Combining Texts

All the ideas for 'Ontology', 'Set Theory' and 'Wittgenstein's 'Tractatus Logico-Philosophicus''

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34 ideas

4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic
23505 Aristotelian logic cannot express 'Everyone loves someone' [White,RM]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
7689 The modal logic of C.I.Lewis was only interpreted by Kripke and Hintikka in the 1960s [Jacquette]
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 / A. Overview of Logic / 1. Overview of Logic
7681 Logic describes inferences between sentences expressing possible properties of objects [Jacquette]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
7682 Logic is not just about signs, because it relates to states of affairs, objects, properties and truth-values [Jacquette]
5. Theory of Logic / F. Referring in Logic / 2. Descriptions / c. Theory of definite descriptions
7697 On Russell's analysis, the sentence "The winged horse has wings" comes out as false [Jacquette]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
7701 Can a Barber shave all and only those persons who do not shave themselves? [Jacquette]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
7707 To grasp being, we must say why something exists, and why there is one world [Jacquette]
7. Existence / A. Nature of Existence / 5. Reason for Existence
7692 Being is maximal consistency [Jacquette]
7687 Existence is completeness and consistency [Jacquette]
7. Existence / D. Theories of Reality / 1. Ontologies
7679 Ontology is the same as the conceptual foundations of logic [Jacquette]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
7678 Ontology must include the minimum requirements for our semantics [Jacquette]
7. Existence / E. Categories / 3. Proposed Categories
7683 Logic is based either on separate objects and properties, or objects as combinations of properties [Jacquette]
7684 Reduce states-of-affairs to object-property combinations, and possible worlds to states-of-affairs [Jacquette]
8. Modes of Existence / B. Properties / 11. Properties as Sets
7703 If classes can't be eliminated, and they are property combinations, then properties (universals) can't be either [Jacquette]
9. Objects / A. Existence of Objects / 1. Physical Objects
7685 An object is a predication subject, distinguished by a distinctive combination of properties [Jacquette]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
7699 Numbers, sets and propositions are abstract particulars; properties, qualities and relations are universals [Jacquette]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
7691 The actual world is a consistent combination of states, made of consistent property combinations [Jacquette]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
7688 The actual world is a maximally consistent combination of actual states of affairs [Jacquette]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / c. Worlds as propositions
7695 Do proposition-structures not associated with the actual world deserve to be called worlds? [Jacquette]
7694 We must experience the 'actual' world, which is defined by maximally consistent propositions [Jacquette]
15. Nature of Minds / B. Features of Minds / 5. Qualia / c. Explaining qualia
7706 If qualia supervene on intentional states, then intentional states are explanatorily fundamental [Jacquette]
17. Mind and Body / E. Mind as Physical / 2. Reduction of Mind
7704 Reduction of intentionality involving nonexistent objects is impossible, as reduction must be to what is actual [Jacquette]
19. Language / D. Propositions / 1. Propositions
7702 The extreme views on propositions are Frege's Platonism and Quine's extreme nominalism [Jacquette]