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A perspective in the philosophy of mathematics is developed from a consideration of the strengths and limitations of both logicism and platonism, with an early focus on Frege’s work. Importantly, although many set-theoretic structures may be developed each of which offers limited isomorphism with the system of natural numbers, no one of them may be identified with it. Furthermore, the timeless, ever present nature of mathematical concepts and results itself offers direct access, in the face of a platonist account which (...) |
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Can there be an objective morality without God? Derek Parfit argues that it can and offers a theory of morality that is neither theistic nor naturalistic. This book provides a critical assessment of Parfit's metaethical theory. Jakobsen identifies some problems in Parfit’s theory – problems concerning moral normativity, the ontological status of morality, and evolutionary influence on our moral beliefs – and argues that theological resources can help solve them. By showing how Parfit’s theory may be improved by the help (...) |
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I survey John Leslie's Platonic thesis that if something sufficiently good possibly exists, then it could be ethically required that it actually exists—along with the pantheistic world‐picture to which this thesis leads. |
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Christian Platonism and Divine Simplicity remain the most commonly discussed views with respect to the way in which Christians ought to conceive of God’s nature and properties. In this essay, I suggest that we ought to consider seriously two versions of a quite different view, namely, what I call “the Nominalized Composite God View.” Both versions of the Nominalized Composite God View share two features: (1) they treat God as metaphysically composite, in opposition to Divine Simplicity, and (2) they deny (...) |
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This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...) |
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Many political theorists believe that a state cannot be neutral when it comes to languages. Legislatures cannot avoid picking a language in which to conduct their business and teachers have to teach their pupils in a language. However, against that, some political liberals argue that liberal neutrality is consistent with the state endorsement of particular languages. Claims to the contrary, they say, are based on a misguided understanding of what neutrality is. I will argue that this line of argument fails, (...) |
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Physicalism, if it is to be a significant thesis, should differentiate itself from key metaphysical contenders which endorse the existence of platonic entities, emergent properties, Cartesian souls, angels, and God. Physicalism can never be true in worlds where things of these kinds exist. David Papineau, David Spurrett, and Barbara Montero have recently developed and defended two influential conceptions of physicalism. One is derived from a conception of the physical as the non-mentally-and-non-biologically identifiable. The other is derived from a conception of (...) |
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Mathematical realism asserts that mathematical objects exist in the abstract world, and that a mathematical sentence is true or false, depending on whether the abstract world is as the mathematical sentence says it is. I raise two objections against mathematical realism. First, the abstract world is queer in that it allows for contradictory states of affairs. Second, mathematical realism does not have a theoretical resource to explain why a sentence about a tricle is true or false. A tricle is an (...) |
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Callard (2007) argues that it is metaphysically possible that a mathematical object, although abstract, causally affects the brain. I raise the following objections. First, a successful defence of mathematical realism requires not merely the metaphysical possibility but rather the actuality that a mathematical object affects the brain. Second, mathematical realists need to confront a set of three pertinent issues: why a mathematical object does not affect other concrete objects and other mathematical objects, what counts as a mathematical object, and how (...) |
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Hutto and Myin have proposed an account of radically enactive (or embodied) cognition (REC) as an explanation of cognitive phenomena, one that does not include mental representations or mental content in basic minds. Recently, Zahidi and Myin have presented an account of arithmetical cognition that is consistent with the REC view. In this paper, I first evaluate the feasibility of that account by focusing on the evolutionarily developed proto-arithmetical abilities and whether empirical data on them support the radical enactivist view. (...) |
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This paper examines Origen's views of “Adam” and considers whether aspects of Origen's views might prove helpful in contemporary debates about Adam and original sin. The question “who was Adam” presents difficult issues for Christian theology. In response to these concerns, many contemporary theologians suggest that “Eastern” traditions, which are less connected to the “Western”/Augustinian view of original sin, can more easily manage these tensions. These gestures towards “Eastern” thought are helpful in the sense that they do highlight the “mythic” (...) No categories |
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Commentators regularly attribute to Frege realist, idealist, and quietist responses to metaphysical questions concerning the abstract objects he calls ‘thoughts’. But despite decades of effort, the evidence offered on behalf of these attributions remains unconvincing. I argue that Frege deliberately avoids commitment to any of these positions, as part of a metaphysical separatist policy motivated by the fact that logic is epistemologically autonomous from metaphysics. Frege’s views and arguments prove relevant to current attempts to argue for epistemological autonomy, particularly that (...) |
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There has been much discussion of late on what exactly the Problem of Universals is and is not. Of course answers to these questions and many more like it depend on what is supposed to be explained by a solution to the Problem of Universals. In this paper, I seek to establish two claims: first, that when the facts (explanada) to be explained and the kind of explanation needed are elucidated, it will be shown that the Problem of Universals is (...) |
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We examine the philosophical disputes among computer scientists concerning methodological, ontological, and epistemological questions: Is computer science a branch of mathematics, an engineering discipline, or a natural science? Should knowledge about the behaviour of programs proceed deductively or empirically? Are computer programs on a par with mathematical objects, with mere data, or with mental processes? We conclude that distinct positions taken in regard to these questions emanate from distinct sets of received beliefs or paradigms within the discipline: – The rationalist (...) |
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In this paper I argue, that if it is metaphysically possible for it to have been the case that nothing existed, then it follows that the right modal logic cannot extend D, ruling out popular modal logics S4 and S5. I provisionally defend the claim that it is possible for nothing to have existed. I then consider the various ways of resisting the conclusion that the right modal logic is weaker than D. |
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The view that abstracta cannot exert causal power is pretty common in metaphysics. According to Friedell (2020), however, this view is mistaken. In a recent paper in this journal, he has argued that at least some abstracta are causally efficacious. My goal in what follows is to demonstrate that, given certain plausible methodological assumptions, Friedell 2020’s argument is not as strong as it might at first seem. No categories |
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Some are attracted to the view that repeatable artworks, such as films, novels, plays, symphonies, photographs, and the like, are a particular kind of abstracta—namely, types. This view, however, is not unproblematic. One of the most serious problems it faces is the so-called "creation problem." The core idea behind this problem is that, on the one hand, it seems reasonable to accept the claims that (1) repeatable artworks are types, (2) types cannot be created, and (3) repeatable artworks are created, (...) |
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In this thesis I argue against unrestricted mereological hybridism, the view that there are absolutely no constraints on wholes having parts from many different logical or ontological categories, an exemplar of which I take to be ‘mixed fusions’. These are composite entities which have parts from at least two different categories – the membered (as in classes) and the non-membered (as in individuals). As a result, mixed fusions can also be understood to represent a variety of cross-category summation such as (...) |
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Logical monism is the view that there is ‘One True Logic’. This is the default position, against which pluralists react. If there were not ‘One True Logic’, it is hard to see how there could be one true theory of anything. A theory is closed under a logic! But what is logical monism? In this article, I consider semantic, logical, modal, scientific, and metaphysical proposals. I argue that, on no ‘factualist’ analysis (according to which ‘there is One True Logic’ expresses (...) |
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I develop two problems, which I call the problem of divine location and the problem of divine age, to challenge the theist belief that God created the universe. The problem of divine location holds that it is not clear where God existed before he created the universe. The problem of divine age holds that it is not clear how old God was when he created the universe. I explore several theist responses to these two problems, and argue that all of (...) |
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I defend a new position in philosophy of mathematics that I call mathematical inferentialism. It holds that a mathematical sentence can perform the function of facilitating deductive inferences from some concrete sentences to other concrete sentences, that a mathematical sentence is true if and only if all of its concrete consequences are true, that the abstract world does not exist, and that we acquire mathematical knowledge by confirming concrete sentences. Mathematical inferentialism has several advantages over mathematical realism and fictionalism. |
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As physical entities that translate symbols into physical actions, computers offer insights into the nature of meaning and agency. • Physical symbol systems, generically known as agents, link abstractions to material actions. The meaning of a symbol is defined as the physical actions an agent takes when the symbol is encountered. • An agent has autonomy when it has the power to select actions based on internal decision processes. Autonomy offers a partial escape from constraints imposed by direct physical influences (...) |
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This dissertation is centered around a set of apparently conflicting intuitions that we may have about mathematics. On the one hand, we are inclined to believe that the theorems of mathematics are true. Since many of these theorems are existence assertions, it seems that if we accept them as true, we also commit ourselves to the existence of mathematical objects. On the other hand, mathematical objects are usually thought of as abstract objects that are non-spatiotemporal and causally inert. This makes (...) No categories |
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