Combining Texts

All the ideas for 'fragments/reports', 'Value Theory' and 'Principles of Arithmetic, by a new method'

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20 ideas

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]
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 / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
To avoid misunderstandings supervenience is often expressed negatively: no A-change without B-change [Orsi]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
By nature people are close to one another, but culture drives them apart [Hippias]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Rather than requiring an action, a reason may 'entice' us, or be 'eligible', or 'justify' it [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / a. Nature of value
Value-maker concepts (such as courageous or elegant) simultaneously describe and evaluate [Orsi]
The '-able' concepts (like enviable) say this thing deserves a particular response [Orsi]
Final value is favoured for its own sake, and personal value for someone's sake [Orsi]
Things are only valuable if something makes it valuable, and we can ask for the reason [Orsi]
A complex value is not just the sum of the values of the parts [Orsi]
Trichotomy Thesis: comparable values must be better, worse or the same [Orsi]
The Fitting Attitude view says values are fitting or reasonable, and values are just byproducts [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / c. Objective value
Values from reasons has the 'wrong kind of reason' problem - admiration arising from fear [Orsi]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
A thing may have final value, which is still derived from other values, or from relations [Orsi]
22. Metaethics / B. Value / 2. Values / a. Normativity
Truths about value entail normative truths about actions or attitudes [Orsi]
The Buck-Passing view of normative values says other properties are reasons for the value [Orsi]
Values can be normative in the Fitting Attitude account, where 'good' means fitting favouring [Orsi]