Penn State University Press
  • Reasoned Grammer, Logic, and Rhetoric at Port-Royal

A substantial distinction between grammar and logic 1 is prima facie conspicuous in the works of the Port-Royal Jansenists, Antoine Arnauld (1612–94), Claude Lancelot (1615–95), and Pierre Nicole (1625–95), if for no other reason than that they coauthored separate works for each discipline. Arnauld and Lancelot published The Reasoned and General Grammar (GGR) in 1660, and, in 1662, Arnauld and Nicole published The Port-Royal Logic (LAP), which the two authors saw fit to revise four times: in 1664, 1668, 1671, and 1683. The distinction is also implied by the dubbing of The Reasoned Grammar as “the art of speaking,” and of The Logic as “the art of thinking”; in the Cartesian world that the authors embrace, it is agreed that, while the material world holds sway over speech, thought uncontroversially belongs to the mental world. Finally, the distinction is explicit when Arnauld and Nicole, before they include, in the fifth edition of The Logic, material borrowed from The Reasoned Grammar, warn the reader that the inclusion does not imply that each discipline does not keep its particularities: “It is of no importance to examine whether they [parts of speech] are the exclusive domain of grammar or of logic, and it is more expedient to say that whatever thing is useful toward comprehending a particular art belongs to that art, whether knowledge of that thing is particular to the art, or whether other arts and sciences use it.” 2

In this paper, I argue that, despite the foregoing evidence, the substantial distinction between reasoned grammar and logic that the Port-Royal authors may desire is not tenable. I maintain that Arnauld, Lancelot, and Nicole are committed to the view that reasoning is an extension of judging and that judging is as much the domain of grammar as it is that of logic; in short, grammar can tell a good inference from a bad one. If the Port-Royalist authors can be held responsible for such a view, then (1) the contribution [End Page 131] made by a book of logic consists in providing a vocabulary of persuasion and (2) the logical structure, which reasoning purports to harbor, must be a quality that language itself generates, rather than an extralinguistic quality. In other words, the three traditional disciplines of grammar, logic, and rhetoric are really only two because grammar and rhetoric can account for all inner and outer workings of language.

Art of speaking and art of thinking

I believe that some of the Port-Royal authors must have been aware of the position I attribute to them, but that they chose not to make it known because it may have proven vexing to two conflicting Cartesian theses that supported their religious views, namely, the thesis of mind/body dualism and the thesis of a unified science. The former thesis requires that speech (a body function) be segregated from thought (a mind function). Yet, the strict separation is unrealistic: speech is more than a function of the body because it stands apart from mere acoustic blasts pretty much the way human beings stand apart from beasts: chirps, meows, roars, and hisses presumably do not signify the way speech does, for speech can be used to explain what it itself signifies. Thus, speech is what it is in virtue of what it signifies and, for the Port-Royal authors, it signifies the contents (ideas, thoughts) or the operations of the mind. Ideas are modes of the substance mind and contain objective reality, and operations of the mind include, but are not limited to, affirmation, denial, conjunction, disjunction, and condition. One cannot discourse about meaningful speech without making reference to the mental world. Likewise, human beings, unlike angels, cannot discourse about ideas without expressing them in language. Thus, language and ideas are correlative and, as such, are really unseparable. That the “art of speaking” lives and dies with the “art of thinking” holds as true as the converse. An admission that logic reduces to grammar would suggest the conflation of speech with thought and would blur the distinction between mind and body.

Arnauld and Nicole underhandedly endorse the latter Cartesian thesis of a unified science or mathesis universalis in the following passage: “Whatever is useful to logic belongs to it; and the trouble, which certain otherwise quite worthy authors, as Ramus and the Ramists, go through so that they may as carefully draw boundaries between disciplines and make sure that one does not infringe another as one sets legal boundaries between [End Page 132] kingdoms or as one distributes the various jurisdictions of Parliament, is entirely ridiculous.” 3 The cavalier attitude, exhibited by the authors toward a division of the sciences, undoubtedly conceals a desire to rejuvenate a Cartesian mathesis universalis: the various arts or sciences are but chapters of one big book (most likely written by God), and each chapter builds up from the foundations laid down in the previous ones. Thus, logic would rely on the foundation laid down by grammar, and logic would become an extension of grammar; rhetoric would rely on the foundation laid down by logic and would extend logic. All disciplines are but extensions of a fundamental science, and so much the worse for Cartesian dualism. At this point, it is interesting to note that Descartes abandoned the project of a mathesis universalis early in his career; he may have anticipated that it would undercut his dualism. Understandably, then, Port-Royal’s desire for the possession and delectation of the same cake of unity and dualism should remain hidden. This desire, however, can be further adduced from the fact that Arnauld and Lancelot never revised The Grammar, but Arnauld and Nicole revised The Logic four times and even included in later editions sections borrowed from The Grammar.

The Grammar, The Logic, and rhetoric

The General and Reasoned Grammar is unique in its not being solely the grammar of a particular language, but also an account of the relation of languages to Cartesian ideas. This explains its title of reasoned grammar. It has two parts: The first part, which occupies one fifth of the book, introduces the various letters, combinations of letters, and other linguistic characters such as accents and punctuation; since each language has its particular characters and combination of characters, one fifth of The Grammar is particular grammar. A particular grammar also assigns each linguistic expressions to a category or part of speech; it gives rules of construction and explains the relationship these parts of speech bear to each other. The second part, which concerns reasoned grammar and occupies the other four fifths of the book, gives an account of the signification of the various parts of speech: nouns, adjectives, pronouns, articles, adverbs, and prepositions signify a reality (an objective reality) whose cause is traceable back to a formally real object. Verbs and logical connectives signify a specific operation of the mind. The first group of ideas, which is representative (it contains objective reality), is entirely dependent on the faculty of [End Page 133] the understanding, and the second group, which is essentially nonrepresentative, depends on the faculty of the will. Verbs and logical connectives manifest a performative quality in the sense that the mind performs the intended operation at the same time the mind thinks the idea.

The Logic or the Art of Thinking is unique in being the first logic manual to reflect the work of the scientific revolution: it reassigns logic to its original function of a tool of justification and it assigns the function of discovery to method. The treatise consists of four more-or-less equal parts. Each attends to the particular operation of the mind it names: conceiving, judging, reasoning, and ordering. The operations of conceiving and judging presuppose knowledge of the signification of various parts of speech and propositions; both operations require language and thought. One conceives simple and complex ideas; one judges propositions. The linguistic expression “prudent men,” which signifies a complex idea, differs from the statement “some men are prudent,” which signifies a judgment, in that the judgment includes an affirmation signified by the verb. Reasoning is necessary when the perception of the two ideas related by a judgment is not clear enough to warrant affirming some relation between the two. Finally, the last operation of ordering examines the new “natural” way of gaining knowledge in the sciences. At this point, then, it becomes clear that reasoned grammar and the mental operations of conceiving and judging overlap.

Tradition relegates reasoning to logic. The Port-Royal authors, however, claim that the inclusion of a book on reasoning in a treatise on logic is inessential, partly because reasoning is an extension of judging and partly because inferential errors are rare. And, of course, logic plays no role in the discovery process. That, which reasoning extends to judging, is a third idea needed to link two ideas that are not conceived well enough; so, reasoning comes to the help of (extends) judging. The Grammar, before The Logic, had argued that reasoning was nothing but an extension of judging: “To reason is to use two judgments to generate a third one. . . . Hence we see that the third operation of the mind is nothing other than an extension of the second.” 4 The Logic later echoed the same sentiment when Arnauld and Nicole argued, in the book devoted to reasoning, (1) that reasoning is a way to clarify judgments that contain confused terms, “when, then, the consideration alone of two ideas is not sufficient to allow us to judge whether one must affirm or deny one of the other, it is necessary to have recourse to a third idea”; 5 (2) that the rules of the syllogism are based on the axioms of propositions (183); and (3) that the dictum de omni et nullo, which validates the syllogisms of the first figure, “has been so elucidated in the chapter where we treated affirmative propositions that it is not necessary to [End Page 134] elucidate it further here [in a book on reasoning].” 6 Finally, and most importantly, the two authors argue that the soundness of an argument can be decided by using the same notion of containment used in deciding the truth of propositions. A proposition is true just in case the subject contains (comprehensionally) the predicate, or the predicate contains (extensionally) the subject; an argument is good just in case the conclusion is contained in one of the premises (compehensionally or extensionally) and the other premise shows it.

The authors not only explicitly articulate that reasoning is reducible to judging, but also question the usefulness of a book on reasoning because “[m]ost human errors, . . . originate more from the fact that they reason from false principles, rather than from the fact that they reason falsely from their principles.” 7

The “extension,” then, arises out of the “necessity to have recourse to a third idea,” which implies the necessity to find a third idea. At this point, therefore, the contribution that a book of logic makes to grammar consists in stressing the need to have a developed method of invention. The conferring of a prominent place to a method of invention in a book of logic was the trademark of the Humanist logicians. But Arnauld and Nicole never manifested a wish to be associated with this tradition; they admit the importance of invention, but also criticize the established topical tradition, which humanists such as Ramus endorsed.

Ramus (1515–72), whose works were quite familiar to the Port-Royal authors, and whose meticulous division of the sciences irked Arnauld and Nicole (see note 3), had taken invention out of rhetoric (where Cicero and Boethius had placed it) and had made it an essential part of logic. Ramistic logic consisted of the two distinct parts that were implicit in Aristotle’s Topics: invention and disposition. Invention suggested places to look for arguments while disposition was a general heading that included all the discussions pertaining to propositions and syllogisms. Arnauld and Nicole distrusted the mechanistic aspect of the topics and places; as a matter of fact, they thought that any mechanistic method aimed at finding a third idea discouraged reflection. They equated such a method with Lullist algorithmic tables, which, rather than help, spoil the mind by cluttering it with an overabundance of ideas: “Nothing stifles more good seeds than the abundance of weeds: nothing makes a mind more sterile of just and solid thoughts than this bad fertility of common places.” 8 They conclude: “It is therefore true that one needs to have a subject matter if one wishes to apply to it the rules of arguments; but it is false that it is necessary to find this subject matter by the method of topics.” 9 The method they advocate is an “attentive [End Page 135] consideration of the subject,” which eventually yields clarity and distinctness of perception.

It is this remark that must have motivated Giambattista Vico (1668–1744), in On the Study of Methods of Our Time, to distinguish between the critical method, which aims at truth, and the method of topics, which aims at eloquence. Vico argued that Arnauld and Nicole were only interested in the critical method, a method that is too restrictive in the sense that it does not permit enough agility in debates. However, Vico and the Port-Royal authors wanted the same thing, namely, an ability to debate controversial ideas under pressure. The former thought that this is best achieved with a ready-at-hand arsenal of topics; the others with a clear and uncluttered mind. 10 An attempt to referee between the two views is tantamount to refereeing between the merits of an abundance of fire power against the merits of sharpness of fire. If one gets the work done, so will the other; the rest is a matter of elegance or eloquence, or the domain of rhetoric.

The Port-Royalist never wrote a general treatise on rhetoric. It is ironic that a treatise on rhetoric, bearing the title De l’Art de Parler and anonymously published in 1675 in Paris, was thought to have been written by the Port-Royal authors until its real author, the Oratorian Bernard Lamy (1640–1715), was disclosed in 1688. 11 The Grammar and The Logic clearly inspired Lamy’s work; De l’Art de Parler makes invention and grammar parts of rhetoric, but rejects the topics as a method of finding arguments. It endorses and makes explicit the view, suggested by Arnauld and Nicole, that meticulous divisions between disciplines are not tenable. In other words, it repeats much of The Logic, which makes numerous allusions to considerations of style in arguments. Undoubtedly, the authors of The Logic must have felt that a separate work on rhetoric would have been redundant. Also, they openly sided with Descartes in believing that eloquence is acquired rather than learned. Furthermore, if grammar was the art of speaking, and logic the art of thinking, what could rhetoric be the art of?

Judging and reasoning

Thus, one way that logic extends grammar is by suggesting ways (methods) of finding arguments: the methods of the Cartesian were contrasted to that of Vico. There is another way in which logic can be said to contribute to grammar and that is by introducing a vocabulary that is specific to it. The point is difficult to make: since all vocabulary strictly belongs to grammar, [End Page 136] how is one to pick the vocabulary that is specific to logic without begging the question? However, if a distinction between conceiving and judging is made on account of the introduction of verbs, as Arnauld and Nicole have made, likewise, a distinction between judging and reasoning could be possible on account of the presence of a vocabulary conspicuously absent in the language of propositions. Sentence connectives signifying conjunction, disjunction, conditionals, and the like are excluded because they are explicitly discussed in the book on propositions. That leaves expressions used to herald a conclusion, such as therefore, so, ergo, and so on. Arnauld and Nicole threw considerable light on this subject when they explained the reduction of argument forms to conditional sentences. The canonical form of an argument is “P1,..., Pn; therefore C,” and the corresponding conditional form of that argument is “If P1,..., and Pn, then C.” Besides changing the punctuation, the tranformation also exchanged some particles by others: the particle therefore replaces the particles and and if...then.... Arnauld and Nicole define the conjunction and the conditional when they describe “copulative” and “conditional” propositions; their definitions reflect the belief that these two connectives are not only truth-functional, but also the bearers of meaning in the form of a function of the mind. For example, the presence of the particle and signifies the operation of joining and the condition that all conjuncts must be true for the conjunction to be true (LAP 132). Nowhere in the books discussing conception or judgment is the meaning of the particle therefore discussed.

The reduction of argument forms to conditional sentences is introduced in a chapter discussing hypothetical syllogisms; Arnauld and Nicole describe two manners of concluding: one “absolute” and one “conditional.” The standard form syllogism illustrates the absolute manner, and the hypothetical statement illustrates the conditional one. They go on showing that a single proposition can enclose a syllogism. Thus, the syllogism “P1, P2 inline graphic C” is contained in one of the following three propositions: “if P1, then C, since P2”; “if P1 and P2, then C”; “C because P1 and P2” (LAP 223). What is telling in their account is that they call the conditionalization reasoning and that they describe it as stylistically more pleasing: “This manner of reasoning is very common and very beautiful; and that is why you cannot suppose that there is reasoning only when three separate propositions are arranged as they are in the schools.” 12

There is, however, a difference, to which the authors point, between an argument and its corresponding conditional statement: the particles that make a sentence a conditional sentence are assigned a meaning whereas the particles that give arguments their identity are not. On one hand, Arnauld [End Page 137] and Nicole argue that in an argument, if one accepts the argument as good, one must accept the conclusion as true. This makes sense, given their position that the soundness of an argument depends on the notion of containment. If the conclusion is contained in one premise and the other premise shows that it is, the conclusion must be true. On the other hand, they argue that in a conditional statement, although one may accept the antecedent and the consequent as true, it still remains to be shown that a condition holds between the two. 13 In other words, the signification, qua operation of the mind, of the particles if...then... must be taken into consideration, and they signify the setting up of one thing as a condition for another (LAP 134). However, The Logic gives no signification for the particle therefore.

It was earlier noted that all vocabulary belongs to grammar, so it is not surprising that The Grammar gives an account of particles such as therefore. They are listed under the heading “Conjunctions and Interjections,” and Arnauld and Lancelot specify that such particles signify an operation of the mind: “They signify the form of our thoughts and not really the objects of our thought.” 14 Arnauld and Lancelot list as conjunctions the particles and, not, or, if...then..., and therefore, and as interjections the words ah, ô, heu, and hélas. But, if if..then... signifies the form of condition, what operation of the mind does therefore signify? If The Grammar had classified therefore as an adverb, rather than as a conjunction, it would modify in some manner the affirmation or denial signified by the verb, but this path is not available. It will not help to say that, because arguments are governed by the relation of containment, therefore signifies the operation of containing, since “containing” would be pretty difficult to explain as an operation of the mind and since containment also governs propositions in the sense that it is the relation that determines their truth or falsity. The only possibility that is left is to take the conjunction/interjection classification less literally and to classify therefore (ergo) as a combination conjunction and interjection.

For Arnauld and Nicole, the movement followed by an argument maker goes from the conclusion to the premises; the conclusion is a quæstio. A third term is required in order to find out whether the relation of containment holds between two others. One may ask the following question: “Are tabbies felines?” Well, tabbies are cats and cats are feline; therefore tabbies are felines. The therefore heralds and flags the answer to the question, and compels the argument maker to believe it. Likewise, the one who hears the argument is expected to be compelled to believe what follows therefore. Therefore and the likes are to the inferential world what voilà is to the world of senses. No such compelling takes place at the level of a conditional statement. This compelling, which is signified by the interjection, [End Page 138] then, may be what distinguishes reasoning from judging; a dramatic break in the flow of speech exacts attention from the argument maker as well as from the argument hearer. Force is what distinguishes reasoning from judging. If this is correct, Plato’s alleged opposition of force to arguments in the opening salvo of book 1 of The Republic (327c) may amount to no more than an opposition of physical force to mental force, and logic is much closer to grammar and rhetoric than it is a discipline sui generis.

Pariente’s objection

The most serious objection to this view comes from Jean Claude Pariente, in his “Grammaire et Logique,” which was published in a collection of essays. Pariente argues that, if the claim made by The Grammar, namely, that reasoning is an extension of judging, is taken seriously, then all arguments can be reduced to a single proposition, and this reduction can be effectuated by means of principles or rules spelled out in The Grammar. However, he finds that a particular distinction, the distinction between “explicative and determinative” judgments is necessary for the reduction to go through, and this distinction is absent from The Grammar. He concludes that the basis for this distinction is what sets logic apart from grammar.

Pariente’s argument has two weaknesses. First, the distinction between determinative and explicative judgments rests, not only on the distinction between comprehension (compréhension) and extension (étendue), but also on the relation the two properties bear to each other. Comprehension and extension are properties of terms, not arguments, and the relation each bears to the other—the extension of t1 is contained in the extension of t2 if and only if the comprehension of t2 is contained in the comprehension of t1—is a property of judgments. Furthermore, the distinction between comprehension and extension is implicit in The Grammar, the discipline traditionally assigned to judgments rather than arguments. Second, as the preceding section demonstrates, arguments can be reduced to propositions by conditionalizing them, that is, without the determinative/explicative distinction. Thus, the transformation schema is superfluous.

That the distinction between comprehension and extension is implicit in The Grammar is evident by looking at the content of the work. Both The Grammar and The Logic anatomize Descartes’s doctrine of ideas and judgments. A judgment binds or separates two ideas. An idea is either singular, when it denotes an individual idea, or universal, when it designates several ideas. A general idea possesses two properties: it has “comprehension,” which [End Page 139] is the set of attributes such that, if any one attribute is removed, the idea is destroyed; and it has “extension,” which is the set of subsets and individuals denoted by the idea. For example, the comprehension of the idea of “cat” includes the ideas of animality, domesticity, and felinity, and its extension consists of the subsets of all breeds of cats and of all individual cats. All categorical judgments have a “comprehensional” and an “extensional” reading: the judgment “All cats are animals,” understood from the point of view of comprehension, means that the attribute of animality is contained in the comprehension of “cat” ideas and, understood from the point of view of extension, that “cat” ideas are contained in the extension of “animal” ideas. Comprehension and extension are related to each other in such a way that, if the comprehension of an idea is increased, its corresponding extension, if it varies at all, varies inversely. Thus, the joining of one idea to another may or may not result in a decrease in the extension of the first. For example, the joining of the idea of “black” to the idea of “cat,” as in the expression “black cat” will restrict the extension of “cat,” but the joining of the idea of “feline” to “cat” will not affect the extension of “cat.” Port-Royal authors call expressions such as “black cat” determinations (LAP 65) and expressions such as “feline cats” explications. 15 A determination turns a general term into a less general one; an explication either brings out part of the comprehension of a general term or modifies a term by a quality that does not affect its extension. 16 Thus, any expression that has a proper name as a principal term is an explication. Furthermore, determinations and explications can be rephrased as relative clauses of complex propositions, for example, “Cats, which are black, are better nocturnal predators” or “Cats, which are feline animals, are not as affectionate as dogs.” The difference between the two propositions is that the second, but not the first, can be turned into a true conjunction: “Cats are feline animals and cats are not as affectionate as dogs.”

Pariente suggests that all syllogisms can be rephrased as complex propositions containing two relative clauses that are framed by the subject and predicate of the conclusion. If the relative clause is an explication, it can be retrenched, since it leaves the extension of the subject unchanged; if the relative clause is a determination, it can also be retrenched, provided the quantifier some prefixes the subject. The change is to take place on the basis of the following interpretation of A, E, I, O propositions: [End Page 140]

All A is B: idea A contains idea B
No A is B: idea A is separated from idea B
Some A is B: few A’s contain idea B
Some A is not B: idea B is separated from few A’s

Pariente’s example of the transformation of the form of Darii can be instantiated as follows:

1 All tabbies are mixed breeds
Some cats are tabbies
inline graphic Some cats are mixed breeds.

Following Pariente’s rules of transformation, this becomes the proposition

1* Those cat ideas, which contain tabby ideas, which tabby ideas contain the idea of mixed breed, contain the idea of mixed breed.

Now, since all tabbies are mixed breeds, the second relative clause, “which tabby ideas contain the idea of mixed breed,” is explicative and can be retrenched; that leaves “Those cat ideas, which contain tabby ideas, contain the idea of mixed breed.” The remaining relative clause is determinative rather than explicative, and Pariente claims that “Those cat ideas which contain tabby ideas” is equivalent to the expression “Some cats.”

According to Pariente, the apparatus that is necessary to carry out the transformation, namely, the distinction between determination and explication, only figures in The Logic; he concludes that this is what must separate reasoning from judging or grammar from logic. But if Pariente is correct with regard to a particular grammar, it is not equally clear that he is correct with regard to reasoned grammar. The reasoned part of The Grammar deals with the signification of terms, and while it is true that the terminology of The Logic does not occur in The Grammar, the ideas expressed by the terminology are very present. One needs only to look at the chapter that discusses the signification of nouns and adjectives (GGR pt. 2, chap. 2). The “two” significations are quite revealing:

I said that adjectives have two significations: one, which is distinct and which is that of the form; and the other, which is confused, and which is that of the subject. 17

This passage clearly is the forerunner of the comprehension/extension distinction. The adjective round means roundness (comprehension) and also the object that is round (extension).

The other weakness of Pariente’s suggestion is parasitic on the first. The transformation rules cannot specify the level of containment present in the reduction. One must, therefore, rely on the properties of terms and judgments in order to operate the transformation. Thus, nothing can be [End Page 141] said to be the exclusive property of logic. This last point becomes clear when we perform the transformation on syllogisms of the fourth figure. Barbari, for example: becomes the following proposition after transformation:

2 All cats are felines
All felines are animals
inline graphic Some animals are cats
2* Those animal ideas, which contain feline ideas, which feline ideas contain cat ideas, contain cat ideas.

In 2*, the containment in the two relative clauses is clearly extensional, making the two determinative and, as such, unretrenchable. In order to confirm the goodness of the argument, we need to appeal to the grammatical apparatus of voices and to the principle that identifies the relation between comprehension and extension, that is, No description available which permits the rephrasing of 2* into the following:

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2** Those animal ideas, which contain feline ideas, which feline ideas are contained in cat ideas, contain ideas.

The second relative clause is explicative, hence retrenchable, and the first relative clause is determinative. The expression “Those animal ideas, which contain feline ideas,” becomes, according to Pariente, “Some animals,” and the goodness of the argument is confirmed. Clearly, a lot more than the explicative/determinative distinction was needed before the argument could be confirmed as good. It is also clear that the transformation rules, as they are given by Pariente, cannot be applied without having knowledge of the content of the argument. Thus, what is presented as resembling a formal procedure cannot be used in a formal manner.

Of course, one could argue that the fourth figure had a controversial status: Aristotle did not recognize it, and many logicians saw it as a perverse version of the first figure. However, Aristotle did not recognize the fourth figure because he classified the figures on the basis of the width of [End Page 142] the middle term compared to that of the other terms. A middle term so construed yields only three possible combinations: in the first figure, it is wider than the predicate of the major premise and narrower than the subject of the minor; in the second figure, it is wider than both subjects and predicates; and in the third figure, it is narrower than both. As to the charge of being perverse versions of the first figure, 18 Arnauld and Nicole do not disagree—they think it is “oh so unnatural” (“si peu naturelle,” 200)—but, nevertheless, they argue for the validity of their moods.

So that, if Pariente wishes to argue that reasoning is not an extension of judging because the reduction of any syllogisms to a proposition requires the distinction between determination and explication, a distinction that belongs only to logic, he must be able to show that all syllogisms recognized as “good” by Port-Royal authors require the distinction to be reduced to a proposition. We have just seen that the fourth figure is controversial. In addition, the underpinnings of the distinction, namely, comprehension and extension, are discussed in principle in The Grammar.

Conclusion

The writings of the Port-Royalists on matters of grammar and logic reflect an important finding of the scientific revolution, namely, that deductive logic is not a logic of discovery, but simply a logic of justification. A logic of discovery became the domain of method, that is, a “critical” method that aimed at truth in the most “natural” way, and an effective justification consisted of good inferences persuasively delivered. A treatise of logic, therefore, had to include procedures to tell good inferences from bad ones, as well as procedures to be persuasive.

With regards to a logic of discovery, Arnauld and Nicole continued the Cartesian tradition: begin with the simple and proceed to the more complex with caution. With regards to a logic of justification, they made an original contribution by proposing a system that could adjudicate inferences on the basis of content rather than form. Moreover, and here echoing Montaigne, their system privileged a “clear,” “well-honed” mind over a mind “full” of ideas. If inferences could be judged on the basis of content, and the meaning or signification of terms determined content, then a grammar or “reasoned” grammar could provide the apparatus that was needed to do the judging; the only thing, then, that was seen as strictly belonging to “logic” was a vocabulary of interjections, which, like therefore, ergo, [End Page 143] and thus, stressed the persuasive, rather than inferential, aspect of a logic of justification. These interjections amount to little more than mental voilàs. Although formal logicians will understandably buck at such a proposal, they will have to admit than a nonformal logic spares them the task of having to account for an ontology of logical forms, schemata, or structures.

Finally, if a “clear” mind is preferred over a “full” mind, as Arnauld and Nicole argued, then logic can adopt a cavalier attitude toward topical considerations. A mind, like a body, acquires clarity (or agility) by doing exercises of a speculative nature and by freeing itself from unnecessary burdens. It is this persuasive part of a logic of justification that Vico criticized, but, as was shown, the criticism was more a question of style than a question of substance.

Bernard Roy
Department of Philosophy
Baruch College of The City University of New York

Footnotes

1. Throughout this paper, the word logic is understood as standing for any system of deductive logic.

2.Il est peu important d’examiner si c’est à la Grammaire ou à la Logique d’en traiter, & il est plus court de dire que tout ce qui est utile à la fin de chaque art lui appartient, soit que la connoissance lui en soit particuliere, soit qu’il y ait aussi d’autres arts & d’autres sciences qui s’en servent” (LAP 103).

3.Tout ce qui sert à la Logique lui appartient; & c’est une chose entierement ridicule que les gehennes que se donnent certains Auteurs, comme Ramus & les Ramistes, quoique d’ailleurs fort habiles gens, qui prennent autant de peine pour borner les jurisdictions de chaque science, & faire qu’elles n’entreprennent pas les unes sur les autres, que l’on prend pour marquer les limites du royaume, & regler les ressorts des Parlemens” (LAP 24).

4.RAISONNER, est se servir de deux jugements pour en faire un troisième: . . . D’où l’on voit que la troisième opération de l’esprit n’est qu’une extension de la seconde” (GGR 23).

5.Lors donc que la seule consideration de ces deux idées ne suffit pas pour faire juger si l’on doit affirmer ou nier l’une de l’autre, il a besoin de recourir à une troisième idée” (LAP 178).

6.Ce principe a été tellement éclairci dans le chapitre où nous avons traité des propositions affirmatives, qu’il n’est pas necessaire de l’éclaircir ici davantage” (LAP 193).

7.La plûpart des erreurs des hommes, . . . viennent bien plus de ce qu’ils raisonnent sur de faux principes, que non pas de ce qu’ils raisonnent mal suivant leurs principes” (LAP 177). This view was criticized by Leibniz in his Letter to Gabriel Wagner on the Value of Logic (1696). Leibniz argued that the existence of paralogisms attest to our propensity to make inferential errors, and that the importance of form is manifest in Aristotle’s reduction of valid forms to truths.

8.Rien n’étouffe plus les bonnes semences que l’abondance de mauvaises herbes: rien ne rend un esprit plus sterile en pensées justes & solides, que cette mauvaise fertilité de pensées communes” (LAP 235).

9.Il est donc vrai qu’il faut avoir une matiere pour y appliquer les regles des argumens; mais il est faux qu’il soit necessaire de trouver cette matiere par la methode des Lieux” (LAP 233).

10. This was a familiar view, but Montaigne, with whose writings Arnauld and Nicole were familiar, articulated it best: “[J]e voudrois aussi qu’on fut soigneux de luy choisir un conducteur qui eust plutost la teste bien faicte que bien pleine (also I would like that special care be taken in selecting for him [the student] a tutor with a well made mind rather than one with a well filled mind)” (1960, 14).

11. Three English translations of Lamy’s work were published in 1684, 1696, and 1708 and presented as the work of the “Messieurs de Port-Royal” (Howell 1961, 378–80).

12.Cette maniere de raisonner est très-commune et très-belle; & c’est ce qui fait qu’il ne faut pas s’imaginer qu’il n’y ait point de raisonnement que lorsqu’on voit trois propositions séparées & arrangées comme dans l’école” (LAP 223).

13.Toute la difference qu’il y a entre les syllogismes absolus, & ceux dont la conclusion est enfermée avec l’une des prémisses dans une proposition conditionnelle, est que les premiers ne peuvent être accordés tous entiers, que nous ne demeurions d’accord de ce qu’on auroit voulu nous persuader; au-lieu que dans les derniers on peut accorder tout, sans que celui qui les fait ait encore rien gagné; parcequ’il lui reste à prouver que la condition d’où dépend la consequence qu’on lui a accordée, est veritable” (LAP 223).

14.[Ils] signifient la forme de nos pensées, et non pas proprement les objets de nos pensées” (GGR 102).

15. In doing so, the authors shift the domain of discourse from one of ideas to one of linguistic terms. But Arnauld and Nicole had warned the reader that ideas and terms could be used interchangeably (LAP 58).

16.elle [explication] ne fait que développer ou ce qui étoit enfermé dans la comprehension de l’idée du premier terme, ou du moins ce qui lui convient comme un de ses accidens, pourvû qu’il lui convienne generalement & dans toute son étendue” (LAP 65).

17.J’ai dit que les adjectifs ont deux significations; l’une distincte, qui est celle de la forme; et l’autre confuse, qui est celle du sujet” (GGR 27).

18. Barbari and Calentes, respectively, become Baralipton and Celantes by switching, not only subject and predicate of the conclusion, but also major for minor premise. Fespamo and Fresisom become Fapesmo and Frisesomorum by simply switching the minor for the major, since their conclusions in the O form cannot be converted.

Works cited

Arnauld, Antoine, and Claude Lancelot. 1969. Grammaire générale et raisonnée, contenant les fondements de l’art de parler, expliqués d’une manière claire et naturelle; les raisons de ce qui est commun à toutes les langues, et des principales différences qui s’y rencontrent, etc. [GGR]. With remarks by Duclos. Rev. ed. Paris: Republications Paulet.
Arnauld, Antoine, and Pierre Nicole. 1981. La Logique ou l’Art de Penser: contenant, outre les règles communes, plusieurs observations nouvelles, propres à former le jugement. [LAP]. Ed. Pierre Clair and François Girbal. 2d, rev. ed. Paris: J. Vrin.
Howell, Wilbur Samuel. 1961. Logic and Rhetoric in England, 1500–1700. New York: Russell & Russell.
Lamy, Bernard. 1969. La Rhétorique; ou l’Art de Parler. Brighton: Falmer.
Leibniz, Gottfried Wilhelm. 1696. “Letter to Gabriel Wagner on the Value of Logic.” In Philosophical Papers and Letters, ed. Leroy E. Loemker, 462–71. Dordrecht: D. Reidel, 1976.
Montaigne. 1960. Essais. 2 vols. Paris: Société des Belles Lettres.
Pariente, Jean Claude. 1985. “Grammaire et Logique.” In L’analyse du langage à Port-Royal: six études logico-grammaticales. Paris: Les Editions de Minuit.
Plato. Complete Works. Ed. J. Cooper. Indianapolis: Hackett, 1997.

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