Gabriele Usberti

Quine famously proposed to represent the intuitive ‘vast difference’ between the notional and the relational reading of the indefinite noun phrase occurring in a belief report of the form “S believes that a P is Q” in terms of the different scope of the existential quantifier, thereby assimilating the intuitive distinction to the theoretical distinction between de dicto and de re interpretation of belief reports. After having highlighted the substantial identity between the notional/relational distinction and the distinction between epistemically nonspecific and specific reading of indefinites in a belief report, the paper addresses two problems. The first is whether the Quinean representation is materially adequate; a negative answer is motivated through the analysis of a famous argument apparently entailing the collapse between de dicto and de re interpretation of belief reports. The second problem is how to represent the ‘vast difference’; the answer that is proposed is based on the adoption of an intuitionistic semantics for first order logic.

In the preceding chapter I argued that Chomskyan motivations for an internalist theory of meaningMeaningtheory of converge with certain motivations for semantical anti-realismAnti-realism. In this chapter, after a detailed characterization of semantical realismRealismsemantical and anti-realism, two varieties of semantical anti-realismAnti-realismsemantical are introduced—mathematical intuitionismIntuitionismand neo-verificationismNeo-verificationism—and the question is discussed of which variety is best suited to the motivations specified in Chap. 1. More precisely, in Sect. 2.1 Dummett’s[aut] Dummett, M. semantic characterization of the the traditional debates between realists and anti-realists (realism/anti-realismAnti-realism debates, for short) is expounded, his proposal of bivalence as the criterion of realism in semantics is justified, and some necessary refinements and qualifications of this basic idea are introduced. The basic ideas of Brouwer[aut] Brouwer, L. E. J.and Heyting[aut] Heyting, A.—the pères fondateurs of intuitionismIntuitionism—about logic and the meaning of the logical constants are outlined in Sect. 2.2, while Sect. 2.3 presents the neo-verificationist program(s) for a theory of meaning elaborated by Dummett, Prawitz[aut] Prawitz, D.and Martin-Löf[aut] Martin-Löf, P. as the outgrowth of some basic results in proof-theoryProof-theory like normalization theoremsTheoremnormalizationfor natural deductionNatural deductionsystems[aut] Curry, H.and Curry-Howard[aut] Howard, W. A.isomorphismCurry-Howard isomorphism. In Sect. 2.4 a comparison is made between intuitionist and neo-verificationist views about some basic issuesTonk (tonk’s problem, the canonical/non-canonical distinctioncanonical/non-canonical distinction, epistemic transparencyTransparency of proofs), from which the rationale is extracted for preferring intuitionism as a source of inspiration for an internalist semantic.

In this chapter the significance of the Paradox of Knowability is discussed with respect to the question of how to conceive truth within an anti-realist conceptual framework. In Sect. 9.1 the Paradox is introduced; Sect. 9.2 articulates the intuitionisticTruthintuitionistic equation of truth with knowledge, first by putting into evidence (Sects. 9.2.1–9.2.3) the conditions at which the equation is acceptable: transparency of knowledge and ‘disquotational property’ of truth; then by showing (Sects. 9.2.4 and 9.2.5) how the charge of inconsistency can be resisted. In Sect. 9.3 the neo-verificationist approaches to the Paradox are discussed, and it is shown how the Paradox hits the neo-verificationist idea of the necessity of a notion of truth irreducible to proof possession. In Sect. 9.4 the Dummettian problem is discussed of how a debate between alternative logics can be rationally shaped.

In the first part of this chapter (Sects. 8.1–8.3) a definition is proposed of the notion of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{C}$$\end{document}-justification for epistemic reports, sentences of the form “S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{S}$$\end{document} knows that α”, and an analysis of Gettier problems. More specifically, in Sect. 8.1 the definition is given; in Sect. 8.2 a representative class of Gettier problems is introduced and analyzed, distinguishing between atomic and logically complex problems; in Sect. 8.3 a comparison is made between the present approach and J. Pollock’s analysis. The second part is devoted to two strictly connected themes: assertibility conditions of empirical sentences (Sect. 8.4), defined in such a way as to result epistemically transparent; and Williamson’s argument(s) against transparency (or luminosity, in his terminology) of knowledge (Sect. 8.5).

The aim of this chapter is to define the theoretical notion of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-justificationJustification (“C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}” for “cognitive”, but also for “computational”) for atomicCognitive stateatomic sentences. As a preliminary the notion of prelinguistic cognitive stateCognitive stateprelinguistic is characterized (Sect. 4.1) in terms of which the basic notions of an internalist ontology—C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-objectObject and C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-conceptConcept—are defined. Linguistic atomic cognitive statesCognitive stateatomic are introduced in Sect. 4.2, and with them the notions of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-authorizationAuthorization to use a singular term to refer to a given object and C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-authorization to use a predicate to apply a manageable concept to C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-objects. Predication is conceived as a case ofInferenceto the best explanation inference to the best explanationExplanationbest, and this, in turn, as a particular kind of computation (Sect. 4.3). The notions of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-justification for, and of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-truth-ground of, an atomic sentence are defined in Sect. 4.4, where it is argued for their epistemic transparency. In Sect. 4.5 it is shown how the ‘uninteresting’ problems generated, according to Chomsky[aut] Chomsky, N., by the realist assumption of externalist semanticsExternalist semantics vanish within the framework of the present internalist semantics, and how, on the other hand, a direction can be suggested for the solution of some ‘interesting’ problems. The next two sections are devoted to a reformulation of Frege’s[aut] Frege, G. distinction between sense and denotationDenotation: in Sect. 4.6 a theoretical explicans of the intuitive notion of synonymy is individuated through an analysis of our intuitions about synonymy of expressions of various categories; in Sect. 4.7 the present approach is compared with the neo-verificationist model of sense, based on a distinction between direct and indirect methods of object identification. The chapter terminates (Sect. 4.8) with a discussion of the so-called frame problemFrame problem as it has been formulated by Fodor.

In the first part of this chapter I illustrate objections to Fregean semantics coming from two very different traditions like Chomsky’s[aut] Chomsky, N. methodological internalismInternalismmethodological, on the one hand, and semantical anti-realismAnti-realism, on the other. In the second part I explain how those objections can be seen as converging to motivate an internalist program for semantics, and I argue that semantical anti-realism can significantly contribute to that program. More specifically, in Sect. 1.1, after a brief review of the reasons of Chomsky’s equation of a scientific approach to the study of language with an internalist one, two objections are distinguished: the lack of explanatory power of the externalist notions of reference and truth, and their giving rise to puzzling and uninteresting questions. In Sect. 1.2 two objections coming from the anti-realist side are expounded: Dummett’s[aut] Dummett, M. so-called anti-realist argumentArgumentanti-realist and a variant of it, and Prawitz’s objection to Tarskian definition of logical consequenceLogical consequenceTarski’s definition of. In Sect. 1.3 two alternative views of the scope of an internalist semantics are introduced, and reasons are adduced to prefer the second, ‘thick semanticsSemanticsthick’, to the first, ‘thin semanticsSemanticsthin’. In the Conclusion the possibility of a convergence between methodological internalism and anti-realismAnti-realism about the external world is individuated in a realist attitude about the ‘internal’ or mental world.

In this chapter the notion of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}}$$\end{document}-justification for logically complex sentences of L\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{L}}$$\end{document} is defined; the definition is inspired to Heyting’s[aut] Heyting, A. inductive definition of the notion of proof of a mathematical sentence α, once that definition is conveniently reinterpreted. In Sect. 5.1 it is argued for the necessity of a reinterpretation; in Sect. 5.2 the notion of evidential factorEvidential factor for α is characterized, and a notion of empirical negationNegationempirical is introduced; in Sect. 5.3 the definition proper is given; Sect. 5.4 contains a characterization of the logical conceptsLogical concepts as they are denoted by the logical constants and a definition of S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{S}}$$\end{document}-validity and logical validity; in Sect. 5.5 it is shown that possession of an S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{S}}$$\end{document}-justification for an arbitrary sentence is epistemically transparent by outlining a ‘non-objectual’ model of evidence possession; as a consequence a way of justifying inference alternative to the neo-verificationist one is suggested.

The purpose of this chapter is to define the notion of justification for doxastic reports, sentences of the form “S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{S}$$\end{document} believes that α”. What makes the problem particularly complex is the presence, in doxastic reports of natural languages, of a well-known ambiguity tracing back to Aristotle, and called in the Middle Age the De Dicto/De Re ambiguity ; it is therefore necessary to analyze preliminarily this ambiguity. In the Introduction (Sect. 7.1) it is argued that the De Dicto/De Re ambiguity conceals in fact two different ambiguities and distinctions: the Transparent/Opaque (TO) one and the Epistemic Specific/Non-specific (ESN) one. Section 7.2 is devoted to the TO ambiguity; in Sects. 7.2.1–7.2.5 it is argued that the foundational puzzles concerning it do not admit an optimal solution within the framework of externalist semantics; in Sects. 7.2.6–7.2.10 the distinction is analyzed and formally represented, within the framework of the internalist semantics outlined in Chaps. 4 and 5, as concerning not two kinds of belief but two different propositions semantically expressed—for the Believer and for the Reporter, respectively—by the subordinate clause of the belief report. In Sect. 7.3 a solution to the Paradox of Analysis is suggested. Sect. 7.4 is devoted to the ESN distinction; in Sect. 7.4.1 it is argued that it cannot be represented in terms of scope; in Sect. 7.4.2 a distinction is introduced between to kinds of cognitive states which can serve as justifications for sentences of the form ∃xα; in Sect. 7.4.3 the distinction is connected to the one between the assertibility conditions, within intuitionistic logic, of ∃xα and ¬∀x¬α; in Sect. 7.4.4 and in Sect. 7.4.5 the distinction is used to account for the ESN ambiguity.

This chapter is concerned with the relation between the intuitive notions of truth and evidence or truth-recognition. While the intuitionists grant no space to the (intuitive) notion of truth of a mathematical sentence (Sect. 6.1), according to many supporters of anti-realist theories of meaning, in particular neo-verificationist ones, the intuitionistic attitude is unacceptable because, on the one hand, it is highly counterintuitive, and on the other hand some notion of truth, irreducible to proof possession, cannot be avoided even within an anti-realist conceptual framework. In Sect. 6.2 two arguments for the necessity of a distinction between truth and truth-recognition are analyzed and criticized: Dummett’s[aut] Dummett, M. argument based on the Paradox of InferenceParadoxof inference, And Prawitz’s[aut] Prawitz, D. considerations concerning the contentContent of assertionsAssertion. Sect. 6.3 discusses the neo-verificationist debate between temporalist and atemporalist conceptions of truth.

The aim of this chapter is to introduce the notion of justification, or warrant, as the key notion of the internalist theory of meaningMeaningtheory of I am going to develop, whose starting idea is that understanding a sentence amounts to having a criterion for establishing what is a justification for that sentence. Because of its intended role, justification has to be introduced as a theoretical notion; but it is clear that the formal notion cannot fail to share some characteristics with the intuitive one. In Sect. 3.1 such characteristics are made explicit: the ex ante nature of (epistemic) justification, its defeasibility, its non-factiveness. In Sect. 3.2 some other features are introduced as indispensable for a theoretical notion of justification: epistemic transparency, k-factiveness, and its consisting in a cognitive state. In the Conclusion (Sect. 3.3) a more explicit formulation is given of the sort of anti-realismAnti-realism about external world and realism about mental world I am advocating.

An intuitionistic solution to the Paradox of Knowability is given. It consists (i) in accepting $$\alpha \mathbin {\rightarrow }{{\mathrm{\mathrm {K}}}}\alpha $$ α → K α, the ordinary formalization of the principle of Radical Anti-Realism (RAR) that “Every truth is known”, since, intuitionistically understood, it means that proofs are epistemically transparent; and (ii) in accepting (RAR) itself, on the basis of the fact that knowledge is an intuitionistic internal truth notion. Some neo-verificationist approaches are criticized. Finally the problem of how to frame a rational discussion between Classicism and Intuitionism is briefly discussed.

The articles of this volume address only some aspects of Nozick's philosophy: his conception of argument, knowledge, rationality, and identity. In examining Nozick's approach to these topics, one has to take issue, ultimately, with his peculiar conception of philosophy whose manifesto appears at the outset of Philosophical Explanations and is echoed in the introduction to philosophical method of Invariances. To transform philosophy into a science or build an impeccable deductive system was not Nozick's dream. He thought of philosophy as aiming at explanation rather than proof. The goal in pursuing philosophy is not to establish one view, but to elaborate theories that can make us understand some phenomena better.

Suppose we are prepared to conceive the meaning of a sentence as a classification criterion which enables us to establish whether something is or is not a justification to believe that sentence. Which properties of the intuitive notion of justification are, from this point of view, essential for believing a sentence? And how might a theoretical notion of justification for a sentence be defined? In Sections 2-5 some properties are suggested as essential, in particular Intentionality (a justification is always a justification for a sentence), Defeasibility (a justification for a sentence A can cease to be a justification for A as new information is received), and Epistemic transparency (a justification for A is not a justification for A unless it is recognized as such by an idealized knowing subject). In Section 6 a sketch of definition is proposed, according to which a justification for a sentence A is a cognitive state in which the subject has at his disposal a certain amount of information, and the hypothesis that A is the best explanation of that information. Section 7 shows how the notion defined escapes a crucial objection to defeasible justifications recently stated by P. Casalegno.

In his paper “Explaining Deductive Inference” Prawitz states what he calls «a fundamental problem of logic and the philosophy of logic»: the problem of explaining «Why do certain inferences have the epistemic power to confer evidence on the conclusion when applied to premisses for which there is evidence already?». In this paper I suggest a way of articulating, and partly modifying, the intuitionistic answer to this problem in such a way as to both answer Prawitz’s problem and satisfy a requirement I argue to be crucial for any epistemic theory of the meaning of the logical constants: the requirement that evidence is epistemically transparent.

Suppose we want to take seriously the neoverificationist idea that an intuitionistic theory of meaning can be generalized in such a way as to be applicable not only to mathematical but also to empirical sentences. The paper explores some consequences of this attitude and takes some steps towards the realization of this program. The general idea is to develop a meaning theory, and consequently a formal semantics, based on the idea that knowing the meaning of a sentence is tantamount to having a criterion for establishing what is a justification for it. Section 1 motivates a requirement of epistemic transparency imposed onto justifications conceived as mental states. In Section 2, the formal notion of justification for an atomic formula is defined, in terms of the notion of cognitive state. In Section 3, the definition is extended to logically complex formulas. In Section 4, the notion of truth-ground is introduced and is used to give a definition of logical validity.

This volume develops a theory of meaning and a semantics for both mathematical and empirical sentences inspired to Chomsky’s internalism, namely to a view of semantics as the study of the relations of language not with external reality but with internal, or mental, reality. In the first part a theoretical notion of justification for a sentence A is defined, by induction on the complexity of A; intuitively, justifications are conceived as cognitive states of a particular kind. The main source of inspiration for this part is Heyting’s explanation of the intuitionistic meaning of logical constants. In the second part the theory is applied to the solution of several foundational problems in the theory of meaning and epistemology, such as Frege’s puzzle, Mates’ puzzle about synonymy, the paradox of analysis, Kripke’s puzzle about belief, the de re/de dicto distinction, the specific/non-specific distinction, Gettier’s problems, the paradox of knowability, and the characterization of truth. On a more general philosophical level, throughout the book the author develops a tight critique of the neo-verificationism of Dummett, Prawitz and Martin-Löf, and defends a mentalist interpretation of intuitionism.

I will be concerned with the following question: are there compelling arguments for postulating a distinction between the truth of a statement and the recognition of its truth, when truth is conceived along the lines of a suitable generalization of the intuitionistic idea that it should be characterized as the existence of a proof? I will argue that the distinction is not necessary within the conceptual framework of intuitionism by replying to two arguments to the contrary, one based on the paradox of inference, the other on considerations concerning the content of a statement

In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability and, on the other, by means of the operator K of epistemic logic. Intuitionistic logic, as reconstructed within this perspective, turns out to be a part of epistemic logic, so that it loses its traditional foundational role, antithetic to that of classical logic. In section 3 we uphold the view that certain consequences of the adoption of atemporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view.