Hume and the nominalist tradition

Many of the central theses of Hume's philosophy – his rejection of real relations, universals, abstract objects and necessary causal relations – had precedents in the later medieval nominalist tradition. Hume and his medieval predecessors developed complex semantic theories to show both how ontologies are apt to become inflated and how, if we understand carefully the processes by which meaning is generated, we can achieve greater ontological parsimony. Tracing a trajectory from those medieval traditions to Hume reveals Hume to be more radical, particularly in his rejection of abstraction and abstract ideas. Hume's denial of general, abstract ideas is consistent with his philosophical principles but fails to appreciate the more sophisticated nominalist approaches to abstraction, the result of which is a theoretically impoverished account of our capacity for generalization.     

Desgabets on Cartesian Minds

George Berkeley maintains both anti-abstractionism (that abstract ideas are impossible) and idealism (that physical objects and their qualities are mind-dependent). Some scholars (including Atherton, Bolton, and Pappas) have argued, in different ways, that Berkeley uses anti-abstractionism as a premise in a simple argument for idealism. In this paper, I argue that the relation between anti-abstractionism and idealism in Berkeley's metaphysics is more complex than these scholars acknowledge. Berkeley distinguishes between two kinds of abstraction, singling abstraction and generalizing abstraction. He then rests his case for idealism, not on the denial of the possibility of generalizing abstraction, but rather on the denial of the possibility of singling abstraction. Moreover, Berkeley's argument does not rest on a blanket rejection of all forms of singling abstraction. Rather, the fundamental anti-abstractionist assumption, for his purposes, is the claim that primary qualities cannot be mentally singled out from secondary qualities. Crucially, the claim that the existence of physical objects cannot be mentally singled out from their being perceived is not a premise in, but rather a consequence of, Berkeley's argument for idealism. Berkeley's argument therefore avoids circularity inasmuch as it appeals to the impossibility of singly abstracting one idea in order to establish the impossibility of singly abstracting another.     

Three Dual Ontologies

In this paper we give an example of intertranslatability between an ontology of individuals (nominalism), an ontology of properties (realism), and an ontology of facts (factualism). We demonstrate that these three ontologies are dual to each other, meaning that each ontology can be translated into, and recaptured from, each of the others. The aim of the enterprise is to raise the possibility that, at least in some settings, there may be no need for considerations of ontological primacy. Whether the world is made up of things, or properties, or facts, may be no more than a matter of how we look at it.     

"不可或缺性论证"与反实在论数学哲学

The indispensability argument for abstract mathematical entities has been an important issue in the philosophy of mathematics. The argument relies on several assumptions. Some objections have been made against these assumptions, but there are several serious defects in these objections. Ameliorating these defects leads to a new anti-realistic philosophy of mathematics, mainly: first, in mathematical applications, what really exist and can be used as tools are not abstract mathematical entities, but our inner representations that we create in imagining abstract mathematical entities; second, the thoughts that we create in imagining infinite mathematical entities are bounded by external conditions. __________ Translated from Zhexue Yanjiu 哲学研究 (Philosophical Researches), 2006, (8): 74–83     

Tropes As Character-Grounders

There is a largely unrecognized ambiguity concerning the nature of a trope. Disambiguation throws into relief two fundamentally different conceptions of a trope and provides two ways to understand and develop each metaphysical theory that puts tropes to use. In this paper I consider the relative merits that result from differences concerning a trope's ability to ground the character of ordinary objects. I argue that, on each conception of a trope, there are unique implications and challenges concerning character-grounding.     

Hume as a trope nominalist

In this paper, I argue that Hume's solution to a problem that contemporary metaphysicians call “the problem of universals” would be rather trope-theoretical than some other type of nominalism. The basic idea in different trope theories is that particular properties, i.e., tropes are postulated to account for the fact that there are particular beings resembling each other. I show that Hume's simple sensible perceptions are tropes: simple qualities. Accordingly, their similarities are explained by these tropes themselves and their resemblance. Reading Hume as a trope nominalist sheds light on his account of general ideas, perceptions, relations and nominalism.     

Ostrich Nominalism and Peacock Realism: A Hegelian Critique of Quine

Abstract

My aim in this paper is to offer a Hegelian critique of Quine’s predicate nominalism. I argue that at the core of Hegel’s idealism is not a supernaturalist spirit monism, but a realism about universals, and that while this may contrast to the nominalist naturalism of Quine, Hegel’s position can still be defended over that nominalism in naturalistic terms. I focus on the contrast between Hegel’s and Quine’s respective views on universals, which Quine takes to be definitive of philosophical naturalism. I argue that there is no good reason to think Quine is right to make this nominalism definitive of naturalism in this way – where in fact Hegel (along with Peirce) offers a reasonably compelling case that science itself requires some commitment to realism about universals, kinds, etc. Furthermore, even if Hegel is wrong about that, at least his case for realism is still a naturalistic one, as it is based on his views on concrete universality, which is an innovative form of in rebus realism about universals.     

Modal Platonism: an Easy Way to Avoid Ontological Commitment to Abstract Entities

Modal Platonism utilizes “weak” logical possibility, such that it is logically possible there are abstract entities, and logically possible there are none. Modal Platonism also utilizes a non-indexical actuality operator. Modal Platonism is the EASY WAY, neither reductionist nor eliminativist, but embracing the Platonistic language of abstract entities while eliminating ontological commitment to them. STATEMENT OF MODAL PLATONISM. Any consistent statement B ontologically committed to abstract entities may be replaced by an empirically equivalent modalization, MOD(B), not so ontologically committed. This equivalence is provable using Modal/Actuality Logic S5@. Let MAX be a strong set theory with individuals. Then the following Schematic Bombshell Result (SBR) can be shown: MAX logically yields [T is true if and only if MOD(T) is true], for scientific theories T. The proof utilizes Stephen Neale’s clever model-theoretic interpretation of Quantified Lewis S5, which I extend to S5@.     

Justification Vindicated Justification: Volume One,Michael Horton,Zondervan, 2018 (ISBN 978‐0‐310‐49160‐6), 400 pp., pb £39.99 Justification: Volume Two,Michael Horton,Zondervan, 2018 (ISBN 978‐0‐310‐57838‐3), 528 pp., pb £39.99

Writing from a classical Reformed perspective, Horton reviews the entire history of ‘Justification’ and then sharply criticizes many fashionable movements in theology that he sees as a betrayal of the doctrine. These include ‘the new perspective on Paul’, the Finnish School of Tuomo Mannermaa, Radical Orthodoxy, and even the Lutheran–Roman Catholic Joint Declaration of 1999. Writing with theological and pastoral passion, Horton is a formidable polemicist who never loses sight of his central concern, so that his book is both an exciting debate and a moving witness to the Pauline, Lutheran, and Calvinist Gospel.