Combining Texts

All the ideas for 'fragments/reports', 'What is Logic?' and 'The Justification of Deduction'

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23 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
19066 Philosophy aims to understand the world, through ordinary experience and science [Dummett]
2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
2. Reason / E. Argument / 6. Conclusive Proof
19067 A successful proof requires recognition of truth at every step [Dummett]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
19060 Truth-tables are dubious in some cases, and may be a bad way to explain connective meaning [Dummett]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11066 Deduction is justified by the semantics of its metalanguage [Dummett, by Hanna]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
19058 Syntactic consequence is positive, for validity; semantic version is negative, with counterexamples [Dummett]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
19063 Beth trees show semantics for intuitionistic logic, in terms of how truth has been established [Dummett]
19059 In standard views you could replace 'true' and 'false' with mere 0 and 1 [Dummett]
19062 Classical two-valued semantics implies that meaning is grasped through truth-conditions [Dummett]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
5. Theory of Logic / K. Features of Logics / 4. Completeness
19065 Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
19061 An explanation is often a deduction, but that may well beg the question [Dummett]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
19064 Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]