Combining Texts

All the ideas for 'Logical Consequence', 'On the Introduction of Transfinite Numbers' and 'The Nature of Existence vol.2'

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23 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
10688 'Equivocation' is when terms do not mean the same thing in premises and conclusion [Beall/Restall]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
10690 Formal logic is invariant under permutations, or devoid of content, or gives the norms for thought [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 2. Types of Consequence
10691 Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10695 Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
10689 A step is a 'material consequence' if we need contents as well as form [Beall/Restall]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10696 A 'logical truth' (or 'tautology', or 'theorem') follows from empty premises [Beall/Restall]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10693 Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers
13489 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
12336 A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10692 Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / g. Von Neumann numbers
18179 For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy]
18180 Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann]
15925 Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine]
7. Existence / B. Change in Existence / 1. Nature of Change
15200 How could change consist of a conjunction of changeless facts? [McTaggart, by Le Poidevin]
14761 Change is not just having two different qualities at different points in some series [McTaggart]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
2608 For McTaggart time is seen either as fixed, or as relative to events [McTaggart, by Ayer]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
22936 A-series time positions are contradictory, and yet all events occupy all of them! [McTaggart, by Le Poidevin]
4231 Time involves change, only the A-series explains change, but it involves contradictions, so time is unreal [McTaggart, by Lowe]
27. Natural Reality / D. Time / 2. Passage of Time / a. Experience of time
8591 There could be no time if nothing changed [McTaggart]
27. Natural Reality / D. Time / 2. Passage of Time / d. Time series
22935 The B-series can be inferred from the A-series, but not the other way round [McTaggart, by Le Poidevin]
7802 A-series uses past, present and future; B-series uses 'before' and 'after' [McTaggart, by Girle]
4230 A-series expressions place things in time, and their truth varies; B-series is relative, and always true [McTaggart, by Lowe]
15199 The B-series must depend on the A-series, because change must be explained [McTaggart, by Le Poidevin]