### All the ideas for Roy Bhaskar, Zeno (Elea) and Leslie H. Tharp

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24 ideas

###### 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
 10775 The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp]
###### 5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
 10766 Logic is either for demonstration, or for characterizing structures [Tharp]
###### 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
 10767 Elementary logic is complete, but cannot capture mathematics [Tharp]
###### 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
 10769 Second-order logic isn't provable, but will express set-theory and classic problems [Tharp]
###### 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
 10762 In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp]
###### 5. Theory of Logic / G. Quantification / 2. Domain of Quantification
 10776 The main quantifiers extend 'and' and 'or' to infinite domains [Tharp]
###### 5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification
 10774 There are at least five unorthodox quantifiers that could be used [Tharp]
###### 5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
 10773 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp]
 10777 Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
###### 5. Theory of Logic / K. Features of Logics / 3. Soundness
 10765 Soundness would seem to be an essential requirement of a proof procedure [Tharp]
###### 5. Theory of Logic / K. Features of Logics / 4. Completeness
 10763 Completeness and compactness together give axiomatizability [Tharp]
###### 5. Theory of Logic / K. Features of Logics / 5. Incompleteness
 10770 If completeness fails there is no algorithm to list the valid formulas [Tharp]
###### 5. Theory of Logic / K. Features of Logics / 6. Compactness
 10771 Compactness is important for major theories which have infinitely many axioms [Tharp]
 10772 Compactness blocks infinite expansion, and admits non-standard models [Tharp]
###### 5. Theory of Logic / K. Features of Logics / 8. Enumerability
 10764 A complete logic has an effective enumeration of the valid formulas [Tharp]
 10768 Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp]
###### 5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
 1507 We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea]
 5109 The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle]
###### 5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
 1512 Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea]
###### 5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
 1508 Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea]
###### 9. Objects / D. Essence of Objects / 5. Essence as Kind
 15143 Kind essences are the categorical bases of a thing's causal powers [Bhaskar, by Chakravartty]
###### 26. Natural Theory / A. Speculations on Nature / 1. Nature
 454 If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea]
###### 27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
 455 That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea]
###### 27. Natural Reality / C. Space / 5. Relational Space
 1511 If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius]