Combining Texts

All the ideas for 'Through the Looking Glass', 'The Thought: a Logical Enquiry' and 'Set Theory'

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

25 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
7740 There exists a realm, beyond objects and ideas, of non-spatio-temporal thoughts [Frege, by Weiner]
3. Truth / A. Truth Problems / 2. Defining Truth
19466 The word 'true' seems to be unique and indefinable [Frege]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
19465 There cannot be complete correspondence, because ideas and reality are quite different [Frege]
3. Truth / H. Deflationary Truth / 1. Redundant Truth
19468 The property of truth in 'It is true that I smell violets' adds nothing to 'I smell violets' [Frege]
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]
7. Existence / A. Nature of Existence / 2. Types of Existence
19470 Thoughts in the 'third realm' cannot be sensed, and do not need an owner to exist [Frege]
7. Existence / A. Nature of Existence / 3. Being / e. Being and nothing
21982 I only wish I had such eyes as to see Nobody! It's as much as I can do to see real people. [Carroll,L]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
19471 A fact is a thought that is true [Frege]
9. Objects / A. Existence of Objects / 3. Objects in Thought
9877 Late Frege saw his non-actual objective objects as exclusively thoughts and senses [Frege, by Dummett]
18. Thought / A. Modes of Thought / 1. Thought
19469 We grasp thoughts (thinking), decide they are true (judgement), and manifest the judgement (assertion) [Frege]
8162 Thoughts have their own realm of reality - 'sense' (as opposed to the realm of 'reference') [Frege, by Dummett]
9818 A thought is distinguished from other things by a capacity to be true or false [Frege, by Dummett]
18. Thought / A. Modes of Thought / 9. Indexical Thought
16379 Thoughts about myself are understood one way to me, and another when communicated [Frege]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
19467 A 'thought' is something for which the question of truth can arise; thoughts are senses of sentences [Frege]
19. Language / D. Propositions / 5. Unity of Propositions
19472 A sentence is only a thought if it is complete, and has a time-specification [Frege]