© The Author 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected]‘Carnap is not completely unknown to us’ comments Richard Creath in his contribution to this book. ‘We often know just enough to be baffled’. It will be no surprise to anyone when I say that this book will not unbaffle us. But it does give us a collection of rewarding papers that each wrestle with the legacy Carnap has (...) left us. The introduction contains a helpful summary of each paper, so rather than giving my own, I will trace one thread of argument that runs through a few of the papers.Perhaps the only feature of Carnap’s views that can be found throughout the book is his distinction between internal and external questions, according to which internal questions are good, external questions are bad and... (shrink)

The paper argues that no second order theory is ontologically commited to anything beyond what its individual variables range over.

There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a (...) liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses. (shrink)

© The Author 2017. Published by Oxford University Press on behalf of The Analysis Trust. All rights reserved. For Permissions, please email: [email protected] Time addresses an exciting topic: what bearing the phenomenology of our experience of time might have on some key disputes over the nature of temporal reality, centrally whether the character of that phenomenology favours an ‘A-theory’ of time, which holds that there is temporal passage, over a ‘B-theory’ or ‘static block’ view. Prosser defends the ‘B-theory’, arguing not (...) only that experience does not favour ‘A-theory’, but also that it could not do so: ‘The passage of time is just the wrong kind of phenomenon to have a selective influence on or connection to a specific mental state, and therefore is not the kind of phenomenon that could be the object of an experience’. He argues further that this makes ‘A-theory’ unintelligible.Prosser’s book... (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

I propose a way of formulating scientific laws and magnitude attributions which eliminates ontological commitment to mathematical entities. I argue that science only requires quantitative sentences as thus formulated, and hence that we ought to deny the existence of sets and numbers. I argue that my approach cannot plausibly be extended to the concrete "theoretical" entities of science.