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.

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)

Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...) most significant philosophers is a remarkable attempt to establish a novel way of thinking. (shrink)

Truths are determined not by what we believe, but by the way the world is. Or so realists about truth believe. Philosophers call such theories correspondence theories of truth. Truthmaking theory, which now has many adherents among contemporary philosophers, is the most recent development of a realist theory of truth, and in this book D. M. Armstrong offers the first full-length study of this theory. He examines its applications to different sorts of truth, including contingent truths, modal truths, truths about (...) the past and the future, and mathematical truths. In a clear, even-handed and non-technical discussion he makes a compelling case for truthmaking and its importance in philosophy. His book marks a significant contribution to the debate and will be of interest to a wide range of readers working in analytical philosophy. (shrink)

During the realist revival in the early years of this century, philosophers of various persuasions were concerned to investigate the ontology of truth. That is, whether or not they viewed truth as a correspondence, they were interested in the extent to which one needed to assume the existence of entities serving some role in accounting for the truth of sentences. Certain of these entities, such as the Sätze an sich of Bolzano, the Gedanken of Frege, or the propositions of Russell (...) and Moore, were conceived as the bearers of the properties of truth and falsehood. Some thinkers however, such as Russell, Wittgenstein in the Tractatus, and Husserl in the Logische Untersuchungen, argued that instead of, or in addition to, truth-bearers, one must assume the existence of certain entities in virtue of which sentences and/or propositions are true. Various names were used for these entities, notably 'fact', 'Sachverhalt', and 'state of affairs'. (1) In order not to prejudge the suitability of these words we shall initially employ a more neutral terminology, calling any entities which are candidates for this role truth-makers. (shrink)