Both traditional and naturalistic epistemologists have long assumed that the examination of human psychology has no relevance to the prescriptive goal of traditional epistemology, that of providing first-person guidance in determining the truth. Contrary to both, I apply insights about the psychology of human perception and concept-formation to a very traditional epistemological project: the foundationalist approach to the epistemic regress problem. I argue that direct realism about perception can help solve the regress problem and support a foundationalist account of justification, (...) but only if it is supplemented by an abstractionist theory of concept-formation, the view that it is possible to abstract concepts directly from the empirically given. Critics of direct realism like Laurence BonJour are correct that an account of direct perception by itself does not provide an adequate account of justification. However a direct realist account of perception can inform the needed theory of concept-formation, and leading critics of abstractionism like McDowell and Sellars, direct realists about perception themselves, fail to appreciate the ways in which their own views about perception help fill gaps in earlier accounts of abstractionism. Recognizing this undercuts both their objections to abstractionism and (therefore) their objections to foundationalism. (shrink)
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. (shrink)
From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special role to atomic formulas containing singular terms. This, we (...) find, secures harmony and uniqueness but militates against the putative realism. (shrink)
According to St. Thomas, the natures of material things are the proper objects of human understanding. 1 And he holds that, at least in this life, humans cognize these natures, not through innate species or by perceiving the divine exemplars, but only by abstraction from phantasms (ST Ia, 84.7, 85.1). 2 More precisely, the human intellects potency to understand. 3 The aim of the present piece is to clarify Thomass antinativism—arguably the most important historical and philosophical legacy of his cognitive (...) psychology. (shrink)
I discuss two arguments against the view that reasons are propositions. I consider responses to each argument, including recent responses due to Mark Schroeder, and suggest further responses of my own. In each case, the discussion proceeds by comparing reasons to answers and goals.
Open future is incompatible with realism about possible worlds. Since realistically conceived (concrete or abstract) possible worlds are maximal in the sense that they contain/represent the full history of a possible spacetime, past and future included, if such a world is actual now, the future is fully settled now, which rules out openness. The kind of metaphysical indeterminacy required for open future is incompatible with the kind of maximality which is built into the concept of possible worlds. The paper discusses (...) various modal realist responses and argues that they provide ersatz openness only, or they lead to incoherence, or they render the resulting theory inadequate as a theory of modality. The paper also considers various accounts of the open future, including rejection of bivalence, supervaluationism, and the ‘thin red line’ view (TRL), and claims that a version of (TRL) can avoid the incompatibility problem, but only at the cost of deflating the notion of openness. (shrink)
Neo-Fregeans such as Bob Hale and Crispin Wright seek a foundation of mathematics based on abstraction principles. These are sentences involving a relation called the abstraction relation. It is usually assumed that abstraction relations must be equivalence relations, so reflexive, symmetric and transitive. In this article I argue that abstraction relations need not be reflexive. I furthermore give an application of non-reflexive abstraction relations to restricted abstraction principles.
This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed intervals (...) is discussed. Finally, it is suggested that one reason there is a common structure between Aristotle's account of the continuum and that found in Cantor's definition of the real number continuum is that our intuitions about the continuum have their source in the experience of the real spatiotemporal world. A plea is made to consider Aristotle's abstractionist philosophy of mathematics anew. (shrink)
How do ordinary objects persist through time and across possible worlds ? How do they manage to have their temporal and modal properties ? These are the questions adressed in this book which is a "guided tour of theories of persistence". The book is divided in two parts. In the first, the two traditional accounts of persistence through time (endurantism and perdurantism) are combined with presentism and eternalism to yield four different views, and their variants. The resulting views are then (...) examined in turn, in order to see which combinations are appealing and which are not. It is argued that the 'worm view' variant of eternalist perdurantism is superior to the other alternatives. In the second part of the book, the same strategy is applied to the combinations of views about persistence across possible worlds (trans-world identity, counterpart theory, modal perdurants) and views about the nature of worlds, mainly modal realism and abstractionism. Not only all the traditional and well-known views, but also some more original ones, are examined and their pros and cons are carefully weighted. Here again, it is argued that perdurance seems to be the best strategy available. (shrink)
The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as abstract (...) objects. (shrink)
What is wrong with abstraction, Michael Potter and Peter Sullivan explain a further objection to the abstractionist programme in the foundations of mathematics which they first presented in their Hale on Caesar and which they believe our discussion in The Reason's Proper Study misunderstood. The aims of the present note are: To get the character of this objection into sharper focus; To explore further certain of the assumptions—primarily, about reference-fixing in mathematics, about certain putative limitations of abstractionist set theory, and (...) about the effects of impredicativity in abstraction principles—which underlie it; and To advance the debate of the issues thereby raised. Thanks for helpful comments to Roy Cook and to an anonymous referee. CiteULike Connotea Del.icio.us What's this? (shrink)
The ideas of fixed points (Kripke in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 53–81, 1975; Martin and Woodruff in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 47–51, 1984) and revision sequences (Gupta and Belnap in The revision theory of truth. MIT, London, 1993; Gupta in The Blackwell guide to philosophical logic. Blackwell, London, pp 90–114, 2001) have been exploited to provide solutions to the semantic paradox and have achieved admirable (...) success. This happy situation naturally encourages one to look for other philosophical areas of their further applications where paradoxical results seem to follow from intuitively acceptable principles. In this paper, I propose to extend the use of these ideas to give two new treatments of abstract objects. Sections 1 and 2 below check several abstractionist theories and their main defects. Section 3 shows how the two ideas can be applied to generate consistent theories of abstract objects without any ad hoc restriction on any principle. (shrink)
The Gestalt principle of isomorphism reveals the primacy of subjective experience as a valid source of evidence for the information encoded neurophysiologically. This theory invalidates the abstractionist view that the neurophysiological representation can be of lower dimensionality than the percept to which it gives rise.
While claiming to refute locke's theory of abstract ideas, Berkeley himself accepts a form of abstractionism. Locke's account of abstraction is indeterminate between two doctrines: 1) abstract ideas are representations of paradigm instances of kinds, 2) abstract ideas are schematic representations of the defining features of kinds. Berkeley's arguments are directed exclusively against 2, And refute only a specific version of it, Which there is no reason to ascribe to locke; berkeley himself accepts abstract ideas of the former type. (...) Locke's theory suffers from circularity and redundancy, Berkeley's from conflation of thought with imagination. (shrink)
A number of formal constraints on acceptable abstraction principles have been proposed, including conservativeness and irenicity. Hume’s Principle, of course, satisfies these constraints. Here, variants of Hume’s Principle that allow us to count concepts instead of objects are examined. It is argued that, prima facie, these principles ought to be no more problematic than HP itself. But, as is shown here, these principles only enjoy the formal properties that have been suggested as indicative of acceptability if certain constraints on the (...) size of the continuum hold. As a result, whether or not these higher-order versions of Hume’s Principle are acceptable seems to be independent of standard (ZFC) set theory. This places the abstractionist in an uncomfortable dilemma: Either there is some inherent difference between counting objects and counting concepts, or new criteria for acceptability will need to be found. It is argued that neither horn looks promising. (shrink)
This article includes a basic overview of possible world semantics and a relatively comprehensive overview of three central philosophical conceptions of possible worlds: Concretism (represented chiefly by Lewis), Abstractionism (represented chiefly by Plantinga), and Combinatorialism (represented chiefly by Armstrong).
This paper presents a critical comparative reading of Ulrich Beck and Herbert Marcuse. Beck's thesis on 'selfcritical society' and the concept of 'sub-politics' are evaluated within the framework of Marcusian critical theory. We argue for the continued relevance of Marcuse for the project of emancipatory politics. We recognise that a focus upon the imminent and spontaneous possibilities for radical social change within the 'sub-political' is a useful provocation to the high abstractionism of much critical theory, but suggest that such (...) possibilities are better captured in a Marcusian theoretical frame than they are in Beck's account. (shrink)
According to Daniel Flage, Berkeley thinks that all necessary truths are founded on acts of will that assign meanings to words. After briefly commenting on the air of paradox contained in the title of Flage’s paper, and on the historical accuracy of Berkeley’s understanding of the abstractionist tradition, I make some remarks on two points made by Flage. Firstly, I discuss Flage’s distinction between the ontological ground of a necessary truth and our knowledge of a necessary truth. Secondly, I discuss (...) Flage’s attempt to show that, according to Berkeley, the resemblance relation does not constitute a necessary connection. (shrink)
Economics has been persistently criticized for its heavy reliance on unrealistic assumptions. Some people reply to this criticism by saying that the unrealistic assumptions of economics result from abstraction from unimportant details, and abstraction is necessary for knowledge of a complex real world. So, far from unrealistic assumptions detracting from the epistemic worth of economics, such assumptions are essential for economic knowledge. I call this line of argument ?the Abstractionist Defense?. After clarifying abstraction, unrealistic assumptions and kindred notions, I show (...) that the Abstractionist Defense does not successfully rebut the position of those who criticize economics for its unrealistic assumptions. (shrink)
Recently much interest has been shown in the notion of intelligible species in the thought of Thomas Aquinas. Intelligible species supposedly explain humanknowing of the world and universals. However, in some cases, the historical context and the philosophical sources employed by Aquinas have been sorely neglected. As a result, new interpretations have been set forth which needlessly obscure an already controversial and perhaps even philosophically tenuous doctrine. Using a recent article by Houston Smit as an example of a novel and (...) anachronistic modern interpretation of Aquinas’s abstractionism, this paper shows that Aquinas follows the intentional transference of Averroes who proposes a genuine doctrine of abstraction of intelligibles from experienced sensible particulars. The paper also shows that Aquinas uses the doctrine of primary and secondary causality from the Liber de causis when he asserts that human abstractive powers function only insofar as they are a participation in Divine illumination. (shrink)
How do we form concepts like those of three, bycicle and red? According to Kant, we form them by carrying out acts of comparison, reflection and abstraction on information provided by the senses. Kant's answer raised numerous objections from philosophers and psychologists alike. "Kant e la formazione dei concetti" argues that Kant is able to rebut those objections. The book shows that, for Kant, it is possible to perceive objects without employing concepts; it explains how, given those perceptions, we can (...) form categories and empirical concepts; and it argues that theories like Kant's - abstractionist theories of concept formation - are more plausible than is often assumed. (shrink)
This book examines the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics. Beginning with an account of the traditional "abstractionist" philosophy of mathematics which Berkeley opposed, it examines his case against abstract ideas as well as his differing accounts of arithmetic and geometry. Berkeley's critique of the calculus is also examined in detail, beginning with a historical treatment of the origins of the calculus, proceeding to analyze Berkeley's objections in his 1734 work "The Analyst", (...) and studying some of the many responses to Berkeley. (shrink)