Combining Texts

All the ideas for 'Mathematical Methods in Philosophy', 'Justice: What's the right thing to do?' and 'Set Theory'

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39 ideas

3. Truth / A. Truth Problems / 3. Value of Truth
21032 Speak truth only to those who deserve the truth [Sandel]
21033 Careful evasions of truth at least show respect for it [Sandel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13030 Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / c. Axiom of Pairing II
13032 Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
13033 Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13037 Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13038 Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / h. Axiom of Replacement VII
13034 Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / i. Axiom of Foundation VIII
13039 Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13036 Choice: ∀A ∃R (R well-orders A) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / k. Axiom of Existence
13029 Set Existence: ∃x (x = x) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13031 Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
13040 Constructibility: V = L (all sets are constructible) [Kunen]
5. Theory of Logic / A. Overview of Logic / 9. Philosophical Logic
18739 Three stages of philosophical logic: syntactic (1905-55), possible worlds (1963-85), widening (1990-) [Horsten/Pettigrew]
5. Theory of Logic / E. Structures of Logic / 1. Logical Form
18741 Logical formalization makes concepts precise, and also shows their interrelation [Horsten/Pettigrew]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
18744 Models are sets with functions and relations, and truth built up from the components [Horsten/Pettigrew]
7. Existence / A. Nature of Existence / 1. Nature of Existence
18740 If 'exist' doesn't express a property, we can hardly ask for its essence [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
18745 A Tarskian model can be seen as a possible state of affairs [Horsten/Pettigrew]
18747 The 'spheres model' was added to possible worlds, to cope with counterfactuals [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
18748 Epistemic logic introduced impossible worlds [Horsten/Pettigrew]
10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds
18746 Possible worlds models contain sets of possible worlds; this is a large metaphysical commitment [Horsten/Pettigrew]
18750 Using possible worlds for knowledge and morality may be a step too far [Horsten/Pettigrew]
23. Ethics / B. Contract Ethics / 1. Contractarianism
21036 Not all deals are fair deals [Sandel]
21038 Does consent create the obligation, or must there be some benefit? [Sandel]
21039 Moral contracts involve both consent and reciprocity; making the deal, and keeping it [Sandel]
23. Ethics / B. Contract Ethics / 2. Golden Rule
21030 The categorical imperative is not the Golden Rule, which concerns contingent desires [Sandel]
23. Ethics / D. Deontological Ethics / 5. Persons as Ends
21031 Man cannot dispose of himself, because he is not a thing to be owned [Sandel]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
21035 Just visiting (and using roads) is hardly ratifying the Constitution [Sandel]
24. Political Theory / B. Nature of a State / 3. Constitutions
21037 A ratified constitution may not be a just constitution [Sandel]
21034 A just constitution harmonises the different freedoms [Sandel]
24. Political Theory / D. Ideologies / 6. Liberalism / d. Liberal freedom
21049 Liberal freedom was a response to assigned destinies like caste and class [Sandel]
25. Social Practice / B. Equalities / 4. Economic equality
21040 Libertarians just want formal equality in a free market; the meritocratic view wants fair equality [Sandel]
25. Social Practice / D. Justice / 1. Basis of justice
21028 We can approach justice through welfare, or freedom, or virtue [Sandel]
21027 Justice concerns how a society distributes what it prizes - wealth, rights, power and honours [Sandel]
21042 Should we redress wrongs done by a previous generation? [Sandel]
21043 Distributive justice concern deserts, as well as who gets what [Sandel]
21052 Justice is about how we value things, and not just about distributions [Sandel]
21048 Work is not fair if it is negotiated, even in a fair situation, but if it suits the nature of the worker [Sandel]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / b. Limited purposes
21045 Teleological thinking is essential for social and political issues [Sandel]