Combining Texts

All the ideas for 'Precis of 'Limits of Abstraction'', 'Law,Liberty and Morality' and 'Set Theory and Its Philosophy'

expand these ideas     |    start again     |     specify just one area for these texts

28 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
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
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 / 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]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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 / 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]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
22. Metaethics / C. The Good / 1. Goodness / g. Consequentialism
23529 Conduct is not isolated from its effect on the moral code [Hart,HLA]
24. Political Theory / D. Ideologies / 5. Democracy / e. Democratic minorities
23530 The great danger of democracy is that the oppression of the minority becomes unobjectionable [Hart,HLA]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
23522 In an organised society all actions have some effect on other people [Hart,HLA]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
23528 The value of liberty allows freedom of action, even if that distresses other people [Hart,HLA]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
23523 The principle of legality requires crimes to be precisely defined in advance of any action [Hart,HLA]
23524 Some private moral issues are no concern of the law [Hart,HLA]
23521 Do morals influence law? Is morality an aspect of law? Can law be morally criticised? [Hart,HLA]
23525 Is the enforcement of morality morally justifiable? [Hart,HLA]
23526 Modern law still suppresses practices seen as immoral, and yet harmless [Hart,HLA]
25. Social Practice / D. Justice / 3. Punishment / b. Retribution for crime
23527 Moral wickedness of an offence is always relevant to the degree of punishment [Hart,HLA]