This chapter begins with a discussion of humanist criticisms of scholastic logic. It then discusses the evolution of the scholastic tradition and the influence of Renaissance Aristotelianism, Descartes and his influence, the Port-Royal Logic, the emergence of a logic of cognitive faculties, logic and mathematics in the late 17th century, Gottfried Wilhelm Leibniz's role in the history of formal logic, and Kant's influence on logic.

This chapter examines the views of seventeenth-century British philosophers on the notion of logic and demonstrative knowledge, particularly Francis Bacon, Thomas Hobbes, and John Locke, offering an overview of traditional Aristotelianism in relation to logic and describing Bacon's approach to demonstration and logic. It also analyzes the contribution of the Cambridge Platonists and evaluates the influence of Cartesianism. The chapter concludes that theorizing about logic and demonstrative knowledge followed an arc familiar from other branches of philosophy such as metaphysics or (...) the philosophy of science. (shrink)

'Mr Bennett, as was to be expected, has written a first-rate book on Kant's Analytic. It is vivid, entertaining, and extremely instructive. It will be found of absorbing interest both by those who already know the Critique and by those - if there are any such - who have a developed interest in philosophy, yet no direct acquaintance with Kant. These last it will surely drive to the text and, as surely, will drive them to approach it in a truly (...) philosophical spirit. Bennett's Kant is not a giant immersed, or frozen, in time. He is a great contemporary - a little out of touch, admittedly, with recent developments in mathematics and physics - but one with whom we can all argue, against him, at his side, or obliquely to him. And so Bennett does argue, continuously, fiercely, and fruitfully; and summons to join in the argument, at appropriate moments, those older contemporaries, Locke, Leibniz, Berkeley, and Hume, and those younger contemporaries, Wittgenstein, Ryle, Ayler, Quine, Quinton, Warnock, and others. This is splendid, and a necessary corrective to that extraordinary isolation in which Kant tends to be islanded, partly indeed, by his own unique qualities, but partly by oceans of the wrong kind of respect. Bennett, continuously engaging his great antagonist, shows the right kind.'. (shrink)

Kant famously declares that “although all our cognition commences with experience, … it does not on that account all arise from experience”. This marks Kant’s disagreement with empiricism, and his contention that human knowledge and experience require both sensation and the use of certain a priori concepts, the Categories. However, this is only the surface of Kant’s much deeper, though neglected view about the nature of reason and judgment. Kant holds that even our a priori concepts are acquired, not from (...) sensation, but “originally,” because our mind has a fundamental capacity to judge that, upon sensory stimulation, generates the Categories through its basic logical functions of judgment. This “epigenesis” of reason and our fundamental capacity to judge that drives it is the topic of Longuenesse’s fascinating book, and the source of her title. (shrink)

"Kant and the Capacity to Judge" will prove to be an important and influential event in Kant studies and in philosophy.

Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...) genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic. (shrink)

This landmark book is now reissued in a new edition that has been vastly rewritten and updated to respond to recent Kantian literature.

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory of the (...) proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

Kant's distinction between intuitive and discursive knowledge precludes his giving intuitions linguistic representation. Singular terms represent concepts given what kant calls a 'singular use' and are analyzable as definite descriptions. That the object described exists and that there is only one such object can be given linguistic representation only through an explicit assertion of existence and uniqueness. As an intuitionist in mathematics kant holds that mathematics proclaims the constructibility and not the existence of its objects.

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

In Kant’s logical texts the reference of the form S is P to an “unknown = x” is well known, but its understanding still remains controversial. Due to the universality of all concepts, the subject as much as the predicate is regarded as predicate of the x, which, in turn, is regarded as the subject of the judgment. In the CPR, this Kantian interpretation of the S-P relationship leads to the question about the relations between intuition and concept in judgment. (...) In contrast to intuition, if no concept, due to its universality, refers immediately to an object, how should one understand the relations of S and P to one another, as well as their relations to intuition, which corresponds to the possible individuality of the object in general = x? To answer this question, it is necessary to understand Kant’s notion of extension, and to prove its irreducibility to the Port-Royal notion of extension as well as to the Fregean one. (shrink)