### All the ideas for Peter B. Lewis, Michael Potter and Keith DeRose

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39 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 / 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 Fresge'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 / 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 / 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]
###### 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]
###### 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 / B. Possibility / 8. Conditionals / c. Truth-function conditionals
 22281 A material conditional cannot capture counterfactual reasoning [Potter]
###### 11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
 21912 Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
 21911 Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
###### 13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
 19513 A contextualist coherentist will say that how strongly a justification must cohere depends on context [DeRose]
###### 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]
###### 13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / a. Contextualism
 19514 Classical invariantism combines fixed truth-conditions with variable assertability standards [DeRose]
 19515 We can make contextualism more precise, by specifying the discrimination needed each time [DeRose]
 19510 In some contexts there is little more to knowledge than true belief. [DeRose]
 19516 Contextualists worry about scepticism, but they should focus on the use of 'know' in ordinary speech [DeRose]
###### 13. Knowledge Criteria / C. External Justification / 6. Contextual Justification / b. Invariantism
 19511 If contextualism is about knowledge attribution, rather than knowledge, then it is philosophy of language [DeRose]
###### 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
 22282 'Direct compositonality' says the components wholly explain a sentence meaning [Potter]
 22283 Compositionality should rely on the parsing tree, which may contain more than sentence components [Potter]
 22296 Compositionality is more welcome in logic than in linguistics (which is more contextual) [Potter]