Combining Texts

All the ideas for 'Physiologia', 'Two-Dimensional Semantics' and 'Principles of Arithmetic, by a new method'

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25 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
13949 All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
18113 PA concerns any entities which satisfy the axioms [Peano, by Bostock]
17634 Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
15653 We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
17635 Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16674 The quantity is just the matter, in that it has extended parts and is diffuse [Charleton]
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]
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
14696 Simple semantics assigns extensions to names and to predicates [Schroeter]
14697 'Federer' and 'best tennis player' can't mean the same, despite having the same extension [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]