The Rootsof Agazzi’s Metaphysics: Formal Logic and Scientific Method
When in 1975 Agazzi writes his first “metaphysical” article, he has already published his most important books: Introduzione ai problemi dell’assiomatica (1961), La logica simbolica (1964) and Temi e problemi di filosofia della fisica (1969), where he sketches the fundamental framework of his thought in the fields of logic and epistemology.
They are three works very deep and rather technical, nonetheless, as we have said, they contain practically all the elements that successively will turn out to be essential to his metaphysics.First of all, in his two logical works Agazzi immediately introduces a concept which may well be considered the real “fil rouge” (cf. Musso 2007) of his whole philosophy (and therefore also of his metaphysics), which here he calls, according to the modern custom, «intentionality». However, in the last years Agazzi has started to speak more and more explicitly of «intellectual intuition», in order to underline that he takes intentionality in a particular sense, very close to that of the medieval philosophers and rather different from that generally accepted nowadays, when it is either completely rejected or in any case tendentially reduced to a mere subjective psychological state or to a socially acquired skill.
In Introduzione ai problemi dell’assiomatica, an exposition and commentary (in my opinion, still the best of all) of the famous Godel’s Theorem, all the discourse about intentionality is contained in very few but nonetheless fundamental pages. Here Agazzi shows that the undecidable proposition G, expressly constructed by Godel to prove the incompleteness of arithmetic, is nonetheless true, since it says of itself precisely that it is undecidable, but nevertheless «it is possible to proof it only by means of metatheoretical arguments and not by deducing G from the axioms of the system P (indeed we know that such deduction is impossible, since G is indemonstrable)» (Agazzi 1961: 186).
It follows that the set of true propositions is wider than the set of demonstrable propositions, i.e. “theorems”, and then also that what human thinking can understand to be true goes necessarily beyond the scope of what can be demonstrated, what is the same than saying that maybe the true distinctive feature of human thinking is not its discursive activity but its capability of “seeing” the truth. In other words, [...] human thinking cannot be replaced by a thinking machine which could execute all the logical operations that it can do (Agazzi 1961: 199).[153]Later, in La logica simbolica Agazzi extends this seminal intuition to the whole problem of the foundations of logic, by questioning the very widespread thesis of the complete conventionality and therefore of the complete meaninglessness of formal systems—what in any case «mathematical logicians had never really stated, while it has become instead the favorite slogan of some philosophical circles» (Agazzi 1964: 356). Furthermore, he also shows that even «the so-called “pure calculus” can be considered well established [...] only if it is “based” on some intuitive evidence» (Agazzi 1964: 355). Consequently, the said capability of “seeing the truth” in an intuitive way is the real basis of all systems of modern mathematical logic, which, in turn, are neither arbitrary nor meaningless, but are based, ultimately, on reality, or, at least, on some properties of reality, in a way which is not very different, after all, from that of scientific theories, as we are going to see immediately.
In Temi e problemi, indeed, Agazzi explains, in a synthetic but substantially complete way, his famous theory of scientific objectivism, firstly clarifying that the objects of scientific theories are not “things” as a whole, but only some properties of theirs, identified through standard operations, which allow the establishment of an intersub- jective agreement among the different observers.
This kind of “weak” objectivity, limited to the ascertainment of the existence of such agreement, without saying anything about its objective ground and therefore without any ontological commitment, is the unique generally accepted by contemporary epistemology. But Agazzi stresses that, as a matter of fact, it can be separated by “strong” objectivity, which instead is based on the relationship with reality, only basing on «epistemological dualism [.] that consists in conceiving the real object as something situated beyond the known object, so that we can never reach it» (Agazzi 1969a: 364-365). Now, it is well known that this presupposition is the basis of modern philosophy, but nonethelessit must be rejected not only because it is dogmatic, but also because it is self-contradictory. Indeed, to say that, beyond the object that I know, there is another that I do not know, I need to have at least ascertained that it exists, but this means already to know it (Agazzi 1969a: 365).
Moreover, if theories
were mere agreements, we may decide (that is, precisely, “agree”) to never modify them, even in the case that new experimental results contradict them. The fact that this never happens and, instead, all recognize that in such cases we must modify the theory, is a proof that, in reality, nobody is ready to seriously admit such conventionality (Agazzi 1969a: 369).
For this reason, a theory, when adequately confirmed, may surely be said true (once again against what is maintained by the overwhelming majority of contemporary epistemology), although never in an absolute sense, since it is always «true or false of a given universe of objects» (Agazzi 1969a: 369) or, as Agazzi likes to say, it is «absolutely true relatively to its objects».[154] So, at last, we can find also a space for philosophy and, particularly, for metaphysics, since
a truth in an absolute sense should be nothing else than a truth which holds for all possible objects, i.e. a truth which, holding for all possible kinds of objectivation, refers to reality not as objectivated, but as such, and therefore, as we have seen, exceeds the field taken in consideration by science and is instead related to philosophy (which, typically, when wanting to assume a cognitive task, aims to investigate reality as such and therefore appears as metaphysics) (Agazzi 1969a: 369-370).[155]
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