Combining Texts

All the ideas for 'reports', 'An Inquiry into Meaning and Truth' and 'First-Order Logic'

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24 ideas

3. Truth / A. Truth Problems / 7. Falsehood
16477 Asserting not-p is saying p is false [Russell]
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 / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
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]
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 / e. or
16480 A disjunction expresses indecision [Russell]
16479 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [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]
16483 Disjunction may also arise in practice if there is imperfect memory. [Russell]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
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 / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
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]
25. Social Practice / D. Justice / 3. Punishment / c. Deterrence of crime
1743 The greatest deterrence for injustice is if uninjured parties feel as much indignation as those who are injured [Solon, by Diog. Laertius]