Combining Texts

All the ideas for 'What is Logic?st1=Ian Hacking', 'Letters to Russell' and 'An Inquiry into Meaning and Truth'

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29 ideas

2. Reason / D. Definition / 3. Types of Definition
13838 A decent modern definition should always imply a semantics [Hacking]
3. Truth / A. Truth Problems / 7. Falsehood
16477 Asserting not-p is saying p is false [Russell]
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]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
16484 There are four experiences that lead us to talk of 'some' things [Russell]
5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
16486 The physical world doesn't need logic, but the mental world does [Russell]
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 / D. Assumptions for Logic / 2. Excluded Middle
2947 Questions wouldn't lead anywhere without the law of excluded middle [Russell]
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 / 2. Logical Connectives / e. or
16479 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell]
16480 A disjunction expresses indecision [Russell]
16483 Disjunction may also arise in practice if there is imperfect memory. [Russell]
16481 'Or' expresses a mental state, not something about the world [Russell]
16487 Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell]
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]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / c. Grelling's paradox
16475 A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
18253 I wish to go straight from cardinals to reals (as ratios), leaving out the rationals [Frege]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
18166 The loss of my Rule V seems to make foundations for arithmetic impossible [Frege]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
18269 Logical objects are extensions of concepts, or ranges of values of functions [Frege]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
16482 All our knowledge (if verbal) is general, because all sentences contain general words [Russell]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / a. Naïve realism
4758 Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
16476 For simple words, a single experience can show that they are true [Russell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
16485 Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell]
20. Action / C. Motives for Action / 3. Acting on Reason / b. Intellectualism
16478 A mother cat is paralysed if equidistant between two needy kittens [Russell]