Combining Texts

All the ideas for 'Set Theory and Its Philosophy', 'Are there propositions?' and 'Noneism or Allism?'

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31 ideas

3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
13985 A true proposition seems true of one fact, but a false proposition seems true of nothing at all. [Ryle]
3. Truth / C. Correspondence Truth / 3. Correspondence Truth critique
13984 Two maps might correspond to one another, but they are only 'true' of the country they show [Ryle]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
13979 Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
15533 We can quantify over fictions by quantifying for real over their names [Lewis]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
15534 We could quantify over impossible objects - as bundles of properties [Lewis]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
7. Existence / A. Nature of Existence / 1. Nature of Existence
15532 'Allists' embrace the existence of all controversial entities; 'noneists' reject all but the obvious ones [Lewis]
7. Existence / A. Nature of Existence / 2. Types of Existence
15535 We can't accept a use of 'existence' that says only some of the things there are actually exist [Lewis]
7. Existence / D. Theories of Reality / 8. Facts / c. Facts and truths
13988 Many sentences do not state facts, but there are no facts which could not be stated [Ryle]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
12. Knowledge Sources / B. Perception / 3. Representation
13983 Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
13980 If you like judgments and reject propositions, what are the relata of incoherence in a judgment? [Ryle]
19. Language / A. Nature of Meaning / 1. Meaning
13978 Husserl and Meinong wanted objective Meanings and Propositions, as subject-matter for Logic [Ryle]
19. Language / A. Nature of Meaning / 3. Meaning as Speaker's Intention
13977 When I utter a sentence, listeners grasp both my meaning and my state of mind [Ryle]
19. Language / D. Propositions / 1. Propositions
13976 'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle]
19. Language / D. Propositions / 4. Mental Propositions
13981 Several people can believe one thing, or make the same mistake, or share one delusion [Ryle]
13987 We may think in French, but we don't know or believe in French [Ryle]
19. Language / D. Propositions / 6. Propositions Critique
13989 There are no propositions; they are just sentences, used for thinking, which link to facts in a certain way [Ryle]
13982 If we accept true propositions, it is hard to reject false ones, and even nonsensical ones [Ryle]