I argue against inferentialism about logic. First, I argue against an analogy between logic and chess, before considering a more basic objection to stipulating inference rules as a way of establishing the meaning of logical constants. The objectionthe Mushroom Omelette Objectionis that stipulative acts are partly constituted by logical notions, and therefore cannot be used to explain logical thought. I then argue that the same problem also attaches to following existing conventional rules, since either those rules (...) have logical contents, or following those conventional rules is done for logical reasons. Lastly, I compare this argument with other arguments found in Quine’s early work, and consider two attempts to reply to Quine. (shrink)

I present a sequent calculus that extends a nonmonotonic reflexive consequence relation as defined over an atomic first-order language without variables to one defined over a logically complex first-order language. The extension preserves reflexivity, is conservative (therefore nonmonotonic) and supraintuitionistic, and is conducted in a way that lets us codify, within the logically extended object language, important features of the base thus extended. In other words, the logical operators in this calculus play what Brandom (2008) calls expressive roles. Expressivist (...) logical systems have already been proposed for propositional logics (see Hlobil, 2016, and Kaplan, 2018) but not for first-order logics. An advantage of this calculus over standard first-order calculi (e.g., those in Gentzen, 1935/1964) is that universally quantified variables behave as they should even in the presence of arbitrary nonlogical axioms. I claim that because of this robust well-behavedness of variables, this calculus also provides logical inferentialists with a way to understand the meanings of variables in terms of the roles those variables play in a wide range of inferences that is not limited to purely logical ones (e.g, mathematical inferences). (shrink)

Inferentialism claims that the rules for the use of an expression express its meaning without any need to invoke meanings or denotations for them. Logical inferentialism endorses inferentialism specically for the logical constants. Harmonic inferentialism, as the term is introduced here, usually but not necessarily a subbranch of logical inferentialism, follows Gentzen in proposing that it is the introduction-rules whch give expressions their meaning and the elimination-rules should accord harmoniously with the meaning (...) so given. It is proposed here that the logical expressions are those which can be given schematic rules that lie in a specific sort of harmony, general-elimination harmony, resulting from applying a certain operation, the ge-procedure, to produce ge-rules in accord with the meaning defined by the I-rules. Griffiths claims that identity cannot be given such rules, concluding that logical inferentialists are committed to ruling identity a non-logical expression. It is shown that the schematic rules for identity given in Read, slightly amended, are indeed ge-harmonious, so confirming that identity is a logical notion. (shrink)

This essay attempts to clarify the project of explaining the possibility of ‘blind reasoning’—namely, of basic logical inferences to which we are entitled without our having an explicit justification for them. The role played by inferentialism in this project is examined and objections made to inferentialism by Paolo Casalegno and Timothy Williamson are answered. Casalegno proposes a recipe for formulating a counterexample to any proposed constitutive inferential role by imaging a subject who understands the logical constant (...) in question but fails to have the capacity to make the inference in question; Williamson’s recipe turns on imagining an expert who continues to understand the constant in question while having developed sophisticated considerations for refusing to make it. It’s argued that neither recipe succeeds. (shrink)

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen (2008) argues that this view - call it logical inferentialism - is undermined by some "very little known" considerations by Carnap (1943) to the effect that "in a definite sense, it is not true (...) that the standard rules of inference" themselves suffice to "determine the meanings of [the] logical constants" (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that "no ordinary formalization of logic ... is sufficient to `fully formalize' all the essential properties of the logical constants" (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap's problem. And although bilateral solutions for classical inferentialists - as proposed by Timothy Smiley and Ian Rumfitt - seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too. (shrink)

This chapter introduces inferential role semantics (IRS) and some of the challenges it faces. It also introduces inferentialism and places it into the wider context of contemporary philosophy of language. The chapter focuses on what is standardly considered both the most important test case for and the most natural application of IRS: logical inferentialism, the view that the meanings of the logical expressions are fully determined by the basic rules for their correct use, and that to (...) understand a logical expression is to use it in accordance with the appropriate rules. It discusses some of the benefits of logical inferentialism, chiefly with regard to the epistemology of logic, and considers a number of objections. The chapter critically examines Robert Brandom's inferentialism about linguistic and conceptual content in general. Finally, it considers a number of general objections to IRS and possible responses on the inferentialist's behalf. (shrink)

Logical inferentialists contend that the meanings of the logical constants are given by their inference rules. Not just any rules are acceptable, however: inferentialists should demand that inference rules must reflect reasoning in natural language. By this standard, I argue, the inferentialist treatment of quantification fails. In particular, the inference rules for the universal quantifier contain free variables, which find no answer in natural language. I consider the most plausible natural language correlate to free variables—the use of variables (...) in the language of informal mathematics—and argue that it lends inferentialism no support. (shrink)

Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about what is told (...) about the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu , and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information. (shrink)

I am presenting a sequent calculus that extends a nonmonotonic consequence relation over an atomic language to a logically complex language. The system is in line with two guiding philosophical ideas: (i) logical inferentialism and (ii) logical expressivism. The extension defined by the sequent rules is conservative. The conditional tracks the consequence relation and negation tracks incoherence. Besides the ordinary propositional connectives, the sequent calculus introduces a new kind of modal operator that marks implications that hold monotonically. (...) Transitivity fails, but for good reasons. Intuitionism and classical logic can easily be recovered from the system. (shrink)

In the mid twentieth century, logical positivists and many other philosophers endorsed a simple equation: something was necessary just in case it was analytic just in case it was a priori. Kripke’s examples of a posteriori necessary truths showed that the simple equation is false. But while positivist-style inferentialist approaches to logic and mathematics remain popular, there is no inferentialist account of necessity a posteriori. I give such an account. This sounds like an anti-Kripkean project, but it is not. (...) Some of Kripke’s remarks even suggest this kind of approach. This inferentialist approach reinstates neither the simple equation nor pure conventionalism about necessity a posteriori. But it does lead to something near enough, a type of impure conventionalism. In recent years, metaphysically heavyweight approaches to modality have been popular, while other approaches have lagged behind. The inferentialist, impure conventionalist theory of necessity I describe aims to provide a metaphysically lightweight option in modal metaphysics. (shrink)

In this essay, we extend earlier inferentialist-expressivist treatments of traditional logical, semantic, modal, and representational vocabulary (Brandom 1994, 2008, 2015; Peregrin 2014) to explanatory vocabulary. From this perspective, Inference to the Best Explanation (IBE) appears to be an obvious starting point. In its simplest formulation, IBE has the form: A best explains why B, B; so A. It thereby captures one of the central inferential features of explanation. An inferentialist-expressivist treatment of “best explains” would treat it as a (...) class='Hi'>logical operator. Analogous to the inferentialist-expressivist treatment of other logical operators, this essay aims to provide introduction and elimination rules for “best explains.” Indeed, by exhibiting a form of detachment, IBE superficially looks like an elimination rule. The sequent calculus LEA+, described in Section 5 below, makes good on this intuition. By showing how “A best explains why B” is related to the underlying, scientific inference “A, so B,” we can purchase the inference ticket of IBE for no more than the cost of science’s material inferences. (shrink)

It is sometimes held that rules of inference determine the meaning of the logical constants: the meaning of, say, conjunction is fully determined by either its introduction or its elimination rules, or both; similarly for the other connectives. In a recent paper, Panu Raatikainen argues that this view—call it logical inferentialism—is undermined by some “very little known” considerations by Carnap (1943) to the effect that “in a definite sense, it is not true that the standard rules of (...) inference” themselves suffice to “determine the meanings of [the] logical constants” (p. 2). In a nutshell, Carnap showed that the rules allow for non-normal interpretations of negation and disjunction. Raatikainen concludes that “no ordinary formalization of logic [... ] is sufficient to ‘fully formalize’ all the essential properties of the logical constants” (ibid.). We suggest that this is a mistake. Pace Raatikainen, intuitionists like Dummett and Prawitz need not worry about Carnap’s problem. And although bilateral solutions for classical inferentialists—as proposed by Timothy Smiley and Ian Rumfitt—seem inadequate, it is not excluded that classical inferentialists may be in a position to address the problem too. (shrink)

In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms.

This paper investigates the relationships between two claims about conditionals that are often discussed separately. One is the claim that conditionals express inferences, in the sense that a conditional holds when its consequent can be inferred from its antecedent. The other is the claim that conditionals intuitively obey the characteristic principles of connexive logic. Following a line of thought that goes back to Chrysippus, we suggest that these two claims may coherently be understood as distinct manifestations of a single and (...) more basic idea, namely, that a conditional holds when its antecedent is incompatible with the negation of its consequent. The account of conditionals we propose is based precisely on this idea. (shrink)

In this paper I present how the normative inferentialist can make the distinction between sentence meaning and content of the utterance. The inferentialist can understand sentence meaning as a role conferred to that sentence by the rules governing inferential transitions and content of the utterance as just a part of sentence meaning. I attempt to show how such a framework can account for prominent scenarios presented by contextualists as a challenge to semantic minimalism/literalism. I argue that inferentialism can address (...) contextualist challenges in a simple and effective manner by understanding sentence meaning as broad, but invariant. (shrink)

In this paper, I show how normative inferentialism could be used to explain several phenomena related to natural languages. First, I show how the distinction between the inferential potential and the inferential significance fits the standard distinction between the meaning of a sentence and the content of an utterance. Second, I show how the distinction could be used to explain ambiguity and free pragmatic enrichment from the perspective of normative inferentialism. The aim of this paper is to establish (...) theoretical foundations that enable normative inferentialism to enter the discussions within the literalism-contextualism debate. As I argue, the biggest advantage of inferentialism is that it provides one general framework for the representation of meaning/content that naturally incorporates contextual information and so it can be used to represent meanings of various types of context-dependent sentences. (shrink)

Brandom's inferentialism provides a semantics that complements Habermas's theory of communicative action without sacrificing its intersubjectivist insights. Pace Habermas, Brandom's conception of communication is robustly intersubjective. At the pragmatic level, interlocutors inherit each other's commitments and entitlements and must justify their claims when challenged; at the semantic level, anaphora show how the web of meaning is knit together, connecting expressions of the language as well as interlocutors. Finally, Habermas's thesis that there are three irreducible types of validity claim is (...) preserved by linking claims to truth and rightness with mutually irreducible patterns of inference. (shrink)

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference (...) and Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates. (shrink)

This paper offers a general model of the semantics of lexicalized social meanings, i.e. semiotic properties of certain expressions in a socio-political context. Examples include slurs, problematically charged expressions such as inner city, as well as terms such as mother, which also carry implicit ideological associations. Insofar as their linguistic properties are concerned, social meanings can be construed as context-structuring devices: without introducing specific at-issue contents, they evoke background assumptions which shape the context of conversation. An inferentialist model of discourse (...) is developed to account for this effect, in which the discursive significance of an utterance is defined as the set of inferences it licenses relative to a discursive context. A discursive context is a set of propositions that can serve as auxiliary premises in material inferences, together with a salience ranking that makes some of these propositions more readily available and therefore more relevant to determining discursive significance. Social meanings are defined as functions on discursive contexts that modify the salience ranking, increasing the salience of certain assumptions and stereotypes. As a result, they impact the discursive significance of utterances indirectly and independently of at-issue contents. They are also largely independent of speaker intentions in virtue of the ideological nature of discursive contexts. (shrink)

This paper provides an inferentialist motivation for a logic belonging in the connexive family, by borrowing elements from the bilateralist interpretation for Classical Logic without the Cut rule, proposed by David Ripley. The paper focuses on the relation between inferentialism and relevance, through the exploration of what we call relevant assertion and denial, showing that a connexive system emerges as a symptom of this interesting link. With the present attempt we hope to broaden the available interpretations for connexive logics, (...) showing they can be rightfully motivated in terms of certain relevantist constraints imposed on assertion and denial. (shrink)

This volume investigates Eric Weil’s innovative conceptualization of the place of violence in the philosophical tradition with a focus on violence’s relationship to language and to discourse. Weil presents violence as the central philosophical problem. According to this reading, the western philosophical tradition commonly conceptualizes violence as an expression of error or as a consequence of the weakness of will. However, by doing so, it misses something essential about the role that violence plays in our conceptual development as well as (...) the place violence holds in our discursive practices. The author draws comparisons between Weil’s work and that of Robert Brandom. Brandom’s inferentialism creates a sophisticated program at the junction of pragmatics and semantics, philosophy of language, logic, and philosophy of mind. The monograph builds on these insights in order to show how an inferentialist reading of Eric Weil is fruitful for both Weilian studies and for inferentialism. This volume will notably be of interest to scholars in philosophy, argumentation theory, and communication studies. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the (...) case of the quantificational logic, the categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.

Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of (...) reality. For naturalists of all stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

For semantic inferentialists, the basic semantic concept is validity. An inferentialist theory of meaning should offer an account of the meaning of "valid." If one tries to add a validity predicate to one's object language, however, one runs into problems like the v-Curry paradox. In previous work, I presented a validity predicate for a non-transitive logic that can adequately capture its own meta-inferences. Unfortunately, in that system, one cannot show of any inference that it is invalid. Here I extend the (...) system so that it can capture invalidities. (shrink)

Logical inferentialism maintains that the formal rules of inference fix the meanings of the logical terms. The categoricity problem points out to the fact that the standard formalizations of classical logic do not uniquely determine the intended meanings of its logical terms, i.e., these formalizations are not categorical. This means that there are different interpretations of the logical terms that are consistent with the relation of logical derivability in a logical calculus. In the (...) case of the quantificational logic, the categoricity problem is generated by the finite nature of the standard calculi and one direction in which it can be solved is to strengthen the deductive systems by adding infinitary rules (such as the ω-rule), i.e., to construct a full formalization. Another main direction is to provide a natural semantics for the standard rules of inference, i.e., a semantics for which these rules are categorical. My aim in this paper is to analyze some recent approaches for solving the categoricity problem and to argue that a logical inferentialist should accept the infinitary rules of inference for the first order quantifiers, since our use of the expressions “all” and “there is” leads us beyond the concrete and finite reasoning, and human beings do sometimes employ infinitary rules of inference in their reasoning. (shrink)

The inferentialist account of the a priori says that basic logical beliefs can be justified by way of rule circular inference. I argue that this account of the a priori fails to skirt the charge of begging the question, that the reasons offered in support of it are weak and that it makes justifying logical beliefs too easy. I also argue that recent modifications to inferentialism spell doom for it as a general theory of a priori justification.

In bilateral systems for classical logic, assertion and denial occur as primitive signs on formulas. Such systems lend themselves to an inferentialist story about how truth-conditional content of connectives can be determined by inference rules. In particular, for classical logic there is a bilateral proof system which has a property that Carnap in 1943 called categoricity. We show that categorical systems can be given for any finite many-valued logic using $n$-sided sequent calculus. These systems are understood as a further development (...) of bilateralism—call it multilateralism. The overarching idea is that multilateral proof systems can incorporate the logic of a variety of denial speech acts. So against Frege we say that denial is not the negation of assertion and, with Mark Twain, that denial is more than a river in Egypt. (shrink)

Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics.

I discuss Prawitz’s claim that a non-reliabilist answer to the question “What is a proof?” compels us to reject the standard Bolzano-Tarski account of validity, andto account for the meaning of a sentence in broadly verificationist terms. I sketch what I take to be a possible way of resisting Prawitz’s claim---one that concedes the anti-reliabilist assumption from which Prawitz’s argument proceeds.

If correct, Christopher Peacocke’s [20] “manifestationism without verificationism,” would explode the dichotomy between realism and inferentialism in the contemporary philosophy of language. I first explicate Peacocke’s theory, defending it from a criticism of Neil Tennant’s. This involves devising a recursive definition for grasp of logical contents along the lines Peacocke suggests. Unfortunately though, the generalized account reveals the Achilles’ heel of the whole theory. By inventing a new logical operator with the introduction rule for the existential quantifier (...) and the elimination rule for the universal quantifier, I am able to show that Peacocke’s theory only avoids verificationism to the extent that it does not satisfy manifestationism. (shrink)

An “inferentialist” semantic theory for some language L aims to account for the meanings of the sentences of L solely in terms of the inferential rules governing their use. A “hyper-inferentialist” theory admits into the semantics only “narrowly inferential” rules that normatively relate sentences of L to other sentences of L. A “strong inferentialist” theory also admits into the semantics “broadly inferential” rules that normatively relate perceptual states to sentences of L or sentences of L to intentional actions. It is (...) widely thought that only the latter of these two sorts of semantic theories is at all viable. I argue here that the opposite is so. Negatively, strong inferentialism is viciously circular: including rules into the semantic theory that relate perceptual states to sentences of the language requires us to appeal, in individuating those perceptual states, to the very meanings for which we are supposed to be inferentially accounting. Hyper-inferentialism does not face this problem because it does not appeal to any nonlinguistic states. Positively, though hyper-inferentialism is widely thought to be a theoretical non-starter, I argue here that it is a genuine theoretical possibility insofar as it essentially includes cross-perspectival inferences, inferences along the lines of the one from the sentences “The ball is in front of n,” “The ball is red,” and “The lighting is good” to the sentence “n sees that the ball is red.” I make the further exegetical claim that Robert Brandom, though unanimously taken to be a strong inferentialist, is in fact a hyper-inferentialist. (shrink)

This book offers new insights into the nature of human rational capacities by engaging inferentialism with empirical research in the cognitive sciences. Inferentialism advocates that humans' unique kind of intelligence is discursive and rooted in competencies to make, assess and justify claims. This approach provides a rich source of valuable insights into the nature of our rational capacities, but it is underdeveloped in important respects. For example, little attempt has been made to assess inferentialism considering relevant scientific (...) research on human communication, cognition or reasoning. By engaging philosophical and scientific approaches in a productive dialogue, this book shows how we can better understand human rational capacities by comparing their respective strengths and weaknesses. In this vein, the author critically revisits and constructively develops central themes from the work of Robert Brandom and other language rationalists: the nature of the assertoric practice and its connection to reasoned discourse, the linguistic constitution of the shared space of reasons, the social nature and function of reasoning, the intersubjective roots of social-normative practices and the nature of objective thought. Practices of Reason will be of interest to scholars and advanced students working in philosophy of mind, philosophy of language and philosophy of logic. (shrink)

The standard inferentialist approaches to modal logic tend to suffer from not being able to uniquely characterize the modal operators, require that introduction and elimination rules be interdefined, or rely on the introduction of possible-world like indexes into the object language itself. In this paper I introduce a hypersequent calculus that is flexible enough to capture many of the standard modal logics and does not suffer from the above problems. It is therefore an ideal candidate to underwrite an inferentialist theory (...) of meaning for modal operators. Here I treat specifically the modal logics K, D, T, S4, B, and S5. I show that the calculi are adequate for each set of models, and show that they meet a large set of criteria that are generally thought necessary for a calculus to underwrite a theory of meaning. (shrink)

The paper presents an exhaustive menu of nonmonotonic logics. The options are individuated in terms of the principles they reject. I locate, e.g., cumulative logics and relevance logics on this menu. I highlight some frequently neglected options, and I argue that these neglected options are particularly attractive for inferentialists.

Inferentialism is a philosophical approach premised on the claim that an item of language acquires meaning in virtue of being embedded in an intricate set of social practices normatively governed by inferential rules. Inferentialism found its paradigmatic formulation in Robert Brandom's landmark book Making it Explicit, and over the last two decades it has established itself as one of the leading research programs in the philosophy of language and the philosophy of logic. While Brandom's version of inferentialism (...) has received wide attention in the philosophical literature, thinkers friendly to inferentialism have proposed and developed new lines of inquiry that merit wider recognition and critical appraisal. From Rules to Meaning brings together new essays that systematically develop, compare, assess and critically react to some of the most pertinent recent trends in inferentialism. The book's four thematic sections seek to apply inferentialism to a number of core issues, including the nature of meaning and content, reconstructing semantics, rule-oriented models and explanations of social practices and inferentialism's historical influence and dialogue with other philosophical traditions. With contributions from a number of distinguished philosophers--including Robert Brandom and Jaroslav Peregrin--this volume is a major contribution to the philosophical literature on the foundations of logic and language. (shrink)

Inferentialism claims that expressions are meaningful by virtue of rules governing their use. In particular, logical expressions are autonomous if given meaning by their introduction-rules, rules specifying the grounds for assertion of propositions containing them. If the elimination-rules do no more, and no less, than is justified by the introduction-rules, the rules satisfy what Prawitz, following Lorenzen, called an inversion principle. This connection between rules leads to a general form of elimination-rule, and when the rules have this form, (...) they may be said to exhibit “general-elimination” harmony. Ge-harmony ensures that the meaning of a logical expression is clearly visible in its I-rule, and that the I- and E-rules are coherent, in encapsulating the same meaning. However, it does not ensure that the resulting logical system is normalizable, nor that it satisfies the conservative extension property, nor that it is consistent. Thus harmony should not be identified with any of these notions. (shrink)

Is logic, feasibly, a product of natural selection? In this paper we treat this question as dependent upon the prior question of where logic is founded. After excluding other possibilities, we conclude that logic resides in our language, in the shape of inferential rules governing the logical vocabulary of the language. This means that knowledge of (the laws of) logic is inseparable from the possession of the logical constants they govern. In this sense, logic may be seen as (...) a product of natural selection: the emergence of logic requires the development of creatures who can wield structured languages of a specific complexity, and who are capable of putting the languages to use within specific discursive practices. (shrink)

This book presents a philosophical conception of logic -- "logical expressivism"-- according to which the role of logic is to make explicit reason relations, which are often neither monotonic nor transitive. It reveals new perspectives on inferential roles, sequent calculi, representation, truthmakers, and many extant logical theories.

What is the source of logical and mathematical truth? This book revitalizes conventionalism as an answer to this question. Conventionalism takes logical and mathematical truth to have their source in linguistic conventions. This was an extremely popular view in the early 20th century, but it was never worked out in detail and is now almost universally rejected in mainstream philosophical circles. Shadows of Syntax is the first book-length treatment and defense of a combined conventionalist theory of logic and (...) mathematics. It argues that our conventions, in the form of syntactic rules of language use, are perfectly suited to explain the truth, necessity, and a priority of logical and mathematical claims, as well as our logical and mathematical knowledge. (shrink)

Both in formal and computational natural language semantics, the classical correspondence view of meaning – and, more specifically, the view that the meaning of a declarative sentence coincides with its truth conditions – is widely held. Truth (in the world or a situation) plays the role of the given, and meaning is analysed in terms of it. Both language and the world feature in this perspective on meaning, but language users are conspicuously absent. In contrast, the inferentialist semantics that Robert (...) Brandom proposes in his magisterial book ‘Making It Explicit’ puts the language user centre stage. According to his theory of meaning, the utterance of a sentence is meaningful in as far as it is a move by a language user in a game of giving and asking for reasons (with reasons underwritten by a notion of good inferences). In this paper, I propose a proof-theoretic formalisation of the game of giving and asking for reasons that lends itself to computer implementation. In the current proposal, I flesh out an account of defeasible inferences, a variety of inferences which play a pivotal role in ordinary (and scientific) language use. (shrink)

This paper explores some of the assumptions orienting the debate about logical pluralism. I argue that these assumptions are grounded in the truth-conditional character of the semantic metavocabularies in which the debate is conducted. Then, I suggest an expressivist strategy to reinterpret the pluralist claim that there are different logics and I show how the expressive role of logical vocabularies can be equally well characterized by means of different expressive resources not involving the notion of truth.

Mark Wilson argues that the standard categorizations of "Theory T thinking"— logic-centered conceptions of scientific organization (canonized via logical empiricists in the mid-twentieth century)—dampens the understanding and appreciation of those strategic subtleties working within science. By "Theory T thinking," we mean to describe the simplistic methodology in which mathematical science allegedly supplies ‘processes’ that parallel nature's own in a tidily isomorphic fashion, wherein "Theory T’s" feigned rigor and methodological dogmas advance inadequate discrimination that fails to distinguish between explanatory structures (...) that are architecturally distinct. One of Wilson's main goals is to reverse such premature exclusions and, thus, early on Wilson returns to John Locke's original physical concerns regarding material science and the congeries of descriptive concern insofar as capturing varied phenomena (i.e., cohesion, elasticity, fracture, and the transmission of coherent work) encountered amongst ordinary solids like wood and steel are concerned. Of course, Wilson methodologically updates such a purview by appealing to multiscalar techniques of modern computing, drawing from Robert Batterman's work on the greediness of scales and Jim Woodward's insights on causation. (shrink)

This new work provides an approachable introduction to the complex system that Making It Explicit mapped out.

I defend logical realism. I begin by motivating the realist approach by underlining the difficulties for its main rival: inferentialism. I then focus on AND and OR, and delineate a realist view of these two logical constants. The realist view is developed in terms of Alexander’s Principleshowing that AND and OR have distinctive determining roles. After that, I say what logic is not. We should not take logic to be essentially about the mind, or language, or exclusively (...) about an abstract realm, or about reasoning, truth, truth-tables, truth-functions, topic-neutrality or form. Lastly, I turn to consider NEGATION and argue that we cannot escape negative facts, and facts conjoining and disjoining negative facts with positive facts. I then give NEGATION a distinctive role, one that contrasts with AND and OR. I reflect on the notion of logic in the coda. (shrink)

The aim of this paper is to provide context for and historical exegesis of Carnap’s alleged move from syntax to semantics. The Orthodox Received View states that there was a radical break, while the Unorthodox Received View holds that Carnap’s syntactical period already had many significant semantical elements. I will argue that both of them are partly right, both of them contain a kernel of truth: it is true that Carnap’s semantical period started after his Logical Syntax of Language (...) — in one sense of semantics. But it is also true that Carnap had already included semantical ideas in LSL: though not in the sense that URV maintains. This latter sense of semantics is related to what is usually called inferentialism, and by getting a clearer picture of Carnap’s original aims, context, and concept-usage, we might be in a better position to approach his alleged inferentialism. (shrink)

A system of logic usually comprises a language for which a model-theory and a proof-theory are defined. The model-theory defines the semantic notion of model-theoretic logical consequence (⊨), while the proof-theory defines the proof- theoretic notion of logical consequence (or logical derivability, ⊢). If the system in question is sound and complete, then the two notions of logical consequence are extensionally equivalent. The concept of full formalization is a more restrictive one and requires in addition the (...) preservation of the standard meanings of the logical terms in all the admissible interpretations of the logical calculus, as it is proof-theoretically defined. Although classical first-order logic is sound and complete, its standard formalizations fall short to be full formalizations since they allow non-intended interpretations. This fact poses a challenge for the logical inferentialism program, whose main tenet is that the meanings of the logical terms are uniquely determined by the formal axioms or rules of inference that govern their use in a logical calculus, i.e., logical inferentialism requires a categorical calculus. This paper is the first part of a more elaborated study which will analyze the categoricity problem from its beginning until the most recent approaches. I will first start by describing the problem of a full formalization in the general framework in which Carnap (1934/1937, 1943) formulated it for classical logic. Then, in sections IV and V, I shall discuss the way in which the mathematicians B.A. Bernstein (1932) and E.V. Huntington (1933) have previously formulated and analyzed it in algebraic terms for propositional logic and, finally, I shall discuss some critical reactions Nagel (1943), Hempel (1943), Fitch (1944), and Church (1944) formulated to these approaches. (shrink)

As the foundation of our rationality, logic has traditionally been considered fixed, stable and constant. This conception of the discipline has been challenged recently by the plurality of logics and in this book, Pavel Arazim extends the debate to offer a new view of logic as dynamic and without a definite, specific shape. The Problem of Plurality of Logics examines the origins of our standard view of logic alongside Kant's theories, the holistic view, the issue of logic's pragmatic significance and (...) Robert Brandom's logical expressivism. Arazim then draws on proof-theoretical approaches to present a convincing argument for a dynamic version of logical inferentialism, which opens space for a new freedom to modify our own logic. He explores the scope, possibilities and limits of this freedom in order to highlight the future paths logic could take, as a motivation for further research. Marking a departure from logical monism and also from the recent doctrine of logical pluralism in its various forms, this book addresses current debates concerning the expressive role of logic and contributes to a lively area of discussion in analytic philosophy. (shrink)