Challenging the myth that mathematical objects can be defined into existence, Bigelow here employs Armstrong's metaphysical materialism to cast new light on mathematics. He identifies natural, real, and imaginary numbers and sets with specified physical properties and relations and, by so doing, draws mathematics back from its sterile, abstract exile into the midst of the physical world.

Consequence is at the heart of logic; an account of consequence, of what follows from what, offers a vital tool in the evaluation of arguments. Since philosophy itself proceeds by way of argument and inference, a clear view of what logical consequence amounts to is of central importance to the whole discipline. In this book JC Beall and Greg Restall present and defend what thay call logical pluralism, the view that there is more than one genuine deductive consequence relation, a (...) position which has profound implications for many linguists as well as for philosophers. We should not search for one true logic, since there are many. (shrink)

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v. 1. Nominalism and realism.--v. 2. A theory of universals.

Totality states of affairs (Russell's 'general facts') are defended against Martin's criticisms. Although higher-order, they are not 'abstract in Quine's sense. If space-time is the whole of being, and if it can be seen as a vast conjunction of states of affairs, then the state of affairs that this is the totality of lower-order states of affairs is not additional to, but completes, space-times. If totality states of affairs are admitted, then there seems no need for any further negative states (...) of affairs additional to totality states of affairs. (shrink)

In this important study D. M. Armstrong offers a comprehensive system of analytical metaphysics that synthesises but also develops his thinking over the last twenty years. Armstrong's analysis, which acknowledges the 'logical atomism' of Russell and Wittgenstein, makes facts the fundamental constituents of the world, examining properties, relations, numbers, classes, possibility and necessity, dispositions, causes and laws. All these, it is argued, find their place and can be understood inside a scheme of states of affairs. This is a comprehensive and (...) rigorously this-worldly account of the most general features of reality, argued from a distinctive philosophical perspective, and it will appeal to a wide readership in analytical philosophy. (shrink)

A realist theory of truth for a class of sentences holds that there are entities in virtue of which these sentences are true or false. We call such entities ‘truthmakers’ and contend that those for a wide range of sentences about the real world are moments (dependent particulars). Since moments are unfamiliar, we provide a definition and a brief philosophical history, anchoring them in our ontology by showing that they are objects of perception. The core of our theory is the (...) account of truthmaking for atomic sentences, in which we expose a pervasive ‘dogma of logical form’, which says that atomic sentences cannot have more than one truthmaker. In contrast to this, we uphold the mutual independence of logical and ontological complexity, and the authors outline formal principles of truthmaking taking account of both kinds of complexity. (shrink)

The Facts of Causation grapples with one of philosophy's most enduring issues. Causation is central to all of our lives. What we see and hear causes us to believe certain facts about the world. We need that information to know how to act and how to cause the effects we desire. D. H. Mellor, a leading scholar in the philosophy of science and metaphysics, offers a comprehensive theory of causation. Many questions about causation remain unsettled. In science, the indeterminism of (...) modern physics and genetics have made such questions considerably harder for philosophers to answer. While progress has been made, a complete account of the nature and cosequences of causation is long overdue. This major study provides that account. (shrink)

David Armstrong's book is a contribution to the philosophical discussion about possible worlds. Taking Wittgenstein's Tractatus as his point of departure, Professor Armstrong argues that nonactual possibilities and possible worlds are recombinations of actually existing elements, and as such are useful fictions. There is an extended criticism of the alternative-possible-worlds approach championed by the American philosopher David Lewis. This major work will be read with interest by a wide range of philosophers.