Analysis and Synthesis

Abstract

In spite of his unusually broad knowledge of the history of science, Peirce did not pay attention to the most significant key idea in the history of heuristic reasoning and problem-solving, viz. the method of analysis and synthesis in Greek geometry. As described by Pappus (c. 300 AD), analysis is inverse inference from a theorem to axioms, or from a problem to its solutions, and synthesis then gives the desired direct proof or construction (Sect. 2.2). This inference resembles the regressive method of Renaissance Aristotelians, consisting of a “resolution” from facts to their causes and a “composition” from causes to effects. These methods influenced also such great figures of modern science as Galileo Galilei, Isaac Newton, and Karl Marx (Sect. 2.1). It is argued in this chapter that Peirce’s description of hypothesis, as a retroductive inference of a cause from its effect, is an instance of what Jaakko Hintikka calls the upward propositional interpretation of theoretical analysis. Further, the backward solution of a crime case by a detective is an instance of problematic analysis. This thesis is vindicated by Edgar Allan Poe’s stories of ratiocination written in the 1840s (Sect. 2.4). Another illustration of the same idea is given in Poe’s essay “Philosophy of Composition” where he describes the analytical construction of his poem The Raven (1845) (Sect. 2.5).