Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'Necessary Truth' and 'Identity'

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11 ideas

6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17447

Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]

16014

It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan]

9. Objects / E. Objects over Time / 4. Four-Dimensionalism

16024

I could have died at five, but the summation of my adult stages could not [Noonan]

9. Objects / E. Objects over Time / 5. Temporal Parts

16023

Stage theorists accept four-dimensionalism, but call each stage a whole object [Noonan]

9. Objects / F. Identity among Objects / 2. Defining Identity

16016

Identity definitions (such as self-identity, or the smallest equivalence relation) are usually circular [Noonan]

16017

Identity is usually defined as the equivalence relation satisfying Leibniz's Law [Noonan]

16015

Problems about identity can't even be formulated without the concept of identity [Noonan]

16020

Identity can only be characterised in a second-order language [Noonan]

9. Objects / F. Identity among Objects / 8. Leibniz's Law

16019

Leibniz's Law must be kept separate from the substitutivity principle [Noonan]

16018

Indiscernibility is basic to our understanding of identity and distinctness [Noonan]

10. Modality / A. Necessity / 11. Denial of Necessity

4577	There is no necessity higher than natural necessity, and that is just regularity [Quine]