Combining Philosophers

All the ideas for Halbach,V/Leigh,G.E, Proclus and Alan Musgrave

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20 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
19125 If we define truth, we can eliminate it [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / b. Satisfaction and truth
19128 If a language cannot name all objects, then satisfaction must be used, instead of unary truth [Halbach/Leigh]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / c. Meta-language for truth
19120 Semantic theories need a powerful metalanguage, typically including set theory [Halbach/Leigh]
3. Truth / F. Semantic Truth / 2. Semantic Truth
19127 The T-sentences are deductively weak, and also not deductively conservative [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
19124 A natural theory of truth plays the role of reflection principles, establishing arithmetic's soundness [Halbach/Leigh]
19126 If deflationary truth is not explanatory, truth axioms should be 'conservative', proving nothing new [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 2. FS Truth Axioms
19129 The FS axioms use classical logical, but are not fully consistent [Halbach/Leigh]
3. Truth / G. Axiomatic Truth / 3. KF Truth Axioms
19130 KF is formulated in classical logic, but describes non-classical truth, which allows truth-value gluts [Halbach/Leigh]
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 / I. Semantics of Logic / 3. Logical Truth
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 / 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 / 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]
8. Modes of Existence / B. Properties / 12. Denial of Properties
19121 We can reduce properties to true formulas [Halbach/Leigh]
8. Modes of Existence / E. Nominalism / 1. Nominalism / c. Nominalism about abstracta
19122 Nominalists can reduce theories of properties or sets to harmless axiomatic truth theories [Halbach/Leigh]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
13165 Geometrical proofs do not show causes, as when we prove a triangle contains two right angles [Proclus]
18. Thought / E. Abstraction / 1. Abstract Thought
9569 The origin of geometry started in sensation, then moved to calculation, and then to reason [Proclus]
19. Language / A. Nature of Meaning / 5. Meaning as Verification
10060 Logical positivists adopted an If-thenist version of logicism about numbers [Musgrave]