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All the ideas for 'Mathematical Methods in Philosophy', 'Introduction to 'Language Truth and Logic'' and 'Sets, Aggregates and Numbers'

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21 ideas

5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17818 How many? must first partition an aggregate into sets, and then logic fixes its number [Yourgrau]
17822 Nothing is 'intrinsically' numbered [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers
17817 Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
17815 We can't use sets as foundations for mathematics if we must await results from the upper reaches [Yourgrau]
17821 You can ask all sorts of numerical questions about any one given set [Yourgrau]
7. Existence / A. Nature of Existence / 1. Nature of Existence
18740 If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
18745 A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
18747 The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
18748 Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
18746 Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
18750 Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
5163 Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
5167 The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
5164 A statement is meaningful if observation statements can be deduced from it [Ayer]
5165 Directly verifiable statements must entail at least one new observation statement [Ayer]
5166 The principle of verification is not an empirical hypothesis, but a definition [Ayer]
19. Language / D. Propositions / 1. Propositions
5162 Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / i. Prescriptivism
5168 Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer]