According to the truthmaker theory that we favour, all contingent truths are made true by existing facts or states of affairs. But if that is so, then it appears that we must accept the existence of the negative facts that are required to make negative truths (such as 'There is no hippopotamus in the room.') true. We deny the existence of negative facts, show how negative truths are made true by positive facts, point out where the (reluctant) advocates of negative (...) facts (Russell, Armstrong, et al.) went wrong, and demonstrate the superiority of our solution to the alternatives. (shrink)

The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...) dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. (shrink)

According to platonists, entities such as numbers, sets, propositions and properties are abstract objects. But abstract objects lack causal powers and a location in space and time, so how could we ever come to know of the existence of such impotent and remote objects? In Knowledge, Cause, and Abstract Objects, Colin Cheyne presents the first systematic and detailed account of this epistemological objection to the platonist doctrine that abstract objects exist and can be known. Since mathematics has such a central (...) role in the acquisition of scientific knowledge, he concentrates on mathematical platonism. He also concentrates on our knowledge of what exists, and argues for a causal constraint on such existential knowledge. Finally, he exposes the weaknesses of recent attempts by platonists to account for our supposed platonic knowledge. This book will be of particular interest to researchers and advanced students of epistemology and of the philosophy of mathematics and science. It will also be of interest to all philosophers with a general interest in metaphysics and ontology. (shrink)

Alan Musgrave has consistently defended two positions that he regards as commonsensical: critical realism and critical rationalism. In this volume a group of internationally-renowned authors discuss themes that are relevant in one way or another to Musgrave’s work. Rather than a standard celebratory festschrift, this book offers a new examination of topics of current interest in philosophy. The contributory essays are followed by responses from Alan Musgrave himself.

By an argument form I shall mean a schema consisting of a string of symbols that are place-­‐holders for either logical terms or non-­‐logical (descriptive/content) terms: substituting terms of the appropriate kind for the symbols yields an argument. A substitution instance of an argument form is an argument that arises as a result of such a substitution. By a valid argument I shall mean an argument such that it is impossible for the premises to be true and the conclusion false. (...) Thus, an invalid argument is an argument such that it is possible for the premises to be true and the conclusion false. (shrink)

The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their (...) dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. Mathematical platonists claim that at least some of the objects which are the subject matter of pure mathematics (e.g. numbers, sets, groups) actually exist. Furthermore, they claim that these objects differ radically from the concrete objects (trees, cats, stars, molecules) which inhabit the material world. We take the standard platonistic position to include the claim that platonic objects lack spatio-temporal location and causal powers. Many (perhaps most) mathematical platonists subscribe to this view.1 But some who call themselves (or might be called) mathematical platonists.. (shrink)

It is widely believed that medically inert treatments (“placebos”) can bring about therapeutic benefits. There is also evidence that medically active treatments may also have “placebo” effects. Since anything that has the potential to benefit patients ought to be exploited, subject to appropriate ethical standards, it has been suggested that more should be done to investigate and exploit the power of the placebo for therapeutic benefit. I explore the acute epistemic and ethical constraints that such exploitation is likely to face, (...) and conclude that effective exploitation is unlikely. (shrink)

Mathematics is about numbers, sets, functions, etc. and, according to one prominent view, these are abstract entities lacking causal powers and spatio-temporal location. If this is so, then it is a puzzle how we come to have knowledge of such remote entities. One suggestion is intuition. But `intuition' covers a range of notions. This paper identifies and examines those varieties of intuition which are most likely to play a role in the acquisition of our mathematical knowledge, and argues that none (...) of them, singly or in combination, can plausibly account for knowledge of abstract entities. (shrink)

According to standard mathematical platonism, mathematical entities (numbers, sets, etc.) are abstract entities. As such, they lack causal powers and spatio-temporal location. Platonists owe us an account of how we acquire knowledge of this inaccessible mathematical realm. Some recent versions of mathematical platonism postulate a plenitude of mathematical entities, and Mark Balaguer has argued that, given the existence of such a plenitude, the attainment of mathematical knowledge is rendered non-problematic. I assess his epistemology for such a profligate platonism and find (...) it unsatisfactory because it lacks an adequate semantics, in particular, an adequate account of reference. (shrink)

Mathematics is about numbers, sets, functions, etc. and, according to one prominent view, these are abstract entities lacking causal powers and spatio-temporal location. If this is so, then it is a puzzle how we come to have knowledge of such remote entities. One suggestion is intuition. But ‘intuition’ covers a range of notions. This paper identifies and examines those varieties of intuition which are most likely to playa role in the acquisition of our mathematical knowledge, and argues that none of (...) them, singly or in combination, can plausibly account for knowledge of abstract entities. (shrink)

The following principles may plausibly be included in a wide range of theories of epistemic justification: (1) There are circumstances in which an agent is justified in believing a falsehood, (2) There are circumstances in which an agent is justified in believing a principle of epistemic justification, (3) Beliefs acquired in compliance with a justifiably-believed epistemic principle are justified. I argue that it follows from these three individually plausible claims that an agent's belief may be both justified and unjustified. I (...) consider how theories may avoid this paradox, and conclude that deontological theories of epistemic justification face considerable, perhaps insurmountable, difficulties. (shrink)

Why are the conditions for propositional knowledge so difficult to discover or devise in this post-Gettier age? Why do not most epistemologists agree on roughly the same analysis as they appear to have done in the pre-Gettier paradise? I argue that the problem lies in that fact that the epistemologists intuitive concept of knowledge appeals to desiderata that probably cannot be satisfied. Unfortunately, if we abandon some of these desiderata, it is difficult to settle on a concept of knowledge which (...) is not too remote from our initial intuitions. I suggest that epistemology may be better off without the concept of knowledge. There are plenty of other interesting notions for us to be going on with. (shrink)

According to mathematical platonism, mathematical entities (e.g. numbers) exist as abstract objects. If numbers are abstract objects, then I doubt our ability to know of their existence.objects lack causal powers and spatio-temporal location. On the other hand, we human knowers exist within the causal nexus and are wholly spatio-temporal. So our epistemic isolation from abstract objects is total and unbridgeable (Benacerraf 1973, Cheyne 2001). Any version of mathematical platonism that is worth taking seriously must claim that we can and do (...) know of the existence of abstract objects. Since I deny that knowledge of the existence of abstract objects is possible, I reject mathematical platonism. (shrink)

Schwartz (1991) argues that the worry that successful reduction would eliminate rather than conserve the mental is a needless worry. He examines cases of reduction from the natural sciences and claims that if reduction of the mental is like any of those cases then it would not be a case of elimination. I discuss other cases of scientific reduction which do involve elimination. Schwartz has not shown that reduction of the mental could not be like such cases, so his argument (...) is not sufficient to dispel the worry of elimination. (shrink)

Book Information The Indispensability of Mathematics. By Mark Colyvan. Oxford University Press. New York. 2001. Pp. 172. Hardback, £30.00.