Combining Texts

All the ideas for 'On the Philosophy of Logic', 'talk' and 'On the Introduction of Transfinite Numbers'

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16 ideas

2. Reason / A. Nature of Reason / 1. On Reason
We reach 'reflective equilibrium' when intuitions and theory completely align [Fisher]
4. Formal Logic / E. Nonclassical Logics / 3. Many-Valued Logic
Three-valued logic says excluded middle and non-contradition are not tautologies [Fisher]
4. Formal Logic / E. Nonclassical Logics / 4. Fuzzy Logic
Fuzzy logic has many truth values, ranging in fractions from 0 to 1 [Fisher]
5. Theory of Logic / A. Overview of Logic / 6. Classical Logic
Classical logic is: excluded middle, non-contradiction, contradictions imply all, disjunctive syllogism [Fisher]
5. Theory of Logic / C. Ontology of Logic / 2. Platonism in Logic
Logic formalizes how we should reason, but it shouldn't determine whether we are realists [Fisher]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
7. Existence / D. Theories of Reality / 10. Vagueness / g. Degrees of vagueness
We could make our intuitions about heaps precise with a million-valued logic [Fisher]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vagueness can involve components (like baldness), or not (like boredom) [Fisher]
10. Modality / B. Possibility / 1. Possibility
We can't explain 'possibility' in terms of 'possible' worlds [Fisher]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
If all truths are implied by a falsehood, then not-p might imply both q and not-q [Fisher]
10. Modality / B. Possibility / 8. Conditionals / d. Non-truthfunction conditionals
In relevance logic, conditionals help information to flow from antecedent to consequent [Fisher]
14. Science / C. Induction / 3. Limits of Induction
Maybe induction is only reliable IF reality is stable [Mitchell,A]