Monday, October 6, 2014

Chapter 23 - Strange Footprints: Part 5 (a) - Bertrand Russell - Reflexiveness and Mapping

Korzybski: A Biography (Free Online Edition)
Copyright © 2014 (2011) by Bruce I. Kodish 
All rights reserved. Copyright material may be quoted verbatim without need for permission from or payment to the copyright holder, provided that attribution is clearly given and that the material quoted is reasonably brief in extent.

In one instance, it was not an origination of Russell’s but a reference he provided that Alfred found of inestimable value. Alfred liberally marked up the page of his copy of Introduction to Mathematical Philosophy, where Russell had written about reflexiveness, referring to Josiah Royce’s “illustration of the map”:
…[H]e [Royce] imagines [making] a map of England upon a part of the surface of England. A map, if it is accurate, has a perfect one-one correspondence with its original; thus our map, which is part, is in one-one relation with the whole, and must contain the same number of points as the whole, which must therefore be a reflexive number. Royce is interested in the fact that the map, if it is correct, must contain a map of a map, which must in turn contain a map of the map of the map, and so on ad infinitum. This point is interesting, but need not occupy us at this moment. In fact, we shall do well to pass from picturesque illustrations to such as are more completely definite, and for this purpose we cannot do better than consider the number series itself. (9) 

Alfred didn’t consider the map illustration merely ‘pictureseque’. At some point—surely after he read the work of Royce (who died in 1916)—he realized Royce’s thought experiment demonstrated the impossibility of a perfect map. On the Eastern Front Alfred’s life had depended on having accurate topographical maps, troop concentration maps, etc. Indeed, he had helped to draw them up with his frontline intelligence reports. He had never seen a map in a ‘perfect’ one-one correspondence with the actual territory it was representing. Indeed, that seemed meaningless in practice. Maps had to be revised—re-mapped—quite regularly. In his copy of Russell’s book he had underlined this sentence in red from the passage above: “Royce is interested in the fact that the map, if it is correct, must contain a map of a map, which must in turn contain a map of the map of the map, and so on ad infinitum.” It would take Alfred years to figure out the details but he knew this mapping business had importance and a deep relationship to Russell’s theory of types; you can make a map of a map, a map of a map is not the original map and is on a different level than the original map, etc. Russell—who conflated “correct” with “perfect”, and whose life may never have depended on having a correct geographical map—didn’t seem to see the significance of these relationships.

You may download a pdf of all of the book's reference notes (including a note on primary source material and abbreviations used) from the link labeled Notes on the Contents page. The pdf of the Bibliography, linked on the Contents page contains full information on referenced books and articles. 
9. Russell 1919, p. 80. 

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