Combining Texts

All the ideas for 'Logical Consequence', 'Letters to Frege' and 'Aristotle and Kant on the Source of Value'

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17 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]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
13365 Russell's Paradox is a stripped-down version of Cantor's Paradox [Priest,G on Russell]
10711 Russell's paradox means we cannot assume that every property is collectivizing [Potter on Russell]
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]
8. Modes of Existence / B. Properties / 11. Properties as Sets
9127 Russell refuted Frege's principle that there is a set for each property [Russell, by Sorensen]
18. Thought / C. Content / 6. Broad Content
7531 We don't assert private thoughts; the objects are part of what we assert [Russell]
22. Metaethics / B. Value / 1. Nature of Value / f. Ultimate value
18225 If we can't reason about value, we can reason about the unconditional source of value [Korsgaard]
18228 An end can't be an ultimate value just because it is useless! [Korsgaard]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
18224 Goodness is given either by a psychological state, or the attribution of a property [Korsgaard]
23. Ethics / C. Virtue Theory / 3. Virtues / g. Contemplation
18233 Contemplation is final because it is an activity which is not a process [Korsgaard]
18226 For Aristotle, contemplation consists purely of understanding [Korsgaard]