Combining Texts

All the ideas for 'fragments/reports', 'Set Theory and Its Philosophy' and 'The Human Condition'

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42 ideas

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]
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]
10. Modality / B. Possibility / 7. Chance
20146 'Luck' is the unpredictable and inexplicable intersection of causal chains [Kekes]
20. Action / B. Preliminaries of Action / 1. Intention to Act / a. Nature of intentions
20169 An action may be intended under one description, but not under another [Kekes]
20. Action / C. Motives for Action / 2. Acting on Beliefs / a. Acting on beliefs
20149 To control our actions better, make them result from our attitudes, not from circumstances [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / c. Purpose of ethics
19738 Values are an attempt to achieve well-being by bringing contingencies under control [Kekes]
20145 Values help us to control life, by connecting it to what is stable and manageable [Kekes]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / g. Moral responsibility
20170 Responsibility is unprovoked foreseeable harm, against society, arising from vicious character [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / b. Rational ethics
20165 Reason and morality do not coincide; immorality can be reasonable, with an ideology [Kekes]
20171 Practical reason is not universal and impersonal, because it depends on what success is [Kekes]
20175 If morality has to be rational, then moral conflicts need us to be irrational and immoral [Kekes]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
20174 Relativists say all values are relative; pluralists concede much of that, but not 'human' values [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
20156 We are bound to regret some values we never aspired to [Kekes]
20150 There are far more values than we can pursue, so they are optional possibilities [Kekes]
20158 Innumerable values arise for us, from our humanity, our culture, and our individuality [Kekes]
20159 Cultural values are interpretations of humanity, conduct, institutions, and evaluations [Kekes]
20161 The big value problems are evil (humanity), disenchantment (cultures), and boredom (individuals) [Kekes]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
20151 Our attitudes include what possibilities we value, and also what is allowable, and unthinkable [Kekes]
20152 Unconditional commitments are our most basic convictions, saying what must never be done [Kekes]
20153 Doing the unthinkable damages ourselves, so it is more basic than any value [Kekes]
22. Metaethics / B. Value / 2. Values / j. Evil
20162 Evil isn't explained by nature, by monsters, by uncharacteristic actions, or by society [Kekes]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
20154 Control is the key to well-being [Kekes]
20157 Well-being needs correct attitudes and well-ordered commitments to local values [Kekes]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / a. Nature of virtue
467 A virtue is a combination of intelligence, strength and luck [Ion]
23. Ethics / F. Existentialism / 4. Boredom
20172 Boredom destroys our ability to evaluate [Kekes]
20173 Boredom is apathy and restlessness, yearning for something interesting [Kekes]
24. Political Theory / A. Basis of a State / 1. A People / c. A unified people
20155 Society is alienating if it lacks our values, and its values repel us [Kekes]
24. Political Theory / B. Nature of a State / 1. Purpose of a State
20164 The ideal of an ideology is embodied in a text, a role model, a law of history, a dream of the past... [Kekes]
20163 Ideologies have beliefs about reality, ideals, a gap with actuality, and a program [Kekes]
25. Social Practice / B. Equalities / 4. Economic equality
20148 Equal distribution is no good in a shortage, because there might be no one satisfied [Kekes]