Combining Texts

All the ideas for 'Good and Evil', 'An Introduction to Modal Logic' and 'Cardinality, Counting and Equinumerosity'

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16 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
A 'value-assignment' (V) is when to each variable in the set V assigns either the value 1 or the value 0 [Hughes/Cresswell]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / d. Basic theorems of PL
The Law of Transposition says (P→Q) → (¬Q→¬P) [Hughes/Cresswell]
4. Formal Logic / B. Propositional Logic PL / 4. Soundness of PL
The rules preserve validity from the axioms, so no thesis negates any other thesis [Hughes/Cresswell]
5. Theory of Logic / K. Features of Logics / 4. Completeness
A system is 'weakly' complete if all wffs are derivable, and 'strongly' if theses are maximised [Hughes/Cresswell]
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]
Is counting basically mindless, and independent of the cardinality involved? [Heck]
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
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]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot]