Limitations of Intensional Logics
After having worked on axiomatization of scientific systems (including the first translation of Godel’s theorem), Agazzi treats intensional logic as a starting point for a better treatment of a good formalization, while at the same time rejecting the “sentential view” of theories, according to which theories are sets of true sentences (the ones deducible from a logico-mathematical axiomatization of a scientific system).
How to develop the idea of intensional logic while, at the same time, rejecting the idea of a scientific theory as a set of true propositions? Agazzi's starting point is the view according to which a physical concept does neither refer to an intension nor to an extension, but a set of operation, following the original idea of Percy W. Bridgman's operationalism: “the concept is synonymous with the corresponding set of operations. If the concept is physical, as of length, the operations are actual physical operations, namely, those by which length is measured” (Bridgman 1927, quoted in Agazzi 1969: 126).However, traditional operationalism, after its first introduction by N.R. Campbell and Bridgman's development, has become too dogmatic and naif, and Agazzi (1969: 132) tries two fundamental corrections of it: (i) on the on side he rejects the idea that every physical concept is operationally defined; (ii) on the other hand he rejects any operationalist reductionism because “actually physically significant measures are always performed inside a theory and get a meaning of physical measure exactly because they are framed inside theories”.
Up to this point the criticism to Bridgman's operationalism is similar to Quine's criticism to the strict verificationism of the first Vienna Circle: in analogy with Quine-Duhem view of holistic evaluation of empirical theories we cannot speak of verification as the meaning of a single proposition and therefore we cannot speak of the meaning of an individual proposition as the set of operations defined for it; only in the context of a physical theory a physical measure has its meaning.
However there is possible a third shortcoming of operationalism, that is defined by Agazzi (1969: 133) as (iii) the risk to “mistake a semantic problem for a methodological problem”. The point is that, from the viewpoint of a standard intensional semantics, we are satisfied to endow a predicate with an intension and an extension, while the problem of the means through which we check the extension is no more of semantic nature and has “no bearing on the problem of meaning”. But this is restricting intensional semantics to a mere formalism of functions and extensions as if they were “given”. Instead of accepting such an assumption Agazzi claims that the means for determining an extension should be taken into account in a theory of meaning of a scientific theory: actually, the intension of an expression of length should contain different kinds of measure operations (for instance comparing rulers, or using a goniometer, or with trigonometry, and so on); therefore referring to such kinds of operations is “not foreign to the meaning of ‘length' but it belongs to it, as part of the its intension”. The main core of operationalism is therefore saved in the following way: “if a physical concept contains intensional components that have no access to verification, neither directly nor through more or less complicated (but actually identifiable) links with operatively defined predicates, they have no right to citizenship in physics” (Agazzi 1969: 135-136).This conclusion is not identical with the empiricist criterion of significance, according to which the meaning of a proposition is its method of verification. The point is that, before accepting or verifying a proposition I need to understand a level of meaning which undergoes (or precedes) any verification. To understand this level of meaning is to understand the kinds of operations that are needed for properly using a concept inside a theory. While keeping a critical attitude to the neopositivistic theory of meaning and assuming a basic holistic view (experimental control concerns a theory in its totality, sometimes with reference to supplementary theories that constitute the “indirect” connection between sentences of the theory and observed facts), Agazzi saves some aspects of opera- tionalism inside a theory of meaning.
The most specific work on the application of an operational view of meaning is the paper “The concept of Empirical Data. Proposals for an Intensional Semantics of Empirical Theories”, published in 1976. In this essay the author claims that the main problem of the intensional logics is that they are unable to univocally determine the intended model. In fact such logics are a representation of what might be called “inferential compe- tence”,[143] that is the ability to find, from meaning postulates, the consequences of the axioms of the theory. However, and this is the key point, they cannot choose among different interpretations, and they can only give what is given inside the language of the theory, where a semantic interpretation cannot give what is intended by a working scientist.The criticism to intensional logics presented by Agazzi (1976) can be considered as an anticipation of the criticism given by Putnam (1981), with a development of the Quinean indeterminacy of reference. Actually Putnam’s analysis is even more clearly revealed in advance in Agazzi (1966) (discussed again in 1978b and 1994) where the author works on the philosophical import of well known results by Lowenheim-Skolem: if a first order theory has a (infinite) model, then it will be true in an indefinite number of isomorphic models; therefore a formal system cannot be characterized by a unique interpretation, but at most it can define the structure of the domain; a formal semantics is a structural semantics and cannot give but an interpretation of the kinds of elements of the domains (what are objects, what properties or classes and how they interact). Agazzi (1966, 1994) and Putnam (1977) discuss the existence of infinite isomorphic models also given the same truth values assignments: no truth value assignments to a class of sentences is sufficient to define the reference of singular terms and predicates; Agazzi (1976) and Putnam (1981) are concerned not only with truth values assignments (extensions) but also truth conditions (intensions).
The general claim therefore holds not only for extensional logics, but also for intensional logics: an intensional logic—also if it specifies the truth values of sentences in all possible worlds, restricting the admissible interpretations through meaning postulates—cannot fix the reference of the expressions of language, and always leaves open the possibility of alternative isomorphic interpretations. Basically “notwithstanding linguistic expedients as enriching meaning postulates to the theoretical sentences, a formal model can never guarantee the uniqueness of the model”. Given that the negative results are used by Putnam to demolish metaphysical realism, Agazzi’s reaction (although we cannot properly speak of “reaction” given that he writes before Putnam) can be interpreted as a defence of metaphysical realism. His main argument is enriching formal theories not only with meaning postulates, but also with operational definitions grounded on observable criteria connected with scientific instruments in the physical environment.3