Combining Texts

All the ideas for 'The Advancement of Learning', 'Intro to Oxford Hndbk of Metaphysics' and 'Elements of Set Theory'

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19 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
12124 Metaphysics is the best knowledge, because it is the simplest [Bacon]
1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
12123 Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon]
1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
12119 Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon]
12120 Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
9217 Modern empirical metaphysics focuses on ontological commitments of discourse, or on presuppositions [Loux/Zimmerman]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
13201 ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton]
13204 The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton]
13206 A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
13200 Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton]
13199 The empty set may look pointless, but many sets can be constructed from it [Enderton]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13202 Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13205 We can only define functions if Choice tells us which items are involved [Enderton]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
12121 We don't assume there is no land, because we can only see sea [Bacon]
14. Science / A. Basis of Science / 3. Experiment
12117 Science moves up and down between inventions of causes, and experiments [Bacon]
14. Science / B. Scientific Theories / 5. Commensurability
12127 Many different theories will fit the observed facts [Bacon]
15. Nature of Minds / C. Capacities of Minds / 5. Generalisation by mind
12126 People love (unfortunately) extreme generality, rather than particular knowledge [Bacon]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / c. Purpose denied
12125 Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
12118 Essences are part of first philosophy, but as part of nature, not part of logic [Bacon]