Combining Philosophers

All the ideas for Xenophanes, Melvin Fitting and R Kaplan / E Kaplan

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19 ideas

4. Formal Logic / E. Nonclassical Logics / 8. Intensional Logic
15375 If terms change their designations in different states, they are functions from states to objects [Fitting]
15376 Intensional logic adds a second type of quantification, over intensional objects, or individual concepts [Fitting]
4. Formal Logic / E. Nonclassical Logics / 9. Awareness Logic
15378 Awareness logic adds the restriction of an awareness function to epistemic logic [Fitting]
4. Formal Logic / E. Nonclassical Logics / 10. Justification Logics
15379 Justication logics make explicit the reasons for mathematical truth in proofs [Fitting]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
15717 Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
11026 Classical logic is deliberately extensional, in order to model mathematics [Fitting]
5. Theory of Logic / F. Referring in Logic / 3. Property (λ-) Abstraction
11028 λ-abstraction disambiguates the scope of modal operators [Fitting]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
15712 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
15711 The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
15714 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
15715 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
15377 Definite descriptions pick out different objects in different possible worlds [Fitting]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
411 If we succeed in speaking the truth, we cannot know we have done it [Xenophanes]
13. Knowledge Criteria / E. Relativism / 1. Relativism
412 If God had not created honey, men would say figs are sweeter [Xenophanes]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / e. The One
1640 The basic Eleatic belief was that all things are one [Xenophanes, by Plato]
28. God / A. Divine Nature / 2. Divine Nature
3055 Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius]
28. God / C. Attitudes to God / 5. Atheism
408 Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes]
407 Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes]