importance in algebra, in the familiar letters such as x, y, z indicating any numbers.  It also appears somewhat tentatively in the Aristotelian syllogisms, where names such as 'Socrates,' indicate 'any man, the same throughout the argument.'
 "The use of the variable is to indicate the self-identity of some use of 'any' throughout a train of reasoning.  For example in elementary algebra when x first appears it means 'any number.'  But in that train of reasoning, the reappearance of x always means 'the same number' as in the original appearance.  Thus the variable is an ingenious combination of the vagueness of any with the definiteness of a particular indication.
 "In logical reasoning, which proceeds by the use of the variable, there are always two tacit presuppositions - one is that the definite symbols of composition can retain the same meaning as the reasoning elaborates novel compositions.  The other presupposition is that this self-identity can be preserved when the variable is replaced by some definite instance.  Complete self-identity can never be preserved in any advance to novelty.  The only question is, as to whether the loss is relevant to the purposes of the argument.  The baby in the cradle, and the grown man in middle age, are in some senses identical and in other senses diverse.  Is the train of argument in its conclusions substantiated by the identity of vitiated by the diversity?
 "We thus dismiss deductive logic as a major instrument for metaphysical discussion.  Such discussion is concerned with the eliciting of self-evidence.  Apart from such self-evidence, deduction fails.  Thus logic presupposes metaphysics."  (Whitehead, Modes of Thought, pp. 105-7)

Ted
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