The idea of a mathematical formalization of logic that dates back to antiquity was only formalized in the 19th century by Charles Boole who proposed a binary system or clear sets. Although the fuzzy set theory is sometimes considered as a simple extension of Boolean algebra, the practical consequences for social science research are fundamental. The QCA has progressively seen the emergence of five increasingly sophisticated variants, the two main ones being the csQCA and the fsQCA. Is what opposes the crisp set qualitative comparative analysis (csQCA) to the fuzzy set qualitative comparative analysis (fsQCA) simply a technical improvement? The answer will be no; beyond different technical tools, there is a paradigm shift affecting in depth the research including epistemological choices, either explicit or implicit. In addition, part of these differences, which at first glance seem essentially methodological, are in fact partly due to a socio-cultural environment and religious values linked to the representation of the world, which is only rarely conscious.
TopAccording to Bocheński (1961) the history of formal logic begins with Aristotle (384-322 BC). Logic is a mathematical discipline stemming from Aristotelian philosophy; this was self-evidence since, according to the Greeks, philosophy was the science that encompassed all the others.
Nevertheless, an intrinsic difficulty in Greek thought in matters of logic, be it Aristotle or other contemporary thinkers or mathematicians, lies in the fact that they did not know the theory of probability (Bernstein, 1996), The probabilities will only be discovered 2,000 years later, notably by two mathematicians the French Pierre-Simon de Laplace (1749-1827) and the Swiss Daniel Bernouilli (1700-1782). Indeed, Sambursky (1956) in the last sentence of his seminal paper express clearly the limits of the ancient Greeks: “Neither the technique of experimentation nor the theory of probability, two cornerstones of modern science, could develop in ancient Greece” (p.48)
Conversely, Aristotle as well as other Greek philosophers were able to develop a rich logical corpus. For McKeon (1941/2001) Aristotle works, notably in “Organon” (the collection of its logical treatises), consist in the development of an inference schemes system (syllogisms) for deduction and widely for reasoning. Organon is composed of 7 logical treaties: Categoriae (Categories), De Interpretatione (On Interpretation), Analytica Priora (Prior Analytics), Analytica Posteriora (Posterior Analytics), Topica (Topics), De Sophisticis Elenchis (On Sophistical Refutations). For Belohlavek et al. (2017): “ In developing his syllogistic, Aristotle fully subscribed to the principle of bivalence”. (p.6) The syllogism is a deductive reasoning based on three propositions which link the premises to a conclusion: for instance, Socrates is a man, men are mortal, therefore Socrates is mortal. The conclusion is therefore always binary because it is or it is not. As stated McKeon (1941/2001), this issue is discussed in the treaty De Interpretatione (On Interpretation): “Everything must either be or not be”.