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Scientific Representation and the Semantic View of Theories
 THEORIA 55: 49–65
, 2006
"... It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent i ..."
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It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought.
Cycling in proofs and feasibility
 Transactions of the American Mathematical Society
, 1998
"... Abstract. There is a common perception by which small numbers are considered more concrete and large numbers more abstract. A mathematical formalization of this idea was introduced by Parikh (1971) through an inconsistent theory of feasible numbers in which addition and multiplication are as usual b ..."
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Abstract. There is a common perception by which small numbers are considered more concrete and large numbers more abstract. A mathematical formalization of this idea was introduced by Parikh (1971) through an inconsistent theory of feasible numbers in which addition and multiplication are as usual but for which some very large number is defined to be not feasible. Parikh shows that sufficiently short proofs in this theory can only prove true statements of arithmetic. We pursue these topics in light of logical flow graphs of proofs (Buss, 1991) and show that Parikh’s lower bound for concrete consistency reflects the presence of cycles in the logical graphs of short proofs of feasibility of large numbers. We discuss two concrete constructions which show the bound to be optimal and bring out the dynamical aspect of formal proofs. For this paper the concept of feasible numbers has two roles, as an idea with its own life and as a vehicle for exploring general principles on the dynamics and geometry of proofs. Cycles can be seen as a measure of how complicated a proof can be. We prove that short proofs must have cycles. 1.
The Role of Ontology in Integrating Semantically Heterogeneous Databases
, 2002
"... More and more enterprises are currently undertaking projects to integrate their applications. They are finding that one of the more difficult tasks facing them is determining how the data from one application matches semantically with the data from the other applications. Currently there are few ..."
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Cited by 4 (0 self)
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More and more enterprises are currently undertaking projects to integrate their applications. They are finding that one of the more difficult tasks facing them is determining how the data from one application matches semantically with the data from the other applications. Currently there are few methodologies for undertaking this task  most commercial projects just rely on experience and intuition. Taking
2003: ‘Everything
 in J. Howthorne and D
"... I am about to take a flight. Everything is packed into my carryon baggage. On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carryon baggage? Probably not. In ordinary language, ‘everything ’ and other quan ..."
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I am about to take a flight. Everything is packed into my carryon baggage. On reading the last sentence, did you interpret me as saying falsely that everything — everything in the entire universe — was packed into my carryon baggage? Probably not. In ordinary language, ‘everything ’ and other quantifiers (‘something’, ‘nothing’, ‘every dog’,...) often carry a tacit restriction to a domain of contextually relevant objects, such as the things that I need to take with me on my journey. Thus a sentence of the form ‘Everything Fs ’ is true as uttered in a context C if and only if everything that is relevant in C satisfies the predicate ‘F’; ‘everything ’ ranges just over the contextually relevant things. Such generality is restricted in a contextrelative way. Is there also absolute generality, without contextual restrictions? In that sense, absolutely everything Fs only if everything that is relevant in any context Fs. To use ‘everything ’ to express absolute generality, we need a context in which absolutely nothing is excluded as irrelevant. Are there such contexts? Bradley describes metaphysics as ‘the effort to comprehend the universe, not simply piecemeal or by fragments, but somehow as a whole ’ ([AR]: 1). How could we comprehend
Frege on knowing the foundations
 Mind
, 1998
"... The paper scrutinizes Frege’s Euclideanism—his view of arithmetic and geometry as resting on a small number of selfevident axioms from which nonselfevident theorems can be proved. Frege’s notions of selfevidence and axiom are discussed in some detail. Elements in Frege’s position that are in ap ..."
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The paper scrutinizes Frege’s Euclideanism—his view of arithmetic and geometry as resting on a small number of selfevident axioms from which nonselfevident theorems can be proved. Frege’s notions of selfevidence and axiom are discussed in some detail. Elements in Frege’s position that are in apparent tension with his Euclideanism are considered—his introduction of axioms in The Basic Laws of Arithmetic through argument, his fallibilism about mathematical understanding, and his view that understanding is closely associated with inferential abilities. The resolution of the tensions indicates that Frege maintained a sophisticated and challenging form of rationalism, one relevant to current epistemology and parts of the philosophy of mathematics. From the start of his career Frege motivated his logicism epistemologically. He saw arithmetical judgments as resting on a foundation of logical principles, and he saw the discovery of this foundation as a discovery of the nature and structure of the justification of arithmetical truths and judg
The role of ontology in semantic integration
 In: Second International Workshop on Semantics of Enterprise Integration at OOPSLA
, 2002
"... Abstract. More and more enterprises are currently undertaking projects to integrate their applications. They are finding that one of the more difficult tasks facing them is determining how the data from one application matches semantically with the other applications. Currently there are few methodo ..."
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Abstract. More and more enterprises are currently undertaking projects to integrate their applications. They are finding that one of the more difficult tasks facing them is determining how the data from one application matches semantically with the other applications. Currently there are few methodologies for undertaking this task – most commercial projects just rely on experience and intuition. Taking semantically heterogeneous databases as the prototypical situation, this paper describes how ontology (in the traditional metaphysical sense) can contribute to delivering a more efficient and effective process of matching by providing a framework for the analysis, and so the basis for a methodology. It delivers not only a better process for matching, but the process also gives a better result. This paper describes a couple of examples of this: how the analysis encourages a kind of generalisation that reduces complexity. Finally, it suggests that the benefits are not just restricted to individual integration projects: that the process produces models which can be used as to construct a universal reference ontology – for general use in a variety of types of projects. 1
Natural Logicism via the Logic of Orderly Pairing by
, 2008
"... Schumm, Timothy Smiley and Matthias Wille. Comments by two anonymous referees have also led to significant improvements. The aim here is to describe how to complete the constructive logicist program, in the author’s book AntiRealism and Logic, of deriving all the PeanoDedekind postulates for arith ..."
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Schumm, Timothy Smiley and Matthias Wille. Comments by two anonymous referees have also led to significant improvements. The aim here is to describe how to complete the constructive logicist program, in the author’s book AntiRealism and Logic, of deriving all the PeanoDedekind postulates for arithmetic within a theory of natural numbers that also accounts for their applicability in counting finite collections of objects. The axioms still to be derived are those for addition and multiplication. Frege did not derive them in a fully explicit, conceptually illuminating way. Nor has any neoFregean done so. These outstanding axioms need to be derived in a way fully in keeping with the spirit and the letter of Frege’s logicism and his doctrine of definition. To that end this study develops a logic, in the GentzenPrawitz style of natural deduction, for the operation of orderly pairing. The logic is an extension of free firstorder logic with identity. Orderly pairing is treated as a primitive. No notion of set is presupposed, nor any settheoretic notion of membership. The formation of ordered pairs, and the two projection operations yielding their left and right coordinates, form a coeval family of logical notions. The challenge is to furnish them with introduction and elimination rules that capture their exact meanings, and no more. Orderly pairing as a logical primitive is then used in order to introduce addition and multiplication in a conceptually satisfying way within a constructive logicist theory of the natural numbers. Because of its reliance, throughout, on senseconstituting rules of natural deduction, the completed account can be described as ‘natural logicism’. 2 1 Introduction: historical