Off-campus access
Using PhilPapers from home?
Click here to configure this browser for off-campus access.
- Jack Arnold & Stewart Shapiro (2007). Where in the (World Wide) Web of Belief is the Law of Non-Contradiction? Noûs 41 (2):276–297.It is sometimes said that there are two, competing versions of W. V. O. Quine’s unrelenting empiricism, perhaps divided according to temporal periods of his career. According to one, logic is exempt from, or lies outside the scope of, the attack on the analytic-synthetic distinction. This logic-friendly Quine holds that logical truths and, presumably, logical inferences are analytic in the traditional sense. Logical truths are knowable a priori, and, importantly, they are incorrigible, and so immune from revision. The other, radical reading of Quine does not exempt logic from the attack on analyticity and a priority. Logical truths and inferences are themselves part of the web of belief, and the same global methodology applies to logic as to any other part of the web, such as theoretical chemistry or ordinary beliefs about ordinary objects. Everything, including logic, is up for grabs in our struggle for holistic confirmation. The purpose of this paper is to examine the law of non-contradiction, and the concomitant principle of ex falso quodlibet, from the perspective of the principles advocated by the radical Quine. I show that he has no compelling reason to accept either of these. To put it bluntly, neither the law of non-contradiction nor the rule of ex falso quodlibet is empirically confirmed, and these principles fare poorly on the various criteria for theory acceptance on the methodology of the radical Quine. So the radical Quine is led rather quickly and rather directly into something in the neighborhood of Graham Priest’s dialetheism.
Similar books and articles
One central strand in Quine's criticism of common-sense notions of linguistic meaning is an argument from the holism of empirical content. This paper explores (with many digressions) the several versions of the argument, and discovers them to be uniformly bad. There is a kernel of truth in the idea that ?holism?, in some sense, ?undermines the analytic?synthetic distinction?, in some sense; but it has little to do with Quine's radical empiricism, or his radical scepticism about meaning.
Conceptions of analytic truth -- Hume's fork -- Kant and the analytic/synthetic distinction -- Synthetic a priori propositions -- Bolzano and analyticity -- Analyticity in frege -- Russell's paradox and the theory of descriptions -- The Vienna circle -- Carnap and logical empiricism -- Carnap and Quine -- Demise of the aufbau -- Philosophy as logical syntax -- Logical and descriptive languages -- Physical languages -- Analyticity in syntax -- Carnap's move to semantics -- Explications -- Analyticity in a semantic setting -- Eliminating metaphysics : Carnap's final try -- W.V. Quine : explication is elimination -- Behaviorists ex officio -- Analyticity in the crosshairs -- Analyticity and its discontents -- Questioning analyticity -- Quine's two dogmas of empiricism -- Objections to the coherence of analytic -- Quine's coherence arguments : Carnap's reply -- Other responses to the coherence objection : Grice and Strawson on Quine -- A second dogma of empiricism -- Responses to the existence objections to analyticity -- Analyticity by convention -- Quine's developed attitude toward analyticity -- Analyticity and ontology -- Quine's naturalized ontology -- The indeterminacy of translation -- Some consequences of the indeterminacy arguments : ontological relativity and analyticity -- Responses to Quine's indeterminacy arguments -- Carnap's empiricism, semantics, and ontology -- Some Quinean and other responses to empiricism, semantics, and ontology -- Some recent connections between conceptual truths and ontology -- Quine's criterion of ontological commitment, causality, and exists -- Eli Hirsch and Ted Sider on mereological principles -- The Canberra Project : a resurrection of Carnap's aufbau -- Analyticity and epistemology -- Analytic truths and their role in epistemology : the classical position -- Objecting to the classical position -- Bonjour on moderate empiricism -- Quine's epistemology naturalized -- Quine and evidence : responses to circularity -- Kripke on a priority, analyticity, and necessity -- Analyticity repositioned -- The concept analytic -- One type of statement that might be reasonably called analytic -- Aside on two dimensionalism -- Analyticity and T-analyticity -- How analyticity avoids many common objections to analyticity -- Some brief comments on two other approaches to analyticity -- Mathematical claims as T-analytic -- A further potential application : pure and impure stipulata.
Conceptions of analytic truth -- Hume's fork -- Kant and the analytic/synthetic distinction -- Synthetic a priori propositions -- Bolzano and analyticity -- Analyticity in frege -- Russell's paradox and the theory of descriptions -- The Vienna circle -- Carnap and logical empiricism -- Carnap and Quine -- Demise of the aufbau -- Philosophy as logical syntax -- Logical and descriptive languages -- Physical languages -- Analyticity in syntax -- Carnap's move to semantics -- Explications -- Analyticity in a semantic setting -- Eliminating metaphysics : Carnap's final try -- W.V. Quine : explication is elimination -- Behaviorists ex officio -- Analyticity in the crosshairs -- Analyticity and its discontents -- Questioning analyticity -- Quine's two dogmas of empiricism -- Objections to the coherence of analytic -- Quine's coherence arguments : Carnap's reply -- Other responses to the coherence objection : Grice and Strawson on Quine -- A second dogma of empiricism -- Responses to the existence objections to analyticity -- Analyticity by convention -- Quine's developed attitude toward analyticity -- Analyticity and ontology -- Quine's naturalized ontology -- The indeterminacy of translation -- Some consequences of the indeterminacy arguments : ontological relativity and analyticity -- Responses to Quine's indeterminacy arguments -- Carnap's empiricism, semantics, and ontology -- Some Quinean and other responses to empiricism, semantics, and ontology -- Some recent connections between conceptual truths and ontology -- Quine's criterion of ontological commitment, causality, and exists -- Eli Hirsch and Ted Sider on mereological principles -- The Canberra Project : a resurrection of Carnap's aufbau -- Analyticity and epistemology -- Analytic truths and their role in epistemology : the classical position -- Objecting to the classical position -- Bonjour on moderate empiricism -- Quine's epistemology naturalized -- Quine and evidence : responses to circularity -- Kripke on a priority, analyticity, and necessity -- Analyticity repositioned -- The concept analytic -- One type of statement that might be reasonably called analytic -- Aside on two dimensionalism -- Analyticity and T-analyticity -- How analyticity avoids many common objections to analyticity -- Some brief comments on two other approaches to analyticity -- Mathematical claims as T-analytic -- A further potential application : pure and impure stipulata.
Quine correctly argues that Carnap's distinction between internal and external questions rests on a distinction between analytic and synthetic, which Quine rejects. I argue that Quine needs something like Carnap's distinction to enable him to explain the obviousness of elementary mathematics, while at the same time continuing to maintain as he does that the ultimate ground for holding mathematics to be a body of truths lies in the contribution that mathematics makes to our overall scientific theory of the world. Quine's arguments against the analytic/synthetic distinction, even if fully accepted, still leave room for a notion of pragmatic analyticity sufficient for the indicated purpose.
I want to analyse the Quine-Carnap discussion on analyticity with regard to logical, mathematical and set-theoretical statements. In recent years, the renewed interest in Carnap’s work has shed a new light on the analytic-synthetic debate. If one fully appreciates Carnap’s conventionalism, one sees that there was not a metaphysical debate on whether there is an analytic-synthetic distinction, but rather a controversy on the expedience of drawing such a distinction. However, on this view, there can be no longer a single analytic-synthetic distinction, because several kinds of statements could be regarded as analytic (L-determinate). L-equivalence between extra-logical linguistic predicates has already been heavily debated. The recent consensus states that Quine’s rejection of this analytic-synthetic is pragmatically grounded in his linguistic behaviorism. However, Carnap’s logical frameworks also contain other kinds of statements, and it is worthwhile to compare both Quine and Carnap’s grounds for considering these statements as analytic or not analytic. First, I will discuss logical statements. I will argue that Quine draws a very sharp distinction between first order logic and set theory, which should be regarded as a (pragmatic) analytic-synthetic distinction (as Quine admits in an interview, see Theoria, 40, 1994, p. 199). In fact, Quine’s major worry is whether identity statements are analytic. Second, I will discuss mathematical statements. In Carnap’s Foundations of Logic and Mathematics, it is clear that mathematical statements are analytic. For Quine, all mathematical statements are reducible to set-theoretical statements. Third, I discuss the analyticity of set-theoretical statements. For Quine, the membership predicate should be regarded as an interpreted extra-logical predicate. Quine’s work in set theory and his later philosophy of set theory naturally lead to the view that set-theoretical statements cannot be analytic. A major complication for the Quine-Carnap comparison is that Carnap has no elaborate reflections on set theory, while the influence of set theory on Quine’s views can hardly be underestimated. I conclude with some lessons for the contemporary debate on analyticity.
The linguistic theory of the logical A Priori: is it obsolete In holistic interpretations, the logical truths are considered as continuous with empirical science: they are revisable, a posteriori, though very near to the centre of our web of belief. In this paper, we consider the merits and demerits of this approach, and we propose that it is necessary to revaluate holistic philosophies of logic. Some arguments are put forward which point in favour of the logical empiricists’ theory of logical truth. We argue (following Hartry Field) that the concept of “correlation between logical facts and logical beliefs” (which is at the heart of the holistic theory) is inconsistent. Finally, we concentrate on the principle of contradiction and argue (following Manley Thompson) that this principle is fundamental for meaning, truth, and thinking. This thesis is derived from considerations on the nature of intentionality.
The Law of Non-Contradiction - that no contradiction can be true - has been a seemingly unassailable dogma since the work of Aristotle, in Book G of the Metaphysics. It is an assumption challenged from a variety of angles in this collection of original papers. Twenty-three of the world's leading experts investigate the 'law', considering arguments for and against it and discussing methodological issues that arise whenever we question the legitimacy of logical principles. The result is a balanced inquiry into a venerable principle of logic, one that raises questions at the very centre of logic itself. The aim of this volume is to present a comprehensive debate about the Law of Non-Contradiction, from discussions as to how the law is to be understood, to reasons for accepting or re-thinking the law, and to issues that raise challenges to the law, such as the Liar Paradox, and a 'dialetheic' resolution of that paradox. The editors contribute an introduction which surveys the issues and serves to frame the debate, and a useful bibliography offering a guide to further reading. This volume will be of interest to anyone working on philosophical logic, and to anyone who has ever wondered about the status of logical laws and about how one might proceed to mount arguments for or against them.
The goals of this paper are two-fold: I wish to clarify the Aristotelian conception of the law of non-contradiction as a metaphysical rather than a semantic or logical principle, and to defend the truth of the principle in this sense. First I will explain what it in fact means that the law of non-contradiction is a metaphysical principle. The core idea is that the law of non-contradiction is a general principle derived from how things are in the world. For example, there are certain constraints as to what kind of properties an object can have, and especially: some of these properties are mutually exclusive. Given this characterisation, I will advance to examine what kind of challenges the law of non-contradiction faces; the main opponent here is Graham Priest. I will consider these challenges and conclude that they do not threaten the truth of the law of non-contradiction understood as a metaphysical principle.
There has been a significant shift in the discussion of a priori knowledge. The shift is due largely to the influence of Quine. The traditional debate focused on the epistemic status of mathematics and logic. Kant, for example, maintained that arithmetic and geometry provide clear examples of synthetic a priori knowledge and that principles of logic, such as the principle of contradiction, provide the basis for analytic a priori knowledge. Quine’s rejection of the analytic-synthetic distinction and his holistic empiricist account of mathematic and logical knowledge undercut the traditional defenses of the a priori in two ways. First, one could no longer defend the view that mathematical and logical knowledge is a priori solely by rejecting Mill’s inductive empiricism. Moreover, holistic empiricism proved to be a more challenging position to refute than inductive empiricism. Second, the rejection of the analytic-synthetic distinction blocked an alternative defense of the a priori status of mathematics and logic that appealed to their alleged analyticity.
W. V. O. Quine's well-known attack upon the analytic-synthetic distinction is held to affect only one of the two species of analytic statements he distinguishes. In particular it is not directed at and does not affect the so-called logical truths. In this paper the scope of Quine's attack is extended so as to embrace the logical truths as well. It is shown that the unclarifiability of the notion of 'synonymy' deprives us not only of "analytic statements that are obtainable from logical truths by the replacement of synonyms with synonyms" but of "logical truths" themselves.
Discussion of Jack Arnold & Stewart Shapiro, Where in the (world wide) web of belief is the law of non-contradiction?
|
|
There are no threads in this forum |
Nothing in this forum yet.

