Combining Texts

All the ideas for 'Logical Consequence', 'Elements of Intuitionism' and 'Community'

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19 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690 Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691 Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689 A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696 A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / c. Potential infinite
15938 Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10692 Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
15939 For intuitionists it is constructed proofs (which take time) which make statements true [Dummett]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / a. Sovereignty
23418 Liberal state legitimacy is based on a belief in justice, not in some conception of the good life [Kymlicka]
24. Political Theory / B. Nature of a State / 5. Culture
23414 Liberals say state intervention in culture restricts people's autonomy [Kymlicka]
24. Political Theory / D. Ideologies / 6. Liberalism / e. Liberal community
23410 Modern liberals see a community as simply a society which respects freedom and equality [Kymlicka]
24. Political Theory / D. Ideologies / 7. Communitarianism / a. Communitarianism
23409 Community can focus on class or citizenship or ethnicity or culture [Kymlicka]
24. Political Theory / D. Ideologies / 7. Communitarianism / b. Against communitarianism
23419 Communitarianism struggles with excluded marginalised groups [Kymlicka]
23413 Feminism has shown that social roles are far from fixed (as communitarians tend to see them) [Kymlicka]
23415 Participation aids the quest for the good life, but why should that be a state activity? [Kymlicka]
25. Social Practice / D. Justice / 1. Basis of justice
23411 Communitarians see justice as primarily a community matter, rather than a principle [Kymlicka]
23412 Justice resolves conflicts, but may also provoke them [Kymlicka]