1,413 research outputs found
Epigenesis of Pure Reason and the Source of Pure Cognitions
Kant describes logic as âthe science that exhaustively presents and strictly proves nothing but the formal rules of all thinkingâ. (Bviii-ix) But what is the source of our cognition of such rules (âlogical cognitionâ for short)? He makes no concerted effort to address this question. It will nonetheless become clear that the question is a philosophically significant one for him, to which he can see three possible answers: those representations are innate, derived from experience, or originally acquired a priori. Although he gives no explicit argument for the third answer, he seems committed to itâespecially given his views on the source of pure concepts of the understanding and on the nature of logic.
It takes careful preparatory work to gather all the essential materials for motivating and reconstructing Kantâs âoriginal acquisitionâ account of logical cognition. I shall proceed in two sections.
In section 1, I analyze Kantâs argument that pure concepts of the understanding (or intellectual concepts)âas one kind of pure cognitionâmust be acquired originally and a priori. My analysis partly concerns his varied attitudes toward Crusiusâs and Leibnizâs versions of the nativist account of such concepts. I give special attention to how Kant characterizes the nativist account and his own âoriginal acquisitionâ account in terms of âpreformationâ and âepigenesisâ. My goal is, firstly, to tease out the sense in which Kant grants that there must be an innate ground (or preformation) for the derivation of pure concepts and, secondly, to introduceâand pave the way for answeringâthe question about the source of logical cognition.
In section 2, in light of Kantâs reference to Locke and Leibniz as the greatest reformers of philosophy (including logic) in their times (Log, AA 9: 32), I examine the Lockean and Leibnizian approaches to logic, respectively. Both approaches are âphysiologicalâ by Kantâs standard and are directly opposed to his own strictly critical method. I explain how this methodological move shapes Kantâs view that representations of logical rules must be originally acquired a priori. This acquisition involves a kind of radical epigenesis of pure reason: unlike the acquisition of pure concepts, it presupposes no further innate ground (or preformation). This view will have important consequences for issues such as the ground of the normativity of logical rules and the boundaries of their rightful use
Leibniz and the Problem of Temporary Truths
Not unlike many contemporary philosophers, Leibniz admitted the existence of temporary truths, true propositions that have not always been or will not always be true. In contrast with contemporary philosophers, though, Leibniz conceived of truth in terms of analytic containment: on his view, the truth of a predicative sentence consists in the analytic containment of the concept expressed by the predicate in the concept expressed by the subject. Given that analytic relations among concepts are eternal and unchanging, the problem arises of explaining how Leibniz reconciled one commitment with the other: how can truth be temporary, if concept-containment is not? This paper presents a new approach to this problem, based on the idea that a concept can be consistent at one time and inconsistent at another. It is argued that, given a proper understanding of what it is for a concept to be consistent, this idea is not as problematic as it may seem at first, and is in fact implied by Leibnizâs general views about propositions, in conjunction with the thesis that some propositions are only temporarily true
Multiple actualities and ontically vague identity
Gareth Evans's argument against ontically vague identity has been picked over on many occasions. But extant proposals for blocking the argument do not meet well-motivated general constraints on a successful solution. Moreover, the pivotal position that defending ontically vague identity occupies vis a vis ontic vagueness more generally has not yet been fully appreciated. This paper advocates a way of resisting the Evans argument meeting all the mentioned constraints: if we can find referential indeterminacy in virtue of ontic vagueness, we can get out of the Evans argument while still preserving genuinely ontically vague identity. To show how this approach can vindicate particular cases of ontically vague identity, I develop a framework for describing ontic vagueness in general in terms of multiple actualities. The effect, overall, is to provide a principled and attractive approach to ontically vague identity that is immune from Evansian worries
Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
Many historians of the calculus deny significant continuity between
infinitesimal calculus of the 17th century and 20th century developments such
as Robinson's theory. Robinson's hyperreals, while providing a consistent
theory of infinitesimals, require the resources of modern logic; thus many
commentators are comfortable denying a historical continuity. A notable
exception is Robinson himself, whose identification with the Leibnizian
tradition inspired Lakatos, Laugwitz, and others to consider the history of the
infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies,
Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly
demonstrating the inconsistency of reasoning with historical infinitesimal
magnitudes. We argue that Robinson, among others, overestimates the force of
Berkeley's criticisms, by underestimating the mathematical and philosophical
resources available to Leibniz. Leibniz's infinitesimals are fictions, not
logical fictions, as Ishiguro proposed, but rather pure fictions, like
imaginaries, which are not eliminable by some syncategorematic paraphrase. We
argue that Leibniz's defense of infinitesimals is more firmly grounded than
Berkeley's criticism thereof. We show, moreover, that Leibniz's system for
differential calculus was free of logical fallacies. Our argument strengthens
the conception of modern infinitesimals as a development of Leibniz's strategy
of relating inassignable to assignable quantities by means of his
transcendental law of homogeneity.Comment: 69 pages, 3 figure
From Logical Calculus to Logical FormalityâWhat Kant Did with Eulerâs Circles
John Venn has the âuneasy suspicionâ that the stagnation in mathematical logic between J. H. Lambert and George Boole was due to Kantâs âdisastrous effect on logical method,â namely the âstrictest preservation [of logic] from mathematical encroachment.â Kantâs actual position is more nuanced, however. In this chapter, I tease out the nuances by examining his use of Leonhard Eulerâs circles and comparing it with Eulerâs own use. I do so in light of the developments in logical calculus from G. W. Leibniz to Lambert and Gottfried Ploucquet. While Kant is evidently open to using mathematical tools in logic, his main concern is to clarify what mathematical tools can be used to achieve. For without such clarification, all efforts at introducing mathematical tools into logic would be blind if not complete waste of time. In the end, Kant would stress, the means provided by formal logic at best help us to express and order what we already know in some sense. No matter how much mathematical notations may enhance the precision of this function of formal logic, it does not change the fact that no truths can, strictly speaking, be revealed or established by means of those notations
The Logic of Opacity
We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show that some of these logics are non-degenerate
LEIBNIZ\u2019S MIRROR THESIS. SOLIPSISM, PRIVATE PERSPECTIVES AND CONCEPTUAL HOLISM
One of the symbolic images to which Leibniz constantly entrusted the synthesis of his philosophy regards the idea of considering one and the same city from various visual perspectives. Such an image is diffused throughout all Leibniz\u2019s writings and clearly reflects the philosopher\u2019s interest for matters regarding perspective as well as optical phenomena. The point of view of its inhabitants can therefore be compared to a mirror that reflects some different portions of reality. But what do the city-viewers really see? Do they all see exactly the same thing? And assuming the plurality of points of view, how one can be sure that they share the same representative content? The paper presented here tries to offer a plausible interpretation of this topic also by linking different and somehow remote Leibnizian doctrines together
Infinite vs. Singularity. Between Leibniz and Hegel
The aim of this paper is to reconsider the controversial problem of the relationship between the philosophy of Hegel and Leibniz. Beyond the thick curtain of historical references (which have been widely developed by scholars), it is in fact possible to assume some guideline concepts (i.e. those of \u2018singularity\u2019 and \u2018infinity\u2019) to reconstruct the deep theoretical influence which Leibniz played in Hegel\u2019s thought since the Jenaer Systementwurf of 1804/05
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