Ideas from 'The Justification of Deduction' by Michael Dummett [1973], by Theme Structure



1. Philosophy / D. Nature of Philosophy / 4. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims to understand the world, through ordinary experience and science
2. Reason / E. Argument / 6. Conclusive Proof
A successful proof requires recognition of truth at every step
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning
Deduction is justified by the semantics of its metalanguage
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
Beth trees show semantics for intuitionistic logic, in terms of how truth has been established
In standard views you could replace 'true' and 'false' with mere 0 and 1
Classical two-valued semantics implies that meaning is grasped through truth-conditions
5. Theory of Logic / K. Features of Logics / 4. Completeness
Soundness and completeness proofs test the theory of meaning, rather than the logic theory
19. Language / B. Meaning / 12. Denial of Meanings
Holism is not a theory of meaning; it is the denial that a theory of meaning is possible