Combining Texts

All the ideas for 'What is Philosophy?', 'On Second-Order Logic' and 'Logicism in the 21st Century'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
8220 Philosophy is in a perpetual state of digression [Deleuze/Guattari]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
8217 Philosophy is a concept-creating discipline [Deleuze/Guattari]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
8242 Philosophy aims at what is interesting, remarkable or important - not at knowledge or truth [Deleuze/Guattari]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
8223 The plague of philosophy is those who criticise without creating, and defend dead concepts [Deleuze/Guattari]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
8247 Phenomenology needs art as logic needs science [Deleuze/Guattari]
2. Reason / C. Styles of Reason / 3. Eristic
8224 'Eris' is the divinity of conflict, the opposite of Philia, the god of friendship [Deleuze/Guattari]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
8246 Logic hates philosophy, and wishes to supplant it [Deleuze/Guattari]
8219 Logic has an infantile idea of philosophy [Deleuze/Guattari]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
14249 Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley]
10830 Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
10829 A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
10832 '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10834 Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos]
5. Theory of Logic / K. Features of Logics / 6. Compactness
13841 Why should compactness be definitive of logic? [Boolos, by Hacking]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10833 Many concepts can only be expressed by second-order logic [Boolos]
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]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
8221 We cannot judge the Cogito. Must we begin? Must we start from certainty? Can 'I' relate to thought? [Deleuze/Guattari]
14. Science / B. Scientific Theories / 4. Paradigm
8222 Concepts are superior because they make us more aware, and change our thinking [Deleuze/Guattari]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / a. Other minds
8218 Other people completely revise our perceptions, because they are possible worlds [Deleuze/Guattari]
18. Thought / C. Content / 6. Broad Content
8248 Phenomenology says thought is part of the world [Deleuze/Guattari]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
8245 The logical attitude tries to turn concepts into functions, when they are really forms or forces [Deleuze/Guattari]
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]
28. God / C. Attitudes to God / 5. Atheism
8243 Atheism is the philosopher's serenity, and philosophy's achievement [Deleuze/Guattari]