Harmonic inferentialism and the logic of identity

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 (ge) 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 (2014) 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 (2004), slightly amended, are indeed ge-harmonious, so confirming that identity is a logical notion.PostprintPeer reviewe

Inferentialism and Structuralism: A Tale of Two Theories

This paper aims to unite two seemingly disparate themes in the philosophy of mathematics and language (and logic) respectively, namely ante rem structuralism and inferentialism. My analysis begins with describing both frameworks in accordance with their genesis in the work of Hilbert. I then draw comparisons between these philosophical views in terms of their similar motivations and similar objections to the referential orthodoxy. I specifically home in on two points of comparison, namely the role of norms and the relation of ontological dependence in both accounts. Lastly, I show that insights from this purported connection can address certain objections to both theories respectively

The poet sings: “resonance” in Paul Valéry’s poietics

This paper analyses Paul Valéry’s theories relating to his stated goal of poetic production: the attainment of “resonance” and a “singing-state”. My intention is to defend Valéry’s theory as a valid and consistent model of the creative process in poetry. To that end, I will draw support from T. W. Adorno’s claim that Valéry’s manner of reflective journalising in his Notebooks can furnish us with what he calls “aesthetic insight”. The consistency of Valéry’s theory will be supported by comparisons with the inferentialist understanding of semantics. Valéry proves to be a reliable exemplar of what might be called a “practice-led” aesthetics

Inferentialism and Structuralism: A Tale of Two Theories

This paper aims to unite two seemingly disparate themes in the philosophy of mathematics and language (and logic) respectively, namely ante rem structuralism and inferentialism. My analysis begins with describing both frameworks in accordance with their genesis in the work of Hilbert. I then draw comparisons between these philosophical views in terms of their similar motivations and similar objections to the referential orthodoxy. I specifically home in on two points of comparison, namely the role of norms and the relation of ontological dependence in both accounts. Lastly, I show that insights from this purported connection can address certain objections to both theories respectively

Rules and Meaning in Quantum Mechanics

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic.Comment: 150 page

Why Should Identity Be Harmonious?

Logical inferentialists have expected identity to be susceptible of harmonious introduction and elimination rules in natural deduction. While Read and Klev have proposed rules they argue are harmonious, Griffiths and Ahmed have criticized these rules as insufficient for harmony. These critics moreover suggest that no harmonious rules are forthcoming. I argue that these critics are correct: the logical inferentialist should abandon hope for harmonious rules for identity. The paper analyzes the three major uses of identity in presumed-logical languages: variable coordination, definitional substitution, and co-reference. We show that identity qua variable coordination is not logical by providing a harmonious natural-deduction system that captures this use through the quantifiers. We then argue that identity qua definitional substitution or co-reference faces a dilemma: either its rules are harmonious but they obscure its actual use in inference, or its rules are not harmonious but they make its actual use in inference plain. We conclude that the inferentialist may have harmonious rules for identity only by disrespecting its inferential use

Rules and Meaning in Quantum Mechanics

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic

Rules and Meaning in Quantum Mechanics

This book concerns the metasemantics of quantum mechanics (QM). Roughly, it pursues an investigation at an intersection of the philosophy of physics and the philosophy of semantics, and it offers a critical analysis of rival explanations of the semantic facts of standard QM. Two problems for such explanations are discussed: categoricity and permanence of rules. New results include 1) a reconstruction of Einstein's incompleteness argument, which concludes that a local, separable, and categorical QM cannot exist, 2) a reinterpretation of Bohr's principle of correspondence, grounded in the principle of permanence, 3) a meaning-variance argument for quantum logic, which follows a line of critical reflections initiated by Weyl, and 4) an argument for semantic indeterminacy leveled against inferentialism about QM, inspired by Carnap's work in the philosophy of classical logic

From Collapse Theorems to Proof-Theoretic Arguments

On some views, we can be sure that parties to a dispute over the logic of `exists' are not talking past each other if they can characterise `exists' as the only monadic predicate up to logical equivalence obeying a certain set of rules of inference. Otherwise, we ought to be suspicious about the reality of their disagreement. This is what we call a proof-theoretic argument. Pace some critics, who have tried to use proof-theoretic arguments to cast doubts about the reality of disagreements about the logic of `exists', we argue that proof-theoretic arguments can be deployed to establish the reality of several such disagreements. Along the way, we will also utilise this technique to establish similar results about some disagreements over the logic of identity

Understanding, normativity, and scientific practice

Understanding, Normativity, and Scientific Practice Harry Lewendon-Evans PhD Thesis Department of Philosophy Durham University 2018 Recent work in epistemology and philosophy of science has argued that understanding is an important cognitive achievement that philosophers should seek to address for its own sake. This thesis outlines and defends a new account of scientific understanding that analyses the concept of understanding in terms of the concept of normativity. The central claim is that to understand means to grasp something in the light of norms. The thesis is divided into two parts: Part I (chapters one to three) addresses the question of the agency of understanding and Part II (chapters four to five) focuses on the vehicles of scientific understanding. Chapter One begins with an account of understanding drawn from the work of Martin Heidegger, which presents understanding as a practical, normative capacity for making sense of entities. Chapter Two builds on Robert Brandom’s normative inferentialism to argue that conceptual understanding is grounded in inferential rules embedded within norm-governed, social practices. Chapter Three argues that normativity should be located in the intersubjective nature of social practices. The chapters in Part II draw on and extend the account of understanding developed in Part I by focusing on how models and explanations function within scientific practice to facilitate scientific understanding. Chapter Four investigates the nature of model-based understanding. It defends the claim that constructing and using models enables a form of conceptual articulation which facilitates scientific understanding by rendering scientific phenomena intelligible. Chapter Five considers the connection between understanding and explanation through the role of explanatory discourse in scientific practice. I argue that the function of explanations is to sculpt and make explicit the norms of intelligibility required for scientific understanding. This thesis concludes that scientific understanding is an inherently norm-governed phenomenon that is unintelligible without reference to the normative dimension of our social and scientific practices