Combining Texts

All the ideas for 'Logical Consequence', 'Letters to Frege' and 'Letters to Des Bosses'

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25 ideas

1. Philosophy / E. Nature of Metaphysics / 5. Metaphysics beyond Science
12780 We can grasp the wisdom of God a priori [Leibniz]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
12774 Without a substantial chain to link monads, they would just be coordinated dreams [Leibniz]
12782 Monads control nothing outside of themselves [Leibniz]
12777 Monads do not make a unity unless a substantial chain is added to them [Leibniz]
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]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
12778 There is active and passive power in the substantial chain and in the essence of a composite [Leibniz]
12783 Primitive force is what gives a composite its reality [Leibniz]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
12775 Things seem to be unified if we see duration, position, interaction and connection [Leibniz]
9. Objects / B. Unity of Objects / 2. Substance / a. Substance
12776 Every substance is alive [Leibniz]
9. Objects / D. Essence of Objects / 6. Essence as Unifier
12753 A substantial bond of powers is needed to unite composites, in addition to monads [Leibniz]
9. Objects / D. Essence of Objects / 12. Essential Parts
12781 A composite substance is a mere aggregate if its essence is just its parts [Leibniz]
10. Modality / B. Possibility / 1. Possibility
12779 There is a reason why not every possible thing exists [Leibniz]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
12785 Truth is mutually agreed perception [Leibniz]
18. Thought / C. Content / 6. Broad Content
7531 We don't assert private thoughts; the objects are part of what we assert [Russell]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
12784 Allow no more miracles than are necessary [Leibniz]