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Towards a general computational theory of musical structure. Unpublished doctoral dissertation
, 1998
"... it may be published without the prior consent of the author The General Computational Theory of Musical Structure (GCTMS) is a theory that may be employed to obtain a structural description (or set of descriptions) of a musical surface. This theory is based on general cognitive and logical principle ..."
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it may be published without the prior consent of the author The General Computational Theory of Musical Structure (GCTMS) is a theory that may be employed to obtain a structural description (or set of descriptions) of a musical surface. This theory is based on general cognitive and logical principles, is independent of any specific musical style or idiom, and can be applied to any musical surface. The musical work is presented to GCTMS as a sequence of discrete symbolically represented events (e.g. notes) without higherlevel structural elements (e.g. articulation marks, timesignature etc.) although such information may be used to guide the analytic process. The aim of the application of the theory is to reach a structural description of the musical work that may be considered as 'plausible ' or 'permissible ' by a human music analyst. As styledependent knowledge is not embodied in the general theory, highly sophisticated analyses (similar to those an expert analyst may provide) are not expected. The theory gives, however, higher rating to descriptions that may be considered more reasonable or acceptable by human analysts and lower to descriptions that are less plausible.
Steps Toward a Computational Metaphysics
 Journal of Philosophical Logic
, 2007
"... In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). Afte ..."
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In this paper, the authors describe their initial investigations in computational metaphysics. Our method is to implement axiomatic metaphysics in an automated reasoning system. In this objects is implemented in prover9 (a firstorder automated reasoning system which is the successor to otter). After reviewing the secondorder, axiomatic theory of abstract objects, we show (1)howtorepresentafragmentofthattheoryinprover9’s firstorder syntax, and (2) how prover9 then finds proofs of interesting theorems of metaphysics, such as that every possible world is maximal. We conclude the paper by discussing some issues for further research. 1.
What does it mean to say that logic is formal?
, 2000
"... Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and ..."
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Much philosophy of logic is shaped, explicitly or implicitly, by the thought that logic is distinctively formal and abstracts from material content. The distinction between formal and material does not appear to coincide with the more familiar contrasts between a priori and empirical, necessary and contingent, analytic and synthetic—indeed, it is often invoked to explain these. Nor, it turns out, can it be explained by appeal to schematic inference patterns, syntactic rules, or grammar. What does it mean, then, to say that logic is distinctively formal? Three things: logic is said to be formal (or “topicneutral”) (1) in the sense that it provides constitutive norms for thought as such, (2) in the sense that it is indifferent to the particular identities of objects, and (3) in the sense that it abstracts entirely from the semantic content of thought. Though these three notions of formality are by no means equivalent, they are frequently run together. The reason, I argue, is that modern talk of the formality of logic has its source in Kant, and these three notions come together in the context of Kant’s transcendental philosophy. Outside of this context (e.g., in Frege), they can come apart. Attending to this
Historical Projects in Discrete Mathematics and Computer Science
"... A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itse ..."
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A course in discrete mathematics is a relatively recent addition, within the last 30 or 40 years, to the modern American undergraduate curriculum, born out of a need to instruct computer science majors in algorithmic thought. The roots of discrete mathematics, however, are as old as mathematics itself, with the notion of counting a discrete operation, usually cited as the first mathematical development
Deduction through the Ages: A History of Truth
"... While the subtitle “A History of Truth ” is far too ambitious for this brief slice through the history of selected topics in deductive thought, this project does offer, in the words of the pioneers, a few passages that explain how modern mathematics has arrived at an understanding of elementary prop ..."
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While the subtitle “A History of Truth ” is far too ambitious for this brief slice through the history of selected topics in deductive thought, this project does offer, in the words of the pioneers, a few passages that explain how modern mathematics has arrived at an understanding of elementary propositional logic. Different cultures have held differing views about deduction, i.e. whether a
Are there Irreducibly Relational Facts?
, 2006
"... Supposing that truths require truthmakers, that true propositions are those which correspond to facts, is there a distinctive domain of facts that make true the relational truths? Or is it rather that, if we had collected the facts required to make true the other truths, the nonrelational ones, tha ..."
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Supposing that truths require truthmakers, that true propositions are those which correspond to facts, is there a distinctive domain of facts that make true the relational truths? Or is it rather that, if we had collected the facts required to make true the other truths, the nonrelational ones, that we would then have enough facts to make all truths true? If the former is the case, let us say that antireductionism about relational facts is true; if the latter, that reductionism about relational facts is true. Let us say that a fact is relational if it makes true some relational proposition (a proposition that asserts that a relation holds between some objects 1), that it is irreducibly relational if, in addition, it does not make true any nonrelational propositions, and that it is monadic if it is not irreducibly relational (if it makes true some proposition that does not assert that a relation holds between some objects). Antireductionism (as we will say for short) holds that there are irreducibly relational facts — reductionism (as we will say for short) that while there may be relational facts, there are no irreducibly relational ones. This is a very fine definition, but is it an interesting issue? Yes, for three reasons: 1. Reasons internal to truthmaker theory. If you are one of those metaphysicians who believes the antecedent of the first sentence of this paper, that truths require truthmakers, you will naturally be interested in what manner of things you are thereby committed to. Different truthmaker theorists offer different ontologies of facts. These ontologies deal with relational facts in different ways, so independent arguments for one or other view of relational facts give us some grip on which truthmaker ontology is likely to be the right one. In particular, irreducibly relational facts could seem nominalistically unrespectable.
On the Ontology of Relations
"... around the dispute on internal and external relations had died away with the decline of Absolute Idealism. Further, in consequence of this, advances in the ontology of relations have not been comparable with the great advances in the topic of the logic of relations. Since Armstrong wrote this, some ..."
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around the dispute on internal and external relations had died away with the decline of Absolute Idealism. Further, in consequence of this, advances in the ontology of relations have not been comparable with the great advances in the topic of the logic of relations. Since Armstrong wrote this, some time has passed by, but the situation is essentially unchanged. Some investigation concerning relations has been done, but I think that many of them were contaminated by old prejudices. This paper is intended as a contribution to minimize this gap. I will defend and argue in favour of some positive claims concerning the ontological status of relations. The main topics – and corresponding sections – of this paper are (1) irreducibility, (2) externality and (3) reality of relations. Thus, my topics exactly coincide with Russell’s main topics in the theory of relations. But my purpose here is not an exegetical investigation of the controversy between classical authors like Russell, Bradley and Leibniz. 1 I will just offer some cursorily historical remarks in order to introduce the questions, but then I will propose some (I hope) original theses and arguments. 1 The irreducibility of relations Aristotle was the first to defend the reducibility of relations. He said in his Categories that, whenever two (or more) substances are related, this is to be explained by means of certain monadic properties or
Chapter 9 Overall Model and Four Analyses
"... In this chapter the computational components of the GCTMS presented in the previous chapters are combined in order to obtain analytic descriptions of four melodies. The main aim of these analytic examples is to highlight the capabilities of the proposed overall model, to give some preliminary eviden ..."
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In this chapter the computational components of the GCTMS presented in the previous chapters are combined in order to obtain analytic descriptions of four melodies. The main aim of these analytic examples is to highlight the capabilities of the proposed overall model, to give some preliminary evidence of the generality of the theory and to present