Combining Texts

All the ideas for 'Perpetual Peace', 'The Philosophy of Mathematics' and 'Logicism Revisited'

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25 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
9193 ZF set theory has variables which range over sets, 'equals' and 'member', and extensionality [Dummett]
9194 The main alternative to ZF is one which includes looser classes as well as sets [Dummett]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
10061 The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
10065 Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
9195 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
9186 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
9187 Logical truths and inference are characterized either syntactically or semantically [Dummett]
10049 Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
10050 A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
9191 Ordinals seem more basic than cardinals, since we count objects in sequence [Dummett]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
10058 No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
9192 The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
10062 Formalism seems to exclude all creative, growing mathematics [Musgrave]
10063 Formalism is a bulwark of logical positivism [Musgrave]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
24. Political Theory / A. Basis of a State / 1. A People / b. The natural life
21075 The state of nature always involves the threat of war [Kant]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
20569 Kant made the social contract international and cosmopolitan [Kant, by Oksala]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / d. General will
21079 The a priori general will of a people shows what is right [Kant]
24. Political Theory / B. Nature of a State / 3. Constitutions
21077 Each nation should, from self-interest, join an international security constitution [Kant]
21078 A constitution must always be improved when necessary [Kant]
25. Social Practice / B. Equalities / 3. Legal equality
21076 Equality is where you cannot impose a legal obligation you yourself wouldn't endure [Kant]
25. Social Practice / C. Rights / 1. Basis of Rights
20570 There is now a growing universal community, and violations of rights are felt everywhere [Kant]
20571 There are political and inter-national rights, but also universal cosmopolitan rights [Kant]
25. Social Practice / E. Policies / 1. War / c. Combatants
21073 Hiring soldiers is to use them as instruments, ignoring their personal rights [Kant]
25. Social Practice / E. Policies / 1. War / e. Peace
21074 Some trust in the enemy is needed during wartime, or peace would be impossible [Kant]