Combining Philosophers

All the ideas for Crawford L. Elder, Jos�� L. Zalabardo and H.L.A. Hart

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36 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10900 Logically true sentences are true in all structures [Zalabardo]
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
8. Modes of Existence / B. Properties / 1. Nature of Properties
13795 Properties only have identity in the context of their contraries [Elder]
9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay
13798 Maybe we should give up the statue [Elder]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
13797 The loss of an essential property means the end of an existence [Elder]
9. Objects / D. Essence of Objects / 9. Essence and Properties
13794 Essential properties by nature occur in clusters or packages [Elder]
13796 Essential properties are bound together, and would be lost together [Elder]
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 / C. Rights / 1. Basis of Rights
21004 Hart (against Bentham) says human rights are what motivate legal rights [Hart,HLA, by Sen]
25. Social Practice / D. Justice / 2. The Law / a. Legal system
20932 Positive law needs secondary 'rules of recognition' for their correct application [Hart,HLA, by Zimmermann,J]
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 / 2. The Law / d. Legal positivism
20931 Hart replaced positivism with the democratic requirement of the people's acceptance [Hart,HLA, by Zimmermann,J]
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]