Introducing Identity

The best-known syntactic account of the logical constants is inferentialism . Following Wittgenstein’s thought that meaning is use, inferentialists argue that meanings of expressions are given by introduction and elimination rules. This is especially plausible for the logical constants, where standard presentations divide inference rules in just this way. But not just any rules will do, as we’ve learnt from Prior’s famous example of tonk, and the usual extra constraint is harmony. Where does this leave identity? It’s usually taken as a logical constant but it doesn’t seem harmonious: standardly, the introduction rule (reflexivity) only concerns a subset of the formulas canvassed by the elimination rule (Leibniz’s law). In response, Read [5, 8] and Klev [3] amend the standard approach. We argue that both attempts fail, in part because of a misconception regarding inferentialism and identity that we aim to identify and clear up.

Ethical Reading of the Tractatus Logico-Philosophicus

The hundred-year history of interpretations of Wittgenstein’s Tractatus Logico-Philosophicus we examine in the article through a gradual approach (through the refusal of researchers from obviously erroneous interpretations) to an ethical (or metaphilosophical) reading of the work. The latter explains Wittgenstein’s unambiguous indication of ethical meaning as the main meaning of the Tractatus and consistently reconciles various parts of the work (ontology, figurative theory of meaning, rejection of the theory of types and logical constants, etc.) with the latest so-called ethical and mystical statements of the Tractatus and with demanding silence. An ethical (metaphilosophical) reading explains the continuing influence and relevance of the Tractatus and is presented in the article as a necessary condition for understanding the continuity between the works of early and late Wittgenstein.

Logical Form, Truth Conditions, and Adequate Formalization

I discuss Andrea Iacona’s idea that logical form mirrors truth conditions, and that logical form, and thus truth conditions, are in turn represented by means of adequate formalization. I criticize this idea, noting that the notion of adequate formalization is highly indefinite, while the pre-theoretic idea of logical form is often much more definite. I also criticize Iacona’s claim that certain distinct sentences, with the same truth conditions and differing only by co-referential names, must be formalized by the same formula (in the same context). I criticize this claim, noting that it imposes implausible demands on adequate formalization. Finally, I offer some brief remarks on the connection between Iacona’s ideas and the distinction between logical and non-logical constants.

Unrestricted Logical Inferentialism

This chapter develops and defends an unrestricted inferentialist theory of the meanings of logical constants. Unlike restricted inferentialism, unrestricted inferentialism puts no constraints on which rules can determine meanings. The foundations of inferentialism are also discussed, including various types of holism and the distinction between basic and derivative rules. In order to develop and defend a detailed inferentialist theory of logic, this chapter provides an inferentialist account of the “logical” constants, solves Carnap’s categoricity problem for the meanings of logical constants, and provides inferentialist approaches to both the psychology and metaphysics of logic. Finally, the chapter briefly discusses the challenge to unrestricted inferentialism posed by tonk and related types of bad company. Building on the foundation provided by Part I (chapters 1-2) of the book, this chapter provides a freestanding development and defense of logical inferentialism.

Boghossian and Casalegno on Understanding and Inference1

In response to Boghossian’s objections in Chapter 6, this chapter defends counterexamples offered by Paolo Casalegno and the author to an inferentialist account of what it is to understand a logical constant, on which Boghossian relied in his explanation of our entitlement to reason according to basic logical principles. The importance for understanding is stressed of non-inferential aspects of the use of logical constants, for example in the description of a perceived scene. Boghossian’s criteria for individuating concepts are also queried, as is the viability of hybrid accounts which mix inferential accounts of the use of some terms with non-inferential accounts of other terms.

Understanding and Inference1

The chapter challenges the inferentialist account of concept possession on which Boghossian relies in Chapter 2 in his account of the transmission of justification by deductive reasoning. Unorthodox speakers who reject the inferences in alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the method developed by Frank Ramsey, Rudolf Carnap, and David Lewis), and pejorative expressions such as ‘Boche’ are examined and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning.

Blind Reasoning

The essay asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ‘blind but blameless’ reasoning. The essay then explores the suggestion that an inferentialist account of the logical constants, according to which an understanding of the constants constitutively involves a disposition to infer according to their characteristic inferential rules, can help explain how such reasoning is possible. Some salient objections are considered and rebutted.

Worlds and Meaning

This chapter discusses the possible world framework for intensional semantics, used for the semantics of ‘would’. It does not depend on any particular metaphysics of worlds, but the standard compositional clauses for the logical constants are a significant constraint. Semantic theories which invoke ‘impossible worlds’ flouting those constraints typically turn out to violate the principle of compositionality; since synonymy is not epistemically transparent to speakers, attempts to craft epistemically possible but metaphysically impossible worlds also tend to violate compositionality. Since worlds are best understood as objectively possible, in a broad sense, the proposed semantics makes counterfactuals with metaphysically impossible antecedents vacuously true; appearances to the contrary are an artefact of the suppositional heuristic (similar phenomena are noted for vacuous universal generalizations). This makes trouble for some prominent versions of fictionalist theories in metaphysics and various other philosophical theories which assume that counterpossibles vary in truth-value.