Combining Texts

All the ideas for 'On Sufficient Reason', 'works' and 'Higher-Order Logic'

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29 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / a. Philosophy as worldly
23027 Ideals and metaphysics are practical, not imaginative or speculative [Green,TH, by Muirhead]
2. Reason / B. Laws of Thought / 1. Laws of Thought
19404 Necessities rest on contradiction, and contingencies on sufficient reason [Leibniz]
3. Truth / D. Coherence Truth / 1. Coherence Truth
23030 Truth is a relation to a whole of organised knowledge in the collection of rational minds [Green,TH, by Muirhead]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
23044 All knowledge rests on a fundamental unity between the knower and what is known [Green,TH, by Muirhead]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
23034 The ultimate test for truth is the systematic interdependence in nature [Green,TH, by Muirhead]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
23032 What is distinctive of human life is the desire for self-improvement [Green,TH, by Muirhead]
23. Ethics / A. Egoism / 2. Hedonism
23033 Hedonism offers no satisfaction, because what we desire is self-betterment [Green,TH, by Muirhead]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
23045 Politics is compromises, which seem supported by a social contract, but express the will of no one [Green,TH]
24. Political Theory / B. Nature of a State / 4. Citizenship
23050 The ideal is a society in which all citizens are ladies and gentlemen [Green,TH]
23052 Enfranchisement is an end in itself; it makes a person moral, and gives a basis for respect [Green,TH]
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
23036 The good is identified by the capacities of its participants [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
23039 A true state is only unified and stabilised by acknowledging individuality [Green,TH, by Muirhead]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
23038 People only develop their personality through co-operation with the social whole [Green,TH, by Muirhead]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
23040 If something develops, its true nature is embodied in its end [Green,TH]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
19403 Each of the infinite possible worlds has its own laws, and the individuals contain those laws [Leibniz]
28. God / A. Divine Nature / 1. God
23031 God is the ideal end of the mature mind's final development [Green,TH]
28. God / C. Attitudes to God / 4. God Reflects Humanity
23041 God is the realisation of the possibilities of each man's self [Green,TH]