Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Clitophon' and 'Aristotle on Matter'

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18 ideas

2. Reason / D. Definition / 3. Types of Definition
A decent modern definition should always imply a semantics [Hacking]
2. Reason / D. Definition / 4. Real Definition
Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K]
2. Reason / D. Definition / 5. Genus and Differentia
Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
Gentzen's Cut Rule (or transitivity of deduction) is 'If A |- B and B |- C, then A |- C' [Hacking]
Only Cut reduces complexity, so logic is constructive without it, and it can be dispensed with [Hacking]
'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
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
First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
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
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
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
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
If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K]
Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K]
22. Metaethics / B. Value / 2. Values / f. Altruism
The just man does not harm his enemies, but benefits everyone [Plato]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
The components of abstract definitions could play the same role as matter for physical objects [Fine,K]