The no-miracles argument for realism and the pessimistic meta-induction for anti-realism pull in opposite directions. Structural Realism---the position that the mathematical structure of mature science reflects reality---relieves this tension.

From the reviews: "A good textbook can improve a lecture course enormously, especially when the material of the lecture includes many technical details. Van Dalen's book, the success and popularity of which may be suspected from this steady interest in it, contains a thorough introduction to elementary classical logic in a relaxed way, suitable for mathematics students who just want to get to know logic. The presentation always points out the connections of logic to other parts of mathematics. The reader (...) immediately see the logic is "just another branch of mathematics" and not something more sacred." Acta Scientiarum Mathematicarum, Hungary. (shrink)

means exhaust the insults. This is unfortunate as their attitude turns a useful book, with valuable contributions from a number of writers, into a polemic.

The Analysis of Matter is perhaps best known for marking Russell's rejection of phenomenalism and his development of a variety of Lockean representationalism–-Russell's causal theory of perception. This occupies Part 2 of the work. Part 1, which is certainly less well known, contains many observations on twentieth-century physics. Unfortunately, Russell's discussion of relativity and the foundations of physical geometry is carried out in apparent ignorance of Reichenbach's and Carnap's investigations in the same period. The issue of conventionalism in its then (...) contemporary form is simply not discussed. The only writers of the period who appear to have had any influence on Russell's conception of the philosophical issues raised by relativity were Whitehead and Eddington. Even the work of A. A. Robb fails to receive any extended discussion;1 although Robb's causal theory is certainly relevant to many of Russell's concerns, especially those voiced in Part 3, regarding the construction of points and the topology of space-time. In the case of quantum mechanics, the idiosyncrasy of Russell's selection of topics is more understandable, since the Heisenberg and Schrödinger theories were only just discovered. Nevertheless, it seems bizarre to a contemporary reader that Russell should have given such emphasis2 to G. N. Lewis's suggestion that an atom emits light only when there is another atom to receive it–-a suggestion reminiscent of Leibniz, and one to which Russell frequently returns. In short, the philosophical problems of modern physics with which Russell deals seem remote from the perspective of post-positivist philosophy of physics. (shrink)

SummaryenThe main argument for scientific realism is that our present theories in science are so successful empirically that they can't have got that way by chance - instead they must somehow have latched onto the blueprint of the universe. The main argument against scientific realism is that there have been enormously successful theories which were once accepted but are now regarded as false. The central question addressed in this paper is whether there is some reasonable way to have the best (...) of both worlds: to give the argument from scientific revolutions its full weight and yet still adopt some sort of realist attitude towards presently accepted theories in physics and elsewhere. I argue that there is such a way - through structural realism, a position adopted by Poincare, and here elaborated and defended. (shrink)

The central contention of this book is that second-order logic has a central role to play in laying the foundations of mathematics. In order to develop the argument fully, the author presents a detailed description of higher-order logic, including a comprehensive discussion of its semantics. He goes on to demonstrate the prevalence of second-order concepts in mathematics and the extent to which mathematical ideas can be formulated in higher-order logic. He also shows how first-order languages are often insufficient to codify (...) many concepts in contemporary mathematics, and thus that both first- and higher-order logics are needed to fully reflect current work. Throughout, the emphasis is on discussing the associated philosophical and historical issues and the implications they have for foundational studies. For the most part, the author assumes little more than a familiarity with logic comparable to that provided in a beginning graduate course which includes the incompleteness of arithmetic and the Lowenheim-Skolem theorems. All those concerned with the foundations of mathematics will find this a thought-provoking discussion of some of the central issues in the field today. (shrink)

The main puzzle about theoretical definitions is that nothing seems to decide which assumptions contribute to such definitions and which do not. I argue that theoretical definitions are indeed imprecise, but that this does not normally matter, since the definitional imprecision does not normally produce indeterminacy of referential value. Sometimes, however, the definitional imprecision is less benign, and does generate referential indeterminacy. In these special cases, but not otherwise, it is necessary to refine the term's definition.

Classical logic has proved inadequate in various areas of computer science, artificial intelligence, mathematics, philosopy and linguistics. This is an introduction to extensions of first-order logic, based on the principle that many-sorted logic (MSL) provides a unifying framework in which to place, for example, second-order logic, type theory, modal and dynamic logics and MSL itself. The aim is two fold: only one theorem-prover is needed; proofs of the metaproperties of the different existing calculi can be avoided by borrowing them from (...) MSL. To make the book accessible to readers from different disciplines, whilst maintaining precision, the author has supplied detailed step-by-step proofs, avoiding difficult arguments, and continually motivating the material with examples. Consequently this can be used as a reference, for self-teaching or for first-year graduate courses. (shrink)

Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...) conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'. (shrink)

Scientific realism is the optimistic view that modern science is on the right track: that the world really is the way our best scientific theories describe it. In his book, Stathis Psillos gives us a detailed and comprehensive study which restores the intuitive plausibility of scientific realism. We see that throughout the twentieth century, scientific realism has been challenged by philosophical positions from all angles: from reductive empiricism, to instrumentalism and to modern sceptical empiricism. _Scientific Realism_ explains that the history (...) of science does not undermine the arguments for scientific realism, but instead makes it reasonable to accept scientific realism as the best philosophical account of science, its empirical success, its progress and its practice. Anyone wishing to gain a deeper understanding of the state of modern science and why scientific realism is plausible, should read this book. (shrink)

Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.