PaperlayerView exact revision on arXiv

Source-linked AI summary

Warrant Theory

Khashayar Irani

arXiv:2609.11667v1cs.LOcs.AI

TL;DR

Truth-based evaluation alone does not explain what entitles propositions to enter inferential analysis. The paper develops warrant theory and a method for tracing inferential standing, then defines logic through legitimate acceptance, rejection, and warranted transitions. It interprets logical consequence and failure through the presence, preservation, or absence of inferential entitlement.

  • Problem

    Truth, falsity, and formal validity do not fully explain what makes a proposition properly available for inferential use.

    Source: §1 · p. 2

  • Method

    The paper frames warrant as inferential entitlement, analyzes how propositions acquire and interact through inferential standing, and uses acceptance and rejection to represent positive and negative positions.

    Source: §2 · p. 7, §3 · p. 10

  • Results

    Logic is defined as the formal and normative study of legitimate acceptance or rejection and the inferential transitions that such legitimacy authorizes.

    Source: §4 · p. 12

  • Takeaways & Limitations

    Logical consequence and failure concern the presence, preservation, or absence of inferential entitlement, rather than only whether a conclusion is true.

    Source: §4 · pp. 13–14

    The account is a foundation rather than an exhaustive theory, leaving systematic warrant-theoretic accounts of logical consequence and logical constants for future research.

    Source: §5 · p. 15

Abstract

from arXiv · show

In this paper, we develop warrant theory as a philosophical discipline concerned with the inferential legitimacy of propositions within logical analysis. Warrant theory reconceptualises logic as a normative framework governing the conditions under which propositions may be introduced, accepted, rejected, and inferentially employed. Warrant is understood as inferential entitlement and is distinguished from truth, belief, and other psychological attitudes, while its relation to inferential use and meaning is examined. Warrant-theoretic analysis is then developed as a systematic method for investigating how propositions acquire inferential standing, how that standing develops, and how inferential positions interact through relations of dependence, compatibility, incompatibility, and exclusion. Acceptance and rejection provide the bilateral vocabulary for representing positive and negative inferential positions and the consequences and commitments associated with them. Finally, these elements are brought together in a warrant-theoretic definition of logic as the formal and normative study of the conditions under which propositions may be legitimately accepted or rejected and of the inferential transitions that such legitimacy warrants. On this account, logical consequence and logical failure are understood through the presence, preservation, or absence of inferential entitlement, thus locating the philosophical subject matter of logic in the systematic governance of inferential legitimacy.

1. What is Warrant Theory?

Warrant theory treats logic as a normative inquiry into what entitles propositions to participate in inferential analysis. It distinguishes inferential entitlement from truth and psychological attitudes, and connects meaning to warranted use.

1. What is Warrant Theory?

  • Warrant theory shifts logic beyond evaluating truth or validity to explaining what makes propositions admissible for inferential use.It addresses a dimension that truth-conditional approaches, as presented here, do not fully explain.Source: §1 · p. 2
  • On a warrant-theoretic reading of Gentzen, introduction rules establish the grounds for accepting propositions, while elimination rules govern warranted inferences from them.Conjunction introduction derives A ∧ B from warranted A and B; elimination recovers either conjunct without adding an independent source of warrant.Source: §1 · pp. 3–5
  • Warrant is the inferential entitlement that licenses a proposition to function within logical analysis.It concerns admissibility for inferential use, not simply meaningfulness or truth.Source: §1 · p. 5
  • Warrant differs from truth and psychological attitudes, so a proposition may be true or believed without being warranted for use in an inferential context.The account treats warrant as part of the public, normative structure of analysis rather than a subjective mental state.Source: §1 · pp. 5–6
  • Warrant theory links meaning to the conditions for legitimate acceptance or rejection and to the warranted inferences and exclusions in which a proposition participates.Understanding a proposition involves grasping its warranted use, not only its truth conditions.Source: §1 · pp. 6–7

2. What is Warrant-Theoretic Analysis?

Warrant-theoretic analysis investigates how propositions acquire, retain, and interact through inferential standing. It reconstructs the grounds and dependencies that determine whether propositions are admissible for continued use.

2. What is Warrant-Theoretic Analysis?

  • The analysis distinguishes a proposition’s mere occurrence from its admissible presence by identifying the grounds for its inferential position.It records where a proposition enters, what it depends on, and which restrictions govern its later use.Source: §2 · pp. 7–8
  • It tracks whether later inferential uses remain continuous with the grounds on which a proposition became available.In disjunction elimination, it reconstructs dependencies across branches and checks whether discharging temporary assumptions leaves the conclusion with standing.Source: §2 · pp. 8–9
  • It examines how inferential positions interact through dependence, compatibility, incompatibility, and exclusion.This relational analysis considers what propositions jointly sustain, what auxiliary claims might reconcile tensions, and what follows when a position is withdrawn or restricted.Source: §2 · p. 9

3. The Role of Acceptance & Rejection in Warrant Theory

Acceptance and rejection articulate positive and negative inferential positions within a bilateral framework. Their orientations carry distinct consequences and commitments, organizing how propositions may be maintained, excluded, or used in analysis.

3. The Role of Acceptance & Rejection in Warrant Theory

  • Acceptance assigns a proposition a positive inferential position, while rejection assigns it a negative one; neither is a psychological attitude or speech act.The signs +A and -A represent positions toward A, distinct from the formula ¬A.Source: §3 · p. 10
  • Acceptance and rejection have different inferential consequences, affecting which transitions remain available and which routes are blocked or excluded.A conclusion depending on an accepted proposition cannot proceed on that basis if the proposition is instead rejected.Source: §3 · p. 11
  • These positions carry commitments and constraints that arise through relations of compatibility, incompatibility, and exclusion.Incompatible accepted positions require the inferential configuration to be reconsidered.Source: §3 · p. 11
  • Together, acceptance and rejection provide a bilateral vocabulary for representing inferential orientation and its consequences without introducing an independent source of warrant.They connect warrant to opposed positions whose effects within analysis can be systematically related.Source: §3 · pp. 11–12

4. A Warrant-Theoretic Definition of Logic

Logic is the formal and normative study of when propositions may be accepted or rejected and which inferential transitions those positions authorize. Consequence and failure turn on whether inferential entitlement authorizes and is preserved through a transition, not merely on a conclusion’s truth.

4. A Warrant-Theoretic Definition of Logic

  • Logic studies the conditions for legitimate acceptance or rejection and the inferential transitions authorized by established positions.Its formal character represents these relations independently of subject matter; its normative character distinguishes warranted transitions from those lacking entitlement.Source: §4 · p. 12
  • Logical consequence is a warranted transition in which premises, together with governing logical principles, authorize the conclusion’s inferential position.The account distinguishes authorization from a proposition merely appearing after premises.Source: §4 · pp. 12–13
  • The bilateral framework represents consequence as both permission for further positions and constraint on positions that cannot be sustained together.Acceptance and rejection express movement among positive and negative positions, with warrant governing that movement.Source: §4 · p. 13
  • An inference fails when its conclusion is not authorized by its starting positions, even if the conclusion is true.In extended reasoning, each stage must preserve inferential entitlement; incompatibility may require rejection or blocking a transition.Source: §4 · p. 13
  • Warrant theory treats successful and unsuccessful inference through the presence, preservation, or absence of inferential entitlement.It examines the authority of truth, validity, derivability, semantics, and proof theory without replacing those notions, and applies across systems with different rules or consequence relations.Source: §4 · p. 14

5. Concluding Remarks

The paper develops warrant theory from inferential entitlement through warrant-theoretic analysis and bilateral acceptance and rejection to a definition of logic. It presents this account as a foundation, with systematic consequence theory and the inferential meaning of logical constants among the future research tasks.

5. Concluding Remarks

  • The paper’s aims are to explain warrant as inferential entitlement, develop warrant-theoretic analysis, clarify acceptance and rejection, and define logic through inferential legitimacy.The concluding account describes a sequence from warrant and its distinction from truth, belief, assertion, and psychological conviction, through analysis and bilateral positions, to the definition of logic.Source: §5 · pp. 14–15
  • Warrant-theoretic analysis investigates how inferential standing is maintained, transferred, restricted, or lost, and how positions interact through dependence, compatibility, incompatibility, and exclusion.Acceptance and rejection articulate the positive and negative orientations of inferential positions.Source: §5 · pp. 14–15
  • The paper interprets logical consequence and failure through the presence, preservation, or absence of inferential entitlement.Logic is defined as the study of legitimate acceptance and rejection and the inferential transitions warranted by established positions.Source: §5 · p. 15
  • The account is a foundation rather than an exhaustive theory; systematic consequence conditions and a warrant-theoretic account of logical constants’ meaning remain future projects.Other proposed directions include warrant and proof-theoretic validity, incompatibility and exclusion, and applications beyond formal logic.Source: §5 · p. 15
Loading 2609.11667v1…