Combining Philosophers

All the ideas for Bonaventura, Michael Potter and C. Anthony Anderson

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42 ideas

2. Reason / D. Definition / 8. Impredicative Definition
22285 Impredicative definitions are circular, but fine for picking out, rather than creating something [Potter]
3. Truth / A. Truth Problems / 2. Defining Truth
22301 The Identity Theory says a proposition is true if it coincides with what makes it true [Potter]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
22324 It has been unfortunate that externalism about truth is equated with correspondence [Potter]
4. Formal Logic / E. Nonclassical Logics / 6. Free Logic
18767 Free logics has terms that do not designate real things, and even empty domains [Anderson,CA]
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 / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
22279 Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents [Potter]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
22291 Deductivism can't explain how the world supports unconditional conclusions [Potter]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
18763 Basic variables in second-order logic are taken to range over subsets of the individuals [Anderson,CA]
5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
18771 Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]
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
22295 Modern logical truths are true under all interpretations of the non-logical words [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]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
22310 The formalist defence against Gödel is to reject his metalinguistic concept of truth [Potter]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
22298 Why is fictional arithmetic applicable to the real world? [Potter]
7. Existence / A. Nature of Existence / 2. Types of Existence
18769 Do mathematicians use 'existence' differently when they say some entity exists? [Anderson,CA]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
22287 If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete [Potter]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
18770 We can distinguish 'ontological' from 'existential' commitment, for different kinds of being [Anderson,CA]
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]
8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
22284 'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers [Potter]
8. Modes of Existence / B. Properties / 8. Properties as Modes
16643 Accidents always remain suited to a subject [Bonaventura]
9. Objects / A. Existence of Objects / 4. Impossible objects
18766 's is non-existent' cannot be said if 's' does not designate [Anderson,CA]
18768 We cannot pick out a thing and deny its existence, but we can say a concept doesn't correspond [Anderson,CA]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
18765 Individuation was a problem for medievals, then Leibniz, then Frege, then Wittgenstein (somewhat) [Anderson,CA]
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]
9. Objects / E. Objects over Time / 6. Successive Things
16696 Successive things reduce to permanent things [Bonaventura]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
18764 The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles [Anderson,CA]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
22281 A material conditional cannot capture counterfactual reasoning [Potter]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
22327 Knowledge from a drunken schoolteacher is from a reliable and unreliable process [Potter]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
22273 Traditionally there are twelve categories of judgement, in groups of three [Potter]
18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
22290 The phrase 'the concept "horse"' can't refer to a concept, because it is saturated [Potter]
19. Language / C. Assigning Meanings / 4. Compositionality
22283 Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter]
22282 'Direct compositonality' says the components wholly explain a sentence meaning [Potter]
22296 Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter]