Wallis: Logic and 17th-century Scientific Thought

Jennifer Ashworth, "Logic in Seventeenth-Century Oxford: What did Wallis contribute?"

In the first part of this paper, I begin by examining the undergraduate logic curriculum in seventeenth-century Oxford, and the texts that were published there for undergraduate use. I then consider the organization and contents of these texts, and remark that Wallis’s logic text, as well as those by his contemporaries John Fell and Henry Aldrich, fell squarely into the standard pattern. In the second part of the paper, I turn to a detailed study of syllogistic, with especial reference to the three different definitions of major and minor terms, and the effect these had on the questions of indirect moods and the legitimacy of the fourth figure. I suggest that in his presentation of formal syllogistic Wallis was inferior to Fell and Aldrich, and that his main contribution was his emphasis on the dispensability of all but the four perfect syllogisms of the first figure together with a few simple rules.

Philip Beeley, “For want of riding the Great Horse…”
John Wallis on the importance of logic in university teaching and for scientific practice

Seventeenth-century attacks on university education often centred on the role they ascribed to traditional disciplines such as logic and grammar, while suggesting at the same time that they failed to provide adequate instruction in modern, more ostensibly useful disciplines such as physiology and the mathematical sciences. As Savilian professor of geometry, John Wallis consistently argued against such attacks. He thereby not only defended the universities’ response to the growth of modern science but also portrayed them as institutions whose intellectual principles were complementary to the scientific aims of the Royal Society. In this paper it will be contended that an essential part of Wallis’s strategy, rooted in the Savilian Statutes, was that a thorough grounding in logic provides an essential basis for rational thought in general and for mathematical thought in particular. Moreover, it will be suggested that he correctly identified deficits in logic and mathematics as being at the root of the Royal Society’s disarray in the 1680s and that he sought to address these problems through publication of his Treatise of Logick. Nor was his stance purely based on theoretical considerations. Drawing on examples from Wallis’s mathematical practice the paper also shows how he used flaws in logical reasoning to refute arguments in mathematics set out by contemporaries such as Thomas Hobbes and James Gregory.

Stephen Clucas, "Hobbes, Logic and Scientific Thought"

In this paper I consider the role of logic in Hobbes’s De corpore – in particular its foundational character. Hobbes’s De corpore, in common with much late-scholastic natural philosophy, is formulated as a ‘science of Causes’, but Hobbes transforms this conception of natural philosophy from within, replacing it with a natural philosophy of bodies in motion, syllogistically-constructed from first principles. I examine Hobbes’s logic as an attempt to discredit and circumvent what he saw as the verbal abuses of contemporary philosophies (such as that of Thomas White) which sought to import metaphysical or religious ideas into their accounts of natural phenomena. I also consider the tension within Hobbes’s work between the demonstrative ideals of Book I, and the probabilistic conception of natural knowledge in Book 4. Finally, I compare the fundamentally different attitudes towards logic to be found in Wallis’s Institutio Logicae, which (I argue) reflects the very different milieux in which the two men were working.

David Cram, "Logic and Grammar in the Seventeenth Century"

This paper will aim to examine how Wallis’s tracts on logic and grammar complement each other with respect to procedure and method, and see what light this can shed on larger questions concerning approaches to the analysis of language in the seventeenth century. There is a salient presentational difference between Wallis’s logic and his grammar. The logic presents itself as a conservative work, defending and working within an Aristotelian tradition; where Wallis strikes new ground, he is at pains to stress that his approach is simply an extension of the Aristotelian approach. In the grammar, by contrast, Wallis draws attention to and emphasizes the innovative nature of his method; and in the 5th edition (1699) he adds a note that this new method has been imitated by the authors of the Port-Royal grammar.
The first part of the paper will survey the places in Wallis’s logic where the author explicitly stresses that grammarians and logicians analyze a particular point in different ways. As illustrative cases, I shall look in particular at the treatment of tense (which is innovative in the grammar) and of the ‘conversion’ of sentences and propositions (which makes an interesting comparison with the Port-Royal approach). In the second part of the paper, I will attempt to position Wallis's treatment of grammar and logic in a larger seventeenth-century context, looking first at his involvement in the discussions about the construction of a universal language, and then at the methodological comparison between Wallis and his (alleged) Port-Royal imitators.

Peter Dvorak, “Wallis, Caramuel, and some Jesuit Logical Texts”

The paper focuses on Wallis’s treatment of oblique statements on the level of the proposition as well as that of the argument. This naturally leads to more general issues such as the logical form of the proposition in opposition to its grammatical form, functions of its constitutive parts, especially those of the copula and the predicate, quantification, modality, etc. The paper will compare Wallis to some selected predecessors: Toledo, Fonseca, Jungius and Caramuel.

Jaap Maat, "Defending Aristotle: singular propositions are really universal, and hypothetical syllogisms are really categorical"

Wallis's treatment of logic was not meant to be innovative. But he indicated that his treatment differed from standard practice regarding two topics: singular propositions and hypothetical syllogisms. The first topic concerns propositions in which terms referring to individuals occur. Aristotle had excluded propositions of this kind from his syllogistic, but later logicians strove to integrate them into the theory. Wallis's strategy was aimed at refuting Ramus's position which maintained that these propositions are to be assigned a class of their own. According to Wallis, they should rather be regarded as a subclass of universal ones. The second topic includes argument forms that centre around conditional statements such as 'If the sun shines, it is day'. Wallis was concerned to show that such argument forms can all be reduced to categorical syllogisms, and that their true logical form, as opposed to their grammatical form, contains universal quantification. In this paper, I set out Wallis's treatment of these two topics in some detail, and compare it with that by some of his contemporaries.

Massimo Mugnai, "Logic and Mathematics in the Seventeenth Century"

According to Joseph Maria Bochenski, the period of what he names classical logic (from the 16th to the second half of the 19th century) is a “decadent form of our science, a kind of dead end in its development.” Logic, in this period, was mainly identified with the theory of syllogism and intertwined with spurious issues concerning psychology, ontology and metaphysics. On a pair with the logic of the early middle age, classical logic - thus Bochenski claims - lacks of any form of originality and may be simply ignored in a history aiming to account for the most relevant topics that have been discussed in the discipline. Of course, Leibniz's logical essays constitute a remarkable exception to this picture: Bochenski, however, emphasizes that this exception does not alter his harsh verdict. In the same vein, William and Martha Kneale, in The Development of Logic observe that “From the 400 years between the middle of the fifteenth and the middle of the nineteenth century we have [...] scores of textbooks but very few works that contain anything at once new and good.” These negative appraisals are motivated by the lack of complexity of modern logic and by the substantial poverty of its achievements. That modern 'classical' logic cannot compete with ancient and medieval logic for what concerns the variety of topics discussed and their philosophical relevance, is too obvious to be put into question. It seems to me, however, that there is a very important feature of modern logic which constitutes its novelty and the main reason (maybe the only one) to positively evaluate it: i.e. the attempt to establish a link between logic and mathematics. In the paper I individuate two aspects of the relationships between logic and mathematics: a 'movement', as it were, of logic towards mathematics and a 'movement' of mathematics towards logic. I examine some authors representative of these two 'movements' and attempt to give an account of their ideas about logic.

Martine Pécharman, "Wallis and the Port-Royal “Logic”"

Wallis may have been well-acquainted with the Port-Royal Logic (16621-16835 / Latine version 16741, 16772 / English version 16851), but his possible familiarity with it did not drive him into an appraisal of its general lines, nor into a discussion of some particular positions defended in it mainly by Arnauld. Reversely, Arnauld may have known Wallis’s theses on the syllogistic universal value of the singular proposition and on the real indistinction between quantity and a quantum, since these two theses appended to the Institutio Logicae in 1687 were first published as soon as 1643. However, they have not exerted an influence on his Logic, even if it similarly argues against the identification of singular propositions with particular ones. Beyond these doubtful questions de facto concerning one another’s mutual acquaintance, I attempt in my paper to highlight the chief theoretical differences between Wallis’s Institutio Logicae and the Port-Royal Logic, in order to show that in any case they could not contribute hand in hand to founding the same logical tradition, in spite of their common design for restating logic on renewed bases. The restored Aristotelian bases that Wallis contended for against Ramism could not adjust to the Cartesian sources of Port-Royal’s redefinition of logic. My analysis focuses on the Art of Thinking’s specific modes of the reform of logic, while wondering whether they remain unanswered in Wallis’s Institutio. I first comment on the logical import of Arnauld’s philosophy of language. Besides putting emphasis on some semantic difficulties that cannot be solved in Arnauld’s eyes but by logic, not by general grammar (e.g. the question of the « complex terms »), I also pick out as particularly representative of the distance between Wallis and Port-Royal the very topic of the formation of judgment, that finalizes Arnauld and Nicole’s Logic. My thesis would be that the Messieurs’s intertwining of a philosophy of mind with the assessment of rules for discerning the sense of propositions allows only ephemeral contacts between their Logic and Wallis’s Institutio.

Siegmund Probst, "Leibniz and Wallis"

The relationship between Leibniz and Wallis was treated by J.E. Hofmann in a comprehensive essay published in 1973. Since this time additional material has become available for research, mainly due to the historical-critical edition of writings and letters of Leibniz. In recent years several studies evaluated specific aspects of this relationship in the fields of mathematics and natural philosophy. The talk aims to give an overview over these new findings and is focused mainly on the reception of Wallis's publications by Leibniz until his departure from Paris in the autumn of 1676.

Richard Serjeantson, "Seventeenth Century Logic and Human Understanding "

Many works of seventeenth-century logic, including Wallis's, rested upon a specific account of human understanding ('intellectus'). This was an account that matched what it took to be the main parts of logic - simple terms, the proposition, and the syllogism - to three 'operations' or 'acts' of the understanding. In this paper I shall say something about nature, development, and significance of this logical tradition down to Wallis's Institutio Logicae (1687). I shall then turn to offer a thesis about the fortunes and transformation of this view of human understanding in the period of Wallis's intellectual maturity, that is, from the later 1630s to the end of the seventeenth century. Although it will take in moral philosophy and theology, the weight of the argument will turn upon the impact of the kind of natural philosophical investigations in which Wallis was closely involved upon his and his contemporaries' view of human understanding.