Combining Texts

All the ideas for 'fragments/reports', 'Ideas, Qualities and Corpuscles' and 'What is Logic?'

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19 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
13834 Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
13835 Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
15959 If the substantial form of brass implies its stability, how can it melt and remain brass? [Alexander,P]
9. Objects / C. Structure of Objects / 2. Hylomorphism / b. Form as principle
15956 The peripatetics treated forms and real qualities as independent of matter, and non-material [Alexander,P]
14. Science / D. Explanation / 2. Types of Explanation / k. Explanations by essence
15975 Can the qualities of a body be split into two groups, where the smaller explains the larger? [Alexander,P]
26. Natural Theory / A. Speculations on Nature / 2. Natural Purpose / a. Final purpose
15963 Science has been partly motivated by the belief that the universe is run by God's laws [Alexander,P]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
15951 Alchemists tried to separate out essences, which influenced later chemistry [Alexander,P]
27. Natural Reality / C. Space / 4. Substantival Space
15981 Absolute space either provides locations, or exists but lacks 'marks' for locations [Alexander,P]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]