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Full Idea
I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism.
Gist of Idea
Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism
Source
Gottlob Frege (Function and Concept [1891], p.30)
Book Ref
Frege,Gottlob: 'Translations from the Writings of Gottlob Frege', ed/tr. Geach,P/Black,M [Blackwell 1980], p.30
A Reaction
This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise.
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| 8492 | Relations are functions with two arguments [Frege] |