Combining Texts

Ideas for 'fragments/reports', 'From Stimulus to Science' and 'Frege Philosophy of Language (2nd ed)'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

2 ideas

4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST

10537	The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett]
	Full Idea: A classic reduction is the class of ordered pairs <x,y> being reduced to the class of sets of the form {{x},{x,y}}.
	From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX

10542	To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett]
	Full Idea: We may suppose that with each set is associated an object as its cardinal number, but we have no systematic way, without appeal to the Axiom of Choice, of selecting a representative set of each cardinality.
	From: Michael Dummett (Frege Philosophy of Language (2nd ed) [1973], Ch.14)