Combining Texts

All the ideas for 'Alfred Tarski: life and logic', 'Two Kinds of Possibility' and 'An Essay in Aesthetics'

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27 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]
10. Modality / A. Necessity / 1. Types of Modality
12205 There are two families of modal notions, metaphysical and epistemic, of equal strength [Edgington]
10. Modality / A. Necessity / 5. Metaphysical Necessity
12207 Metaphysical possibility is discovered empirically, and is contrained by nature [Edgington]
10. Modality / A. Necessity / 6. Logical Necessity
12206 Broadly logical necessity (i.e. not necessarily formal logical necessity) is an epistemic notion [Edgington]
12208 An argument is only valid if it is epistemically (a priori) necessary [Edgington]
16. Persons / C. Self-Awareness / 3. Limits of Introspection
20429 Most of us are too close to our own motives to understand them [Fry]
21. Aesthetics / A. Aesthetic Experience / 2. Aesthetic Attitude
20424 Imaginative life requires no action, so new kinds of perception and values emerge in art [Fry]
20427 Everyone reveals an aesthetic attitude, looking at something which only exists to be seen [Fry]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
20433 'Beauty' can either mean sensuous charm, or the aesthetic approval of art (which may be ugly) [Fry]
21. Aesthetics / A. Aesthetic Experience / 6. The Sublime
20430 In life we neglect 'cosmic emotion', but it matters, and art brings it to the fore [Fry]
21. Aesthetics / B. Nature of Art / 2. Art as Form
20431 Art needs a mixture of order and variety in its sensations [Fry]
21. Aesthetics / B. Nature of Art / 3. Art as Imitation
20423 If graphic arts only aim at imitation, their works are only trivial ingenious toys [Fry]
20428 Popular opinion favours realism, yet most people never look closely at anything! [Fry]
21. Aesthetics / C. Artistic Issues / 1. Artistic Intentions
20432 When viewing art, rather than flowers, we are aware of purpose, and sympathy with its creator [Fry]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
20425 In the cinema the emotions are weaker, but much clearer than in ordinary life [Fry]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
20426 For pure moralists art must promote right action, and not just be harmless [Fry]