Combining Philosophers

All the ideas for Archimedes, Feferman / Feferman and H.H. Price

expand these ideas     |    start again     |     specify just one area for these philosophers

26 ideas

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]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
13007 Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz]
8. Modes of Existence / C. Powers and Dispositions / 2. Powers as Basic
14329 Some dispositional properties (such as mental ones) may have no categorical base [Price,HH]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
9032 Before we can abstract from an instance of violet, we must first recognise it [Price,HH]
9035 If judgement of a characteristic is possible, that part of abstraction must be complete [Price,HH]
9034 There may be degrees of abstraction which allow recognition by signs, without full concepts [Price,HH]
9036 There is pre-verbal sign-based abstraction, as when ice actually looks cold [Price,HH]
9037 Intelligent behaviour, even in animals, has something abstract about it [Price,HH]
18. Thought / A. Modes of Thought / 1. Thought
9033 Recognition must precede the acquisition of basic concepts, so it is the fundamental intellectual process [Price,HH]
18. Thought / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
10645 We reach concepts by clarification, or by definition, or by habitual experience [Price,HH]
18. Thought / E. Abstraction / 1. Abstract Thought
9030 Abstractions can be interpreted dispositionally, as the ability to recognise or imagine an item [Price,HH]
9029 If ideas have to be images, then abstract ideas become a paradoxical problem [Price,HH]
18. Thought / E. Abstraction / 2. Abstracta by Selection
10644 A 'felt familiarity' with universals is more primitive than abstraction [Price,HH]
10646 Our understanding of 'dog' or 'house' arises from a repeated experience of concomitances [Price,HH]
9031 The basic concepts of conceptual cognition are acquired by direct abstraction from instances [Price,HH]