Aristotle's Syllogism and the Creation of Modern Logic by Lukas M. Verburgt;Matteo Cosci;

Author:Lukas M. Verburgt;Matteo Cosci;
Language: eng
Format: epub, pdf
Publisher: Bloomsbury UK

8

Hugh MacColl: Never twist the syllogism again

Jean-Marie C. Chevalier

1 Introduction

Christine Ladd-Franklin thought it ‘unfortunate that Mr. MacColl’s valuable work in Logic should have met with almost complete neglect in England’.1 Hugh MacColl still deserves a better place in the history of logic than he currently has, for his achievements are not few. He is famous for having developed a modern propositional logic a few years prior to the publication of Frege’s Begriffsschrift, claiming that logic should not be a calculus of classes but of propositions. Russell called him ‘the first to have found symbolic logic on propositions and implication’.2 Another of his contemporaries acknowledged that ‘in making the proposition the unit of thought, he has brought the symbolic logic into line with the general theory of modern logic to-day’.3 He is also known for debating with Russell the problem of the existential import of propositions and for their controversy on ‘if’ and ‘imply’. MacColl challenged the use of material implication, used the notion of propositional function, and opened the way to non-classical and modal logics and to logical pluralism.4 It has been claimed by specialists that ‘MacColl’s definition of the syllogism as an inference defined in terms of implication, however, was perhaps his more significant contribution to the over-all development of logic’.5 Ladd-Franklin too considered it one of MacColl’s greatest accomplishments to have defined universal affirmative propositions in terms of implication, writing that ‘[t]he logic of the non-symmetrical affirmative copula, “all a is b,” was first worked out by Mr. MacColl’.6 Nevertheless, MacColl’s goal was not to produce a new theory of syllogism, which he considered one of the many fields of application of his new symbolic logic: ‘No part of logic has received so much attention and given rise to so much discussion as the syllogisms of Aristotle. This is why I have selected them as illustrations of the application of my symbolical method.’7 But there may be more to it: his insistence on the subject may also be ‘justified by the fact that syllogistics is configured as a complete and structured deductive system, capable of providing a term of comparison for the deductive possibilities of a logical system’.8 He considered that the best illustration of the advantages of his symbolic logic was that he was not obliged, as so many logicians of time were, ‘to twist and torture simple sentences in order to adapt them for syllogistic reasoning’.9

Starting from MacColl’s treatment of the syllogism (Section 3), this chapter intends to show how his theory of implication and of hypothetical propositions was embodied (Section 4), what his conception of ‘formal certainty’ in syllogistic reasoning was (Section 5), how this came with a new conception of pure logic as propositional logic (Section 6), and finally how he could provide a solution to the problem of the presupposition of existence in syllogistic propositions (Section 7).

2 Biographical sketch

The Scottish mathematician and logician Hugh MacColl (1837–1909) lived in the northern French city of Boulogne-sur-Mer from 1865 until his death in 1909. His logical activity is usually divided into two periods, separated by an interval of literary creation.

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