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All the ideas for 'Structures and Structuralism in Phil of Maths', 'What is Philosophy?' and 'Discourse on Metaphysics'

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45 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophy is in a perpetual state of digression [Deleuze/Guattari]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Philosophy is a concept-creating discipline [Deleuze/Guattari]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
Philosophy aims at what is interesting, remarkable or important - not at knowledge or truth [Deleuze/Guattari]
1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
The plague of philosophy is those who criticise without creating, and defend dead concepts [Deleuze/Guattari]
1. Philosophy / H. Continental Philosophy / 2. Phenomenology
Phenomenology needs art as logic needs science [Deleuze/Guattari]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Reason avoids multiplying hypotheses or principles [Leibniz]
2. Reason / C. Styles of Reason / 3. Eristic
'Eris' is the divinity of conflict, the opposite of Philia, the god of friendship [Deleuze/Guattari]
3. Truth / F. Semantic Truth / 2. Semantic Truth
While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price]
5. Theory of Logic / A. Overview of Logic / 3. Value of Logic
Logic has an infantile idea of philosophy [Deleuze/Guattari]
Logic hates philosophy, and wishes to supplant it [Deleuze/Guattari]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
'Analysis' is the theory of the real numbers [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Mereological arithmetic needs infinite objects, and function definitions [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
Set-theory gives a unified and an explicit basis for mathematics [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price]
There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price]
Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price]
There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price]
Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price]
Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price]
8. Modes of Existence / C. Powers and Dispositions / 1. Powers
The immediate cause of movements is more real [than geometry] [Leibniz]
8. Modes of Existence / E. Nominalism / 6. Mereological Nominalism
A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
The complete notion of a substance implies all of its predicates or attributes [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
Substances mirror God or the universe, each from its own viewpoint [Leibniz]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
Forms are of no value in physics, but are indispensable in metaphysics [Leibniz]
9. Objects / D. Essence of Objects / 1. Essences of Objects
Subjects include predicates, so full understanding of subjects reveals all the predicates [Leibniz]
10. Modality / E. Possible worlds / 3. Transworld Objects / d. Haecceitism
Leibniz is some form of haecceitist [Leibniz, by Cover/O'Leary-Hawthorne]
11. Knowledge Aims / B. Certain Knowledge / 4. The Cogito
We cannot judge the Cogito. Must we begin? Must we start from certainty? Can 'I' relate to thought? [Deleuze/Guattari]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
Knowledge doesn't just come from the senses; we know the self, substance, identity, being etc. [Leibniz]
14. Science / B. Scientific Theories / 4. Paradigm
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
Other people completely revise our perceptions, because they are possible worlds [Deleuze/Guattari]
16. Persons / D. Continuity of the Self / 2. Mental Continuity / a. Memory is Self
If a person's memories became totally those of the King of China, he would be the King of China [Leibniz]
16. Persons / F. Free Will / 1. Nature of Free Will
Future contingent events are certain, because God foresees them, but that doesn't make them necessary [Leibniz]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
People argue for God's free will, but it isn't needed if God acts in perfection following supreme reason [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
Mind and body can't influence one another, but God wouldn't intervene in the daily routine [Leibniz]
18. Thought / C. Content / 6. Broad Content
Phenomenology says thought is part of the world [Deleuze/Guattari]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
The logical attitude tries to turn concepts into functions, when they are really forms or forces [Deleuze/Guattari]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / a. Preconditions for ethics
Animals lack morality because they lack self-reflection [Leibniz]
28. God / C. Attitudes to God / 5. Atheism
Atheism is the philosopher's serenity, and philosophy's achievement [Deleuze/Guattari]