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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
Is there a good epistemological argument against platonism
 Analysis
, 2006
"... [This is the final draft of an article that appeared in Analysis 66.2 (April 2006), 13541. The definitive version is available to subscribers at Oxford Journals: ..."
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[This is the final draft of an article that appeared in Analysis 66.2 (April 2006), 13541. The definitive version is available to subscribers at Oxford Journals:
THE RELIABILITY CHALLENGE AND THE EPISTEMOLOGY OF LOGIC
"... This paper concerns a problem in the epistemology of logic. This problem is an analogue of the BenacerrafField problem for mathematical Platonism. It is also an analogue of ..."
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This paper concerns a problem in the epistemology of logic. This problem is an analogue of the BenacerrafField problem for mathematical Platonism. It is also an analogue of
1 Knowledge and the Heuristics of Folk Epistemology
"... Epistemologists, like other philosophers, sometimes try to convince us of the truth of their claims about the nature of knowledge by appeals to our epistemic intuitions. Sometimes intuitions are gathered and deployed against an epistemological theory: as, for example, when our ..."
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Epistemologists, like other philosophers, sometimes try to convince us of the truth of their claims about the nature of knowledge by appeals to our epistemic intuitions. Sometimes intuitions are gathered and deployed against an epistemological theory: as, for example, when our
1 PYTHAGOREAN POWERS or A CHALLENGE TO PLATONISM
"... I have tried to apprehend the Pythagorean power by which number holds sway above the flux. Bertrand Russell, Autobiography, vol. 1, Prologue. The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot ..."
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I have tried to apprehend the Pythagorean power by which number holds sway above the flux. Bertrand Russell, Autobiography, vol. 1, Prologue. The Quine/Putnam indispensability argument is regarded by many as the chief argument for the existence of platonic objects. We argue that this argument cannot establish what its proponents intend. The form of our argument is simple. Suppose indispensability to science is the only good reason for believing in the existence of platonic objects. Either the dispensability of mathematical objects to science can be demonstrated and, hence, there is no good reason for believing in the existence of platonic objects, or their dispensability cannot be demonstrated and, hence, there is no good reason for believing in the existence of mathematical objects which are genuinely platonic. Therefore, indispensability, whether true or false, does not support platonism. Mathematical platonists claim that at least some of the objects
Chapter 3
"... In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and in ..."
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In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and indicate how this suggests a structural realist interpretation of spacetime. 1.
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"... This is a draft. Do not quote without permission. In Being Realistic About Reasons, T.M. Scanlon develops a nonnaturalistic realist account of normative reasons. A crucial part of that account is Scanlon’s contention that there is no deep epistemological problem for nonnaturalistic realists, and t ..."
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This is a draft. Do not quote without permission. In Being Realistic About Reasons, T.M. Scanlon develops a nonnaturalistic realist account of normative reasons. A crucial part of that account is Scanlon’s contention that there is no deep epistemological problem for nonnaturalistic realists, and that the method of reflective equilibrium suffices to explain the possibility of normative knowledge. In this critical notice we argue that this is not so: on a realist picture, normative knowledge presupposes a significant correlation between distinct entities, namely between normative beliefs and normative facts. This correlation calls for an explanation. We show that Scanlon does not have the resources to offer such an explanation.
Epistemically Selfdefeating Arguments and Skepticism about Intuition
, 2012
"... An argument is epistemically selfdefeating when either the truth of an argument’s conclusion or belief in an argument’s conclusion defeats one’s justification to believe at least one of that argument’s premises. Some extant defenses of the evidentiary value of intuition have invoked considerations ..."
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An argument is epistemically selfdefeating when either the truth of an argument’s conclusion or belief in an argument’s conclusion defeats one’s justification to believe at least one of that argument’s premises. Some extant defenses of the evidentiary value of intuition have invoked considerations of epistemic selfdefeat in their defense. I argue that there is one kind of argument against intuition, an unreliability argument, which, even if epistemically selfdefeating, can still imply that we are not justified in thinking intuition has evidentiary value. 1 Intuition and Epistemic SelfDefeat Let us say an argument is epistemically selfdefeating when either the truth of an argument’s conclusion or belief in an argument’s conclusion defeats one’s justification to believe at least one of that argument’s premises.1 Accordingly, unless one has some other source of justification for the conclusion of such an argument one lacks justification to believe that conclusion. We are not
Springer, New York 2009. Indiscrete Variations on GianCarlo Rota’s Themes
"... I never met GianCarlo Rota but I have often made references to his writings on the philosophy of mathematics, sometimes agreeing, sometimes disagreeing. In this paper I will discuss his views concerning four questions: the existence of mathematical objects, definition in mathematics, the notion of ..."
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I never met GianCarlo Rota but I have often made references to his writings on the philosophy of mathematics, sometimes agreeing, sometimes disagreeing. In this paper I will discuss his views concerning four questions: the existence of mathematical objects, definition in mathematics, the notion of
Mathematics, Language and Translation
"... aussi aux termes de la langue naturelle. Les textes mathématiques relèvent de combinaisons de symboles, de langue naturelle, de représentations graphiques, etc. Pour arriver à une lecture cohérente de ces textes, il faut passer par la traduction. Les mathématiques appliquées, comme la physique, pass ..."
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aussi aux termes de la langue naturelle. Les textes mathématiques relèvent de combinaisons de symboles, de langue naturelle, de représentations graphiques, etc. Pour arriver à une lecture cohérente de ces textes, il faut passer par la traduction. Les mathématiques appliquées, comme la physique, passent continuellement d’une langue (et culture) à une autre, et par conséquent, elles sont mieux comprises quand elles relèvent du domaine de la traduction. The mathematical discourse is not possible without a fertile use of natural language. Its symbols, first and foremost, refer to natural language terms. Its texts are a combination of symbols, natural language, diagrams and so on. To coherently read these texts is to be involved in the activity of translation. Applied mathematics, as in physics, constantly shifts from one language (and culture) to another and, therefore, is best understood within the ambit of translation studies. MOTSCLÉS/KEYWORDS mathematical discourse, natural language, symbols, translation studies