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All the ideas for 'Mathematical Methods in Philosophy', 'Logicism in the 21st Century' and 'Sophistical Refutations'

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21 ideas

2. Reason / A. Nature of Reason / 1. On Reason
2676 Didactic argument starts from the principles of the subject, not from the opinions of the learner [Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
2675 Reasoning is a way of making statements which makes them lead on to other statements [Aristotle]
2. Reason / C. Styles of Reason / 1. Dialectic
2677 Dialectic aims to start from generally accepted opinions, and lead to a contradiction [Aristotle]
2. Reason / C. Styles of Reason / 3. Eristic
2674 Competitive argument aims at refutation, fallacy, paradox, solecism or repetition [Aristotle]
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 / E. Structures of Logic / 2. Logical Connectives / d. and
16967 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle]
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 / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
8784 Neo-logicism founds arithmetic on Hume's Principle along with second-order logic [Hale/Wright]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem
8787 The Julius Caesar problem asks for a criterion for the concept of a 'number' [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8788 Logicism is only noteworthy if logic has a privileged position in our ontology and epistemology [Hale/Wright]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
8783 Logicism might also be revived with a quantificational approach, or an abstraction-free approach [Hale/Wright]
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]
9. Objects / D. Essence of Objects / 10. Essence as Species
16149 Generic terms like 'man' are not substances, but qualities, relations, modes or some such thing [Aristotle]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
11840 Only if two things are identical do they have the same attributes [Aristotle]
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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
8786 One first-order abstraction principle is Frege's definition of 'direction' in terms of parallel lines [Hale/Wright]