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