Combining Texts

All the ideas for 'works', 'Set Theory and Its Philosophy' and 'Real Essence'

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40 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
19693 There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb]
2. Reason / A. Nature of Reason / 2. Logos
1575 For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle]
2. Reason / A. Nature of Reason / 4. Aims of Reason
1589 Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle]
2. Reason / D. Definition / 4. Real Definition
8200 Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine]
16030 'Nominal' definitions identify things, but fail to give their essence [Jones,J-E]
2. Reason / D. Definition / 5. Genus and Differentia
4385 Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10702 Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10713 Usually the only reason given for accepting the empty set is convenience [Potter]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13044 Infinity: There is at least one limit level [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10708 Nowadays we derive our conception of collections from the dependence between them [Potter]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13546 The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter]
4. Formal Logic / G. Formal Mereology / 1. Mereology
13282 Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki]
10707 Mereology elides the distinction between the cards in a pack and the suits [Potter]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10704 We can formalize second-order formation rules, but not inference rules [Potter]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4730 For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
5. Theory of Logic / H. Proof Systems / 3. Proof from Assumptions
10703 Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
10712 If set theory didn't found mathematics, it is still needed to count infinite sets [Potter]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17882 It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
8. Modes of Existence / A. Relations / 4. Formal Relations / a. Types of relation
13043 A relation is a set consisting entirely of ordered pairs [Potter]
9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
13042 If dependence is well-founded, with no infinite backward chains, this implies substances [Potter]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
13276 The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / d. Form as unifier
13277 The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13041 Collections have fixed members, but fusions can be carved in innumerable ways [Potter]
10. Modality / A. Necessity / 1. Types of Modality
10709 Priority is a modality, arising from collections and members [Potter]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
5991 For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
11239 The notion of a priori truth is absent in Aristotle [Aristotle, by Politis]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
23312 Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
16111 Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML]
14. Science / B. Scientific Theories / 1. Scientific Theory
16971 Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik]
14. Science / D. Explanation / 1. Explanation / a. Explanation
11243 Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
3320 Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
12000 Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung]
18. Thought / A. Modes of Thought / 5. Rationality / c. Animal rationality
23300 Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji]
19. Language / E. Analyticity / 2. Analytic Truths
11240 The notion of analytic truth is absent in Aristotle [Aristotle, by Politis]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
6559 Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
11150 It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle]
25. Social Practice / E. Policies / 5. Education / b. Education principles
3037 Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
8660 There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
12058 Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
22729 The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus]