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OPERATIONAL QUANTUM LOGIC: AN OVERVIEW
, 2000
"... The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform presentation of what we call operational quantum logic, highlighting bo ..."
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The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform presentation of what we call operational quantum logic, highlighting both its concrete physical origins and its purely mathematical structure. To orient readers new to this subject, we shall recount some of the historical development of quantum logic, attempting to show how the physical and mathematical sides of the subject have influenced and enriched one another.
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
Nonrelativistic quantum mechanics
 In J. Butterfield & J. Earman (Eds.), Philosophy of Physics Part A. Elsevier
, 2006
"... Abstract. This chapter is a discussion of the philosophical and foundational issues that arise in nonrelativistic quantum theory. After introducing the formalism of the theory, I consider: characterizations of the quantum formalism, empirical content, uncertainty, the measurement problem, and non ..."
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Abstract. This chapter is a discussion of the philosophical and foundational issues that arise in nonrelativistic quantum theory. After introducing the formalism of the theory, I consider: characterizations of the quantum formalism, empirical content, uncertainty, the measurement problem, and nonlocality. In each case, the main point is to give the reader some introductory understanding of some of the
Quantum Mechanics: From Realism to Intuitionism  A mathematical and philosophical investigation
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PLURALISM IN LOGIC
"... Abstract. A number of people have proposed that we should be pluralists about logic, but there are several things this can mean. Are there versions of logical pluralism that are both high on the interest scale and also true? After discussing some forms of pluralism that seem either insufficiently in ..."
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Abstract. A number of people have proposed that we should be pluralists about logic, but there are several things this can mean. Are there versions of logical pluralism that are both high on the interest scale and also true? After discussing some forms of pluralism that seem either insufficiently interesting or quite unlikely to be true, the paper suggests a new form which might be both interesting and true; however, the scope of the pluralism that it allows logic is extremely narrow. There are quite a few theses about logic that are in one way or another pluralist: they hold (i) that there is no uniquely correct logic, and (ii) that because of this, some or all debates about logic are illusory, or need to be somehow reconceived as not straightforwardly factual. Pluralist theses differ markedly over the reasons offered for there being no uniquely correct logic. Some such theses are more interesting than others, because they more radically affect how we are initially inclined to understand debates about logic. Can one find a pluralist thesis that is high on the interest scale, and also true? §1. The boundaries of logic. One form of pluralism that strikes me as true though of somewhat limited interest is Tarski’s (1936) thesis that there is no principled division of concepts into the logical and the nonlogical, and the related view that there is no principled
Quine’s challenge and Logical Pluralism
, 2010
"... Anumberofdeviantdeductivesystemshavebeenproposedwhichdiffer in some way from classical logic. An influential philosophical interpretation of plurality in logic has been developed by Quine, who introduced the meaningchange thesis, summarized in his "Change of logic, change of subject". We s ..."
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Anumberofdeviantdeductivesystemshavebeenproposedwhichdiffer in some way from classical logic. An influential philosophical interpretation of plurality in logic has been developed by Quine, who introduced the meaningchange thesis, summarized in his "Change of logic, change of subject". We show that if Quine is right about the consequences of his thesis, then the systems of classical logic can only be rejected as unscientific or meaningless, and not refined as inadequate. We show that there are good reasons both for and against his thesis. We argue against Local Pluralism, on the basis that it is incompatible with the universality and normativity of logic. We then assess Beall and Restall’s logical pluralism, which is shown to be not sufficiently finegrained in that it leads to relativism in logic. We finally introduce Dalla Pozza’s Global Pluralism, where deviant logics are viewed as dealing with specific pragmatic metaconcepts, which are distinct from
1 Semantic Paradoxes and Abductive Methodology
"... Understandably absorbed in technical details, discussion of the semantic paradoxes risks losing sight of broad methodological principles. This essay sketches a general approach to the comparison of rival logics, and applies it to argue that revision of classical propositional logic has much higher c ..."
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Understandably absorbed in technical details, discussion of the semantic paradoxes risks losing sight of broad methodological principles. This essay sketches a general approach to the comparison of rival logics, and applies it to argue that revision of classical propositional logic has much higher costs than its proponents typically recognize.