Combining Texts

All the ideas for 'works (fragments)', 'The Art of the Infinite' and 'What is the Source of Knowledge of Modal Truths?'

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26 ideas

2. Reason / D. Definition / 6. Definition by Essence
A definition of a circle will show what it is, and show its generating principle [Lowe]
Defining an ellipse by conic sections reveals necessities, but not the essence of an ellipse [Lowe]
An essence is what an entity is, revealed by a real definition; this is not an entity in its own right [Lowe]
2. Reason / D. Definition / 11. Ostensive Definition
Simple things like 'red' can be given real ostensive definitions [Lowe]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
The essence of lumps and statues shows that two objects coincide but are numerically distinct [Lowe]
The essence of a bronze statue shows that it could be made of different bronze [Lowe]
9. Objects / D. Essence of Objects / 4. Essence as Definition
Grasping an essence is just grasping a real definition [Lowe]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
Explanation can't give an account of essence, because it is too multi-faceted [Lowe]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
If we must know some entity to know an essence, we lack a faculty to do that [Lowe]
10. Modality / A. Necessity / 3. Types of Necessity
Logical necessities, based on laws of logic, are a proper sub-class of metaphysical necessities [Lowe]
10. Modality / A. Necessity / 5. Metaphysical Necessity
'Metaphysical' necessity is absolute and objective - the strongest kind of necessity [Lowe]
10. Modality / B. Possibility / 2. Epistemic possibility
'Epistemic' necessity is better called 'certainty' [Lowe]
10. Modality / C. Sources of Modality / 6. Necessity from Essence
If an essence implies p, then p is an essential truth, and hence metaphysically necessary [Lowe]
Metaphysical necessity is either an essential truth, or rests on essential truths [Lowe]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
We could give up possible worlds if we based necessity on essences [Lowe]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
'Intuitions' are just unreliable 'hunches'; over centuries intuitions change enormously [Lowe]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
18. Thought / D. Concepts / 1. Concepts / a. Nature of concepts
A concept is a way of thinking of things or kinds, whether or not they exist [Lowe]
19. Language / B. Reference / 3. Direct Reference / a. Direct reference
Direct reference doesn't seem to require that thinkers know what it is they are thinking about [Lowe]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
H2O isn't necessary, because different laws of nature might affect how O and H combine [Lowe]