Combining Texts

All the ideas for 'An Inquiry into Meaning and Truth', 'Leibniz' and 'Cardinality, Counting and Equinumerosity'

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28 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 / 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 / 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 / a. Numbers
17453 The meaning of a number isn't just the numerals leading up to it [Heck]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / f. Cardinal numbers
17457 A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
17448 In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
17455 Is counting basically mindless, and independent of the cardinality involved? [Heck]
17456 Counting is the assignment of successively larger cardinal numbers to collections [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
17450 Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
17451 We can know 'just as many' without the concepts of equinumerosity or numbers [Heck]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17459 Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
17454 Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
17458 Equinumerosity is not the same concept as one-one correspondence [Heck]
17449 We can understand cardinality without the idea of one-one correspondence [Heck]
10. Modality / B. Possibility / 1. Possibility
19378 Early modern possibility is what occurs sometime; for Leibniz, it is what is not contradictory [Arthur,R]
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]
17. Mind and Body / A. Mind-Body Dualism / 4. Occasionalism
19380 Occasionalism contradicts the Eucharist, which needs genuine changes of substance [Arthur,R]
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]