more from this thinker | more from this text
Full Idea
The true principle is that we can assign to every object its determined characteristic number.
Gist of Idea
We can assign a characteristic number to every single object
Source
Gottfried Leibniz (Towards a Universal Characteristic [1677], p.18)
Book Ref
Leibniz,Gottfried: 'Leibniz Selections', ed/tr. Wiener,Philip P. [Scribners 1951], p.18
A Reaction
I add this as a predecessor of Gödel numbering. It is part of Leibniz's huge plan for a Universal Characteristic, to map reality numerically, and then calculate the truths about it. Gödel seems to allow metaphysics to be done mathematically.
| 19391 | We can assign a characteristic number to every single object [Leibniz] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 17883 | Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10609 | Two routes to Incompleteness: semantics of sound/expressible, or syntax of consistency/proof [Smith,P] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 15353 | The first incompleteness theorem means that consistency does not entail soundness [Horsten] |
| 10755 | A deductive system is only incomplete with respect to a formal semantics [Rossberg] |
| 13852 | Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't [Engelbretsen/Sayward] |