Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving (...) a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optinal sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in logic, mathematics, philosophy, and computer science. (shrink)
[Ian Rumfitt] Frege's logicism in the philosophy of arithmetic consisted, au fond, in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already needs to appeal in order to justify paradigmatically logical truths and paradigmatically logical forms of inference. Using ideas of Gentzen to spell out what these methods and principles might include, I sketch a strategy for vindicating this logicist claim for the special case of the arithmetic of the (...) finite cardinals. /// [Timothy Williamson]The paper defends the intelligibility of unrestricted quantification. For any natural number n, 'There are at least n individuals' is logically true, when the quantifier is unrestricted. In response to the objection that such sentences should not count as logically true because existence is contingent, it is argued by consideration of cross-world counting principles that in the relevant sense of 'exist' existence is not contingent. A tentative extension of the upward Löwenheim-Skolem theorem to proper classes is used to argue that a sound and complete axiomatization of the logic of unrestricted universal quantification results from adding all sentences of the form 'There are at least n individuals' as axioms to a standard axiomatization of the first-order predicate calculus. (shrink)
This article explores the proposal offered by Ian Hacking for the distinction between natural and social sciences—a proposal that he has defined from the outset as complex and different from the traditional ones. Our objective is not only to present the path followed by Hacking's distinction, but also to determine if it constitutes a novelty or not. For this purpose, we deemed it necessary to briefly introduce the core notions Hacking uses to establish his strategic approach to (...) social sciences, under the assumption that they are less well known that the ones corresponding to his treatment of natural sciences. Key Words: Ian Hacking • natural sciences • social sciences • distinction. (shrink)
I use Ian Hacking's views to explore ways of classifying people, exploiting his distinction between indifferent kinds and interactive kinds, and his accounts of how we 'make up' people. The natural kind/essentialist approach to indifferent kinds is explored in some depth. I relate this to debates in psychiatry about the existence of mental illness, and to educational controversies about the credentials of learner classifications such as 'dyslexic'. Claims about the 'existence' of learning disabilities cannot be given a clear, simple (...) and unambiguous interpretation. In particular I show that science cannot deliver a definitive taxonomy of learner categories, and that this has important implications for teachers and policy makers. (shrink)
While Ludwik Fleck's Genesis and Development of a Scientific Fact is mainly concerned with social elements in science, a central argument depends on his case study of the development of a serum test for syphilis, the Wasserman Reaction, which Fleck argues was the product of skill and of laboratory practice, not a simple discovery. Ian Hacking interprets the creation of new phenomena in science very differently, arguing that it can seen as an argument for scientific realism. Hacking's argument shows that (...) Fleck's case study does not lead to the conclusion Fleck expects, and may solve one of the main problems in Fleck's work, how to define an objective element of knowledge. (shrink)
This paper examines Ian Hacking's arguments in favor of entity realism. It shows that his examples from science do not support his realism. Furthermore, his proposed criterion of experimental use is neither sufficient nor necessary for conferring a privileged status on his preferred unobservables. Nonetheless his insight is genuine; it may be most profitably seen as part of a more general effort to create a space for a new form of scientific and philosophical certainty, one that does not require foundations.
This article examines the ethical implications of Ian Mitroff's scholarly contribution to the study of Organizational Communication. Although Mitroff does not specifically ground his work in ethics, this article considers an ethic of choicemaking to be a significant interpretive key for understanding the contribution of his research. In addition, this article provides another conceptual key for understanding the considerable quantity of Mitroff's work by organizing it around three major themes: science, decision-making, and myth. The goal of this article is to (...) make explicit two conceptual keys to Mitroff's scholarship, an ethic of choice and a three-fold division of his work that exemplifies his commitment to maximizing choice in organizational settings. (shrink)
Representing and Reconstructing: A Hermeneutical Reply to Ian Hacking. Hacking published in 1983 Representing and Intervening which has provoked, particularly in the US, the so called realism/anti-realism debate which is still alive today. He lays claim to anti-realism for theory and to realism for the experiment. Following him, only that which can be used for manipulating something (e.g., the path of an electon) is realistic. H. Putnam is a severe critic of this dualism. In my paper I am (...) going to take the Hacking-Putnam controversy as a starting-point for the problem about the determination of the relation between theory and experiment in the natural sciences. I shall then follow M. Schlick's discussion of this problem and the current solution to the problem as offered by H. Pietschmann. The differing interpretation of Kant according to the three perspectives shall be the guideline for the argumentation. The goal of my argumentation is that theory and experiment do not live their own lives, that in experimenting one always continues traditional chains of action, and that natural science cannot be regarded independently of the life world it takes place in. This insight into the representing and reconstructing overturns in natural science, due to the necessity of human decisions, opens up their hermeneutical dimension. (shrink)
Reply to Ian Johnston Content Type Journal Article Pages 1-2 DOI 10.1007/s11712-012-9274-1 Authors Dan Robins, School of Arts and Humanities, The Richard Stockton College of New Jersey, 101 Vera King Farris Drive, Galloway, NJ 08205, USA Journal Dao Online ISSN 1569-7274 Print ISSN 1540-3009.
Frederick R. Steiner (ed): The Essential Ian McHarg: Writings on Design and Nature, 2006 Content Type Journal Article Pages 1-10 DOI 10.1007/s10806-009-9217-y Authors Ruth Beilin, University of Melbourne Landscape Sociologist, Department of Resource Management and Geography, Melbourne School of Land and Environment Melbourne VIC 3010 Australia Journal Journal of Agricultural and Environmental Ethics Online ISSN 1573-322X Print ISSN 1187-7863.
Ian Inkster (ed.): History of technology. Vol. 29. London: Continuum, 2009, 232pp, £90.00 HB Content Type Journal Article Pages 1-2 DOI 10.1007/s11016-011-9523-7 Authors Aristotle Tympas, Department of Philosophy and History of Science, University of Athens, University Campus, 157 71 Athens, Greece Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
The context for these interviews was a seminar [Peter Gratton] conducted on speculative realism in the Spring 2010. There has been great interest in speculative realism and one reason Gratton surmise[s] is not just the arguments offered, though [Gratton doesn't] want to take away from them; each of these scholars are vivid writers and great pedagogues, many of whom are in constant contact with their readers via their weblogs. Thus these interviews provided an opportunity to forward student questions about their (...) respective works. Though each were conducted on different occasions, the interviews stand as a collected work, tying together the most classical questions about “realism” to ancillary movements about the non-human in politics, ecology, aesthetics, and video gaming—all to point to future movements in this philosophical area. (shrink)
Hiding behind the anodyne title of this book is a work of large scope and considerable interest for the Hegelian reader. Its main purpose is to vindicate a dialectical interpretation of Marxism in the context of recent analytical Marxism. The book falls into two parts. The first contains a detailed account of the dialectical philosophy implicit in Marx's work, and of its background in the philosophies of Kant and Hegel. The second shows how this account of Marx's approach can (...) be used to resolve some of the major issues in Marxist philosophy and to illuminate some of the central topics in Marxist social, political and economic thought. (shrink)
The paper discusses the version of entity realism presented by Ian Hacking in his book, Representing and Intervening. Hacking holds that an ontological form of scientific realism, entity realism, may be defended on the basis of experimental practices which involve the manipulation of unobservable entities. There is much to be said in favour of the entity realist position that Hacking defends, especially the pragmatist orientation of his approach to realism. But there are problems with the position. The paper explores two (...) issues that reflect negatively on Hacking’s version of the entity realist position. The first issue relates to the role of description in fixing the reference of theoretical terms. The second issue relates to Hacking’s claim that the argument for entity realism based on experiment is a different kind of argument from the standard argument for scientific realism based on the success of science. (shrink)
This paper examines the ways in which social scientific discourse and classification interact with the objects of social scientific investigation. I examine this interaction in the context of the traditional philosophical project of demarcating the social sciences from the natural sciences. I begin by reviewing Ian Hacking’s work on interactive classification and argue that there are additional forms of interaction that must be treated.
This comment responds to Shapiro?s State of Democratic Theory. First, it argues that the map of democratic possibilities in the book, dividing forms of democracy into aggregative and deliberative, conflates and obscures important democratic alternatives. Second, I argue that one of the possibilities this map obscures, deliberation with aggregation, avoids the critique Shapiro directs at deliberative democracy. While some of his criticisms are appropriate to other categories, they do not apply to this one. Third, I argue that the empirical work (...) conducted under this category undermines Shapiro?s claims about how democracy can be expected to lead to violations of transitivity in actual practice. Fourth, I argue that there are other lines of defense for deliberative democracy in response to the combination of arguments that Shapiro offers in critique of deliberative democracy. (shrink)
This article entitled “History's `So it seems'” explores the potential of phenomenology for the framing of histories which privilege partcipant perspectives. The theory agenda of the article adapts insights drawn from Heidegger's ontological hermeneutic of Da-sein - the human condition of being-there and being-aware (or not aware). The theory agenda also adapts Heidegger's readings of Heraclitus. The practical agenda of the article illustrates this potential of Heidegger's phenomenology for history by contrasting `so it once seemed' senses of the Emperor Julian (...) the Apostate's Roman pagan self-hood. The contrasts are autobiographical (Julian's Misopogon ), contemporary biographical (Ammianus Marcellinus's history), and long-lag biographical (Gore Vidal's novel avowedly constrained by the sources). (shrink)