Harry K. Wells on the History of Logic

by Ralph Dumain

A former student of the Marxist philosopher Harry Wells sent me a paper Wells distributed in his course, before McCarthyism caught up to Wells:

Wells, Harry K. "Historical Origins of the Logic of Classification and the Logic of Genesis." Oneonta, New York, Dept. of Philosophy, Hartwick College. October 1961. 53 pp. Based on chapters 6 & 7 of the author's 1950 dissertation "Process and Unreality."

Introduction: Stages in the Science of Logic
Chapter 1: Logical and Ontological Principles: Laws of Thought and Laws of Being
Chapter 2: Plato and Heraclitus
Chapter 3: Aristotle's Logic of Classification
Chapter 4: Hegel and Aristotle
Chapter 5: Hegel's Logic of Genesis
Conclusion: The Logic of Genesis and the Twentieth Century Crisis in Thought

This is my capsule review.

(1) First, I'm impressed with the distinction between laws of being (ontological view) and laws of thought (propositional view), and the historical relation posited between them. It is interesting to see the views of Jevons and Cohen and Nagel. My own position on formal logic has always been propositional, not ontological, but apparently this is at variance with many other philosophers throughout history. Wells poses the question, whether one can maintain ontological and propositional perspectives at variance with one another (p. 9-10). He seems to think that this won't work. I don't know.

(2) It's interesting that he identifies the logic of genesis with Marxism and Existentialism, both philosophies exiled from mainstream western philosophy. I don't know what else to say about this, though.

(3) The chapter on the ancient Greeks is fascinating, particularly the war of Plato against Heraclitus and Plato' dubious ontological motives. Similarly interesting is Aristotle's logic of classification.

(4) The summary of Hegel's logic of genesis is also of great interest.

(5) I am unhappy with the conclusion, though. First, the posited connection between logic and the sciences disturbs me. Secondly, the historical development of both. I can see the hiatus between the development of logic in Aristotle and the redefinition of the subject in Hegel's time. However, the connection between the development of logic and the development of the sciences is not at all clear to me.

(6) Wells claims that science emerges from classification at the beginning of the 19th century. Also that logic, outside of Hegel, never caught up. But I see two great omissions. First, there is the development of modern physics from Galileo and Newton on. This is hardly a taxonomic science. Secondly, the development of physics is congruent with the development of the calculus, which is hardly a formalism of stasis. This is all completely missing from Wells' survey.

(7) The next question would be the relation between logic and mathematics (calculus). Well, we know that calculus could not overcome its logical contradictions until well into the 19th century, but I'm not aware that logic itself was basically revised during this period. Mathematicians had to tolerate contradictions until they could overcome them. Calculus did not deal with qualitative change, of course, but it did learn how to overcome the logical contradictions of motion.

(8) Logic itself began to evolve late in the 19th century, both with new formalisms—Frege, etc.—and with developments in the foundations of mathematics. The criticism of formal logic overlooks all of these developments and is hence way out of date.

(9) All the sciences of course have developed way beyond taxonomy for a long time. They seem to have gotten along without any major preoccupations with logic, although there have been conceptual crises yet to be resolved. For example, quantum mechanics yielded attempts to apply three-valued logic to apply to indeterminate states, not to mention the (dialectical?) principle of complementarity. There might be an interesting conceptual crisis to which a new conception of logic might apply, but I'm not aware that any particular innovation has definitively taken root. Wells' examples (p. 49-50) are rather lame in comparison to these problems.

(10) The question of why Hegel is completely overlooked by modern logic is well worth asking. G.H. von Wright gives some credit to Hegel even though Hegel is not part of his purview. But modern logic involves a number of developments of conceivable relevance to dialectics, not just in foundations of mathematics, but in many-valued logics, tense logic, paraconsistent logic (which admits contradictions), etc. Whether these can be considered the old static logics is debatable, but either way they should be investigated and compared to Hegel's logic and determined whether they adequately convey genesis and not merely classification. In logic there have also been opposing schools of ontological thought from the atomism of Russell to the holism of Quine.

(11) Some of these developments in formal logic have been deemed to be applications of dialectical logic (e.g. Graham Priest's paraconsistent logic). Conversely, others have attempted to formalize Hegel's logic. Whether or not such efforts encapsulate the essence of dialectical thinking or whether formalization is fundamentally beside the main point, I'm not certain. There are also claims that Hegelian logic is a concrete logic (logic of content), while others are abstract logics. One would have to understand both areas in order to evaluate the alleged shortcomings of formal logic with respect to something else. There may well be a substantive issue here, but it is difficult to determine in light of the amateurishness that plagues Marxist thinkers about logic.

(12) In sum, I think Wells raises important issues, but his conclusions are unconvincingly argued. The need for dialectical thinking may or may not be related to the need for development of a different logic. The persistence of outmoded ways of thinking may or may not be related to the practice of formal logic. I myself don't really know much about the relation between the ontological and propositional outlooks in modern logic, but perhaps there is an issue here where further inspection is indicated. Ontology itself may be the primary issue. Lack of a dialectical perspective may also be important, per Wells' dissertation, where he finds Whitehead way behind Hegel.


"The goal of Stalinism is to make yourself anonymous."
--- R. Dumain to Jim Murray, 6/28/03

13 November 2003

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Pragmatism and Its Discontents: Annotated Selected Bibliography

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Process and Unreality: A Criticism of Method in Whitehead's Philosophy
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