Combining Texts

All the ideas for 'That Politics may be reduced to a Science', 'Constructibility and Mathematical Existence' and 'Putnam's Paradox'

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12 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
We could talk of open sentences, instead of sets [Chihara, by Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A consistent theory just needs one model; isomorphic versions will do too, and large domains provide those [Lewis]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro]
We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro]
7. Existence / D. Theories of Reality / 4. Anti-realism
Anti-realists see the world as imaginary, or lacking joints, or beyond reference, or beyond truth [Lewis]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
A gerrymandered mereological sum can be a mess, but still have natural joints [Lewis]
19. Language / B. Reference / 3. Direct Reference / b. Causal reference
Causal theories of reference make errors in reference easy [Lewis]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
Descriptive theories remain part of the theory of reference (with seven mild modifications) [Lewis]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
Friendship without community spirit misses out on the main part of virtue [Hume]
24. Political Theory / B. Nature of a State / 3. Constitutions
It would be absurd if even a free constitution did not impose restraints, for the public good [Hume]
24. Political Theory / C. Ruling a State / 2. Leaders / d. Elites
Nobility either share in the power of the whole, or they compose the power of the whole [Hume]