Comments on: Parsons’s Mathematical Thought: Secs 31, 32, Numbers as objects http://www.logicmatters.net/2008/09/parsonss-mathematical-thought-secs-31-32-numbers-as-objects/ Logic, enthusiasms, sceptical thoughts, and a little LaTeX geekery Mon, 06 Feb 2012 19:23:02 +0000 hourly 1 http://wordpress.org/?v=3.1 By: Christopher F. S. Maligec http://www.logicmatters.net/2008/09/parsonss-mathematical-thought-secs-31-32-numbers-as-objects/comment-page-1/#comment-379 Christopher F. S. Maligec Sun, 14 Sep 2008 22:47:00 +0000 http://www.logicmatters.net/?p=355#comment-379 What about this conception: If we take a graph with the nodes being objects and the edges non-equality relations (NOT=), numbers would be cliques (fully connected graphs). Perhaps numerosity results from perceiving non-equalities; otherwise, everything would simply be ONE (implying a distinction from NOTHING). Addition could be seen as indicating subgraphs (2+2 indicates that the graph defining FOUR can be seen as containing subgraphs TWO and TWO). Numbers themselves can be counted if a graph can be taken as a node. (e.g. “two numbers” being the graph TWO with graphs pertaining to other numbers as nodes). If you assume that all nodes are distinct a priori, the graphs collapse into sets of nodes (or variables).<br/><br/>Please drop me a line about this if it is of interest. What about this conception: If we take a graph with the nodes being objects and the edges non-equality relations (NOT=), numbers would be cliques (fully connected graphs). Perhaps numerosity results from perceiving non-equalities; otherwise, everything would simply be ONE (implying a distinction from NOTHING). Addition could be seen as indicating subgraphs (2+2 indicates that the graph defining FOUR can be seen as containing subgraphs TWO and TWO). Numbers themselves can be counted if a graph can be taken as a node. (e.g. “two numbers” being the graph TWO with graphs pertaining to other numbers as nodes). If you assume that all nodes are distinct a priori, the graphs collapse into sets of nodes (or variables).

Please drop me a line about this if it is of interest.

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