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 (...) object that changes its shape from a triangle to a circle, and then back to a triangle with every second. (shrink)

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 (...) we can have knowledge about an unchanging object. (shrink)

Abstract objects are standardly taken to be causally inert, however principled arguments for this claim are rarely given. As a result, a number of recent authors have claimed that abstract objects are causally efficacious. These authors take abstracta to be temporally located in order to enter into causal relations but lack a spatial location. In this paper, I argue that such a position is untenable by showing first that causation requires its relata to have a temporal location, but second, that (...) if an entity is temporally located then it is spatiotemporally located since this follows from the theory of Relativity. Since abstract objects lack a spatiotemporal location, then if something is causally efficacious, it is not abstract. (shrink)

Beach's Gaelic Symphony is plausibly an abstract object that Beach created. The view that people create some abstract objects is called abstract creationism. There are abstract creationists about many kinds of objects, including musical works, fictional characters, arguments, words, internet memes, installation artworks, bitcoins, and restaurants. Alternative theories include materialism and Platonism. This paper discusses some of the most serious objections against abstract creationism. Arguably, these objections have ramifications for questions in metaphysics pertaining to the abstract/concrete distinction, time, causation, vague (...) existence, vague identity, and inadvertent creation. (shrink)

Many philosophers think all abstract objects are causally inert. Here, focusing on novels, I argue that some abstracta are causally efficacious. First, I defend a straightforward argument for this view. Second, I outline an account of object causation—an account of how objects cause effects. This account further supports the view that some abstracta are causally efficacious.

In an earlier paper I suggested that we can solve the Benacerraf Problem – the problem of explaining how mathematical knowledge is possible on the assumption that the objects of mathematics are abstract and immaterial – by positing efficient causal relations between those abstract objects and our brains. The burden of the paper was to remove the appearance that relations between abstracta and concreta, far from being actual, are inconceivable. This alleged inconceivability has been derived from some putative conditions on (...) efficient causation: physical contact, energy transfer, reciprocal effects on the cause, and the idea that the cause must exist in time if its effects do. I argued that none of these conditions are a priori conditions on efficient causation, and thus do not pose an obstacle to the conceivability or metaphysical possibility of efficient causal relations between platonic objects and brains. In this essay I reply to three published challenges to this proposed solution to the Benacerraf Problem. (shrink)

Benjamin Callard has recently suggested that causation between Platonic objects—standardly understood as atemporal and non-spatial—and spatio-temporal objects is not ‘a priori’ unintelligible. He considers the reasons some have given for its purported unintelligibility: apparent impossibility of energy transference, absence of physical contact, etc. He suggests that these considerations fail to rule out a priori Platonic-object causation. However, he has overlooked one important issue. Platonic objects must causally affect different objects differently, and different Platonic objects must causally affect the same objects (...) differently. How are Platonic objects—ones outside space and time—supposed to do that? CiteULike Connotea Del.icio.us What's this? (shrink)

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.

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

In this thesis, I will explore the epistemological evolutionary debunking arguments in meta-ethics. I will defend these arguments by accomplishing two tasks: I will offer the best way to understand the EDA and I will also respond to two strongest objections to the EDA. Firstly, in Part I of this thesis, I will offer my account of how the EDA should be best formulated. I will start from how evolution has significantly influenced our moral beliefs. I will then explain why, (...) due to their evolutionary origin, our moral beliefs are not tracking the moral truth reliably. Furthermore, I will argue that the fact that our moral beliefs are not tracking the moral truth also provides an undercutting and a higher-order defeater for those beliefs. As a result, I will conclude that the epistemic status of our moral beliefs is undermined because of these two kinds of defeaters. Secondly, in Part II of this thesis, I will turn my attention to the two strongest objections to the EDA – the Conceptual Truth Objection and the Third Factor Objection. I will first offer two responses to the Conceptual Truth Objection and, based on these two responses, I will argue that the Conceptual Truth Objection fails as a challenge to the EDA. I will then also argue that there currently doesn’t exist an acceptable version of the Third Factor Objection and it is also unlikely that such a version could be constructed in the future. I will finally conclude that both objections are problematic and they are thus unable to give us reason to doubt the EDA. (shrink)