Combining Texts

All the ideas for 'The Intrinsic Quality of Experience', 'Truth Rehabilitated' and 'Introduction to Mathematical Logic'

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29 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
23291 Without truth, both language and thought are impossible [Davidson]
23284 Plato's Forms confused truth with the most eminent truths, so only Truth itself is completely true [Davidson]
23286 Truth can't be a goal, because we can neither recognise it nor confim it [Davidson]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
23292 Correspondence can't be defined, but it shows how truth depends on the world [Davidson]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
23288 When Tarski defines truth for different languages, how do we know it is a single concept? [Davidson]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
23287 Disquotation only accounts for truth if the metalanguage contains the object language [Davidson]
4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
17749 Post proved the consistency of propositional logic in 1921 [Walicki]
17765 Propositional language can only relate statements as the same or as different [Walicki]
4. Formal Logic / B. Propositional Logic PL / 3. Truth Tables
17764 Boolean connectives are interpreted as functions on the set {1,0} [Walicki]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
17752 The empty set is useful for defining sets by properties, when the members are not yet known [Walicki]
17753 The empty set avoids having to take special precautions in case members vanish [Walicki]
4. Formal Logic / F. Set Theory ST / 6. Ordering in Sets
17759 Ordinals play the central role in set theory, providing the model of well-ordering [Walicki]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
17741 To determine the patterns in logic, one must identify its 'building blocks' [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
17747 A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
17748 The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17758 Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki]
17755 Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki]
17756 The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki]
17760 Two infinite ordinals can represent a single infinite cardinal [Walicki]
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17762 In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
17754 Inductive proof depends on the choice of the ordering [Walicki]
7. Existence / D. Theories of Reality / 8. Facts / e. Facts rejected
23285 If we try to identify facts precisely, they all melt into one (as the Slingshot Argument proves) [Davidson]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
15. Nature of Minds / B. Features of Minds / 5. Qualia / b. Qualia and intentionality
8130 Qualities of experience are just representational aspects of experience ('Representationalism') [Harman, by Burge]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
23289 Knowing the potential truth conditions of a sentence is necessary and sufficient for understanding [Davidson]
19. Language / A. Nature of Meaning / 6. Meaning as Use
23290 It could be that the use of a sentence is explained by its truth conditions [Davidson]