## Sunday, March 07, 2004

### What Is Linear Reasoning?

Justice Souter thinks (see my previous two posts) that reasoning about the relevance of evidence does not involve linear reasoning.

What is linear reasoning?

Is it Linear Logic? See, e.g., Trobin Brauener, Preface, INTRODUCTION TO LINEAR LOGIC v (1996):

Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it is a logical way of coping with resources and resource control.

Does linear reasoning amount to reasoning with linear equations? See, e.g., hyperdictionary at http://www.hyperdictionary.com/dictionary/linear+equation:

[n] a polynomial equation of the first degree

Is linear reasoning, reasoning about spaces defined by two or more rectilinear coordinates? Reasoning with linear differential equations? Is nonlinear reasoning, reasoning about spaces defined by curvilinear coordinates? Does nonlinear reasoning involve equations that generate curved lines in rectilinear space? ...

What, precisely, is a "linear scheme of reasoning"? And is all analysis or argument about evidence linear? What makes Souter (or his law clerks) think so?

Does Souter believe that reason cannot portray (i) exponential increases or (ii) the influence of multiple variables?

Does Souter believe that logic cannot "handle" scenarios?

• Decision theory deals with alternative scenarios. Judea Pearl's subtle logic certainly deals with causal scenarios. So does Glenn Shafer's. [Souter said that a syllogism is not a story. This is true. {Did anyone ever assert the contrary?} But even if a syllogism is not a story, does it follow that deliberation about alternative scenarios or about alternative stories lies entirely beyond logic? If so, what makes Souter (or you) think so?]