Combining Texts

All the ideas for 'fragments/reports', 'Alfred Tarski: life and logic' and 'Ontological Dependence'

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26 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
14255 We understand things through their dependency relations [Fine,K]
1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
14250 Metaphysics deals with the existence of things and with the nature of things [Fine,K]
2. Reason / D. Definition / 4. Real Definition
14259 Maybe two objects might require simultaneous real definitions, as with two simultaneous terms [Fine,K]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10147 The Axiom of Choice is consistent with the other axioms of set theory [Feferman/Feferman]
10148 Axiom of Choice: a set exists which chooses just one element each of any set of sets [Feferman/Feferman]
10149 Platonist will accept the Axiom of Choice, but others want criteria of selection or definition [Feferman/Feferman]
10150 The Trichotomy Principle is equivalent to the Axiom of Choice [Feferman/Feferman]
10146 Cantor's theories needed the Axiom of Choice, but it has led to great controversy [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10158 A structure is a 'model' when the axioms are true. So which of the structures are models? [Feferman/Feferman]
10162 Tarski and Vaught established the equivalence relations between first-order structures [Feferman/Feferman]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10160 Löwenheim-Skolem says if the sentences are countable, so is the model [Feferman/Feferman]
10159 Löwenheim-Skolem Theorem, and Gödel's completeness of first-order logic, the earliest model theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 4. Completeness
10161 If a sentence holds in every model of a theory, then it is logically derivable from the theory [Feferman/Feferman]
5. Theory of Logic / K. Features of Logics / 7. Decidability
10156 'Recursion theory' concerns what can be solved by computing machines [Feferman/Feferman]
10155 Both Principia Mathematica and Peano Arithmetic are undecidable [Feferman/Feferman]
7. Existence / A. Nature of Existence / 3. Being / b. Being and existence
14253 An object's 'being' isn't existence; there's more to an object than existence, and its nature doesn't include existence [Fine,K]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
14261 There is 'weak' dependence in one definition, and 'strong' dependence in all the definitions [Fine,K]
14251 A natural modal account of dependence says x depends on y if y must exist when x does [Fine,K]
14257 An object depends on another if the second cannot be eliminated from the first's definition [Fine,K]
14254 Dependency is the real counterpart of one term defining another [Fine,K]
9. Objects / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
14252 We should understand identity in terms of the propositions it renders true [Fine,K]
9. Objects / D. Essence of Objects / 2. Types of Essence
14256 How do we distinguish basic from derived esssences? [Fine,K]
14258 Maybe some things have essential relationships as well as essential properties [Fine,K]
9. Objects / D. Essence of Objects / 4. Essence as Definition
14260 An object only essentially has a property if that property follows from every definition of the object [Fine,K]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]