Combining Texts

All the ideas for 'Logical Pluralism', 'Set Theory and Its Philosophy' and 'Classical Cosmology (frags)'

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38 ideas

3. Truth / A. Truth Problems / 1. Truth
13252 Some truths have true negations [Beall/Restall]
3. Truth / B. Truthmakers / 5. What Makes Truths / b. Objects make truths
13247 A truthmaker is an object which entails a sentence [Beall/Restall]
4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
13249 (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall]
4. Formal Logic / E. Nonclassical Logics / 5. Relevant Logic
13243 Excluded middle must be true for some situation, not for all situations [Beall/Restall]
13245 Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall]
13246 Relevant logic does not abandon classical logic [Beall/Restall]
13254 A doesn't imply A - that would be circular [Beall/Restall]
13255 Relevant logic may reject transitivity [Beall/Restall]
13242 It's 'relevantly' valid if all those situations make it true [Beall/Restall]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
13250 Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall]
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
13235 Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall]
13238 Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 2. History of Logic
13234 The view of logic as knowing a body of truths looks out-of-date [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13232 Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall]
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 / A. Overview of Logic / 8. Logic of Mathematics
13241 The model theory of classical predicate logic is mathematics [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
13253 There are several different consequence relations [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
13240 A sentence follows from others if they always model it [Beall/Restall]
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]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
13236 Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / d. The Preface paradox
13237 Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall]
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]
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]
10. Modality / A. Necessity / 3. Types of Necessity
13244 Relevant necessity is always true for some situation (not all situations) [Beall/Restall]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
13239 Judgement is always predicating a property of a subject [Beall/Restall]
19. Language / C. Assigning Meanings / 8. Possible Worlds Semantics
13248 We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall]
19. Language / D. Propositions / 1. Propositions
13233 Propositions commit to content, and not to any way of spelling it out [Beall/Restall]
27. Natural Reality / E. Cosmology / 1. Cosmology
5994 Is the cosmos open or closed, mechanical or teleological, alive or inanimate, and created or eternal? [Robinson,TM, by PG]