Combining Texts

All the ideas for 'Are Freedom and Equality Compatible?', 'Sentences' and 'The Philosophy of Mathematics'

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15 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
Intuitionists reject excluded middle, not for a third value, but for possibility of proof [Dummett]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
First-order logic concerns objects; second-order adds properties, kinds, relations and functions [Dummett]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths and inference are characterized either syntactically or semantically [Dummett]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
8. Modes of Existence / A. Relations / 1. Nature of Relations
The single imagined 'interval' between things only exists in the intellect [Auriol]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
The right-wing conception of freedom is based on the idea of self-ownership [Cohen,GA]
Plenty of people have self-ownership, but still lack autonomy [Cohen,GA]
25. Social Practice / C. Rights / 4. Property rights
It is doubtful whether any private property was originally acquired legitimately [Cohen,GA]
It is plausible that no one has an initial right to own land and natural resources [Cohen,GA]
Every thing which is now private started out as unowned [Cohen,GA]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol]
28. God / A. Divine Nature / 4. Divine Contradictions
God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol]