123 research outputs found
Indispensability Without Platonism
According to Quineâs indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quineâs criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrongâs criterion of ontological commitment rather than Quineâs. According to Armstrongâs criterion, âto be is to be a truthmaker (or part of one)â. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage
Maurinian Truths : Essays in Honour of Anna-Sofia Maurin on her 50th Birthday
This book is in honour of Professor Anna-Sofia Maurin on her 50th birthday. It consists of eighteen essays on metaphysical issues written by Swedish and international scholars
We donât need no explanation
Explanation has played myriad roles in truthmaker theory. The notion of explanation is sometimes thought to give content to the very idea of truthmaking, and is sometimes used as a weapon to undermine the entire point of truthmaker theory. I argue that the notion of explanation is dialectically useless in truthmaker theory: while itâs true that truthmaking offers a form of explanation, this claim is theoretically unilluminating, and leaves truthmaker theorists vulnerable to various kinds of attack. I advocate an alternative approach to truthmaker theory that downplays the role of explanation, and show how it releases the enterprise from a variety of problematic commitments that have troubled truthmaker theorists. The âontology-firstâ approach to truthmaking that I advocate not only restores the initial impulse behind truthmaking, but also has a number of theoretical advantages. Most prominently, it dodges the infamous problem of negative existentials, and lessens truthmaker theoryâs dependence on contentious intuitive judgments about both explanation and truthmaking
Explanation, Extrapolation, and Existence
Mark Colyvan (2010) raises two problems for âeasy roadâ nominalism about mathematical objects. The first is that a theoryâs mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the âcould beâ, but not (or not yet) the âisâ. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theoryâs mathematical aspects to obtain, as remainder, what it says âmathematics asideâ. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quineâs three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvanâs example that the third grade really obtains
Structural Parsimony
Many metaphysicians often appeal to Humeâs dictum (HD), according to which there are no necessary connections between distinct entities (or states of entities), in order to resist theories that commit us to such connections. Some have argued that HD is an unsupported dogma of metaphysics. But theories that commit us to necessary connections between distinct goings-on can also be resisted by invoking a normative twist on HD, which I call the Humean Solvent (HS): âDo not connect distinct entities (or states of entities) beyond necessityâ. HS is a principle of structural parsimony â assuming that a theory is structurally more parsimonious than another when the latter is committed to a more connected ontology than the former is. Just as Ockhamâs ârazorâ encourages us to cut down superfluous ontological commitments, the Humean âsolventâ encourages us to dissolve dispensable metaphysical glue: we ought not to glue elements of our ontology beyond necessity. HS has both a qualitative and a quantitative dimension: qualitatively, it encourages us to avoid using metaphysical glues that are unnecessarily strong, the strongest of which being metaphysically necessary connections; quantitatively, it encourages us not to metaphysically glue things that need no gluing. Thus, given HS, other things being equal, what is worst is a theory that entails that everything is metaphysically necessarily connected to anything else and what is best is a theory that leaves all things loose and separable. In this paper, I will first compare HD and HS as grounds for paradigmatic Humean doctrines in contemporary metaphysics, then I will argue that structural parsimony is neither a variety of ontological nor of ideological parsimony; finally, I will offer an argument for HS
Constructing a Religious Worldview: Why Religious Antirealism is Still interesting
After a short overview of anti-realist positions within the philosophy of religion, the following paper argues in favour of a moderate version of religious anti-realism. especially the notions of ârevelationâ and âreligious experienceâ seem to suggest that certain dichotomies that are typical for realism cannot be upheld consistently within philosophy of religion. However, the end of the paper shows a different route, which might overcome the realism/antirealism dichotomy as such
Logic and/of Truthmaking
The purpose of this paper is to explore the question of how truthmaker theorists ought to think about their subject in relation to logic. Regarding logic and truthmaking, I defend the view that considerations drawn from advances in modal logic have little bearing on the legitimacy of truthmaker theory. To do so, I respond to objections Timothy Williamson has lodged against truthmaker theory. As for the logic of truthmaking, I show how the project of understanding the logical features of the truthmaking relation has led to an apparent impasse. I offer a new perspective on the logic of truthmaking that both explains the problem and offers a way out
Groundless Truth
We defend two claims: (1) if one is attracted to a strong non-maximalist view about truthmaking, then it is natural to construe this as the view that there exist fundamental truths; (2) despite considerable aversion to fundamental truths, there is as yet no viable independent argument against them. That is, there is no argument against the existence of fundamental truths that is independent of any more specific arguments against the ontology accepted by the strong non-maximalist. Thus there is no argument that the strong non-maximalist herself will find dialectically motivating
The uncanny accuracy of God's mathematical beliefs
I show how mathematical platonism combined with belief in the God of classical theism can respond to Field's epistemological objection. I defend an account of divine mathematical knowledge by showing that it falls out of an independently motivated general account of divine knowledge. I use this to explain the accuracy of God's mathematical beliefs, which in turn explains the accuracy of our own. My arguments provide good news for theistic platonists, while also shedding new light on Field's influential objection
- âŠ