Combining Texts

All the ideas for 'New system of communication of substances', 'Which Logic is the Right Logic?' and 'Summa quaestionum super Sententias'

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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
10777 Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp]
10773 The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
16659 Relations do not add anything to reality, though they are real aspects of the world [Olivi]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
13168 My formal unifying atoms are substantial forms, which are forces like appetites [Leibniz]
13169 I call Aristotle's entelechies 'primitive forces', which originate activity [Leibniz]
9. Objects / A. Existence of Objects / 5. Simples
13170 The analysis of things leads to atoms of substance, which found both composition and action [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / c. Types of substance
13171 Substance must necessarily involve progress and change [Leibniz]
9. Objects / C. Structure of Objects / 4. Quantity of an Object
16673 Quantity just adds union and location to the extension of parts [Olivi]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
13167 We need the metaphysical notion of force to explain mechanics, and not just extended mass [Leibniz]
27. Natural Reality / G. Biology / 5. Species
16663 Things are limited by the species to certain modes of being [Olivi]