Combining Texts

All the ideas for 'Attacks (frags)', 'Logical Consequence' and 'Schopenhauer'

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17 ideas

4. Formal Logic / A. Syllogistic Logic / 2. Syllogistic Logic
'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
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
Logical consequence needs either proofs, or absence of counterexamples [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
Logical consequence is either necessary truth preservation, or preservation based on interpretation [Beall/Restall]
5. Theory of Logic / B. Logical Consequence / 8. Material Implication
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
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
Models are mathematical structures which interpret the non-logical primitives [Beall/Restall]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea]
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')
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
Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Hilbert proofs have simple rules and complex axioms, and natural deduction is the opposite [Beall/Restall]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
26. Natural Theory / A. Speculations on Nature / 1. Nature
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
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
If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius]