Combining Texts

All the ideas for 'Logicism Revisited', 'Of Miracles' and 'Computing Machinery and Intelligence'

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11 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
The If-thenist view only seems to work for the axiomatised portions of mathematics [Musgrave]
Perhaps If-thenism survives in mathematics if we stick to first-order logic [Musgrave]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
Logical truths may contain non-logical notions, as in 'all men are men' [Musgrave]
A statement is logically true if it comes out true in all interpretations in all (non-empty) domains [Musgrave]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
No two numbers having the same successor relies on the Axiom of Infinity [Musgrave]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
Formalism seems to exclude all creative, growing mathematics [Musgrave]
Formalism is a bulwark of logical positivism [Musgrave]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / b. Turing Machines
The Turing Machine is the best idea yet about how the mind works [Fodor on Turing]
18. Thought / B. Mechanics of Thought / 6. Artificial Thought / c. Turing Test
In 50 years computers will successfully imitate humans with a 70% success rate [Turing]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
It can't be more rational to believe in natural laws than miracles if the laws are not rational [Ishaq on Hume]