Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Letters to Paul Pellison-Fontinier' and 'Fourfold Root of Princ of Sufficient Reason'

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21 ideas

2. Reason / B. Laws of Thought / 2. Sufficient Reason
21918 Sufficient Reason can't be proved, because all proof presupposes it [Schopenhauer, by Lewis,PB]
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]
7. Existence / E. Categories / 1. Categories
21920 No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB]
10. Modality / A. Necessity / 3. Types of Necessity
21362 Necessity is physical, logical, mathematical or moral [Schopenhauer, by Janaway]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
21361 For Schopenhauer, material things would not exist without the mind [Schopenhauer, by Janaway]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
21919 Object for a subject and representation are the same thing [Schopenhauer]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
21917 The four explanations: objects by causes, concepts by ground, maths by spacetime, ethics by motive [Schopenhauer, by Lewis,PB]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
21921 Concepts are abstracted from perceptions [Schopenhauer, by Lewis,PB]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
21363 Motivation is causality seen from within [Schopenhauer]
27. Natural Reality / A. Classical Physics / 1. Mechanics / c. Forces
12719 Clearly, force is that from which action follows, when unimpeded [Leibniz]
27. Natural Reality / D. Time / 1. Nature of Time / i. Denying time
12720 Time doesn't exist, since its parts don't coexist [Leibniz]