Combining Texts

All the ideas for 'Croce and Collingwood', 'Alfred Tarski: life and logic' and 'The Relation of Sense-Data to Physics'

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34 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]
7. Existence / C. Structure of Existence / 8. Stuff / a. Pure stuff
6472 Continuity is a sufficient criterion for the identity of a rock, but not for part of a smooth fluid [Russell]
9. Objects / A. Existence of Objects / 1. Physical Objects
6473 Physical things are series of appearances whose matter obeys physical laws [Russell]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
6465 We need not deny substance, but there seems no reason to assert it [Russell]
6471 The assumption by physicists of permanent substance is not metaphysically legitimate [Russell]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
6466 Where possible, logical constructions are to be substituted for inferred entities [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / b. Nature of sense-data
6467 No sensibile is ever a datum to two people at once [Russell]
6483 Russell held that we are aware of states of our own brain [Russell, by Robinson,H]
8244 Sense-data are qualities devoid of subjectivity, which are the basis of science [Russell, by Deleuze/Guattari]
6462 Sense-data are not mental, but are part of the subject-matter of physics [Russell]
6463 Sense-data are objects, and do not contain the subject as part, the way beliefs do [Russell]
6464 Sense-data are usually objects within the body, but are not part of the subject [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / c. Unperceived sense-data
6459 We do not know whether sense-data exist as objects when they are not data [Russell]
6460 'Sensibilia' are identical to sense-data, without actually being data for any mind [Russell]
6461 Ungiven sense-data can no more exist than unmarried husbands [Russell]
12. Knowledge Sources / B. Perception / 4. Sense Data / d. Sense-data problems
6458 Individuating sense-data is difficult, because they divide when closely attended to [Russell]
6469 Sense-data may be subjective, if closing our eyes can change them [Russell]
21. Aesthetics / A. Aesthetic Experience / 1. Aesthetics
20416 By 1790 aestheticians were mainly trying to explain individual artistic genius [Kemp]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
20417 Expression can be either necessary for art, or sufficient for art (or even both) [Kemp]
20419 We don't already know what to express, and then seek means of expressing it [Kemp]
20418 The horror expressed in some works of art could equallly be expressed by other means [Kemp]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
6470 Matter is the limit of appearances as distance from the object diminishes [Russell]
27. Natural Reality / C. Space / 2. Space
6468 There is 'private space', and there is also the 'space of perspectives' [Russell]