Combining Philosophers

All the ideas for Hermarchus, Cheryl Misak and Giuseppe Peano

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21 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Modern pragmatism sees objectivity as possible, despite its gradual evolution [Misak]
3. Truth / E. Pragmatic Truth / 1. Pragmatic Truth
Truth makes disagreements matter, or worth settling [Misak]
For pragmatists the loftiest idea of truth is just a feature of what remains forever assertible [Misak]
'True' is used for emphasis, clarity, assertion, comparison, objectivity, meaning, negation, consequence... [Misak]
'That's true' doesn't just refer back to a sentence, but implies sustained evidence for it [Misak]
Truth isn't a grand elusive property, if it is just the aim of our assertions and inquiries [Misak]
Truth is proper assertion, but that has varying standards [Misak]
3. Truth / F. Semantic Truth / 1. Tarski's Truth / a. Tarski's truth definition
Disquotation is bivalent [Misak]
Disquotations says truth is assertion, and assertion proclaims truth - but what is 'assertion'? [Misak]
Disquotationalism resembles a telephone directory [Misak]
3. Truth / H. Deflationary Truth / 2. Deflationary Truth
Deflating the correspondence theory doesn't entail deflating all the other theories [Misak]
Deflationism isn't a theory of truth, but an account of its role in natural language [Misak]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Numbers have been defined in terms of 'successors' to the concept of 'zero' [Peano, by Blackburn]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
All models of Peano axioms are isomorphic, so the models all seem equally good for natural numbers [Cartwright,R on Peano]
PA concerns any entities which satisfy the axioms [Peano, by Bostock]
Peano axioms not only support arithmetic, but are also fairly obvious [Peano, by Russell]
0 is a non-successor number, all successors are numbers, successors can't duplicate, if P(n) and P(n+1) then P(all-n) [Peano, by Flew]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
We can add Reflexion Principles to Peano Arithmetic, which assert its consistency or soundness [Halbach on Peano]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
Arithmetic can have even simpler logical premises than the Peano Axioms [Russell on Peano]
7. Existence / D. Theories of Reality / 4. Anti-realism
The anti-realism debate concerns whether indefeasibility is a plausible aim of inquiry [Misak]
25. Social Practice / F. Life Issues / 6. Animal Rights
Animals are dangerous and nourishing, and can't form contracts of justice [Hermarchus, by Sedley]