This paper advances the view that the history of philosophy is both a kind of history and a kind of philosophy. Through a discussion of some examples from epistemology, metaphysics, and the historiography of philosophy, it explores the benefit to philosophy of a deep and broad engagement with its history. It comes to the conclusion that doing history of philosophy is a way to think outside the box of the current philosophical orthodoxies. Somewhat paradoxically, far from imprisoning its students in outdated and crystallized views, the history of philosophy trains the mind to think differently and alternatively about the fundamental problems of philosophy. It keeps us alert to the fact that latest is not always best, and that a genuinely new perspective often means embracing and developing an old insight. The upshot is that the study of the history of philosophy has an innovative and subversive potential, and that philosophy has a great deal to gain from a long, broad, and deep conversation with its history.
This paper aims to show that a proper understanding of what Leibniz meant by "hypercategorematic infinite" sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz's distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is "God himself" in conjunction with other key statements about God. I then discuss the issue of whether the hypercategorematic infinite is a "whole", comparing the four kinds of infinite outlined by Leibniz in 1706 with the three degrees of infinity outlined in 1676. In the last section, I discuss the relationship between the hypercategorematic infinite and created simple substances. I conclude that, for Leibniz, only a being beyond all determinations but eminently embracing all determinations can enjoy the pure positivity of what is truly infinite while constituting the ontological grounding of all things.In a striking passage of 1706 meant for his Jesuit correspondent, Bartholomew Des Bosses, Leibniz writes:There is a syncategorematic infinite or passive power having parts, namely, the possibility of further progress by dividing, multiplying, subtracting, or adding. In addition, there is a hypercategorematic infinite, or potestative infinite, and active power having, as it were, parts eminently but not formally or actually. This infinite is God himself. But there is not a categorematic infinite or one actually having infinite parts formally.There is also an actual infinite in the sense of a distributive whole but not a collective one [per modum totius distributivi non collectivi]. Thus, something can be stated of all numbers, though not collectively. In this way it can be said that for every 2 even number there is a corresponding odd number, and vice versa; but it is not therefore accurately said that there is an equal multitude of even and odd numbers. 1 This text has attracted significant attention in recent years, especially in the context of the discussion on Leibniz's theory of the infinite sparked by seminal papers by Laurence Carlin, Gregory Brown, and Richard Arthur published in the Leibniz Review. 2 The debate has broadened to other important contributions while retaining a focus on Leibniz's notions of syncategorematic infinite and actual infinite, and on their key implications for Leibniz's conception of bodies, composite substances, and more, generally, the physical world. 3 Little attention has been devoted, however, to the intriguing notion of "hypercategorematic infinite"introduced by Leibniz in this passage. 4 In this paper, after revisiting Leibniz's distinction Four kinds of infiniteIn the passage quoted above, Leibniz outlines four kinds of infinite: the syncategorematic infinite, the categorematic infinite, the hypercategorematic infinite, and the actual infinite. Of these four kinds of infinite, one (the categorematic infinite) is rejected.T...
The aim of this chapter is to provide a first impression of Leibniz’s long and deep engagement with history and historiography, in the hope of stimulating a more thorough investigation of this poorly studied aspect of his oeuvre. After a brief account of Leibniz’s work as an historian, the second section of the chapter explores Leibniz’s conception of history, which is shown to be profoundly embedded in his philosophical thought. The last section focuses on epistemological issues, namely, on Leibniz’s view of testimony as the epistemological ground of historical reconstruction, on the problem of historical credibility and scepticism, and on the role of sources in historiography.
Drawing inspiration from a well-attested historical tradition, I propose an account of cognition according to which knowledge is not only prior to belief; it is also, and crucially, not a kind of belief. Believing, in turn, is not some sort of botched knowing, but a mental state fundamentally different from knowing, with its own distinctive and complementary role in our cognitive life. I conclude that the main battle-line in the history of epistemology is drawn between the affirmation of a natural mental state in which there is a contact between ‘mind’ and ‘reality’ (whatever the ontological nature of this ‘reality’) and the rejection of such a natural mental state. For the former position, there is a mental state which is different in kind from belief, and which is constituted by the presence of the object of cognition to the cognitive subject, with no gap between them. For the latter position, all our cognition is belief, and the question becomes how and when belief is permissible.
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