Combining Texts

All the ideas for 'Introduction to 'Properties'', 'works' and 'Cardinality, Counting and Equinumerosity'

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16 ideas

1. Philosophy / H. Continental Philosophy / 1. Continental Philosophy
Some continental philosophers are relativists - Baudrillard, for example [Baudrillard, by Critchley]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
Ockham's Razor is the principle that we need reasons to believe in entities [Mellor/Oliver]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
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
A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck]
Counting is the assignment of successively larger cardinal numbers to collections [Heck]
Is counting basically mindless, and independent of the cardinality involved? [Heck]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / e. Counting by correlation
Understanding 'just as many' needn't involve grasping one-one correspondence [Heck]
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
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
Children can use numbers, without a concept of them as countable objects [Heck]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Equinumerosity is not the same concept as one-one correspondence [Heck]
We can understand cardinality without the idea of one-one correspondence [Heck]
8. Modes of Existence / B. Properties / 6. Categorical Properties
Properties are respects in which particular objects may be alike or differ [Mellor/Oliver]
8. Modes of Existence / B. Properties / 12. Denial of Properties
Nominalists ask why we should postulate properties at all [Mellor/Oliver]
18. Thought / E. Abstraction / 5. Abstracta by Negation
Abstractions lack causes, effects and spatio-temporal locations [Mellor/Oliver]