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All the ideas for 'Epistemological Disjunctivism', 'Making It Explicit' and 'Elements of Geometry'

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26 ideas

2. Reason / E. Argument / 1. Argument
My modus ponens might be your modus tollens [Pritchard,D]
2. Reason / E. Argument / 6. Conclusive Proof
Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Facts can't make claims true, because they are true claims [Brandom, by Kusch]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC
If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / m. One
A unit is that according to which each existing thing is said to be one [Euclid]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
Postulate 2 says a line can be extended continuously [Euclid, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid]
Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend]
Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid]
Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays]
Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / b. Greek arithmetic
Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik]
10. Modality / B. Possibility / 9. Counterfactuals
An improbable lottery win can occur in a nearby possible world [Pritchard,D]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
Moore begs the question, or just offers another view, or uses 'know' wrongly [Pritchard,D, by PG]
13. Knowledge Criteria / A. Justification Problems / 2. Justification Challenges / c. Knowledge closure
We can have evidence for seeing a zebra, but no evidence for what is entailed by that [Pritchard,D]
Favouring: an entailment will give better support for the first belief than reason to deny the second [Pritchard,D]
Maybe knowledge just needs relevant discriminations among contrasting cases [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
Epistemic internalism usually says justification must be accessible by reflection [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / b. Pro-externalism
Externalism is better than internalism in dealing with radical scepticism [Pritchard,D]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / c. Disjunctivism
Disjunctivism says perceptual justification must be both factual and known by the agent [Pritchard,D]
Metaphysical disjunctivism says normal perceptions and hallucinations are different experiences [Pritchard,D]
13. Knowledge Criteria / C. External Justification / 10. Anti External Justification
Epistemic externalism struggles to capture the idea of epistemic responsibility [Pritchard,D]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
We assess error against background knowledge, but that is just what radical scepticism challenges [Pritchard,D]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
Radical scepticism is merely raised, and is not a response to worrying evidence [Pritchard,D]