Combining Philosophers

All the ideas for Euclid, Carrie Jenkins and Richard Cartwright

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48 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy
Philosophers working like teams of scientists is absurd, yet isolation is hard [Cartwright,R]
1. Philosophy / F. Analytic Philosophy / 4. Conceptual Analysis
Examining concepts can recover information obtained through the senses [Jenkins]
2. Reason / A. Nature of Reason / 6. Coherence
A false proposition isn't truer because it is part of a coherent system [Cartwright,R]
2. Reason / E. Argument / 6. Conclusive Proof
Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege]
3. Truth / A. Truth Problems / 5. Truth Bearers
Are the truth-bearers sentences, utterances, ideas, beliefs, judgements, propositions or statements? [Cartwright,R]
Logicians take sentences to be truth-bearers for rigour, rather than for philosophical reasons [Cartwright,R]
3. Truth / C. Correspondence Truth / 2. Correspondence to Facts
Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins]
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]
Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins]
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]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
Arithmetic concepts are indispensable because they accurately map the world [Jenkins]
Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
We can learn about the world by studying the grounding of our concepts [Jenkins]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG]
7. Existence / E. Categories / 4. Category Realism
The concepts we have to use for categorising are ones which map the real world well [Jenkins]
8. Modes of Existence / B. Properties / 11. Properties as Sets
While no two classes coincide in membership, there are distinct but coextensive attributes [Cartwright,R]
9. Objects / B. Unity of Objects / 3. Unity Problems / a. Scattered objects
Clearly a pipe can survive being taken apart [Cartwright,R]
Bodies don't becomes scattered by losing small or minor parts [Cartwright,R]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
Essentialism says some of a thing's properties are necessary, and could not be absent [Cartwright,R]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
The difficulty in essentialism is deciding the grounds for rating an attribute as essential [Cartwright,R]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is said to be unintelligible, because relative, if necessary truths are all analytic [Cartwright,R]
9. Objects / F. Identity among Objects / 3. Relative Identity
An act of ostension doesn't seem to need a 'sort' of thing, even of a very broad kind [Cartwright,R]
9. Objects / F. Identity among Objects / 4. Type Identity
A token isn't a unique occurrence, as the case of a word or a number shows [Cartwright,R]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins]
13. Knowledge Criteria / C. External Justification / 1. External Justification
Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
The physical effect of world on brain explains the concepts we possess [Jenkins]
Grounded concepts are trustworthy maps of the world [Jenkins]
19. Language / A. Nature of Meaning / 1. Meaning
For any statement, there is no one meaning which any sentence asserting it must have [Cartwright,R]
People don't assert the meaning of the words they utter [Cartwright,R]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins]
19. Language / C. Assigning Meanings / 2. Semantics
Success semantics explains representation in terms of success in action [Jenkins]
19. Language / D. Propositions / 1. Propositions
We can pull apart assertion from utterance, and the action, the event and the subject-matter for each [Cartwright,R]
'It's raining' makes a different assertion on different occasions, but its meaning remains the same [Cartwright,R]
19. Language / D. Propositions / 4. Mental Propositions
We can attribute 'true' and 'false' to whatever it was that was said [Cartwright,R]
To assert that p, it is neither necessary nor sufficient to utter some particular words [Cartwright,R]
19. Language / E. Analyticity / 1. Analytic Propositions
'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins]
19. Language / F. Communication / 2. Assertion
Assertions, unlike sentence meanings, can be accurate, probable, exaggerated, false.... [Cartwright,R]