Formal Logic

I came across the book I want to discuss here by an odd route.

In his autobiography The Thousand-Petalled Lotus, Sangharakshita relates that, shortly after his ordination as a sramanera (novice monk), he had an academic interlude at the Benares Hindu University, studying Abhidhamma (Buddhist scripture), Pali (the language in which it was written), and Logic with Bhikkhu Kashyap. He explains the enjoyment he got from the last of these:

Though in my early and middle ‘teens I had read quite widely in philosophy, for some reason I had completely neglected this ancient and venerable partner of metaphysics, ethics, politics, aesthetics, and rhetoric. It was therefore with some trepidation that I set about making good the omission. But I need not have worried. Once I had emerged from the thickets of Formal Logic I found myself in one of the most fascinating and enjoyable stretches of the intellectual terrain in which it had ever been my lot to wander, and with companions among the most delightful it had ever been my good fortune to meet. Bradley, admittedly, was a little forbidding, but Mill and Carveth Read I found exhilarating in the extreme, while F. C. S. Schiller’s Formal Logic, a radical empiricist’s brilliant exposure of the aridities and absurdities of the subject, as traditionally expounded, was undoubtedly one of the most hilarious books I had ever encountered. While I was reading it there escaped me from time to time chuckles—even guffaws—which Kashyapji, in his room next door, never heard when I was studying Pali.

What? A book on logic that makes you laugh out loud? This I must read!

So I ordered it from Amazon.

The author, Ferdinand Canning Scott Schiller, M.A., D.Sc., Fellow and Senior Tutor of Corpus Christi College, Oxford, describes himself as a teacher of Formal Logic. Thus, he was my predecessor by about sixty years. (In the mid-1970s, I lectured on Logic to an audience of students of mathematics intermingled with philosophy students on various courses.) The book is a sustained attack on a subject which I simply don’t recognise.

The first sentence of Chapter 1 is:

The derivation of Logic from the ambiguous Greek word λογικη would seem to suggest that it is a study either of words or reasoning.

Already it appears that he is attacking a straw man, criticising logic because it does not contain psychology and linguistics within it. When I do geometry, I am under no illusion that I am measuring the Earth by my endeavours.

Later in this chapter, he says:

… in real life the distinction between true and false is always present to consciousness, and to discriminate between the true and the false is one of our most pressing and vital concerns. … A logic of real truth must, therefore, be possible. But once it is constructed, it must supersede Formal Logic and condemn it to unutterable triviality.

I beg to differ. Here are two simple declarative propositions of whose truth value I have no idea.

  • It will rain on the opening ceremony of the London Olympics next year.
  • Purple is fashionable this year.

But perhaps the subject he attacks really did exist, and was swept away in less than sixty years. After all, the book was published 563 years after the death of Ockham (who is name-checked only in connection with the triumph of Nominalism), 196 after that of Leibniz and 48 after that of Boole (neither of whom are mentioned). On the other hand, Aristotle is quoted often and extensively. If it were true that the subject has made no essential progress in over two millennia, perhaps it deserved to be swept away!

(I should add here that I remember looking at one of my sister’s high school textbooks, and seeing Barbara, Celarent, and all the rest in it. She denies ever having such a book.)

Chapter 2 is on terms (or “concepts”). The classical subdivisions of terms into relative and absoute, positive, negative and privative, are rightly criticised. However, part of this criticism is on the basis of ambiguity, which the author subdivides into equivocation, indefiniteness and indeterminateness, in a passage which seems to be as much “logic-chopping” as the analysis he criticises. However, his main criticism is that terms don’t have meaning; nothing below propositions can have meaning. Rather simplistically, this just seems to confuse “meaning” and “truth”.

In several places he asserts that the proposition P is identical with the proposition “P is true”, that is, P asserts its own truth. Has he never seen a proof by contradiction?

In a section entitled “Darwin v Formal Logic”, he claims that Darwin initiated a greater upheaval in logic than in biology, by discrediting the belief in the fixity of species. Really? He clearly thinks well of this argument, since Darwin is indexed six further times.

The subtitle of the book is A Scientific and Social Problem, and the last chapter blames Formal Logic for the stultification of science and for religious dogmatism and the Inquisition. A trifle harsh?

All this is a pity, since interspersed with the vitriol are some valuable analyses. For example, having identified “ambiguity of the middle term” as a defect which allows the premisses of a syllogism to be true but the conclusion false, he says,

The advantage of putting the argument in syllogistic form is that experience shows that when we have done wrong the mischief shows itself as an ambiguity in the middle term. And in this shape it may be easier to detect.

But reading the book is like anthropology of a lost civilisation rather than the record of a vital academic debate. I never caught myself guffawing, or even chuckling, though there were sentences that might pass as jokes, for example,

If I define a “Grabberwock” as “an etherialization of a Brolliwag”, and deny that I am making personal remarks about any one, I shall be understood to be either joking or insane


The division of food into “fish, flesh, fowl, and good red herring” is used to illustrate the horrors of Cross Division, and the “University, family and pork butcher” in the Cowley Road in Oxford is solemnly censured as illogical, without regard either to the excellence of the advertisement or the ease with which the joke is seen, and seen through, by the obtusest intelligence.

I do not think that Formal Logic, rightly construed, is as arid as Schiller maintains. When I taught Logic in Oxford (which I did chiefly to learn it myself, since I thought it would be useful to me), I proved to the students, using propositional logic, that the Four-Colour Theorem for finite maps implies the same theorem for infinite maps. I still think this is a simple case where logic generates real novelty!

A clear statement of my own view on the relation between logic and “real life” is given by Julian Jaynes, from The Origin of Consciousness in the Breakdown of the Bicameral Mind, which I already quoted in an earlier discussion of logic, but bears repeating here:

Reasoning and logic are to each other as health is to medicine, or—better—as conduct is to morality. Reasoning refers to a gamut of natural thought processes in the everyday world. Logic is how we ought to think if objective truth is our goal—and the everyday world is very little concerned with objective truth. Logic is the science of the justification of conclusions we have reached by natural reasoning. My point here is that, for such natural reasoning to occur, consciousness is not necessary. The very reason we need logic at all is because most reasoning is not conscious at all.

About Peter Cameron

I count all the things that need to be counted.
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2 Responses to Formal Logic

  1. Isn’t Google wonderful? I just discovered that “Grabberwock” occurs in a poem, parodying Lewis Carroll, on the Nazi invasion of Poland in 1939.

  2. Here is my Open Access pdf LOGIC GALLERY. It has a page for each of virtually every logician since Aristole. I think most of you will like it………

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