Combining Texts

All the ideas for 'Philosophical Explanations', 'works' and 'What is Logic?'

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20 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
13833 'Thinning' ('dilution') is the key difference between deduction (which allows it) and induction [Hacking]
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]
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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
13445 Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
16774 Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau]
11. Knowledge Aims / A. Knowledge / 4. Belief / c. Aim of beliefs
3570 Maybe knowledge is belief which 'tracks' the truth [Nozick, by Williams,M]
12. Knowledge Sources / B. Perception / 3. Representation
7400 Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck]
13. Knowledge Criteria / C. External Justification / 4. Tracking the Facts
2748 A true belief isn't knowledge if it would be believed even if false. It should 'track the truth' [Nozick, by Dancy,J]
16. Persons / F. Free Will / 4. For Free Will
4310 We have inner awareness of our freedom [Descartes]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
6553 Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19676 Nature is devoid of thought [Descartes, by Meillassoux]
26. Natural Theory / A. Speculations on Nature / 7. Later Matter Theories / c. Matter as extension
6518 Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes]