Combining Texts

All the ideas for 'The Justification of Deduction', 'W.V. Quine' and 'An Analysis of Knowledge and Valuation'

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30 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 / 1. Propositional Logic
8472 Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
8476 Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein]
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 / D. Modal Logic ML / 4. Alethic Modal Logic
8480 S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
8474 Unlike elementary logic, set theory is not complete [Orenstein]
4. Formal Logic / G. Formal Mereology / 1. Mereology
8465 Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein]
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 / 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 / 1. Quantification
8452 Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
8475 The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein]
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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8454 The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8473 The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
7. Existence / E. Categories / 3. Proposed Categories
8458 Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein]
12. Knowledge Sources / E. Direct Knowledge / 4. Memory
21500 We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI]
21501 If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
6556 If anything is to be probable, then something must be certain [Lewis,CI]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
21498 Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI]
14. Science / B. Scientific Theories / 1. Scientific Theory
8457 The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein]
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]
18. Thought / C. Content / 8. Intension
5828 Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
8477 People presume meanings exist because they confuse meaning and reference [Orenstein]
19064 Holism is not a theory of meaning; it is the denial that a theory of meaning is possible [Dummett]
19. Language / C. Assigning Meanings / 3. Predicates
8471 Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein]
19. Language / D. Propositions / 4. Mental Propositions
8484 If two people believe the same proposition, this implies the existence of propositions [Orenstein]