Combining Texts

All the ideas for '', 'Intellectual Autobiography' and 'works'

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19 ideas

2. Reason / A. Nature of Reason / 1. On Reason
17892 For clear questions posed by reason, reason can also find clear answers [Gödel]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18901 Truthmakers are facts 'of' a domain, not something 'in' the domain [Sommers]
4. Formal Logic / A. Syllogistic Logic / 3. Term Logic
18904 'Predicable' terms come in charged pairs, with one the negation of the other [Sommers, by Engelbretsen]
18895 Logic which maps ordinary reasoning must be transparent, and free of variables [Sommers]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
11211 If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
9188 Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
18897 Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18893 Translating into quantificational idiom offers no clues as to how ordinary thinkers reason [Sommers]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
11210 Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
11212 The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18903 Sommers promotes the old idea that negation basically refers to terms [Sommers, by Engelbretsen]
5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic
18894 Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10620 Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17883 Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17885 Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
10614 The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
7. Existence / D. Theories of Reality / 2. Realism
18900 Unfortunately for realists, modern logic cannot say that some fact exists [Sommers]
19. Language / B. Reference / 1. Reference theories
18898 In standard logic, names are the only way to refer [Sommers]
19. Language / F. Communication / 3. Denial
11214 We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]