This paper describes a theory of accuracy or approximate truth and applies it to problems in the realist interpretation of scientific theories. It argues not only that realism requires approximate truth, but that an adequate theory of approximation also presupposes some elements of a realist interpretation of theories. The paper distinguishes approximate truth from vagueness, probability and verisimilitude, and applies it to problems of confirmation and deduction from inaccurate premises. Basic results are cited, but details appear elsewhere. Objections are surveyed, (...) including arguments by Miller, Laymon, and Laudan. Comparison is made with Niiniluoto's theory of verisimilitude, and the utility of his theory for realism assessed. (shrink)

The major point of contention among the philosophers and mathematicians who have written about the independence results for the continuum hypothesis (CH) and related questions in set theory has been the question of whether these results give reason to doubt that the independent statements have definite truth values. This paper concerns the views of G. Kreisel, who gives arguments based on second order logic that the CH does have a truth value. The view defended here is that although Kreisel's conclusion (...) is correct, his arguments are unsatisfactory. Later sections of the paper advance a different argument that the independence results do not show lack of truth values. (shrink)

The technical results presented here on continuity and approximate implication are obviously incomplete. In particular, a syntactic characterization of approximate implication is highly desirable. Nevertheless, I believe the results above do show that the theory has considerable promise for application to the areas mentioned at the top of the paper.Formulation and defense of realist interpretations of science, for example, require approximate truth because we hardly ever have evidence that a particular scientific theory corresponds perfectly with a portion of the real (...) world. Realists need to assert, then, that evidence for a theory is evidence for its approximate truth, not its truth (see [3] and [18]). Approximate truth is, however, a vague notion, and specification of quantity terms and of a sense of approximation are needed to make precise applications of it. Suitability of both vocabulary and sense of approximation depend on the subject matter, and their selection is a partly empirical matter that raises complex issues. In light of the number of common inferences which are not continuous, realists also need to be concerned about indiscriminate use of deductive logic to derive consequences from approximately true theories. These issues will be considered further in a future paper.Approximate truth also has potential application in areas of artificial intelligence that require inference from inaccurate data. In the ‘qualitative’ physical theories of de Kleer and Brown [6], for example, ‘qualitative’ values are derived by partitioning the real numbers into regions. Inferences leading from inside to outside a region must be identified and avoided, and approximate implication and continuity may prove useful in doing this. More generally, growing use of predicate logic as a programming language invites application of the theory of approximate truth as a symbolic substitute for numerical evaluation of computation errors. This too will be the subject of a future paper. (shrink)

It is a widespread view that Marx did not apply dialectics to nature, and that Engels’s writings on this subject are a distortion of his outlook. This paper examines Marx’s discussion of elliptical motion and some other physical phenomena, and shows that he did indeed find contradictions and oppositions in nature, and thus recognised a dialectics of nature. In addition to analysing relevant passages in Marx’s texts, his study of the physics and mathematics of elliptical motion is reviewed and compared (...) with Hegel’s position. Marx’s conception of how dialectical contradictions are resolved is reviewed in order to interpret his claim that the contradiction in elliptical motion is ‘solved’ but not ‘overcome’ by that motion. Textual evidence is presented that Marx regarded ‘real contradictions’ as resolved only by ‘development’, a process in which the conflict between the opposing sides of the contradiction becomes more intense. The consequences of this interpretation for Marx’s analysis of elliptical motion are explored, and some alternative interpretations are discussed. (shrink)

The concept of "non-antagonistic contradiction" (NAC) was developed in the early 1930s in the Soviet Union to describe the social contradictions of Soviet society. This concept was employed to claim that Soviet social contradictions could be resolved without becoming intense or leading to social upheavals. The numerous attempts by Soviet philosophers to explain the NAC concept resulted in theories that are subject to decisive objections. In particular, the contradictions among the working class, the peasantry, and the intelligentsia of the USSR (...) did not prove to be non-antagonistic according to any of the theories designed to support that characterization. The reasons for the failure of the NAC concept are not confined to the Soviet context, and suggest that the NAC concept represents an important error in dialectical theory. (shrink)

As the subtitle suggests, the book is organized around the themes of judgment, inference and truth. Material for the first two topics is largely taken from the second edition of Bradley's Principles of Logic. The discussion of his conception of truth relies on essays written in reply to various authors. In general, the book is to be welcomed by students of Bradley for its remarkably clear and unpretentious exposition of central themes in these difficult topics.Much of the book is taken (...) up with discussion of the views of Bradley's precursors and contemporaries in British and German idealism, material that is important for understanding Bradley's own views. Hegel scholars may cringe, however, at the oft-repeated claim, stated without qualification, that Hegel regarded thought and reality as identical. Allard argues that Hegel must maintain this because his view of deductive inference required that objects be self-determining, and self-determining objects require the identity of thought and being. The argument is particularly puzzling in the light of the fact that Bradley's view of inference also requires the self-development of its objects, although he denied that thought and reality are identical. (shrink)