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Bayle’s Use of Logic - Pierre Bayle, A Philosophical Commentary on These Words of the Gospel, Luke 14.23, ‘Compel Them to Come In, That My House May Be Full’ [1686]

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A Philosophical Commentary on These Words of the Gospel, Luke 14.23, ‘Compel Them to Come In, That My House May Be Full’, edited, with an Introduction by John Kilcullen and Chandran Kukathas (Indianapolis: Liberty Fund, 2005).

About Liberty Fund:

Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.


Bayle’s Use of Logic

Seventeenth-century French education included a more or less thorough training in logic, the art of thinking. Medieval logic textbooks were rivaled by new texts, notably the famous work of the Jansenists Arnauld and Nicole, The Logic of Port-Royal.1 Bayle frequently comments on the logic of his arguments, using the terminology common at the time. Argument was thought of as disputation, an “adversary procedure” with opposing parties (though sometimes the opponent might be imaginary).

An argument, inference, or “consequence” (see p. 75) is a set of prem-ises from which a conclusion “follows.” The premises of a valid argument “necessitate” or “compel” the conclusion: if you accept the premises as true, you must also accept the conclusion. This characteristic of a valid argument is sometimes called its “consequence”; see p. 186. (Thus “consequence” has two meanings: the argument and its validity.) A valid argument with true and accepted premises is “cogent” or “compelling.”2

Various kinds of arguments were distinguished, including the syllogism (with two premises, called in order the “major” and the “minor,” arranged in “mood and figure”; see p. 333, pp. 430–31), the enthymeme (an argument with one or more of its premises not expressly stated; see p. 186, p. 218, p. 428), and the dilemma (“either p or q, if p then r, and if q then s, therefore either r or s,” and other variants; see p. 142).

The premises of an argument were called “antecedents” (p. 75). The fundamental premises of a chain of arguments, or of all reasoning in a field, were called its “principles” (p. 72), or “common notions” (p. 68), or “maxims” (p. 416). It is pointless to try to convince people by an argument the principles of which they do not believe. Since the proposer of the argument (normally) also believes its premises, its principles must therefore be “common” to both parties (p. 43).3 Bayle often insists that discussion cannot achieve persuasion unless the issues are traced up to “common principles” (p. 134). Premises likely to be acceptable to almost anyone were called “commonplaces.”4 A “topic” is as it were a pigeon-hole in which commonplaces are stored, a magazine of premises (p. 276).

An argument that fails by using a premise that no one will believe unless they already believe the conclusion was called a “petitio principii” (p. 333), literally a “begging of the principle” (p. 23), usually called in English “begging the question” (p. 54, p. 510), or “assuming” or “supposing the thing in question” (p. 42, p. 45). (Note that “begging the question” does not mean raising a question, but assuming as premise something that will not be believed by anyone the argument is meant to convince.)

A “direct” proof argues positively from premises which imply the desired conclusion (p. 150, p. 199, p. 412). An “indirect” proof shows that a proposition is true by assuming “for the sake of argument” the truth of the proposition that contradicts the one you wish to prove, and then on that assumption constructing a hypothetical argument to a conclusion the other party will admit is absurd or impossible. Such indirect proof was called “reductio ad absurdum” (p. 72, p. 211, p. 512).

The other party’s argument could be undermined by showing that it “proves too much” (p. 175), that it implies “inconveniences,” conclusions that the other party cannot accept (p. 134). Or the argument can be “retorted,” i.e. adapted to prove conclusions inconsistent with the position of the party using it (p. 347). Or a counter-argument can be “objected” (literally “thrown up against”) its premises or its conclusion. The other party might well reply to such “difficulties,” and the reply might provoke a counter-reply; the reply might be characterized as an “evasion” (p. 37), meaning an unsuccessful attempt to avoid the force of the objection.

Some arguments are faulty because the conclusion they lead to is simply not relevant or “not to the point.” In such a case the arguer is accused of “impertinence” (see p. 42), of “changing the question” (see p. 301), or of “ignoratio elenchi” (not knowing what a proof is); see p. 348.

If an argument is unsuccessful, not because its premises are false or not accepted, but because even if they were accepted its conclusion would not follow, it is said to be a fallacy, paralogism, or sophism (p. 54, p. 411). Often Bayle is at pains to point out that even if something is accepted that in fact might well be challenged, still the opponent’s conclusion will not follow. One virtue of such an analysis is that it clears the ground, brings into sharper focus the issues in dispute: there is no need to argue about various things the parties might in fact disagree about, because they make no difference to the point in question. For examples of Bayle’s passing over disagreements that do not need to be pursued, see p. 88, p. 200, p. 480.

On moral questions a common method of argument is by example, parallel, or analogy. “If you accept that in situation X one ought to make moral judgment J, then you must also accept that in this similar situation one ought to make the same judgment.” The counter to such an argument is to point out a “disparity” between the two situations (p. 361). The practice of comparing situations and analyzing similarities and disparities was called “casuistry,” the analysis of “cases” (p. 70). Though this was recognized as a legitimate activity in principle, it was often felt that casuists were “too clever by half.” Jesuit casuists, in particular, were accused of working to make the demands of morality less exacting than they really were (pp. 245, 319).5

The fierce contests fought with the aid of the art of logic were often carried on unfairly, in Bayle’s opinion. Hence his warning that he will not accept that his book has been “answered” if opponents merely find various minor faults of reasoning—they must come to grips with his main and best arguments for toleration; see p. 38, p. 478. On the other hand, he claims that he himself does not treat his opponents unfairly (pp. 175–76, p. 423). Compare DHC, art. “Chrysippus,” rem. G.

[1. ]Arnauld, Antoine, and Pierre Nicole, Logic or the Art of Thinking (first edition 1662). Translated into English by Jill Buroker (Cambridge: Cambridge University Press, 1996).

[2. ]If one or more of the premises is not asserted but merely “supposed” (“for the sake of argument”), the argument is hypothetical, useful for showing what would follow from what, but not proving anything.

[3. ]If the arguer does not believe one or more of the premises but supposes that the other party does, the argument is “ad hominem”—not a proof, but an argument suitable for shaking the other party’s current belief, or, as Bayle says, a “Representation importing that they did not act consistently with their own Principles” (p. 417; see also pp. 124, 331).

[4. ]However, this term (as also “maxims”) was often used contemptuously, since what some people think is obvious to everyone may be just prejudice; see p. 147.

[5. ]The reputation of the Jesuit casuists was attacked especially by Blaise Pascal’s Letters of a Provincial, for which material was provided by the Jansenist Antoine Arnauld; it was later translated into Latin by Arnauld’s colleague Nicole.