Interpretation and reconstruction of S. Carnot's Réflexions through original sentences belonging to non-classical Logic.

Antonino Drago and Raffaele Pisano
Group of History of Physics - Department of Physical Sciences -
University "Federico II" of Naples


We examine the first part of Réflexions sur la Puissance Motrice du Feu (Carnot S. 1978, pp. 1-112); our purpose is to find out in the book all occurrences of double negated sentences (DNSs), which we show to be typical of a theory based on non-classical logic.

Abstract

We examine the first part of Réflexions sur la Puissance Motrice du Feu (Carnot S. 1978, pp. 1-112); our purpose is to find out in the book all occurrences of double negated sentences (DNSs), which we show to be typical of a theory based on non-classical logic. We have collected 63 DNSs (see Appendix). This kind of analysis highlights what author's presentation implicitly presupposes; and therefore it reveals his fundamental hypotheses beyond his exposition.

This great number of DNSs is an extraordinary result, in comparison with previous analyses performed on original books of different physical theories. They are enough for representing the whole content of Sadi Carnot's theory (flow-chart A). Moreover, we have obtained six basic steps in the development of Carnot's theory as represented through an ordered groups of DNSs (flow-chart Bs).

The occurrences of DNSs since the beginning of the exposition, qualifies the theory as being organized upon a basic problem. Since the beginnings Sadi Carnot questions the existence or not of an upper bound for transforming heat in work, and how to determine it. These problems are put through a DNS. Then, some methodological principles are enunciated through DNSs belonging to non-classical logic. In total, the analysis shows that Sadi Carnot consistently follows his theoretical choice, that is to work within non-classical logic. A relevant result of this investigation is the discovery of five methodological principles instead of the commonly considered two principles.
Two of them (DNSs 9, 39) - ignored by previous historians - concern the relationship physics-mathematics. Indeed, our study on theory through DNSs has shown that the whole first part of Sadi's book is aimed to solve a fundamental problem of mathematical physics: by relying upon empirical date, to study whether the efficiency function can be considered as a mathematical function representing the efficiency of a heat machine that depends on few variables: Q, t, P, V (flow-chart C). On the other hand, contrarily to our expectations, DNSs don't suggest anything about the problem that impassioned many historians, from Ostwald (Ostwald) onwards: why S. Carnot uses two words (calorique and chaleur) when he referred to heat?


Info

Antonino Drago and Raffaele Pisano:
Interpretation and reconstruction of S. Carnot's Réflexions through original sentences belonging to non-classical Logic, 2004, Ronchi Found. 615-644.