Combining Texts

All the ideas for 'Two-Dimensional Semantics', 'Introduction to Mathematical Logic' and 'Protocol Sentences'

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40 ideas

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
17763 Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki]
17761 A compact axiomatisation makes it possible to understand a field as a whole [Walicki]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
17757 Members of ordinals are ordinals, and also subsets of ordinals [Walicki]
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]
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]
10. Modality / A. Necessity / 2. Nature of Necessity
17742 Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki]
10. Modality / A. Necessity / 3. Types of Necessity
14703 Superficial necessity is true in all worlds; deep necessity is thus true, no matter which world is actual [Schroeter]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / b. Conceivable but impossible
14714 Contradictory claims about a necessary god both seem apriori coherent [Schroeter]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
14704 2D semantics gives us apriori knowledge of our own meanings [Schroeter]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
10486 If we are rebuilding our ship at sea, we should jettison some cargo [Boolos on Neurath]
8485 We must always rebuild our ship on the open sea; we can't reconstruct it properly in dry-dock [Neurath]
18. Thought / C. Content / 5. Twin Earth
14706 Your view of water depends on whether you start from the actual Earth or its counterfactual Twin [Schroeter]
18. Thought / C. Content / 7. Narrow Content
14711 Rationalists say knowing an expression is identifying its extension using an internal cognitive state [Schroeter]
19. Language / A. Nature of Meaning / 1. Meaning
14717 Internalist meaning is about understanding; externalist meaning is about embedding in a situation [Schroeter]
19. Language / C. Assigning Meanings / 2. Semantics
14720 Semantic theory assigns meanings to expressions, and metasemantics explains how this works [Schroeter]
19. Language / C. Assigning Meanings / 4. Compositionality
14695 Semantic theories show how truth of sentences depends on rules for interpreting and joining their parts [Schroeter]
19. Language / C. Assigning Meanings / 7. Extensional Semantics
14697 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [Schroeter]
14696 Simple semantics assigns extensions to names and to predicates [Schroeter]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
14698 Possible worlds semantics uses 'intensions' - functions which assign extensions at each world [Schroeter]
14699 Possible worlds make 'I' and that person's name synonymous, but they have different meanings [Schroeter]
14709 Possible worlds semantics implies a constitutive connection between meanings and modal claims [Schroeter]
14719 In the possible worlds account all necessary truths are same (because they all map to the True) [Schroeter]
19. Language / C. Assigning Meanings / 10. Two-Dimensional Semantics
14701 Array worlds along the horizontal, and contexts (world,person,time) along the vertical [Schroeter]
14702 If we introduce 'actually' into modal talk, we need possible worlds twice to express this [Schroeter]
14705 Do we know apriori how we refer to names and natural kinds, but their modal profiles only a posteriori? [Schroeter]
14715 2D fans defend it for conceptual analysis, for meaning, and for internalist reference [Schroeter]
14716 2D semantics can't respond to contingent apriori claims, since there is no single proposition involved [Schroeter]