On the Prospects for Ontology: Deflationism,Pluralism, and Carnap's Principle of Tolerance

In this paper, I critically discuss recent work on the role that the principle of tolerance plays in Rudolf Carnap's philosophy. Specifically, I consider how two prominent interpretations of Carnap's principle of tolerance can be used to argue for Carnap's anti‐metaphysical views. I then argue that there are serious problems with these arguments, and I diagnose those problems as resulting, in part, from a tension between competing goals of Carnap's philosophical project.     

A Note on Hahn's Philosophy of Logic

Hans Hahn, mathematician, philosopher and co-founder of the Vienna Circle, attempted to reconcile the validity and applicability of both logic and mathematics with a strict empiricism. This article begins with a review of this attempt, focusing on his view of the relation of language to logic and his answer to the question of why we need logic. I then turn to some recent work by Stephen Yablo in an attempt to show that Yablo's fictionalism, and in particular his use of metaphor, can shed light on Hahn's philosophy of logic.     

Two Dogmas'–All Bark and No Bite? Carnap and Quine on Analyticity1

Recently O'Grady aigued that Quine's “Two Dogmas” misses its mark when Carnap's use of the analyticity distinction is understood in the light of his deflationism. While in substantial agreement with the stress on Camap's deflationism, I argue that O'Grady is not sufficiently sensitive to the difference between using the analyticity distinction to support deflationism, and taking a deflationary attitude towards the distinction itself; the latter being much more controversial. Being sensitive to this difference, and viewing Quine as having reason to insist on a non‐arbitrary analyticity distinction, we see that “Two Dogmas” makes direct contact with Carnap's deflationism. We must look beyond “Two Dogmas” to Quine's other critiques of analyticity to understand why the arbitrariness of the distinction threatens to undermine or overextend Carnap's deflationism, collapsing it into a view much like Quine's. Quine is then seen to achieve many of Carnap's ends, with the important exception of deflationism.     

How Tolerant Can You Be? Carnap on Rationality

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well‐defined form of language or linguistic framework we please. A linguistic framework defines framework‐internal standards of correct reasoning that guide us in our first‐order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not itself constrained by these (framework‐internal) standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance.     

For Want of an ‘And’: A Puzzle about Non-Conservative Extension

The paper analyses Frege's approach to the identity conditions for the entity labelled by him as Sinn. It starts with a brief characterization of the main principles of Frege's semantics and lists his remarks on the identity conditions for Sinn. They are subject to a detailed scrutiny, and it is shown that, with the exception of the criterion of intersubstitutability in oratio obliqua, all other criteria have to be discarded. Finally, by comparing Frege's views on Sinn with Carnap's method of extension and intension and the method of intensional isomorphism, it is proved that these methods do not provide a criterion for the identity of Frege's Sinn, even for extensional contexts, that the concept of intension does not coincide, as stated by Carnap, in these contexts, with Frege's concept of Sinn, and that Carnap's claim that in oratio obliqua Frege's semantics leads to an infinite hierarchy of Sinn entities can be questioned at least hypothetically in the light of certain new historical facts.     

Carnap's inductive probabilities as a contribution to decision theory

Common probability theories only allow the deduction of probabilities by using previously known or presupposed probabilities. They do not, however, allow the derivation of probabilities from observed data alone. The question thus arises as to how probabilities in the empirical sciences, especially in medicine, may be arrived at. Carnap hoped to be able to answer this question byhis theory of inductive probabilities. In the first four sections of the present paper the above mentioned problem is discussed in general. After a short presentation of Carnap's theory it is then shown that this theory cannot claim validity for arbitrary random processes. It is suggested that the theory be only applied to binomial and multinomial experiments. By application of de Finetti's theorem Carnap's inductive probabilities are interpreted as consecutive probabilities of the Bayesian kind. Through the introduction of a new axiom the decision parameter λ can be determined even if no a priori knowledge is given. Finally, it is demonstrated that the fundamental problem of Wald's decision theory, i.e., the determination of a plausible criterion where no a priori knowledge is available, can be solved for the cases of binomial and multinomial experiments.     

James and Carnap on philosophical systems and the role of temperaments

The relationship between American pragmatism and logical empiricism is complicated at best. The received view is that by around the late 1930s or early 1940s pragmatism had been replaced, supplanted, or eclipsed by the younger and more logic-oriented form of empiricism developed in interwar Vienna. Recently, however, this picture has been challenged, and this paper offers further reasons for thinking that the received view is inadequate. Through a critical examination of William James's Pragmatism and “The Sentiment of Rationality” and Rudolf Carnap's “Elimination of Metaphysics Through Logical Analysis of Language” and other works, the paper builds a case for the existence of a rather striking correspondence between the work of one of pragmatism's most vaunted figures and the thought of logical empiricism's most famous advocate. Not only were both philosophers interested in what might be called metaphilosophy or the psychology of philosophy, both held very similar deflationary views.     

Comments on the paradox of analysis

A version of the so‐called paradox of analysis is enunciated which involves two principles of synonymy, referred to respectively as that of substitution and that of triviality. It is argued that for most “familiar” concepts of synonymy the former principle can be maintained whereas the latter one has to be rejected. I deal with some solutions to the paradox that have been proposed or discussed by Carnap, Lewy, Feyerabend and Hare, and adhere to Carnap's view that the puzzle arises from the use of unclarified and imprecise notions of synonymy.     

On Wittgenstein's and Carnap's Conceptions of the Dissolution of Philosophical Problems,and against a Therapeutic Mix: How to Solve the Paradox of the Tractatus

In this article, I distinguish Wittgenstein's conception of the dissolution of philosophical problems from that of Carnap. I argue that the conception of dissolution assumed by the therapeutic interpretations of the Tractatus is more similar to Carnap's than to Wittgenstein's for whom dissolution involves spelling out an alternative in the context of which relevant problems do not arise. To clarify this I outline a non‐therapeutic resolute reading of the Tractatus that explains how Wittgenstein thought to be able to make a positive contribution to logic and the philosophy thereof without putting forward any (ineffable) theses. This explains why there is no paradox in the Tractatus.     

Feminism and Carnap's Principle of Tolerance

The logical empiricists often appear as a foil for feminist theories. Their emphasis on the individualistic nature of knowledge and on the value‐neutrality of science seems directly opposed to most feminist concerns. However, several recent works have highlighted aspects of Carnap's views that make him seem like much less of a straightforwardly positivist thinker. Certain of these aspects lend themselves to feminist concerns much more than the stereotypical picture would imply.     

Metacognition and mathematics strategy use

The role of children's metacognitive knowledge in their mathematics strategy use was studied by a longitudinal examination of second graders' effort attributions, metacognition for mathematics, and strategy use while solving mathematics problems. Children's correct use of retrieval, internal and external strategies, and the prevalence of strategy use were assessed in September and the following January. Effort attributions for success and failure were also assessed at both points in time. In January, metacognitive knowledge about mathematics strategies was measured. Second graders possess metacognitive knowledge about mathematics strategies, and this knowledge is correlated most strongly with the tendency to use internal strategies in September and correct internal strategy use in September. Effort attributions measured at both timepoints were significantly related to metacognition. Effort attributions in January also correlated with the tendency to use internal strategies in January. In general, the results are consistent with self-system theories, which posit that metacognition, motivation, and strategy use work together to promote learning.     

LOT 2: The Language of Thought Revisited

A main thread of the debate over mathematical realism has come down to whether mathematics does explanatory work of its own in some of our best scientific explanations of empirical facts. Realists argue that it does; anti-realists argue that it doesn't. Part of this debate depends on how mathematics might be able to do explanatory work in an explanation. Everyone agrees that it's not enough that there merely be some mathematics in the explanation. Anti-realists claim there is nothing mathematics can do to make an explanation mathematical; realists think something can be done, but they are not clear about what that something is.

I argue that many of the examples of mathematical explanations of empirical facts in the literature can be accounted for in terms of Jackson and Pettit's [1990] notion of program explanation, and that mathematical realists can use the notion of program explanation to support their realism. This is exactly what has happened in a recent thread of the debate over moral realism (in this journal). I explain how the two debates are analogous and how moves that have been made in the moral realism debate can be made in the mathematical realism debate. However, I conclude that one can be a mathematical realist without having to be a moral realist.     

Hypatia's silence

Hartry Field distinguished two concepts of type‐free truth: scientific truth and disquotational truth. We argue that scientific type‐free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non‐classical logical treatment.     

The German Reformation and the Mathematization of the Created World

This article explores the emergence of mathematics and mathematical method as a means of defining authoritative truth in the thought of some scholars in the German Reformation. Against the background of Martin Luther's critique of Aristotelian philosophy, Philip Melanchthon presented mathematics as an ideal discipline for preparing the mind to understand God. His approach drew on the work of humanist mathematicians such as Regiomontanus. It finds resonances in the work of the Basel humanist Simon Grynaeus, and (in a less mathematically informed way) in the thought of Peter Ramus. These discussions about the divine nature and certainty of mathematical truth formed the context within which Johannes Kepler's Platonist astronomy emerged.     

Kant and Kantian Themes in Recent Analytic Philosophy

This article notes six advances in recent analytic Kant research: (1) Strawson's interpretation, which, together with work by Bennett, Sellars, and others, brought renewed attention to Kant through its account of space, time, objects, and the Transcendental Deduction and its sharp criticisms of Kant on causality and idealism; (2) the subsequent investigations of Kantian topics ranging from cognitive science and philosophy of science to mathematics; (3) the detailed work, by a number of scholars, on the Transcendental Deduction; (4) the clearer understanding of transcendental idealism sparked by reactions to Allison's epistemic account; (5) the resulting need—prompted also by new studies of the thing in itself—to face up to the old question of the philosophical defensibility of such idealism; and (6) the active engagement with Kant's ethics and political philosophy that derives from Rawls's and others' work.     

Putnam, Peano, and the Malin Génie: could we possibly bewrong about elementary number-theory?

This article examines Hilary Putnam's work in the philosophy of mathematics and - more specifically - his arguments against mathematical realism or objectivism. These include a wide range of considerations, from Gödel's incompleteness-theorem and the limits of axiomatic set-theory as formalised in the Löwenheim-Skolem proof to Wittgenstein's sceptical thoughts about rule-following (along with Saul Kripke's ‘scepticalsolution’), Michael Dummett's anti-realist philosophy of mathematics, and certain problems – as Putnam sees them – with the conceptual foundations of Peano arithmetic. He also adopts a thought-experimental approach – a variant of Descartes' dream scenario – in order to establish the in-principle possibility that we might be deceived by the apparent self-evidence of basic arithmetical truths or that it might be ‘rational’ to doubt them under some conceivable (even if imaginary) set of circumstances. Thus Putnam assumes that mathematical realism involves a self-contradictory ‘Platonist’ idea of our somehow having quasi-perceptual epistemic ‘contact’ with truths that in their very nature transcend the utmost reach of human cognitive grasp. On this account, quite simply, ‘nothing works’ in philosophy of mathematics since wecan either cling to that unworkable notion of objective (recognition-transcendent) truth or abandon mathematical realism in favour of a verificationist approach that restricts the range of admissible statements to those for which we happen to possess some means of proof or ascertainment. My essay puts the case, conversely, that these hyperbolic doubts are not forced upon us but result from a false understanding of mathematical realism – a curious mixture of idealist and empiricist themes – which effectively skews the debate toward a preordained sceptical conclusion. I then go on to mount a defence of mathematical realism with reference to recent work in this field and also to indicate some problems – as I seethem – with Putnam's thought-experimental approach as well ashis use of anti-realist arguments from Dummett, Kripke, Wittgenstein, and others.     

Problems for Logical Pluralism

I argue that Beall and Restall's logical pluralism fails. Beall–Restall pluralism is the claim that there are different, equally correct logical consequence relations in a single language. Their position fails for two, related, reasons: first, it relies on an unmotivated conception of the ‘settled core’ of consequence: they believe that truth-preservation, necessity, formality and normativity are ‘settled’ features of logical consequence and that any relation satisfying these criteria is a logical consequence relation. I consider historical evidence and argue that their position relies on an unmotivated conception of the settled features of logical consequence. There are many features that are just as settled but which are inconsistent with pluralism. Second, I argue that Beall–Restall pluralism fails to hold in a single language with a single selection of logical constants, which they require for the position to be distinct from Carnap's. I consider various ways in which Beall and Restall can resist this meaning variance, particularly for negation, but argue that the strongest way relies on an unmotivated conception of the settled features of the logical constants.