[FOM] Standard Language of Euclid

Sara L. Uckelman S.L.Uckelman at uva.nl
Sun Sep 27 14:26:20 EDT 2009

A. MANI wrote:
> You are not being very correct in using "standard language of Euclid".
> In the original language of Euclid it is not possible to remove the schematic 
> figures from the proof. It definitely possess a 'logic of diagrams' component. 
> It seems nobody has actually formalized it. 'School geometry' like in some of 
> the older British texts (Hall & Stevans for e.g) is in the language you 
> describe.

It's not clear whether you're referring to the "logic of diagrams" in
Euclid when you say that no one has formalized it, or to Euclid's
geometry more generally.  Either way, you would probably find the
following article interesting:

"A formal system for Euclid's Elements"
Jeremy Avigad, Edward Dean, John Mumma, to appear in the Review of
Symbolic Logic

The article presents a formal system, which they call "E", that models
both the linguistic and the diagrammatic reasoning of Euclid's


Dr. Sara L. Uckelman
Insitute for Logic, Language, & Computation

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