Combining Texts

All the ideas for 'The Justification of Deduction', 'Plural Quantification Exposed' and 'Metaphysical Foundations of Mathematics'

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17 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 / E. Argument / 6. Conclusive Proof
19067 A successful proof requires recognition of truth at every step [Dummett]
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]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
10779 A comprehension axiom is 'predicative' if the formula has no bound second-order variables [Linnebo]
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
10781 A 'pure logic' must be ontologically innocent, universal, and without presuppositions [Linnebo]
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 / G. Quantification / 6. Plural Quantification
10778 Can second-order logic be ontologically first-order, with all the benefits of second-order? [Linnebo]
10783 Plural quantification depends too heavily on combinatorial and set-theoretic considerations [Linnebo]
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 / K. Features of Logics / 4. Completeness
19065 Soundness and completeness proofs test the theory of meaning, rather than the logic theory [Dummett]
9. Objects / A. Existence of Objects / 1. Physical Objects
10782 The modern concept of an object is rooted in quantificational logic [Linnebo]
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]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
22908 When one element contains the grounds of the other, the first one is prior in time [Leibniz]