Combining Philosophers

All the ideas for Oliver,A/Smiley,T, Anaximenes and Charles Parsons

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19 ideas

4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
9470 Modal logic is not an extensional language [Parsons,C]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14240 The empty set is something, not nothing! [Oliver/Smiley]
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13418 The old problems with the axiom of choice are probably better ascribed to the law of excluded middle [Parsons,C]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
9469 Substitutional existential quantifier may explain the existence of linguistic entities [Parsons,C]
9468 On the substitutional interpretation, '(∃x) Fx' is true iff a closed term 't' makes Ft true [Parsons,C]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17447 Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
18201 General principles can be obvious in mathematics, but bold speculations in empirical science [Parsons,C]
6. Mathematics / C. Sources of Mathematics / 8. Finitism
13419 If functions are transfinite objects, finitists can have no conception of them [Parsons,C]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems
13417 If a mathematical structure is rejected from a physical theory, it retains its mathematical status [Parsons,C]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
1497 For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius]