Combining Texts

Ideas for 'In Defense of Essentialism', 'Grundgesetze der Arithmetik 2 (Basic Laws)' and 'Remarks on the Foundations of Mathematics'

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

display all the ideas for this combination of texts

---

7 ideas

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number

9886	Cardinals say how many, and reals give measurements compared to a unit quantity [Frege]

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers

9889	Real numbers are ratios of quantities [Frege, by Dummett]

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers

10553

A number is a class of classes of the same cardinality [Frege, by Dummett]

10020

Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege]

6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism

11073

Two and one making three has the necessity of logical inference [Wittgenstein]

6. Mathematics / C. Sources of Mathematics / 7. Formalism

9887	Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett]

8751	Only applicability raises arithmetic from a game to a science [Frege]