Combining Texts

All the ideas for 'Semantic Relationism', 'Set Theory' and 'The Theory of Objects'

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

35 ideas

4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
8250 So-called 'free logic' operates without existence assumptions [Meinong, by George/Van Evra]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
15592 The usual Tarskian interpretation of variables is to specify their range of values [Fine,K]
15593 Variables can be viewed as special terms - functions taking assignments into individuals [Fine,K]
15590 It seemed that Frege gave the syntax for variables, and Tarski the semantics, and that was that [Fine,K]
15591 In separate expressions variables seem identical in role, but in the same expression they aren't [Fine,K]
15595 The 'algebraic' account of variables reduces quantification to the algebra of its component parts [Fine,K]
15594 'Instantial' accounts of variables say we grasp arbitrary instances from their use in quantification [Fine,K]
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
15599 Cicero/Cicero and Cicero/Tully may differ in relationship, despite being semantically the same [Fine,K]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
8719 There can be impossible and contradictory objects, if they can have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 3. Objects in Thought
8971 There are objects of which it is true that there are no such objects [Meinong]
8718 Meinong says an object need not exist, but must only have properties [Meinong, by Friend]
9. Objects / A. Existence of Objects / 4. Impossible objects
7756 Meinong said all objects of thought (even self-contradictions) have some sort of being [Meinong, by Lycan]
15781 The objects of knowledge are far more numerous than objects which exist [Meinong]
9. Objects / F. Identity among Objects / 1. Concept of Identity
15603 I can only represent individuals as the same if I do not already represent them as the same [Fine,K]
9. Objects / F. Identity among Objects / 5. Self-Identity
15604 If Cicero=Tully refers to the man twice, then surely Cicero=Cicero does as well? [Fine,K]
18. Thought / B. Mechanics of Thought / 5. Mental Files
15602 Mental files are devices for keeping track of basic coordination of objects [Fine,K]
18. Thought / C. Content / 1. Content
15588 You cannot determine the full content from a thought's intrinsic character, as relations are involved [Fine,K]
19. Language / C. Assigning Meanings / 2. Semantics
15596 The standard aim of semantics is to assign a semantic value to each expression [Fine,K]
15587 That two utterances say the same thing may not be intrinsic to them, but involve their relationships [Fine,K]
15589 The two main theories are Holism (which is inferential), and Representational (which is atomistic) [Fine,K]
15598 We should pursue semantic facts as stated by truths in theories (and not put the theories first!) [Fine,K]
15600 Referentialist semantics has objects for names, properties for predicates, and propositions for connectives [Fine,K]
15601 Fregeans approach the world through sense, Referentialists through reference [Fine,K]
19. Language / C. Assigning Meanings / 9. Indexical Semantics
15605 I take indexicals such as 'this' and 'that' to be linked to some associated demonstration [Fine,K]