map ≢ territory
June 24, 2024 12:02 PM Subscribe
Welcome to the Principia Mathematica Maps and Table Site (PM-MATS). The goal of this project is to make clear structural connections between different parts of Principia and to make analyzable data about the theorems, definitions, and primitive postulates in its text.
We do this by providing three digital tools:
A map of Principia that allows you to see the whole book.
9,944 mini-maps (one for every starred number in Principia) that show you everything used to prove it and everything that it is used to prove (❋13.1 for example).
A table of Principia that allows users to search for specific starred numbers, sections, chapters, and more, and also allows exportation of search results to JSON or CSV files.
Via Trivium
We do this by providing three digital tools:
A map of Principia that allows you to see the whole book.
9,944 mini-maps (one for every starred number in Principia) that show you everything used to prove it and everything that it is used to prove (❋13.1 for example).
A table of Principia that allows users to search for specific starred numbers, sections, chapters, and more, and also allows exportation of search results to JSON or CSV files.
Via Trivium
I think this, 110.643, is the entry for their celebrated proof of 1 + 1 = 2. Click on original text there to show the source page from the printed Principia: "The above proposition is occasionally useful."
I don't pretend to understand this. There is an explanation here.
As I understand it, Principia Mathematica is now regarded as an historic curiosity. Modern mathematics and logic do not follow this approach. Proving 1 + 1 = 2 in a modern framework should only take a page or two.
posted by JonJacky at 6:05 PM on June 24 [1 favorite]
I don't pretend to understand this. There is an explanation here.
As I understand it, Principia Mathematica is now regarded as an historic curiosity. Modern mathematics and logic do not follow this approach. Proving 1 + 1 = 2 in a modern framework should only take a page or two.
posted by JonJacky at 6:05 PM on June 24 [1 favorite]
JonJacky, some complexity may be due to ultimate incompatibility between the philosophical viewpoints of Bertrand Russell and Alfred Whitehead: "Whitehead’s main philosophical doctrine—that the world is composed of deeply interdependent processes and events, rather than mostly independent material things or objects—turned out to be largely the opposite of Russell’s doctrine of logical atomism..." [Stanford]
Giuseppe Peano, who is mentioned in a link you shared, has neat connections with Antonio Gramsci & structuralist linguist Ferdinand Saussure [pdf, L'Università di Urbino, Italy]. Saussure, of course, significantly explores territories & maps, with/in language.
zamboni, thank you for this resource. the map/territory distinction continues to be interesting, e.g. "in the case of the Nazca geoglyphs [unesco], Clarkson notes the extensive overlapping of the geoglyphs and says it 'raises an interesting and in many ways important question of why certain areas of the pampa look like a chalkboard used for many different lessons but never erased between each lesson. Was the act of construction as or more important than the recognizability of individual geoglyphs?'" [The History of Cartography, via U. Chicago]
was the map/territory pairing partly for effect above? mathematics seems somewhat beyond territory, yet (symbolic) maps guide us through math
posted by HearHere at 6:49 PM on June 24 [2 favorites]
Giuseppe Peano, who is mentioned in a link you shared, has neat connections with Antonio Gramsci & structuralist linguist Ferdinand Saussure [pdf, L'Università di Urbino, Italy]. Saussure, of course, significantly explores territories & maps, with/in language.
zamboni, thank you for this resource. the map/territory distinction continues to be interesting, e.g. "in the case of the Nazca geoglyphs [unesco], Clarkson notes the extensive overlapping of the geoglyphs and says it 'raises an interesting and in many ways important question of why certain areas of the pampa look like a chalkboard used for many different lessons but never erased between each lesson. Was the act of construction as or more important than the recognizability of individual geoglyphs?'" [The History of Cartography, via U. Chicago]
was the map/territory pairing partly for effect above? mathematics seems somewhat beyond territory, yet (symbolic) maps guide us through math
posted by HearHere at 6:49 PM on June 24 [2 favorites]
As you suggest, the title is of course riffing on the map-territory relation, what it might mean to map the
As I understand it, Principia Mathematica is now regarded as an historic curiosity. Modern mathematics and logic do not follow this approach.
Historic curiosity is the point. PM-MATS is related to the Principia Rewrite project, which is partially about investigating PM as part of the history of philosophy and mathematics, and making it accessible to a modern audience. As a byproduct, they've produced a TeX package just so they can write PM's now idiosyncratic notation.
On a side note, wittgenstein in particular might also be eponysterically interested in the tangentially related University of Iowa Tractatus Map.
posted by zamboni at 8:33 AM on June 25
territoryof Principia, and the lazy joke of rendering
is not thewith a non-equivalency symbol.
As I understand it, Principia Mathematica is now regarded as an historic curiosity. Modern mathematics and logic do not follow this approach.
Historic curiosity is the point. PM-MATS is related to the Principia Rewrite project, which is partially about investigating PM as part of the history of philosophy and mathematics, and making it accessible to a modern audience. As a byproduct, they've produced a TeX package just so they can write PM's now idiosyncratic notation.
On a side note, wittgenstein in particular might also be eponysterically interested in the tangentially related University of Iowa Tractatus Map.
posted by zamboni at 8:33 AM on June 25
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posted by wittgenstein at 1:04 PM on June 24 [6 favorites]