The price of inscrutability

In our reasoning we depend on the stability of language, the fact that its signs do not arbitrarily change in meaning from moment to moment.(Campbell, 1994, p.82) Some philosophers offer arguments contending that ordinary names such as “London” are radically indeterminate in reference. The conclusion of such arguments is that there is no fact of the matter whether “London” refers to a city in the south of England, or whether instead it refers to Sydney, Australia. Some philosophers have even suggested that we accept the conclusion of these arguments. Such a position seems crazy to many; but what exactly goes wrong if one adopts such a view? This paper evaluates the theoretical costs incurred by one who endorses extreme inscrutability of reference (the ‘inscrutabilist’). I show that there is one particular implication of extreme inscrutability which pushes the price of inscrutabilism too high. An extension of the classic ‘permutation’ arguments for extreme inscrutability allow us to establish what I dub ‘extreme indexical inscrutability’. This result, I argue, unacceptably undermines the epistemology of inference. The first half of the paper develops the background of permutation arguments for extreme inscrutability of reference and evaluates some initial attempts to make trouble for the inscrutabilist. Sections 1 and 2 describe the setting of the original permutation arguments for extreme inscrutability. Sections 3 and 4 survey four potential objections to extreme inscrutability of reference, including some recently raised in Vann McGee’s excellent (2005a). Sections 5 sketches how the permutation arguments can be generalized to establish extreme indexical inscrutability; and shows how this contradicts a ‘stability principle’—that our words do not arbitrarily change their reference from one moment to the next—which I claim plays a vital role in the epistemology of inference. The second half of the paper develops in detail the case for thinking that language is stable in the relevant sense. In section 6, I use this distinction to call into question the epistemological relevance of validity of argument types; Kaplan’s treatment of indexical validity partially resolves this worry, but there is a residual problem. In section 7, I argue that stability is exactly what is needed to bridge this final gap, and so secure the relevance of validity to good inferential practice. Section 8 responds to objections to this claim. An appendix to the paper provides formal backing for the results cited in this paper, including a generalization of permutation arguments to the kind of rich setting required for a realistic semantics of natural language.1 Extreme indexical inscrutability results can be proved within this setting. The first half of the paper shows that the inscrutabilist is committed to extreme indexical inscrutability, which implies that language not determinately ‘stable’. The second half of the paper argues that good inference requires stability. The price of inscrutabilism, therefore, is to sever the connection between the validity of argument-forms and inferential practice: and this is too high a price to pay

What is a logical diagram?

Robert Brandom’s expressivism argues that not all semantic content may be made fully explicit. This view connects in interesting ways with recent movements in philosophy of mathematics and logic (e.g. Brown, Shin, Giaquinto) to take diagrams seriously - as more than a mere “heuristic aid” to proof, but either proofs themselves, or irreducible components of such. However what exactly is a diagram in logic? Does this constitute a semiotic natural kind? The paper will argue that such a natural kind does exist in Charles Peirce’s conception of iconic signs, but that fully understood, logical diagrams involve a structured array of normative reasoning practices, as well as just a “picture on a page”

A Peirce for the 21st century

Review of Peirce’s Speculative Grammar: Logic as Semiotics by Francesco Bellucci. New York, London: Routledge, 2017, 388 pages

A constructive modal semantics for contextual verification

This paper introduces a non-standard semantics for a modal version of constructive KT for contextual (assumptions-based) verification. The modal fragment expresses verifiability under extensions of contexts, enjoying adapted validity and (weak) monotonicity properties depending on satisfaction of the contextual data

Stable Semantics of Temporal Deductive Databases

We define a preferential semantics based on stable generated models for a very general class of temporal deductive databases. We allow two kinds of temporal information to be represented and queried: timepoint and timestamp formulas, and show how each of them can be translated into the other. Because of their generality, our formalism and our semantics can serve as a basis for comparing and extending other temporal deductive database frameworks

Reasoning about Rational, but not Logically Omniscient Agents

We propose in the paper a new solution to the so-called Logical Omniscience Problem of epistemic logic. Almost all attempts in the literature to solve this problem consist in weakening the standard epistemic systems: weaker systems are considered where the agents do not possess the full reasoning capacities of ideal reasoners. We shall argue that this solution is not satisfactory: in this way omniscience can be avoided, but many intuitions about the concepts of knowledge and belief get lost. We shall show that axioms for epistemic logics must have the following form: if the agent knows all premises of a valid inference rule, and if she thinks hard enough, then she will know the conclusion. To formalize such an idea, we propose to \dynamize' epistemic logic, that is, to introduce a dynamic component into the language. We develop a logic based on this idea and show that it is suitable for formalizing the notion of actual, or explicit knowledge

The Relevant Logic E and Some Close Neighbours: A Reinterpretation

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven

Anti-realism : the manifestation of semantic knowledge

Realistic views are fashionable. In this thesis, I defend a view opposed to realism, which Dummett calls "anti-realism". My defence of anti-realism depends on the assumption that a theory of meaning should explain how speakers understand one another. The theory should therefore describe linguistic abilities in terms of communicable features of linguistic practice: those which are exhaustively manifest in use. I call this the manifestation argument. In the first Chapter, I apply the manifestation argument not only to theories of meaning which yield specifications of the content of sentences of a language (1.2), but also to theories which aim primarily to define linguistic behaviour as a species of intentional activity (I.3). The manifestation argument tells against the realist assumption of verification transcendent truth: that there may be truths which speakers could never be in a position to verify (1.2.3,I.3.3). However, holistic theories are exempted from the anti-realist argument. Alternative characterisations of realism are also mentioned(1.4). Dummett's theory of meaning is tailored to ensure that knowledge of meaning can be manifested. I endorse this account, with minor modifications (II.l-II.5). The revisionary consequences of the account are, I think, more extreme than Dummett supposes (II.6). Dummett takes Intuitionism in mathematics to be the paradigm of an anti-realist account of meaning (III.l-III.2). Two accounts of the meaning of the intuitionist logical constants are discussed. The first, which Dummett prefers, is in terms of canonical proof conditions (III.3-III.4); the second is an intuitionist analogue of a Tarski style truth definition (III.5). I argue that the former is required for justifying the intuitionist account, even though the latter adequately captures the intuitionist notion of truth. Chapter IV concerns the motivation of the manifestation argument (IV.l). I discuss the acquisition argument for anti-realism used by Dummett; namely, that it must be possible to acquire a grasp of the meaning of a sentence of a language from experience of its use (IV.2). I suggest that the manifestation argument is prior to the acquisition argument. I argue that anti-realism need not be reductionist (IV.4), and that vagueness suggests a modification of the manifestation argument. When intuitionism in mathematics provides the model of a theory of meaning for natural language, various notions of assertibility replace that of provability. Dummett considers conclusive verifiability (V.2) and falsifiability (V.3). Both fail to provide an acceptable account of negation, and do not allow for those assertions of natural language evidence for which is inconclusive (V.4). I take conditions of verification and falsification to determine meaning (V. 5). The intuitionist analogy is applied to time in Chapter VI. I discuss the analysis of temporal modification (VI.Z), and argue that tensed sentences involve indexical reference to time (VI.3). This suggests a generalised anti-realism about spatial and personal indexicals, which I reject (VI.4). I also reject Dummett's treatment of tense-links, but endorse a modified anti-realism about time (VI.5). I conclude with a discussion of holism. According to Dummett, holistic theories are objectionable because they are not molecular (VII.l). There are three strands in Dummett's notion of molecularity, and I discuss the role of each in rejecting varieties of holism (VII.2-VII.4). Dummett has doubts about anti-realist molecular theories which I dismiss, but I argue that the anti-realist cannot explain what I call 'radical' meaning change (VII.5)