Definition and Determination • 15

Re: Ontolog ForumRichard McCullough

In some early math course I learned a fourfold scheme of Primitives (undefined terms), Definitions, Axioms, and Inference Rules.  But later excursions tended to run the axioms and definitions together, speaking for example of mathematical objects like geometries, graphs, groups, topologies, etc. ad infinitum as defined by so many axioms.  And later still I learned correspondences between axioms and inference rules that blurred even that line, making the distinction appear more a matter of application and interpretation than set in stone.

In any case, the pervasive theme running through all the variations remains (1) whether the formal system inaugurated by the ritual of choice is a system of consequence or not, (2) whether and how well it determines a category of mathematical objects and, (3) if you bear an applied mind, whether those objects serve the end of understanding that reality which does not cease to press on us.

Resource

cc: Ontolog Forum

This entry was posted in C.S. Peirce, Comprehension, Constraint, Definition, Determination, Extension, Form, Geometry, Graph Theory, Group Theory, Indication, Information = Comprehension × Extension, Inquiry, Inquiry Driven Systems, Intension, Logic, Logic of Relatives, Logical Graphs, Mathematics, Peirce, Relation Theory, Semiotics, Sign Relations, Topology and tagged , , , , , , , , , , , , , , , , , , , , , , , . Bookmark the permalink.

2 Responses to Definition and Determination • 15

  1. Pingback: Definition and Determination : 16 | Inquiry Into Inquiry

  2. Pingback: Survey of Definition and Determination • 1 | Inquiry Into Inquiry

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