This paper presents a new approach to the class-theoretic paradoxes. In the first part of the paper, I will distinguish classes from sets, describe the function of class talk, and present several reasons for postulating type-free classes. This involves applications to the problem of unrestricted quantification, reduction of properties, natural language semantics, and the epistemology of mathematics. In the second part of the paper, I will present some axioms for type-free classes. My approach is loosely based on the Gödel–Russell idea (...) of limited ranges of significance. It is shown how to derive the second-order Dedekind–Peano axioms within that theory. I conclude by discussing whether the theory can be used as a solution to the problem of unrestricted quantification. In an appendix, I prove the consistency of the class theory relative to Zermelo–Fraenkel set theory. (shrink)

The article, first, reconstructs and criticizes Sandro Nannini’s incompatibilistic concept of freedom of decision and, second, develops a compatibilistic alternative, a synthesis of a rationalistic and an autonomous approach. Nannini justifies his conception primarily from a naturalistic point of view: it reflects our sense of agency, so he says. This is criticized as empirically wrong and methodically mistaken: The theory of freedom of decision is, actually, normative; it is about good decisions; naturalism cannot establish normative claims. The alternative is based, (...) methodically, on an idealizing hermeneutics, which tries to reconstruct the point of free decisions, and then justifies the resulting concept practically: Free decisions, conceived in this way, realize optimally our autonomous desires. (shrink)

In his 1936 paper,On the Concept of Logical Consequence, Tarski introduced the celebrated definition oflogical consequence: “The sentenceσfollows logicallyfrom the sentences of the class Γ if and only if every model of the class Γ is also a model of the sentenceσ.” [55, p. 417] This definition, Tarski said, is based on two very basic intuitions, “essential for the proper concept of consequence” [55, p. 415] and reflecting common linguistic usage: “Consider any class Γ of sentences and a sentence which (...) follows from the sentences of this class. From an intuitive standpoint it can never happen that both the class Γ consists only of true sentences and the sentenceσis false. Moreover, … we are concerned here with the concept of logical, i.e.,formal, consequence.” [55, p. 414] Tarski believed his definition of logical consequence captured the intuitive notion: “It seems to me that everyone who understands the content of the above definition must admit that it agrees quite well with common usage. … In particular, it can be proved, on the basis of this definition, that every consequence of true sentences must be true.” [55, p. 417] The formality of Tarskian consequences can also be proven. Tarski's definition of logical consequence had a key role in the development of the model-theoretic semantics of modern logic and has stayed at its center ever since. (shrink)

I distinguish two ways of developing anti-exceptionalist approaches to logical revision. The first emphasizes comparing the theoretical virtuousness of developed bodies of logical theories, such as classical and intuitionistic logic. I'll call this whole theory comparison. The second attempts local repairs to problematic bits of our logical theories, such as dropping excluded middle to deal with intuitions about vagueness. I'll call this the piecemeal approach. I then briefly discuss a problem I've developed elsewhere for comparisons of logical theories. Essentially, the (...) problem is that a pair of logics may each evaluate the alternative as superior to themselves, resulting in oscillation between logical options. The piecemeal approach offers a way out of this problem andthereby might seem a preferable to whole theory comparisons. I go on to show that reflective equilibrium, the best known piecemeal method, has deep problems of its own when applied to logic. (shrink)

1. What are called ‘intuitions’ in philosophy are just applications of our ordinary capacities for judgement. We think of them as intuitions when a special kind of scepticism about those capacities is salient. 2. Like scepticism about perception, scepticism about judgement pressures us into conceiving our evidence as facts about our internal psychological states: here, facts about our conscious inclinations to make judgements about some topic rather than facts about the topic itself. But the pressure should be resisted, for it (...) rests on bad epistemology: specifically, on an impossible ideal of unproblematically identifiable evidence. 3. Our resistance to scepticism about judgement is not simply epistemic conservativism, for we resist it on behalf of others as well as ourselves. A reason is needed for thinking that beliefs tend to be true. 4. Evolutionary explanations of the tendency assume what they should explain. Explanations that appeal to constraints on the determination of reference are more promising. Davidson’s truth-maximizing principle of charity is examined but rejected. 5. An alternative principle is defended on which the nature of reference is to maximize knowledge rather than truth. It is related to an externalist conception of mind on which knowing is the central mental state. 6. The knowledge-maximizing principle of charity explains why scenarios for scepticism about judgement do not warrant such scepticism, although it does not explain how we know in any particular case. We should face the fact that evidence is always liable to be contested in philosophy, and stop using talk of intuition to disguise this unpleasant truth from ourselves. (shrink)

The axiom of reducibility plays an important role in the logic of Principia Mathematica, but has generally been condemned as an ad hoc non-logical axiom which was added simply because the ramified type theory without it would not yield all the required theorems. In this paper I examine the status of the axiom of reducibility. Whether the axiom can plausibly be included as a logical axiom will depend in no small part on the understanding of propositional functions. If we understand (...) propositional functions as constructions of the mind, it is clear that the axiom is clearly not a logical axiom and in fact makes an implausible claim. I look at two other ways of understanding propositional functions, a nominalist interpretation along the lines of Landini and a realist interpretation along the lines of Linsky and Mares. I argue that while on either of these interpretations it is not easy to see the axiom as a non-logical claim about the world, there are also appear to be difficulties in accepting it as a purely logical axiom. (shrink)

The Löwenheim-Hilbert-Bernays theorem states that, for an arithmetical first-order language L, if S is a satisfiable schema, then substitution of open sentences of L for the predicate letters of S...

In a growing number of papers, one encounters arguments to the effect that certain philosophical views are objectionable because they would imply that there are necessary truths for whose necessity there is no explanation. That is, they imply that there are propositions p such that (a) it is necessary that p, but (b) there is no explanation why it is necessary that p. For short, they imply that there are “brute necessities.” Therefore, the arguments conclude, the views in question should (...) be rejected in favor of rival views under which the necessities would be explained. This style of argument raises a number of important and difficult questions. Do necessary truths really require explanation? Are they not paradigms of truths that either need no explanation or automatically have one, being in some sense self‐explanatory? If some necessary truths do require or admit of explanation, what types of explanation, are available? Are some necessary truths explained by other necessary truths? Are some necessary truths self‐explanatory? Are all necessary truths either self‐explanatory or explained by others? Or are there some necessary truths that are truly brute? This article surveys several representative arguments from brute necessity as well as a variety of answers to the questions above, noting their bearing on arguments from bruteness. (shrink)

I examine the thesis that Otto Neurath anticipated the programme of naturalised epistemology already at the time of the Vienna Circle and consider the relation between Neurath's proposals and those of two contemporary theorists whose research programmes he would thus have broadly anticipated. The thesis is confirmed by reference to Neurath's own writings. The connection between Neurath's programme and the programmes of his two successors considered here, however, is found to be highly indirect in one case and nonexistent in the (...) other — despite their undeniable overlap. (shrink)

Michael Friedman’s Dynamics of Reason is a welcome contribution to the ongoing articulation of philosophical perspectives for understanding the sciences in the context of post-positivist philosophy of science. Two perspectives that have gained advocacy since the demise of the “received view” are Quinean naturalism and Kuhnian relativism. In his 1999 Stanford lectures, Friedman articulates and defends a neo-Kantian perspective for philosophy of science that opposes both of these perspectives. His proffered neo-Kantian perspective is presented within the context of the problem (...) of theory change or “scientific revolutions,” and its main feature is a conception of scientific knowledge that requires “relativized constitutive a priori principles.” The lectures make up the first part of the book; the second part of the book, “Fruits of Discussion,” is a further elaboration and defence of the ideas advanced in the lectures. The resulting book serves as a useful sequel to Friedman’s impressive historical studies in Foundations of Space-Time Theories, Kant and the Exact Sciences, and Reconsidering Logical Positivism. In the preface, Friedman tells us that this book represents the philosophical viewpoint that he has arrived at as a result of completing these works. As such, it is not surprising that the prominent themes of the book are ones that have occupied Friedman’s attention in the past, viz., the importance of a priori principles in the exact sciences, the conventionalism of the logical positivists, and, more generally, an articulation of what remains defensible in neo-Kantian philosophy of science. (shrink)

Beliefs have what I will call ‘propositional content’. A belief is always a belief that so-and-so: a belief that grass is green, or a belief that snow is white, or whatever. Other things have propositional content too, such as sentences, judgments and assertions. The Standard View amongst philosophers is that what it is to have a propositional content is to stand in an appropriate relation to a proposition. Moreover, on this view, propositions are objects, i.e. the kind of thing you (...) can refer to with singular terms. For example, on the Standard View, we should parse the sentence ‘Simon believes that Sharon is funny’ as: [Simon] believes [that Sharon is funny]; ‘Simon’ is a term referring to a thinking subject, ‘that Sharon is funny’ is a term referring to a proposition, and ‘x believes y’ is a dyadic predicate expressing the believing relation. In this paper, I argue against the Standard View. This is how I think we should parse ‘Simon believes that Sharon is funny’: [Simon] believes that [Sharon is funny]; here we have a singular term, ‘Simon’, a sentence ‘Sharon is funny’, and a ‘prenective’ joining them together, ‘x believes that p’. On this Prenective View, we do not get at the propositional content of someone’s belief by referring to a reified proposition with a singular term; we simply use the sentence ‘Sharon is funny’ to express that content for ourselves. I argue for the Prenective View in large part by showing that an initially attractive version of the Standard View is actually vulnerable to the same objection that Wittgenstein used against Russell’s multiple-relation theory of judgment. (shrink)

A neutralist framework is an account of the second-order quantifiers which does not by itself tell us what the ontological commitments of second-order quantification are, but which does tell us that those commitments cannot exceed those of predication. Recently, Wright has suggested that an inferentialist account of the second-order quantifiers is an adequate neutralist framework. I show that we do not have to become inferentialists in the pursuit of a neutralist framework: such a framework can be established within the semantic (...) tradition. (shrink)

Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by at least (...) some of these sentences as infectious. This leads us to consider four distinct four-valued logics: one where truth-value gaps are infectious, but gluts are not; one where truth-value gluts are infectious, but gaps are not; and two logics where both gluts and gaps are infectious, in some sense. Additionally, we focus on the proof theory of these systems, by offering a discussion of two related topics. On the one hand, we prove some limitations regarding the possibility of providing standard Gentzen sequent calculi for these systems, by dualizing and extending some recent results for infectious logics. On the other hand, we provide sound and complete four-sided sequent calculi, arguing that the most important technical and philosophical features taken into account to usually prefer standard calculi are, indeed, enjoyed by the four-sided systems. (shrink)

In recent work on a priori justification, one thing about which there is considerable agreement is that the notion of truth in virtue of meaning is bankrupt and infertile. (For the sake of more readable prose, I will use ‘TVM’ as an abbreviation for ‘the notion of truth in virtue of meaning’.) Arguments against the worth of TVM can be found across the entire spectrum of views on the a priori, in the work of uncompromising rationalists (such as BonJour (1998)), (...) of centrist moderates (such as Boghossian (1997)), and of uncompromising empiricists (such as Devitt (2004)). My aim is to dispute this widespread opinion. The outline is as follows: First, §§2-3 consist of preliminary stage-setting. Then, in §4 I will argue that some of the most prevalent arguments against the worth of TVM – in particular, one which is given clear expression by Quine (1970), and is recently reinforced by Boghossian (1997) – do not engage with the core idea motivating TVM. After deflecting this charge of incoherence, the aim of §§5-8 is to work toward developing a useful conception of TVM. (shrink)

In the recent literature on all things metaontological, discussion of a notorious Meinongian doctrine—the thesis that some objects have no kind of being at all—has been conspicuous by its absence. And this is despite the fact that this thesis is the central element of the noneist metaphysics of Richard Routley (1980) and Graham Priest (2005). In this paper, we therefore examine the metaontological foundations of noneism, with a view to seeing exactly how the noneist's approach to ontological inquiry differs from (...) the orthodox Quinean one. We proceed by arguing that the core anti-Quinean element in noneism has routinely been misidentified: rather than concerning Quine's thesis that to be is to be the value of a variable, the real difference is that the noneist rejects what we identify as Quine's “translate-and-deflate” methodology. In rejecting this aspect of Quinean orthodoxy, the noneist is in good company: many of those who think that questions of fundamentality should be the proper focus of ontological inquiry can be read as rejecting it too. Accordingly, we then examine the differences between the noneist's conception of ontology and that offered by the fundamentalist. We argue that these two anti-Quinean approaches differ in terms of their respective conceptions of the theoretical role associated with the notion of being. And the contrast that emerges between them is, in the end, an explanatory one. (shrink)

NeoFregeanism is an intriguing but elusive philosophy of mathematical existence. At crucial points, it goes cryptic and metaphorical. I want to put forward an interpretation of neoFregeanism—perhaps not one that actual neoFregeans will embrace—that makes sense of much of what they say. NeoFregeans should embrace quantifier variance.

The paper seeks to answer two new questions about truth and scientific change: What lessons does the phenomenon of scientific change teach us about the nature of truth? What light do recent developments in the theory of truth, incorporating these lessons, throw on problems arising from the prevalence of scientific change, specifically, the problem of pessimistic meta-induction?

Knowledge requires both freedom and friction . Freedom to set up our epistemic goals, choose the subject matter of our investigations, espouse cognitive norms, design research programs, etc., and friction (constraint) coming from two directions: the object or target of our investigation, i.e., the world in a broad sense, and our mind as the sum total of constraints involving the knower. My goal is to investigate the problem of epistemic friction, the relation between epistemic friction and freedom, the viability of (...) foundationalism as a solution to the problem of friction, an alternative solution in the form of a neo-Quinean model, and the possibility of solving the problem of friction as it applies to logic and the philosophy of logic within that model. (shrink)

It is often claimed that nominalistic programmes to reconstruct mathematics fail, since they will at some point involve the notion of logical consequence which is unavailable to the nominalist. In this paper we use an idea of Goodman and Quine to develop a nominalistically acceptable explication of logical consequence.

It is sometimes mentioned that Bernard Bolzano’s work on grounding anticipates many insights of the current debate on metaphysical grounding. The present paper discusses a certain part of Bolzano’s theory of grounding that has thus far not been discussed in the literature. This part does not so much anticipate what are nowadays common assumptions about grounding, but rather goes beyond them. Central to the discussion will be a thesis of Bolzano’s by which he tries to establish a connection between grounding (...) and unification. The paper spells out this thesis in detail and discusses the assumptions on which it rests. Next to this mainly historical aim, the paper also presents reasons why philosophers who are not interested in the historical Bolzano should find the thesis interesting by relating it to a certain view on unification and explanation that has been put forward by Kim. A final part of the paper provides a critical evaluation of the thesis against the background of current accounts of grounding. (shrink)

Is understanding epistemic in nature? Does a correct account of what constitutes understanding of a concept mention epistemological notions such as knowledge, justification or epistemic rationality? We defend the view that understanding is epistemic in nature – we defend epistemological conceptions of understanding. We focus our discussion with a critical evaluation of Tim Williamson's challenges to epistemological conceptions of understanding in The Philosophy of Philosophy. Against Williamson, we distinguish three kinds of epistemological conceptions and argue that Williamson's arguments succeed against (...) only the most heavily committed kind, and leave the less heavily committed kinds untouched. Further, we argue that Williamson's elaboration of lessons from his arguments point in a direction opposite of his own conclusions and give vivid articulation and support to epistemological conceptions. We suggest also that skepticism about Williamson's larger metaphilosophical conclusions – according to which understanding plays no special role in the epistemology of philosophy – may be in order. (shrink)

...its identity in the pragmatics of elucidation, and not in some sort of special knowledge...yer's essay (`Implicit Thoughts: Quine, Frege and Kant on Analytic Propositions...by Quine, and attributed to Kant, Frege and Carnap, has nothing in common..

It is a consequence of Quine’s confirmation holism that the logical laws are in principle revisable. Some have worried this is at odds with another dictum in Quine, viz., that any translation which construes speakers as systematically illogical is ipso facto inadequate. In this paper, I try to formulate exactly what the problem is here, and offer a solution to it by (1) disambiguating the term ‘logic,’ and (2) appealing to a Quinean understanding of ‘necessity.’ The result is that the (...) different theses in Quine’s philosophy of logic are to be situated within different contexts of inquiry. (shrink)

In this essay I focus on the idea of the univocity of being, championed by Duns Scotus and given prominence more recently by Deleuze. Although I am interested in how this idea can be established, my primary concern is with something more basic: how the idea can even be properly thought. In the course of exploring this issue, which I do partly by borrowing some ideas about logical syntax from Wittgenstein's Tractatus, I try to show how there can be dialogue (...) between analytic philosophers and those of other traditions. (shrink)

Isabelle Delpla a écrit une étude critique riche et généreuse de mon ouvrage Les fondements empiriques de la signification. Cette étude regorge d’analyses fines et de critiques subtiles des positions que je défends. Son titre défaitiste ne m’apparaît toutefois pas motivé, et je vais montrer pourquoi ses principales attaques échouent.

The project of antirealism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of the excluded third and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity. Using principles of intuitionistic mathematics and employing only intuitionistically correct inferences, we show that prima facie reasonable formulations of (1), (2), and (3) are inconsistent. Therefore, it should (...) not be assumed that the project of anti-realism as it bears upon intuitionistic mathematics and logic can be accomplished. (shrink)

I defend the Received View on scientific theories as developed by Carnap, Hempel, and Feigl against a number of criticisms based on misconceptions. First, I dispute the claim that the Received View demands axiomatizations in first order logic, and the further claim that these axiomatizations must include axioms for the mathematics used in the scientific theories. Next, I contend that models are important according to the Received View. Finally, I argue against the claim that the Received View is intended to (...) make the concept of a theory more precise. Rather, it is meant as a generalizable framework for explicating specific theories. (shrink)

Restrictionism is a response to the Liar and other paradoxes concerning truth. Restrictionists—as I will call proponents of the strategy—respond to these paradoxes by giving up instances of the schema -/- <p> is true iff p. -/- My aim is to show that the current unpopularity of restrictionism is undeserved. I will argue that, whilst cautious versions of the strategy may face serious problems, a radical and previously overlooked version of restrictionism provides a strong and defensible response to the paradoxes.

Thanks to the work of Kendall Walton, appeals to the notion of pretence (or make-believe) have become popular in philosophy. Now the notion has begun to appear in accounts of truth. My aim here is to assess one of these accounts, namely the ‘constructive methodological deflationism’ put forward by Jc Beall. After introducing the view, I argue that Beall does not manage to overcome the problem of psychological implausibility. Although Beall claims that constructive methodological deflationism supports dialetheism, I argue that (...) it does not, and I show that it in fact provides a classical response to the Liar paradox. (shrink)

Ascriptions of truth give rise to an explanatory asymmetry. For instance, we accept ‘ is true because Rex is barking’ but reject ‘Rex is barking because is true’. Benjamin Schnieder and other philosophers have recently proposed a fresh explanation of this asymmetry : they have suggested that the asymmetry has a conceptual rather than a metaphysical source. The main business of this paper is to assess this proposal, both on its own terms and as an option for deflationists. I offer (...) a pair of objections to the proposal and defend them from counter-objections. To conclude, I discuss how else to explain the asymmetry, and set out the implications for deflationism and correspondence theories of truth. (shrink)

In the paper I defend the idea of metametasemantics against the arguments recently presented by Ori Simchen. Simchen attacks the view, according to which metametasemantics incorporating all possible metasemantic accounts is necessary to protect the metasemantic theories from the notorious problem of inscrutability of reference. Simchen claims that if metametasemantics is allowed it ‘absorbs’ metasemantic theories to the extent that it diminishes their explanatory value. Furthermore, in this way Simchen sets up two main metasemantic paradigms i.e. productivism and interpretationism as (...) the rival theories inevitably excluding each other. I endeavour to undermine Simchen’s point by demonstrating that his argumentation mixes up deflationary reading of the predicate ‘is true’ with its substantial reading. Consequently, I demonstrate that accepting metametasemantics does not diminish explanatory value of various metasemantic theories and thus that there is no good reason to forbid metametasemantics. I also argue that even if we ignore the above-mentioned confusion in Simchen’s reasoning, his arguments still fail when considering various problems with the notion of diminishment of explanatory value and because the analogy that his arguments are based on is fairly weak. Eventually, I conclude that metametasemantics does not pose any danger to metasemantics and that it provides a solid ground for developing a theory that benefits from both productivism and interpretationism. (shrink)

Notice that each of (1)–(4) is an instance of a more general pattern. For example, we could replace ‘black’ in (1) with any of a wide range of other adjectives such as ‘furry’ or ‘hungry’ or ‘three-legged’, without rendering the entailment invalid or any less obvious. Similarly, there are a number of verbs that occur in entailments parallel to (3): ‘Moe boiled the water; so the water boiled’; ‘Bart blew up the school; so the school blew up’; ‘Homer sank the (...) boat; so the boat sank’ and so on. (shrink)

A common objection against deflationist theories of truth is that they cannot do justice to the correspondence intuition, i.e. the intuition that there is an explanatory relationship between, for instance, the truth of ‘Snow is white’ and snow's being white. We scrutinize two attempts to meet this objection and argue that both fail. We then propose a new response to the objection which, first, sheds doubt on the correctness of the correspondence intuition and, second, seeks to explain how we may (...) nonetheless have come to have that intuition. (shrink)

The difference between Carnap and Quine over analyticity is usually thought to turn on a disagreement as to whether there is a notion of meaning, or rules of language, which enable us to define that idea. This paper argues that the more important disagreement is epistemological. Quine came to accept a notion of analyticity. That leaves him in a position somewhat like Putnam's in ‘The Analytic and the Synthetic’: that there is a notion of analyticity, but that it is of (...) no philosophical importance. But their reasons for thinking analyticity unimportant are quite different: for Putnam it is because all analytic truths are trivial; for Quine, the notion of analyticity itself is unimportant. I contrast Putnam's position with that of Carnap, and also contrast Carnap and Quine. Analyticity only has the force that it has for Carnap because he accepts the Principle of Tolerance, the idea that changes within a language and changes of language are subject to justification in different senses. Quine rejects that idea. That is why he does not take analyticity to be philosophically important or useful. (shrink)

Logical pluralism has been in vogue since JC Beall and Greg Restall 2006 articulated and defended a new pluralist thesis. Recent criticisms such as Priest 2006a and Field 2009 have suggested that there is a relationship between their type of logical pluralism and the meaning-variance thesis for logic. This is the claim, often associated with Quine 1970, that a change of logic entails a change of meaning. Here we explore the connection between logical pluralism and meaning-variance, both in general and (...) for Beall and Restall's theory specifically. We argue that contrary to what Beall and Restall claim, their type of pluralism is wedded to meaning-variance. We then develop an alternative form of logical pluralism that circumvents at least some forms of meaning-variance. (shrink)

In recent discussions of the problem of truth, Austin's views have been largely overlooked. This is unfortunate, since many of his criticisms aimed at Strawson's redundancy theory carry over to more recent incarnations of deflationism. And unlike contemporary versions of the correspondence theory of truth, Austin's manages properly to situate truth in its conceptual neighbourhood wherein it belongs to “a whole dimension of different appraisals which have something or other to do with the relation between what we say and the (...) facts.” A proper analysis of truth cannot be given apart from a broader study of speech acts. (shrink)

I examine various claims to the effect that Cantor's Continuum Hypothesis and other problems of higher set theory are ill-posed questions. The analysis takes into account the viability of the underlying philosophical views and recent mathematical developments.

Virtually all currently discussed accounts advert to a shift or replacement of a property or properties in describing what happens to the ordinary words in metaphors. And the mechanism of this shift tends to involve an overt or sometimes hidden appeal to similarity, or to some notion that is essentially connected to it. In the first part of the paper, I argue that this route is a dead end, and in the second part I offer my own preferred alternative. That (...) alternative is not argued for, or developed in detail – that is done in my book Objects of Metaphor – but my main aim in the paper is simply showing how radically it differs from the property route. (shrink)