Combining Philosophers

All the ideas for H.Putnam/P.Oppenheim, Oliver,A/Smiley,T and Avicenna (Abu Ibn Sina)

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15 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Understanding begins with the notion of being and essence [Avicenna]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
The empty set is something, not nothing! [Oliver/Smiley]
We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
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
The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
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
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 / g. Applying mathematics
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
Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
9. Objects / A. Existence of Objects / 5. Simples
The simple's whatness is its very self [Avicenna]
9. Objects / C. Structure of Objects / 3. Matter of an Object
The ultimate material of things has the unity of total formlessness [Avicenna]
9. Objects / D. Essence of Objects / 2. Types of Essence
An essence can either be universal (in the mind) or singular (in concrete particulars) [Avicenna, by Panaccio]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson]