PSI - Issue 68

Tamás Fekete et al. / Procedia Structural Integrity 68 (2025) 915–921 T. Fekete / Structural Integrity Procedia 00 (2025) 000–000

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On the contrary, a key step in the development of the methodology of SIC s is the transformation from an already existing theoretical framework to a new one, such that: (1) the transformation involves a Conceptual Shift ; (2) the new theoretical framework generalizes the old one in such a way that the new one is compatible with the old one within its domain of validity – Rovelli (2024 44.). Therefore, the new concept needed a research method that was more general than –but at the same time backward compatible with– the Aristotelian ASM , which is now considered by many people to be the most general. The philosophical literature – e.g. Cellucci (2013), (2017), (2022) – shows that such a method exists, namely a contemporary version of the Analytic Method ( AM ) –first described by Plato in the 4 th century BC– adapted to the contemporary context – see Cellucci (2013 55–67.), (2017 149–160.), (2022 121–157.). What the AM has to say that is relevant to scientific research is that the solution to a scientific problem always begins with an analysis of the problem, from which a hypothesis is derived using a non-deductive rule based on data directly available from the problem and other external sources. A hypothesis is plausible if the arguments for it are stronger than those against it. The plausibility of a hypothesis is checked by the plausibility test procedure, and if, and only if, it is found to be plausible, statements are derived from it using deductive rules. Of paramount importance in plausibility testing is the question of whether the plausibility of a hypothesis is supported by experience. One of the most important features of the AM is that it recognizes the finite and fallible nature of human understanding and knowledge, and the open ended nature of problem solving. The open-ended nature of problem solving is easy to see because after a problem has been solved once using given methods, new knowledge may emerge that justifies revisiting the problem and solving it in light of that new knowledge. The AM takes everything as a hypothesis, it does not single out certain hypotheses as Aristotle did in his ASM . Figure 2 shows a version of the AM that illustrates how this method is fundamentally similar to the Aristotelian ASM in the development of a physical or other theory. It is clear that the investigation of a given problem or set of problems begins with ‘ Analysis ’ – comparing Figure 1(a) with Figure 2. This is the ‘ Inductive ’ phase of inquiry, in which the causes of phenomena are primarily investigated. In both methods, this phase is expressed as a progression from hypothesis to hypothesis. In the ASM , hypotheses are called premises. The ‘ Deductive ’ phase of research in the Aristotelian method is called ‘ Synthesis ’, and it is now widely believed that only deductive methods are used in this phase. In contrast, Figure 2 shows that the mathematically dominated phase of theory development is driven by the AM in the same way as the earlier ‘ Inductive ’ phase. To bring the AM more in line with the experience of the natural sciences, the hypotheses that stand out from the rest are those that are both deep and the most trustworthy so far, having survived the plausibility tests. In the ‘ Inductive ’ part, these hypotheses are called ‘ Core Hypotheses ’. On the starting end of the ‘ Deductive ’ part, the corresponding versions of these are called ‘ Principles ’, just as in the ASM . The conceptual difference between the AM and the ASM is that whereas in the AM ‘ Core Hypotheses ’ and ‘ Principles ’ belong to the class of hypotheses , Aristotle argues: ‘ Prime Premises ’ and ‘ Principles ’ are definite and absolutely ‘true’, proven by intuition – Cellucci (2017 165). This implies that the AM leaves open the possibility of revising even the principles of a theory, if necessary, whereas the ASM excludes this issue. According to Cellucci (2017 179), in the AM a scientific theory is interpreted as an open system, while in the ASM it is interpreted as a closed system, since the ‘ Synthesis ’ part is equivalent to the Axiomatic Method – Cellucci (2017 295.). The model presented on Figure 2 can be referred to as the Double AM or the Generalized Scientific Method .

Fig. 2. The Double Analytical Method or Generalized Scientific Method