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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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Cited by 8 (3 self)
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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.
A Language for Specifying and Comparing Table Recognition Strategies
, 2004
"... Table recognition algorithms may be described by models of table location and structure, and decisions made relative to these models. These algorithms are usually defined informally as a sequence of decisions with supporting data observations and transformations. In this investigation, we formalize ..."
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Cited by 7 (3 self)
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Table recognition algorithms may be described by models of table location and structure, and decisions made relative to these models. These algorithms are usually defined informally as a sequence of decisions with supporting data observations and transformations. In this investigation, we formalize these algorithms as strategies in an imitation game, where the goal of the game is to match table interpretations from a chosen procedure as closely as possible. The chosen procedure may be a person or persons producing ‘ground truth, ’ or an algorithm. To describe table recognition strategies we have defined the Recognition Strategy Language (RSL). RSL is a simple functional language for describing strategies as sequences of abstract decision types whose results are determined by any suitable decision method. RSL defines and maintains interpretation trees, a simple data structure for describing recognition results. For each interpretation in an interpretation tree, we annotate hypothesis histories which capture the creation, revision, and rejection of individual hypotheses, such as the logical type and structure of regions. We present a proofofconcept using two strategies from the literature. We demonstrate how RSL allows strategies to be specified at the level of decisions rather than ii algorithms, and we compare results of our strategy implementations using new techniques. In particular, we introduce historical recall and precision metrics. Conventional recall and precision characterize hypotheses accepted after a strategy has finished. Historical recall and precision provide additional information by describing all generated hypotheses, including any rejected in the final result. iii
Representing Scientific Representation
, 2003
"... Scientific discourse is rife with passages that appear to be ordinary descriptions of systems of interest in a particular discipline. Equally, the pages of textbooks and journals are filled with discussions of the properties and the behavior of those systems. Students of mechanics investigate at len ..."
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Cited by 3 (2 self)
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Scientific discourse is rife with passages that appear to be ordinary descriptions of systems of interest in a particular discipline. Equally, the pages of textbooks and journals are filled with discussions of the properties and the behavior of those systems. Students of mechanics investigate at length the dynamical properties of a
NonStandard Models of Arithmetic: a Philosophical and Historical perspective MSc Thesis (Afstudeerscriptie)
, 2010
"... 1 Descriptive use of logic and Intended models 1 1.1 Standard models of arithmetic.......................... 1 1.2 Axiomatics and Formal theories......................... 3 1.3 Hintikka and the two uses of logic in mathematics.............. 5 ..."
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1 Descriptive use of logic and Intended models 1 1.1 Standard models of arithmetic.......................... 1 1.2 Axiomatics and Formal theories......................... 3 1.3 Hintikka and the two uses of logic in mathematics.............. 5
From Hilbert’s Program to a Logic Tool Box
"... www.cs.technion.ac.il/∼janos Abstract. In this paper I discuss what, according to my long experience, every computer scientists should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic tools should look lik ..."
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www.cs.technion.ac.il/∼janos Abstract. In this paper I discuss what, according to my long experience, every computer scientists should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic tools should look like for a computer scientist who is involved in designing and analyzing reliable systems. We shall conclude that many classical topics dear to logicians are less important than usually presented, and that less known ideas from logic may be more useful for the working computer scientist. For Witek Marek, first mentor, then colleague and true friend, on the occasion of his 65th birthday.
Philosophia Mathematica (III) 13 (2005), 115–134. doi:10.1093/philmat/nki010 ‘Mathematical Platonism ’ Versus Gathering the Dead: What Socrates teaches Glaucon †
"... Glaucon in Plato’s Republic fails to grasp intermediates. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. He says mathematical objects are eternal. Socrates urges a seriously debatable, and seriously defensible, alternative centered on the destruction of hyp ..."
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Glaucon in Plato’s Republic fails to grasp intermediates. He confuses pursuing a goal with achieving it, and so he adopts ‘mathematical platonism’. He says mathematical objects are eternal. Socrates urges a seriously debatable, and seriously defensible, alternative centered on the destruction of hypotheses. He offers his version of geometry and astronomy as refuting the charge that he impiously ‘ponders things up in the sky and investigates things under the earth and makes the weaker argument the stronger’. We relate his account briefly to mathematical developments by Plato’s associates Theaetetus and Eudoxus, and then to the past 200 years ’ developments in geometry. Plato was much less prodigal of affirmation about metaphysical ultimates than interpreters who take his myths literally have supposed. (Paul Shorey [1935], p. 130) Mathematics views its most cherished answers only as springboards to deeper questions. (Barry Mazur [2003], p. 225)
MATHEMATICAL TRUTH REGAINED
"... Benacerraf’s Dilemma (BD), as formulated by Paul Benacerraf in “Mathematical Truth, ” is about the apparent impossibility of reconciling a “standard ” (i.e., classical Platonic) semantics of mathematics with a “reasonable ” (i.e., causal, spatiotemporal) epistemology of cognizing true statements. In ..."
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Benacerraf’s Dilemma (BD), as formulated by Paul Benacerraf in “Mathematical Truth, ” is about the apparent impossibility of reconciling a “standard ” (i.e., classical Platonic) semantics of mathematics with a “reasonable ” (i.e., causal, spatiotemporal) epistemology of cognizing true statements. In this paper I spell out a new solution to BD. I call this new solution a positive Kantian phenomenological solution for three reasons: (1) It accepts Benacerraf’s preliminary philosophical assumptions about the nature of semantics and knowledge, as well as all the basic steps of BD, and then shows how we can, consistently with those very assumptions and premises, still reject the skeptical conclusion of BD and also adequately explain mathematical knowledge. (2) The standard semantics of mathematically necessary truth that I offer is based on Kant’s philosophy of arithmetic, as interpreted by Charles Parsons and by me. (3) The reasonable epistemology of mathematical knowledge that I offer is based on the phenomenology of logical and mathematical selfevidence developed by early Husserl in Logical Investigations and
Everything you always wanted to know about structural realism but were afraid to ask
 EURO JNL PHIL SCI (2011 ) 1:227–276
, 2011
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