Ideas of Michael Potter, by Theme
[British, fl. 2004, Senior Lecturer at Cambridge, and Fellow of Fitzwilliam College.]
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2. Reason / D. Definition / 8. Impredicative Definition
22285
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Impredicative definitions are circular, but fine for picking out, rather than creating something
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3. Truth / A. Truth Problems / 2. Defining Truth
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The Identity Theory says a proposition is true if it coincides with what makes it true
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3. Truth / C. Correspondence Truth / 1. Correspondence Truth
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It has been unfortunate that externalism about truth is equated with correspondence
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4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713
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Usually the only reason given for accepting the empty set is convenience
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
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Infinity: There is at least one limit level
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
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Nowadays we derive our conception of collections from the dependence between them
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects
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4. Formal Logic / G. Formal Mereology / 1. Mereology
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Mereology elides the distinction between the cards in a pack and the suits
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5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
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We can formalize second-order formation rules, but not inference rules
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5. Theory of Logic / B. Logical Consequence / 3. Deductive Consequence |-
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Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents
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5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
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Deductivism can't explain how the world supports unconditional conclusions
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5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703
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Supposing axioms (rather than accepting them) give truths, but they are conditional
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5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
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Modern logical truths are true under all interpretations of the non-logical words
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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712
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If set theory didn't found mathematics, it is still needed to count infinite sets
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6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms
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6. Mathematics / C. Sources of Mathematics / 7. Formalism
22310
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The formalist defence against Gödel is to reject his metalinguistic concept of truth
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6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
22298
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Why is fictional arithmetic applicable to the real world?
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7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
22287
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If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete
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8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043
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A relation is a set consisting entirely of ordered pairs
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8. Modes of Existence / A. Relations / 4. Formal Relations / c. Ancestral relation
22284
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'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers
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9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042
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If dependence is well-founded, with no infinite backward chains, this implies substances
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9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041
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Collections have fixed members, but fusions can be carved in innumerable ways
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10. Modality / A. Necessity / 1. Types of Modality
10709
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Priority is a modality, arising from collections and members
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10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
22281
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A material conditional cannot capture counterfactual reasoning
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13. Knowledge Criteria / C. External Justification / 3. Reliabilism / b. Anti-reliabilism
22327
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Knowledge from a drunken schoolteacher is from a reliable and unreliable process
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18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
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Traditionally there are twelve categories of judgement, in groups of three
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18. Thought / D. Concepts / 3. Ontology of Concepts / c. Fregean concepts
22290
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The phrase 'the concept "horse"' can't refer to a concept, because it is saturated
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19. Language / C. Assigning Meanings / 4. Compositionality
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Compositionality should rely on the parsing tree, which may contain more than sentence components
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22282
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'Direct compositonality' says the components wholly explain a sentence meaning
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22296
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Compositionality is more welcome in logic than in linguistics (which is more contextual)
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