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Full Idea
The primitive truths contain the core of arithmetic because their constituents are simples which define the essential boundaries of the subject. …The primitive truths are the most general ones, containing the basic, essence determining elements.
Gist of Idea
The primitive simples of arithmetic are the essence, determining the subject, and its boundaries
Source
report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Robin Jeshion - Frege's Notion of Self-Evidence 2
Book Ref
-: 'Mind' [-], p.947
A Reaction
This presents Frege as explicable in essentialist terms, as identifying the core of an abstract discipline, from which the rest of it is generated. Jeshion says 'simples are the essence'.
| 16891 | Despite Gödel, Frege's epistemic ordering of all the truths is still plausible [Frege, by Burge] |
| 16906 | The primitive simples of arithmetic are the essence, determining the subject, and its boundaries [Frege, by Jeshion] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 17807 | To study formal systems, look at the whole thing, and not just how it is constructed in steps [Curry] |
| 10595 | A 'theorem' of a theory is a sentence derived from the axioms using the proof system [Smith,P] |
| 14620 | Theories in logic are sentences closed under consequence, but in truth discussions theories have axioms [Fine,K] |
| 10973 | A theory is logically closed, which means infinite premisses [Read] |
| 15328 | A theory is 'non-conservative' if it facilitates new mathematical proofs [Horsten] |
| 16310 | A theory is some formulae and all of their consequences [Halbach] |