Combining Texts

All the ideas for 'Function and Concept', 'On the True Doctrine (Against Christians)' and 'What is Cantor's Continuum Problem?'

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21 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
18806 Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
8490 First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
8492 Relations are functions with two arguments [Frege]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8487 Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18899 Frege takes the existence of horses to be part of their concept [Frege, by Sommers]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
4028 Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege]
9. Objects / A. Existence of Objects / 3. Objects in Thought
8489 The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
9947 Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman]
10319 An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale]
8488 A concept is a function whose value is always a truth-value [Frege]
18. Thought / D. Concepts / 4. Structure of Concepts / a. Conceptual structure
9948 Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman]
19. Language / B. Reference / 5. Speaker's Reference
4972 I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege]
25. Social Practice / F. Life Issues / 6. Animal Rights
1868 The world was made as much for animals as for man [Celsus]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
8491 The Ontological Argument fallaciously treats existence as a first-level concept [Frege]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
1867 Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus]