Abstract
In the course of our presentation we have often used expressions such as “meaning,” “reference,” “denotation,” “intension,” “extension,” and so on. All these (and related) terms are far from having unique, standard meanings in the philosophical literature, and so we must clarify the way we are using them in this work.
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Notes
- 1.
It would take us too far afield to reconstruct the history of this approach. However, at least certain points deserve mention since they throw light on issues relevant to our discussion. As we have noted on earlier occasions, twentieth century positivist philosophy of science was deeply influenced not only by the ‘linguistic turn’ of contemporary philosophy, but especially by the creation of mathematical logic and the ‘formalistic’ trends of Hilbert’s philosophy of mathematics. The adhesion to the linguistic turn produced the conviction that a full understanding of science could be provided by an analysis of the language of science. The fascination of mathematical logic led to the creation of what has been called the mythology of deductivism (see Harré 1970, Chap. 1), which in particular has led to what has been termed the statement view of theories and the hypothetico-deductive model of scientific explanation (Hanson 1958, p. 70 ff.), and in general to an abhorrence of the idea that “vehicles for thought are not wholly propositional but ‘pictorial’ as well” (Harré 1970, p. 2). In short, the empire of formal deduction, which was seen to cover all mathematical disciplines, was extended to encompass all of the exact sciences, including the empirical ones. But the last step was even more drastic. In his Logical Construction of the World, Carnap explicitly says that “science is concerned only with the structural properties of objects” (see his 1928, p. 12 ff.), and makes explicit reference to the spirit of mathematics and to Hilbert’s doctrine of “axiomatic definitions” (which we have already mentioned, particularly in Sect. 2.8 of this work). But this doctrine had been created in order to dispense with reference in mathematics, and how could it be applied to the empirical sciences? We know that a possibility in this sense is not excluded, and that already Poincaré, e.g., had maintained that science is able to discover objective relations in nature (therefore considering a ‘content’ overstepping the simple syntactic domain). This is the central idea of that ‘realism of structures’ that has known interesting developments recently but was not the idea that Carnap was advocating in his work. Carnap says—and logical empiricists have repeated after him—that a scientific theory is a formal calculus to which ‘interpretations’ may afterwards be assigned (by means of ‘correspondence rules’ or otherwise). But how can these interpretations actually be selected and applied? Mathematical logic (and in particular its branch known as model theory) has a reply to this question, since the interpretation of formal systems is conceived of extensionally and in purely set-theoretical terms, so that the nature of the elements of the set is immaterial, and their properties and relations may be (extensionally) defined in an arbitrary way in order to construct the interpretation. But this cannot be satisfactory for the interpretation of empirical theories, in which the referents are intended and endowed with attributes which the theory is meant to express and describe, and in which no formal tools are able to single out this ‘intended’ model among the other infinite models of the theory. For more details regarding the efforts and the difficulties which emerge in the realisation of this programme, see Przelecki (1969); for a more general survey see Agazzi (1981). For a discussion of the inadequacy of the model-theoretic approach in order to single out the ‘intended model’ see Agazzi (1976), reproduced also as Appendix in the present work, whose arguments are similar to those presented later by Putnam in Chap. 2 and the Appendix of Putnam (1981).
- 2.
Actually Morris does not define semantics as the study of the meaning of signs, but says that “semantics deals with the relation of signs to their designata and so to the objects which they may or do denote” (Morris 1938, p. 35 of the 1971 reprint). Therefore, semantics is introduced with a tacit referential connotation. But this is not surprising, if we consider the general behaviouristic background of Morris’s thought, in which meaning could not really play any role. It is worth noting, however, that Morris was considering meaningful languages, that is, languages for which the problem is not that of attributing a meaning (be it understood in a referential sense or otherwise), but that of explaining in what meaning consists. On the other hand, the use of the term “semantics” in the field of logic, methodology and philosophy of science, introduced by Tarski in the 1930s, was then, in a certain sense, codified in Carnap’s Introduction to Semantics (1942). Carnap makes direct reference to Morris’s work in the first pages of his book, where he introduces his discourse on semantics. But he is also particularly sensitive to the different trend in the philosophy of mathematics and formal logic characterised by the formalistic outlook, according to which formal systems are meaningless constructions to which a meaning may be artificially assigned through interpretations, as we have indicated in the preceding note. To a certain extent this was also Tarski’s attitude when he first introduced semantic considerations into the methodology of the exact sciences—though, on his view, this expressed the need to overcome the purely syntactic approach that still characterised Carnap’s work at that time. In particular, a merit of the Polish School is that of having established and vindicated semantics as a particular part of the methodology of science and as a specific discipline of logic (see Tarski 1933 and 1936, and Kokoszynska 1936).
- 3.
Actually the German word Bedeutung is normally translated as “meaning,” (in the sense of ‘significance’) which would make it synonymous with Sinn, or “sense,” like the corresponding English terms. However, Frege, in his famous paper Über Sinn und Bedeutung (1892), wanted to avoid all ‘identities’ being tautologies on his view, and used these terms to make a distinction which he though would allow him to do this. As a consequence, it has become customary in recent literature to reflect this technical distinction by translating the Fregean “Bedeutung” as “reference” (even in German it is now replaced by the term “Referenz”), leaving “meaning” to be synonymous with “sense,” as it is in everyday language. We can note, however, Feigl’s translation of that paper, where he, following Carnap, uses the term “denotatum,” and we may also remember that early authors used to translate Frege’s terminology as the difference between “meaning” and “denotation” (see, e.g., Russell in ‘On Denoting’).The issue is not trivial because “reference” can be considered a poor translation of Bedeutung if one means by reference the ‘act of referring,’ since Frege’s Bedeutung means the object, not the act, of referring. A few authors advocate this view, as a consequence of their having taken into special consideration the concrete activity of speaking. By “term,” therefore, they mean something written or spoken which can be used (by speakers) in referring (listeners) to referents or in expressing senses. Referents (more generally, objects) are what listeners are referred to, using terms, by speakers. Therefore “reference” is one linguistic expression of the more general category of intention; it consists in the directing of a listener’s attention (referring the listener) to a referent by a speaker. In conclusion, reference is an act (involved in e.g., stating, judging and describing), while a referent is an object. This view, proposed by Strawson and shared, e.g., by Austin and Searle, is certainly of interest as far as it concerns the use of statements, but its limits consist precisely in making of reference just a property of such a use, strictly depending, in particular, on the concrete circumstances of this use. It seems to us, however, that if one wants to draw attention on this concrete use, one might better speak of referring (that has all the normal features of an act), leaving reference to indicate in general the domain of objects denoted by a term, a domain to which one or more referents can belong. (By the way, the title of the paper where Strawson proposed his thesis (Strawson 1950) has the title “On referring” and not “On reference.”) Owing to this situation, one must admit that “there is ambiguity about the term ‘reference,’ an ambiguity which threatens the validity of many observations usually made on the nature and conditions of reference. But we need not worry too much about it if our question is what it is, viz. whether definite descriptions would ever allow singular reference. If the question is understood as a question regarding the reference of the definite description, it is a purely semantical question,… If, on the other hand, the question is understood as a question regarding the speaker’s reference, it is also a question about the speaker’s ability to refer.” (Sen 1991, pp. 25–26). After having recognised this ambiguity, however, we prefer to eliminate it in our work by deciding to intend reference according to its semantical sense. This choice is recommendable for the same reasons that induce us to speak of the sense or the meaning of a term without caring about the particular speaker or listener that is exchanging these private mental contents. Therefore we shall conform to the more widespread practice in this work for the sake of simplicity, and use “reference” almost as a synonymous of “referents” or, more precisely, as indicating the domain to which the referents of a term (if any) belong.
Coming now to the second expression of Frege’s paper (Sinn), our preference would be to use “meaning” in the most general sense, so that one could include in the meaning of a linguistic expression (as different ‘aspects’ of the meaning) both the sense and the reference. We shall refrain from adopting this more complicated convention here, and shall only make an occasional mention of it when we speak of intension and extension.
- 4.
Already before his 1892 article, ‘On Sense and Reference,’ Frege had very clearly expressed his views on the objective nature of concepts and on the primacy of understanding concepts over the task of indicating referents. See for example this passage: “The concept is something objective that we do not construct and which does not construct itself in us, but rather that we try to comprehend and, hopefully, to really comprehend, if we do not erroneously seek something which is not there” (Frege 1891, p. 158).
- 5.
Valuable accounts of the historical and conceptual links between semantic conceptions which originated and were developed in the field of phenomenology on the one hand, and in the logico-analytic tradition on the other, are presented in two articles by Guido Küng (1972, 1973). In these papers one may also find a useful explanation of certain systematic and terminological distinctions which we have hinted at only briefly in some passages of this work. It is perhaps not superfluous to note that the term noema, that we relate especially to Husserl because of his important analysis of the nature and relevance of this notion, is already present, with nearly the same meaning, in Aristotle.
- 6.
A documentation and discussion of this trend may be found in Zalta (1988).
- 7.
A recent presentation of this latter trend is provided in Wettstein (1991). This work not only offers a reconstruction of the central views and aims of the Fregean and Russellian approach, but also presents an illuminating interpretation of the philosophical insights which are only partially made explicit in the referentialist approach of people such as Kripke, Donnellan, Kaplan, Perry and Putnam who, developing Mill’s conception that proper names have only reference without any meaning (contrary to Frege’s claim) have elaborated a ‘new semantics’ in which mental contents, intensions, and thoughts tend to be dispensed with (we are not interested here in analysing the possible exceptions to this rule).
- 8.
For some information regarding these more recent trends let us simply refer to a few works such as McGinn (1982), Davidson (1986), Block (1986), Lepore and Loewer (1987).
- 9.
We shall consider this Aristotelian doctrine again in Sect. 4.4, where we shall also give a few textual references.
- 10.
Wettstein, for example, maintains that the central role attributed by Frege to sense is a consequence of the fact that Frege and Russell (and in his view even several ‘conservative’ anti-Fregeans who are unable to renounce a ‘cognitive fix’) are still prisoners of that ‘representationalism’ which he (correctly) traces back essentially to Descartes. However, it is certainly mistaken to attribute such a conception to Frege. Indeed, not only is there no plausible evidence for this in his major works, but in other writings he strongly criticises the thesis that representations are the objects of our knowledge (see, for example, “representations cannot be seen or touched, neither smelled, nor tasted, nor heard. I take a walk with a friend. I see a green meadow; I have in such a way the visual impression of the green. I have it, but I do not see it.” Frege 1918, p. 67; my italics).
But it is after all not that important to decide this question regarding Frege, since the admission—and indeed the elaborate and rigorous introduction—of the ontological world of meanings was performed by a scholar, namely Husserl, who certainly counts among the most decided opponents of representationalism and epistemological dualism in contemporary philosophy. Precisely because he realises that that which we intend in a perceptual act is the referent, but that in a certain different sense we also intend the meaning of such a referent, Husserl introduces the notion of the intentional object which, starting with his Ideen of 1913, becomes the noema. This remains very distinct from the referent, since the referent belongs, so to speak, to the external world, while the noema belongs to the world of meaning. A clear presentation of these passages is offered in the already cited article, Küng (1973).
- 11.
As a conclusion of our discourse we can say: if one considers ‘meaning’ as a general notion, including as its ‘aspects’ both sense and reference, one can consistently maintain that semantics studies meaning, and that in so doing it has a legitimate (and necessary) part that is concerned with sense, as well as a legitimate (and necessary) part concerned with reference. Let us also recall that in presenting certain of our views on ‘intensional semantics’ we have explicitly stressed that the ‘relation to the referents’ is part of the intensional meaning of concepts (we have qualified it the ‘referential part,’ as distinct from the ‘contextual part,’ of this meaning).
- 12.
This is not only conceptually, but also historically true. In fact William Hamilton, starting his lectures on logic in 1837–1838, introduced intension in his discussion of the “quantity of concepts,” explicitly equating it with the notion of comprehension, which was common in the tradition. Let us consider a few remarks from his Lectures on Logic, published after his death:
This quantity is of two kinds; as it is either … Intensive or Extensive .… The former (the Intensive Quantity) is called … by the Latin logical writers the comprehension (comprehensio, quantitas comprehensionis, complexus, or quantitas complexus). The latter (the Extensive Quantity) is called … by the logical writers of the Western or Latin world, the extension or circuit (extensio, quantitas extensionis, ambitus, quantitas ambitus) and likewise the domain or sphere of a notion (regio, sphaera) .… The Internal Quantity of a notion—its Intension or Comprehension, is made up of those different attributes of which the concept is the conceived sum, that is, the various characters connected by the concept itself into a single whole in thought. The External Quantity of a notion or its Extension is, on the other hand, made up of the number of objects which are thought mediately through a concept. (See Hamilton 1860. The quotation is made from the 2nd revised edition, 1866, vol. 3, pp. 141–142.)
The Scholastic tradition had actually known the use both of “intentio” and “intensio.” The second term had been used by certain authors in order to eliminate the ambiguity of the meaning of “intentio” which, after having for centuries meant ‘purpose’ or ‘goal,’ had started to be used to indicate the representational content of a concept in general. For this second meaning, they proposed to use “intensio.” Therefore Hamilton’s terminology was in fact resuming a certain tradition, and his influence was such that it practically replaced the use of “comprehension” in the English-speaking logical community. This explains why Carnap, when promoting the circulation of this notion in the literature of contemporary logic, did not even mention “comprehension,” and made use of the term “intension,” which was then adopted, as is clear from what he says:
Now we shall introduce the terms “extension” and “intension” with respect to predicators.… The use of “intension” varies still more than that of “extension.” It seems in agreement with at least one of the existing usages to speak of the same intension in the case of L-equivalence. Thus we lay down the following conventions.… The extension of a predicator (of degree one) is the corresponding class.… The intension of a predicator (of degree one) is the corresponding property [pp. 18–19]…. The extension of a sentence is its truth value.… The intension of a sentence is the proposition expressed by it. (Carnap 1947; from the 2nd enlarged edition of 1956, pp. 26–27).
In fact, it suffices to recall, for example, that Tarski speaks of the ‘extension’ and ‘intension’ of the concept of truth in his 1944 paper (Tarski 1944, p. 342), without feeling the need to explain the sense of these words, which means that they were in common use.
- 13.
In this respect, one can note that, while Carnap relates extensions directly to linguistic expressions, and not to the properties or relations they express, Frege, on the contrary, associated the extension with concepts.
- 14.
For example, the complex predicative expressions, “the red coloured sky at sunset” and “the golden mountain” are both abstract objects or noemata, resulting from the composition of concepts that, individually taken, have their reference, but while the first complex noema has obviously a referent, the second does not.
- 15.
Radical empiricists are not ready to admit the ‘intermediate level’ of sense and intensional objects, but this can bring them into difficulties when they elaborate their most sophisticated doctrines. A case in point is van Fraassen’s empirical structuralism whose clear understanding should obviously rely upon a satisfactory definition of the notion of structure itself. However no such definition is provided by the author, who simply uses the undefined word “structure,” and expressions such as “abstract structure” and “mathematical structure.” Let us consider, however, a significant passage (van Fraassen 2008, p. 238):
Essential to an empiricist structuralism is the following core construal of the slogan that all we know is structure:
-
I.
Science represents the empirical phenomena as embeddable in certain abstract structures (theoretical models).
-
II.
Those abstract structures are describable only up to structural isomorphism.
This way of speaking would incline one to conceive of these ‘abstract structures’ as intensional objects, as noemata, to use our preceding terminology, but a strict empiricist—as the author is—does not want to admit this ontological qualification. Thus one does not know what ‘kind of reality’ these abstract structures have since, after all, they are different from nothing and can even be embedded into one another. Moreover, why are they called “abstract” if there is no mention in that book of “concrete structures”? We are told that phenomena are “embedded” into abstract structures, but this might have something like an analogical sense if phenomena also had a structure, but this is explicitly excluded a few lines below this quotation. On the contrary, we would say that models and mathematical structures are abstract objects that can be exemplified by phenomena that become their referents thanks to certain operations.
Van Fraassen, however, neatly rejects such an idea. For instance, discussing the example of an assertion stating that a table top is square, he says, “That is true, but simply because this table top is square—c’est tout! It is true because the top’s sides are of equal length and the angles between them are right angles. It could be paraphrased as ‘the table top instantiates the Euclidean square form,’ but the cash value of the assertion carries no metaphysical commitment: it is just that the table top is square” (2008, p. 249). One could object that the operations of measuring the sides and the angles of the table can allow me to say that the table top is square because they lead to exemplifications of the properties encoded in the concept of square, and not, for instance, of circle. We think that an empiricist could come to accept this position, provided that some (for him) palatable explanations were offered regarding how such abstract concepts are arrived at, but in such a way the discussion would be limited to the domain of epistemology, and would not concern ontology. What is transparent in van Fraassen’s position, therefore, is an ontological stand, in which one could recognise the features of nominalism; and if one also notes his allergy to “metaphysical commitment” (which is declared also in other passages of his work) one can interpret his position as a development of the neo-positivist tradition. This is by no means a negative appreciation; on the contrary, the intelligent, original and creative elaborations that this philosopher has been able to produce during many years attest to the internal wealth of that tradition, a wealth that can be gladly recognised also by those who criticise the tradition, point out its limits, and advance different proposals.
-
I.
- 16.
We note that recognising the ‘intentional’ nature of cognitive acts and their products (i.e. representations) can be limited to recognising the ‘directionality’ of such acts and products, and to these products even the qualification of ‘intensional’ can be applied without the further step of admitting an ‘intensional reality’ as such. This is typical of radical empiricists and is well demonstrated in van Fraassen (2008) where intention and intension are very parsimoniously mentioned in this limited sense (pp. 21–22), whereas an ‘ontological status’ for such intensional entities as representations and models is not provided, and this is a critical point in his doctrine that we have considered in the preceding note.
- 17.
In the first chapter of Zalta (1988) one finds a discussion of some additional reasons which support the merging of ‘intentionality’ and ‘intensionality’ in contemporary logical research.
- 18.
See, for example, Agazzi (1969, 1976).
- 19.
The most significant example is Zalta (1988). His book provides for the first time an extensive and rigorous formal treatment of relations, stating in particular the conditions under which there are relations, and the conditions for their identity. In this way, the traditional set-theoretic treatment (for which relations coincide with their exemplification-extension) is no longer the only rigorous tool available for the study of relations, not to mention the fact that the exclusive use of this tool had reinforced the wrong idea that relations are ‘strongly extensional,’ while it is intuitively clear (and Zalta’s theory accounts for this) that even logically equivalent properties or relations are not identical from an intensional point of view, that is, from the point of view of their sense.
- 20.
Also Zalta, for example, makes this identification.
- 21.
Let us note that we are here going to use the concept ‘knowledge’ in its broadest sense, i.e., including both ‘knowledge by acquaintance’ and ‘propositional knowledge,’ therefore admitting the existence also of a subjective knowledge, as well as the fact that knowledge does not necessarily entail the subsumption of the particular under a universal. This ‘tolerant’ attitude is adopted because we do not need, here, to enter into more detailed issues that might impose a more refined analysis.
- 22.
An analysis of the Fregean ‘tripartition’ is presented in Thiel (1965), where the author sees a one-to-one correspondence between the distinction ‘sign, sense, reference,’ and the distinction ‘subjective-real, objective-non-real, objective-real,’ and charges Frege with having introduced a “completely unacceptable contamination” by his “allowance of a participation of ontology in the doctrine of sense and reference” (pp. 151–152 of the English edition). A persuasive argument that Frege did not perform such a contamination, accompanied by a vindication of the legitimacy of considering the ontological counterparts of a semantic analysis, is contained in a critical appraisal of Thiel’s thesis in Carl (1982), pp. 61–65.
- 23.
This does not overlook what Frege stressed concerning the ‘unsaturated’ character of concepts, as contrasted with the saturated character of objects, but at the same time accounts for an ontological feature which was somewhat obscured by Frege’s purely linguistic analysis, that is, that properties often have a rather unproblematic intrinsic determinability. (Frege recognised, on the other hand, that concepts may also become objects saturating a second-order concept.) As to the ontological analysis, we think that the traditional distinction of esse per se and esse in alio still provides a sensible tool for the ontological analysis of properties, which does not endow only individuals with ontological relevance. Let us point out, by the way, that our semantic analysis is partially in keeping with Frege’s theory, at least in the sense that he claims that a predicate, being an unsaturated expression, cannot have as referent an object, and therefore must denote a concept. But since a concept is an entity whose kind of existence consists in being true or false of some object, the result is that for Frege a concept is a property or a function (in our vocabulary, an attribute). As a result, both Frege’s semantics and ours state that the referent of a predicate is an attribute. However, our agreement with Frege is only very partial, for concepts are for him the referents, and not the senses, of predicates (contrary to what we maintain). Frege is obliged to maintain this position in order to be consistent with his fundamental distinction between concept and object. However, unfortunately, he never formulated a clear view on the ontological status of concepts, remaining content with the fact that their existence is justified by the possibility of quantifying over them (which is a purely linguistic justification). On the contrary, we do have such a concern for ontology, and give to concepts the ontological status of intensional objects (on the level of sense); and at the same time we say that they refer (or may refer) to concretely existing attributes.
- 24.
This explains why it would be problematic (contrary to one’s first impression) to say that the reference of a predicate is its extension. In fact, for Frege, while the sense of a predicate is “its way of being given,” and its reference is the concept (equated with a property or relation), the extension (which he calls Umfang) has no semantic relation to the predicate. Carnap, on the other hand, does not use the distinction of sense and reference. The classical tradition was actually more sophisticated than contemporary approaches: the ‘comprehension’ of a concept (that is, its ‘content,’ its ‘intention,’ to use our vocabulary) was the class of its characteristics, that is, the class of those upper-concepts which occur in its definition (let us say, e.g., concepts such as ‘animal’ or ‘rational’ in the case of the intension of ‘man’). The ‘extension’ was instead the class of its lower-concepts (such as, e.g., ‘European,’ ‘musician’), among which appear, on the bottom-level, the individual concepts. Therefore, the classical notions of extension and intension only denoted relations between concepts and did not involve such an ‘ontological jump’ as is implicit in considering the extension of a concept as constituted by concrete individuals, instead of concepts.
- 25.
We are aware of the double sense in which we are using the term data. In the preceding sections we have qualified as data the results given by the immediate application of operational devices; here we include among data also the instruments and all non-problematised things. We are doing this on purpose, in order to underscore the common character of ‘givenness’ of all these different entities. This will not be done in the sequel, however, when we return to using “data” in its more technical sense of operationally established states of affairs.
- 26.
See Agazzi (1969).
- 27.
See in particular Husserl (1913) and Meinong (1904). The solutions adopted by Husserl and Meinong are often said to be divergent. But they are not really. Rather, they correspond to the differences in approach we have just mentioned, and it is possible to reconcile them if a more positive interpretation of Meinong’s claims is made by resorting to certain elements of his ontology which are not really clear in his writings, but were fully specified by his student Ernst Mally (see Mally 1912). This is shown in a short but valuable presentation of the debate about intentionality, which took place at the turn of the century, provided in Chap. 6 of Zalta (1988). Zalta himself (as we have already said) develops his own theory of intentionality by using both Meinong’s distinction between being and existing (so that ‘abstract objects’ do not exist), and Mally’s distinction between determining and satisfying, which he reproduces in his notions of encoding and exemplifying. Thanks to this elaboration Zalta can give a theory of ‘abstract objects’ (which do not exist, in spite of encoding precise properties), and ‘ordinary objects’ (which exist and exemplify certain properties), as well as a fully-fledged theory of relations, which enables him to eliminate (in the most direct and convincing way we know of) all the usual difficulties connected with the principles of existential generalisation and substitutivity in intensional contexts. As we have already occasionally noted, there are many points of similarity between our theory of scientific objects and Zalta’s theory of intentionality. However, there are also differences, which will be discussed soon, and which in particular are also differences between our conception and Meinong’s, in spite (again) of several points of similarity.
- 28.
See Harré (1964), p. 48 ff.
- 29.
The page numbers quoted are from Zalta (1988).
- 30.
We should not like to give the impression of being particularly critical of Zalta. In fact his position not only has its clear and acknowledged historical roots in the works of Meinong and Mally, but is amply consonant with a rich production regarding ‘non-existent objects’ which is current in modern literature, where an emblematic title could be, for example, that of Parsons’ (very valuable) book Non-existent Objects (Parsons 1980). The reason we have discussed Zalta at length is that his approach constitutes, in our view, perhaps the best treatment of this kind of problem, and at the same time the one in which it is possible to see how this strange denigration of existence to certain things which ‘there are’ can actually be dispensed with.
- 31.
As an example of the second doctrine we could mention the Scholastic doctrine of the phantasmata (which we could translate as “sensory images”). These are not id quod cognoscitur (that which is known), but id quo cognoscitur (that through which one knows), and this in spite of our intellect not being able to know things unless it passes through these images (nisi convertendo se ad phantasmata). The other doctrine is explicit in Descartes, who claims that we know our ‘ideas’ and sees them as something whose origin must be causally explained. From the logical analysis of these ideas he believes it possible to infer the existence of things (e.g., of God and the external world) from their causes. Only the thinking subject escapes this fate, since it is present to itself in the act of cogito. This approach, as we have already said, was retained by the majority of modern philosophers up to Kant, and constitutes the philosophical doctrine that we have called epistemological dualism or representationalism. As we already said in a preceding note, these themes have been revisited in the contemporary theory of intentionality, but they are also to be found, for instance, in the Fregean distinction of Sinn (sense) and Bedeutung (reference), in several works of Russell, and so on (sometimes in a ‘representationalistic’ sense as in Russell, sometimes not). In addition to the literature already cited, let us mention here Searle (1983) and Dreyfus (1982).
- 32.
Let us note, however, that this identification is very different from that which characterises the referentialist and extensionalist semantics we have discussed in the preceding section. In that case, intension was actually eliminated, and it was maintained that meaning coincides with reference. In the case of epistemological dualism, instead, intension is present, and is indeed so dominant that it precludes access to the referent, and itself becomes the referent.
- 33.
Due to this fact, noemata may be at the same time ‘objective,’ that is, independent of the subjective ‘act of thinking,’ and from mental or psychological images of different kinds. But they cannot help being at the same time reality’s ‘way of being present to thinking’ in its various aspects. This was expressed by Frege when he tried to explain in what sense not only concrete referents, but also thoughts, are endowed with objective existence: “I understand by objectivity an independence from our perceptions, intuitions, and ideas, from the establishment of internal images, from the remembering of earlier perceptions, but not an independence from reason: for to say that things are independent of reason is to judge them without judging, which is like trying to wash the fur without getting it wet.” (Frege 1884, p. 36). In this Fregean statement we can find a short but significant formulation of the spirit of a non-naive realism, i.e. of a realism that does not reduce reality to simple ideas but at the same time does not overlook that we can state existence only of known realities.
- 34.
What we are explaining here is a brief presentation of the traditional distinction between intentio prima and intentio secunda, which we have already mentioned in a preceding section.
- 35.
We recognise, therefore, that existence statements may also be advanced, and are actually often advanced, on the ground of faith or belief, that is, on grounds that we here call noncognitive.
- 36.
See the discussion on the Kantian theory of the noumenon sketched in Sect. 1.7. It is interesting to note, in this context, that Husserl, precisely because he was anti-dualist, could not admit that if an external world exists it may be constituted by things-in-themselves that are in principle unknowable. This is possibly one of the reasons why, in the last stage of his philosophy, he became an idealist. A possible explanation of this fact (which, however, is not admitted by certain interpreters of Husserl) is that he thought that realism was untenable because the external world can be known by human beings only partially, in the sense that such knowledge could never be complete. Our comment is that this conclusion would not be logically correct. In fact, the incompleteness of our knowledge of the external world does not provably depend on the fact that there are, so to speak, parts of this world that are epistemologically inaccessible, but rather on the fact that the objectifications we can make of this world are potentially infinite, and that, as a consequence, our knowledge is inexhaustible even though it is always realistically referred to this world. We shall return to this issue in our discussion of realism (and, in any case, we do not maintain that this is a precise criticism of Husserl’s doctrine).
- 37.
In order not to complicate our discourse, we do not mention here those particular images which may be obtained by abstraction, and which could lead us to apply the present reasoning to abstract entities such as those of mathematics. Therefore we are not adhering to a basic empiricist view, as might have been suggested by the elementary examples used here.
- 38.
See, for example, Ingarden (1964/1965), vol. 1: Existentialontologie, p. 33.
- 39.
Certain authors have insisted that realism (be it common-sense or scientific realism) is a ‘metaphysical’ position and, as such, must not be confused with an epistemological or a semantic view, nor made dependent upon a particular theory of truth (such as a correspondence theory). This, in particular, is the position advocated in Devitt (1984). We can agree, to a certain extent, with this view, especially because in the examination of the literature on realism and anti-realism it often appears that anti-realist positions are taken as a consequence of the holding of particular semantic or epistemological tenets. This fact, however, cannot prevent one from recognising that a simple ‘metaphysical’ defence of realism, such as the one advocated by Devitt in the form of a very general ‘naturalistic defence,’ falls short of providing cogent arguments in favour of realism (though he is often rather convincing in his criticisms of particular forms of anti-realism). This is why we are convinced that a good deal of semantic analysis (and in particular a clarification of the issue of reference), as well as a close scrutiny of the notion of truth, are needed for a correct understanding of the issues at stake in the realism debate, and for the evaluation of the ‘arguments’ produced by the opposed parties in this debate.
- 40.
This ‘holistic’ conception of meaning has been particularly stressed, as we have seen, by those recent scholars who have made of it the fulcrum for advocating the theory-ladenness of every scientific term, the incommensurability of theories due to meaning variance, and so on. It is fair to recognise, however, that this doctrine is not that new. In fact it was already contained in the conception Frege himself considered to be the major novelty of his logic with respect to his predecessors, and even the reason why his logic was (to a certain extent) in opposition to that of Aristotle and the tradition.
This conception maintained the primacy of the proposition over the concept. The primitive unit of meaning is the proposition, in which a judgment (i.e., a content of thought) is expressed, and only by analysing this primitive meaning can we determine which concepts occur in the proposition, and establish their meanings. Traditionally, things were seen the other way round: by abstraction we first obtain concepts, and then we combine concepts to form judgements. The rejection of this conception certainly begins, philosophically, with the primacy of judgment explicitly stressed by Kant; but Kant was unable to translate this view into his way of conceiving of logic (his logic remains structured according to the traditional patterns, and so does his doctrine of judgment, which he still sees as consisting in the attribution of a predicate to a subject). It was only with Frege that the Kantian novelty found its recognition in logic (and in fact the relation subject-predicate is replaced in Frege by the relation function-argument). Concepts are regarded as unsaturated logical entities, and as such cannot be the primary bearers of meaning. Of course, this does not prevent, in the subsequent steps of the construction of a language, compound concepts’ being obtained by combining the senses of already available concepts and, similarly, determining the sense of a proposition on the basis of the senses of its constitutive parts, including concepts.
- 41.
As Schopenhauer pointed out, the German word for reality, i.e. “Wirklichkeit,” involves the idea of action (Wirkung). The same is true of the English “actual.”
- 42.
This conception of the pragmatic and operational nature of reference, which we have presented and defended for many years, has several affinities with doctrines that have been elaborated more recently. For example, it is not accidental that the ‘new semantics,’ or anti-Fregean semantics, of which we have spoken in Sect. 4.1—and which is typically a semantics of reference as opposed to a semantics of meaning—explicitly maintains that reference has ultimately to do with ostension, since all that matters as regards a referent is to identify it. This identification occurs in the context of a social communicative practice whose task, however, is not that of improving our understanding of a meaning: “the circumstances of utterance do help to provide us with an identification of a referent, but not by providing some descriptive characterisation of it” (Wettstein 1991, p. 26). The context of utterance, moreover, is only partially linguistic, not only because natural languages are conceived of as social institutions governed by a complex system of rules and conventions, but also because in concrete situations the identification of the referent is primarily bound to material gestures: “the pointing gestures not only provide cues as to the reference but actually determine the reference” (Wettstein, op. cit., p. 78; in general this work offers a well-developed account of these concepts).
But also Rom Harré has expressed a similar view of reference: “Referring is a human deictic practice, by which, with any means at hand, one person tries to draw the attention of another person to a being in their common public space” (Harré 1986, p. 97; the title of Chap. 4 of this work has the significant title: ‘Referring as a material praxis’). With respect to these and similar positions, we note that our theory is more elaborate and has the essential feature of relating reference to the more precise notion of operation, which is much more than simple gestures or a general ‘picking out’ as, for instance, in Harré’s example. This is why, in particular, we believe that our position is better suited for treating the problem of reference in the sciences, and better equipped for granting the stability of the referent—in spite of ‘meaning variance’—which we have already discussed.
- 43.
This explains why in the Foundations of Arithmetic (1884), where Frege was concerned only with the meaning of mathematical concepts, that is, of abstract objects, could he defend a purely contextualistic theory of meaning, while he opened a space for the consideration of the referent when he enlarged his considerations, for example in the paper ‘On Sense and Reference’ (1892).
- 44.
Let us recall that, according to the view proposed in this work, every scientific discipline is characterised by the specific ‘point of view’ from which it considers reality, which entails the adoption of certain specific predicates. They make the ‘specificity’ of the language of this discipline, in which the presence of several elements of an everyday language is simply a tool for communication and referentiality. Therefore, the ‘discourses’ formulated in a discipline certainly contain many expressions of common language, but are disciplinary only to the extent that they contain the specific predicates of the given discipline.
- 45.
It is obviously possible that a certain ‘point of view’ takes shape within another point of view, so that the two languages are more significantly interconnected than just through a community of reference; but we are not interested in discussing this point here.
- 46.
In the Second Day of the Dialogue Concerning the Two Chief World Systems, Sagredo (who expresses Gaileo’s position) celebrates the use of mathematics in the study of natural phenomena, and the Aristotelian Simplicio objects that to use mathematics is wrong, since in the realm of material things no geometrical properties really hold, due to the imperfections of matter. For instance, in the physical world it is never the case that a sphere touches a plane at a single point, as geometry would demand. This objection is rejected by Salviati, who remarks that this happens because in the material world no perfect spheres or planes exist, but this does not invalidate the geometrical reasoning, for “even in the abstract, an immaterial sphere which is not a perfect sphere can touch an immaterial plane, which is not perfectly flat, not in one point, but over a part of its surface, so that what happens in the concrete, up to this point, happens the same way in the abstract” (Galileo 1632, Opere VII, p. 233; English translation, p. 207).
Here we see that, while it is recognised that no concrete object could encode abstract properties, but only exemplify them within a certain limit, it is also possible to mirror the properties exemplified by a concrete object in an abstract object where they may be studied in full generality and in terms of logical necessity. The discussion in Galileo’s work continues with its being said that “the mathematical scientist (filosofo geometra), when he wants to recognise in the concrete the effects which he has proved in the abstract, must deduct (diffalcare) the material hindrances, and if he is able to do so, I assure you that things are no less in agreement than in the arithmetical computations.” (op. cit., p. 234; English translation, p. 207). Here we find the indication of the necessity of non-trivial efforts to find the exemplification of encoded ‘abstract properties’ in the realm of ‘concrete objects.’
- 47.
The considerations presented in this section enable us to propose a critical appraisal of a famous distinction advocated by Wilfrid Sellars in his paper ‘Philosophy and the Scientific Image of Man’ (1963, pp. 1–40). According to Sellars, the self-consciousness through which man-in-the-world realises the identification of his proper nature depends on a complex idealised view in which perceptual elements, conceptualisations, classifications, categorisations and theories of various kinds are deeply interrelated to form a global ‘image,’ an image which has gradually evolved from pre-historical times up to the present, and which we take for granted and consider obvious. This is the ‘manifest image’ of the world. With the creation of modern science, however, a new image of the world has rapidly emerged, the ‘scientific image,’ which is not in keeping with, but at variance with, the manifest image shared by common sense. According to Sellars, however, the manifest image (though being unavoidably the accepted frame of reference of our daily life) is wrong, and should be replaced by the scientific image, which gives us the true representation of reality.
Several criticisms have been levelled against this doctrine. They include that the manifest image is the ground on which the scientific image itself is founded; the different sciences offer different images of the world, so it is hardly sensible to speak of the scientific image; and science is in a continuous state of revision such that the scientific image capable of replacing the manifest image is at best an ideal and rather utopian end-state whose features and time of realisation we cannot even imagine.
We are not interested in discussing these (and similar) criticisms, since we see certain deeper reasons for disagreement with Sellars. The first is that his separation fails to consider the distinction between things and objects and, in particular, ignores that the sciences investigate only a limited number of specific attributes of things (e.g., physical attributes). But also common sense cannot do otherwise: the manifest image of the world is that which is elaborated starting from a rather large, but still limited, number of attributes, and contains those conceptualisations and theories that are considered adequate for understanding and explaining the world as characterised through such attributes. Moreover, both science and common sense do not limit themselves to producing intellectual constructions, but try to secure their access to reality (and truth) by means of their criteria of referentiality. In the case of the sciences they are standardised and few in number, but common sense too relies upon a variety of commonly shared operations and ways of doing things that enable people to ‘meet’ things and refer to them in the concrete.
This common situation becomes even clearer if we consider that the operational criteria of referentiality are of a practical nature, not only in the elementary sense of constituting a concrete way of acting, but also in the sense of belonging to praxis, i.e., of being determined by the needs and the ends of a particular human activity. Therefore their adequacy must be measured according to their ability to satisfy these needs and fulfil these ends. Once this is clear, it is also clear that the manifest image of the world is cognitively right and adequate for the conduct of man in the multiple activities of his ordinary life (and it also easily absorbs several contents of the scientific image when this is needed). These considerations, by the way, capture the reasons for which social/pragmatic relativism is partially right. In other words, the pluralistic ontology we have advocated as a consequence of considering the different sets of attributes of reality and their different conditions of referentiality justify a view according to which the manifest and the scientific images of the world are complementary rather than in opposition. The deeper reason for Sellars’ position is that it is a combination of metaphysical realism and partial epistemological dualism. It is obvious that he is a ‘scientific realist’ (in the strongest sense of maintaining that science gives us a true representation of reality as it is). But at the same time he is also an epistemological dualist, since he maintains that the manifest image of the world that humans have in their most common way of knowing is not a true portrayal of reality. This amounts to saying that reality exists independently of our knowledge of it (metaphysical realism), and that knowledge cannot be had of reality by ordinary means. However, this reality can be faithfully represented (though only in an idealised limit-situation) by science.
It is not accidental that Sellars himself recognises the affinity of his position with that of Kant. He agrees with Kant that the world of common sense is a ‘phenomenal’ world, but he submits that ‘scientific objects,’ rather than the metaphysical unknowables, constitute the true things-in-themselves, which science is able to know (see Sellars 1968, p. 143).
- 48.
A rather detailed analysis of this issue may be found in Agazzi (1988b). We shall return to this discussion in a later section.
- 49.
See Meinong (1902) and Marty (1908).
- 50.
See Husserl (1901), pp. 288–289 of the English translation. An interesting study of this view of Husserl on states of affairs is contained in Mulligan (1989). It is not sufficient to admit autonomy to the world of meaning in order to preserve the difference between sentence, proposition, and state of affairs. Indeed, states of affairs and propositions may be identified not only when one neglects the autonomy of the intermediate level of sense, but also if one overlooks the specificity of the world of referents. This was already done by Frege. A more recent example is to be found in Zalta (1988). We can say that such an identification of proposition and state of affairs results in a kind of trivialisation. Instead of designation, of reference, an ontological identity is introduced, instead of an identity which is only intentional. Husserl was aware of this difference (which was already clear to Scholastic philosophy), and did not make this mistake.
- 51.
It is perhaps not superfluous to compare our approach with Carnap’s, which is still the most commonly followed in standard epistemology of the empirical sciences. In Carnap (1942), an appendix is devoted to terminological remarks, where the terminological variations concerning the meanings of “sentence” and “proposition”—to be found in different authors and dictionaries—are reviewed. Carnap particularly recommends using “(declarative) sentence” as a linguistic expression, and “proposition” as the designatum of the sentence, that is, “that which is expressed (signified, formulated, represented, designated) by a (declarative) sentence” (p. 235), which is explicitly equated with Wittgenstein’s notion of state of affairs. Here we find on the one hand a certain recognition that only statements (i.e., declarative sentences) matter in the epistemology of the sciences, and on the other hand an identification of propositions with states of affairs, which reflects the elimination of the ‘second level’ already discussed in Sect. 4.1. An account of the complexity of the topic sketched here may be profitably read, for instance, in Cohen (1962).
- 52.
We shall see that theories are closer to the semantic than to the apophantic logos to the extent that they have a ‘representational’ rather than explicitly ‘declarative’ character. In this sense a theory—like a concept, which typically belongs to the semantic and not to the apophantic logos—is always incomplete, and involves a certain degree of implicitness. It is incomplete in the sense that it always intends to express a certain ‘way of seeing’ a given field of reality, leaving many other aspects out of consideration. It is largely implicit because it consists, as we shall see later, in the proposal of a certain global Gestalt, which can only partially be translated into a finite set of explicit declarative sentences, though it must undergo such a translation if it is to be submitted to tests or, in general, to a critical examination. These considerations will become clearer in Sects. 5.4 and 5.5, where more will be said about the nature of theories.
- 53.
This fact should be obvious: “London is a city,” and “Londres est une ville” are different sentences (they even belong to different languages), but have the same sense, that is, they express the same proposition. It is because this common proposition is true that we can say of these sentences (in an extended but acceptable sense) that they are true, as are all other sentences, in all possible languages, that express the same proposition. This seems to be a small detail, but it removes the difficulty of defining truth only relative to a given language which is, as we shall see, a shortcoming of the usual definitions of truth, which define truth directly for sentences, rather than indirectly, through the proposition which is expressed or denoted by the sentence. This is also the case as regards the Tarskian definition of truth, and Tarski is fully aware of this fact (see Tarski 1944, p. 342). The necessity of in some way obtaining a proposition when using only a sentential semantics is often alluded to in the philosophical literature in terms of the notion of semantic ascent, which will not be discussed here.
- 54.
This is tantamount to saying that sentences (and, we say, propositions) are truth-bearers, but that there must be something in virtue of which they are true. This something may be called the truth-maker of the sentence. As to the determination of these truth-makers, different proposals have been put forward. On our view—which distinguishes a purely linguistic level (sentence), a noematic level (proposition), and a referential level (state of affairs)—what makes a sentence true is not its related proposition (which is only its sense), but the state of affairs to which the sentence refers. Indeed, we maintain that the state of affairs makes the proposition true (or false) and, indirectly and automatically, makes true or false all sentences which express this proposition in any possible language.
However, in those conceptions in which the three levels are reduced to two, this option may be impossible to adopt. For example, Zalta gives full space to the world of noemata, but fails to seriously provide a space for the world of referents, so that he accepts the identification of propositions with states of affairs, and claims that they are both ‘abstract,’ since both are constituted by properties and relations, which are abstract objects. As a consequence, he is led to say that propositions possess in themselves a “metaphysical truth or falsity [which] is basic. If a proposition is true, there is nothing else that ‘makes it true.’ Its being true is just the way things are (arranged)” (Zalta 1988, p. 56). According to this view, the basic ‘metaphysical’ truth of propositions is what assures the derivative ‘semantic’ truth of sentences. Needless to say, we have here to do with a rather peculiar and unclear notion of ‘metaphysical truth,’ which creates certain difficulties even with other aspects of Zalta’s theory. But the reason for adopting this position seems to reside in the fact that referentiality has been considered impossible in the case of properties and relations.
This does not happen, for example, in the case of those authors who have developed a theory of ‘truth-makers’ in which attributes (in our terminology; or moments in the authors’ terminology) function as truth-makers (see, e.g., Simons 1982, Mulligan et al. 1984). This theory may be considered a significant refinement of a position which Russell expressed in a well known passage of The Philosophy of Logical Atomism, where he said: “When I speak of a fact… I mean the kind of thing that makes a proposition true or false” (Russell 1918, p. 36), a position which is interesting to the extent that it shows that also for Russell (at least at a certain stage in his intellectual development) propositions were truth-bearers and not truth-makers. More about this problem will be said in the Sect. 4.4.5.
- 55.
Two fundamental works must be taken into consideration in order to understand the Tarskian theory: Tarski (1933, 1944). The first contains the complete and technical development of Tarski’s definition of truth for formalised languages; the second is devoted to the discussion of some relevant philosophical aspects of the notion of truth. For our purposes it will be sufficient to consider the 1944 paper.
- 56.
We are here following Tarski (1944), with the following slight modification. Tarski introduces (T) as a sentence ‘schema’:
(T) X is true if, and only if, p,
where p is a sentence and “X” is the name of this sentence. From (T) actual sentences may be obtained by substituting for “X” and “p” in the way just indicated. Our example involves such a substitution and (as Tarski himself says) may be considered for that reason to be a “partial definition of truth,” that is, a definition of truth for the particular sentence considered (here, “Snow is white”).
- 57.
We have said that this distinction has been neglected, but we do not say that it has been totally ignored in contemporary philosophy. Indeed, we have already mentioned Frege’s insistence on the difference between declarative sentence (Behauptungssatz), simple thought (Gedanke), and even judgment (Urteil). A declarative sentence is a kind of ‘notification’ or ‘announcement’ (Kundgebung) of a judgment (see Frege 1918, p. 62). And while declarative sentences must always be either true or false, this is not the case with thoughts. Another, even more explicit, recognition of the difference we are speaking about is to be found in Husserl, who uses the term “apophantics” to indicate that part of formal logic which is concerned with the predicative judgment, following in this way the Aristotelian and, in general, traditional terminology (see Husserl 1929, p. 63). One can also say that recognition of the difference between a statement and a sentence—which we have explicitly accepted, and which has a certain circulation in the philosophy of language—indicates an awareness of this distinction. However, we still have the impression that this difference has not really been thoroughly exploited, as we shall try to do in what follows of this section. For more details on this distinction, see Agazzi (1989).
- 58.
Tarski (1944), p. 341.
- 59.
After having explained that the definition of truth must be given in the metalanguage, Tarski says:
It is desirable for the meta-language not to contain any undefined terms except such as are involved explicitly or implicitly in the remarks above, i.e., terms of the object-language; terms referring to the form of the expressions of the object-language, and used in building names for these expressions; and terms of logic. In particular, we desire semantic terms (referring to the object-language) to be introduced into the meta-language only by definition. For, if this postulate is satisfied, the definition of truth, or of any other semantic concept, will fulfill what we intuitively expect from every definition, that is, it will explain the meaning of the term being defined in terms whose meaning appears to be completely clear and unequivocal. And, moreover, we have then a kind of guarantee that the use of semantic concepts will not involve us in any contradictions (Tarski 1944, pp. 350–351).
- 60.
“It may seem strange that we have chosen a roundabout way of defining the truth of a sentence, instead of trying to apply, for instance, a direct recursive procedure. The reason is that compound sentences are constructed from simpler sentential functions, but not always from simpler sentences; hence no general recursive method is known which applies specifically to sentences.” (Tarski 1944, p. 353).
- 61.
Tarski (1944), pp. 361–362.
- 62.
A good analysis of this point is provided in Keuth (1978), pp. 64–72.
- 63.
That Tarki’s semantics is of this kind may be easily seen from the few lines where he explains why his definition of truth is to be called “semantic”:
I should like to propose the name “the semantic conception of truth” for the conception of truth which has just been discussed.
Semantics is a discipline which, speaking loosely, deals with certain relations between expressions of a language and the objects (or “states of affairs”) referred to by those expressions. As typical examples of semantic concepts we may mention the concepts of designation, satisfaction, and definition. (Tarski 1944, p. 345.)
It is evident that we here have to do with a ‘two-level’ semantics, considering only the language-world relation, and ignoring the mediation of the senses (and the existence of speakers and listeners). This was already clear at the beginning of the paper, where Tarski declines attempting to define truth for propositions, since,
as regards the term “proposition,” its meaning is notoriously a subject of lengthy disputations by various philosophers and logicians, and it seems never to have been made quite clear and unambiguous. For several reasons it appears most convenient to apply the term “true” to sentences, and we shall follow this course. (ibid., p. 342).
It is therefore embarrassing (but not surprising, as we know) that such a semantics remains unable to justify a notion of truth in which reference to the world is actually made, as we shall see in the sequel.
- 64.
Tarski (1944), p. 343.
- 65.
Tarski (1944), p. 344.
- 66.
Tarski says: “Much more serious difficulties are connected with the problem of the meaning (or the intension) of the concept of truth” (Tarski 1944, p. 342).
- 67.
Among the most famous writers who have interpreted Tarski as a supporter of the correspondence theory let us mention Popper (especially Popper 1972) and Davidson (see Davidson 1969). Among those who have denied this qualification, let us mention Black (1949), Field (1972), Harré (1986) and Keuth (1978). At any rate, what is certainly undeniable is that Tarski himself explicitly intended his theory to be a specification of what he indicates as the classical, Aristotelian correspondence theory of truth, as is clearly stated not only in the more ‘philosophical’ paper of 1944, but already in the introduction of his extensive and technically complex 1933 monograph:
I would only mention that throughout this work I shall be concerned exclusively with grasping the intuitions which are contained in the so-called classical conception of truth (‘true—corresponding with reality’) in contrast, for example, with the utilitarian conception (‘true—in a certain respect useful’). (Tarski 1933, p. 153 of the English translation.)
I mean a definition which we can express in the following words: a true sentence is one which says that the state of affairs is so and so, and the state of affairs indeed is so and so (ibid., p. 155).
All that is to be done therefore is to see whether the result he obtained actually corresponded to his intentions. What we have seen (and what his critics after all are able to show) is that his definition does not necessarily imply a correspondence theory of truth, that it is also compatible with other doctrines. But it would be unjustified to say that it does not provide a suitable framework for an acceptable formulation of that theory, and that it is naturally oriented in such a direction.
- 68.
Before passing on to this analysis, however, let us briefly discuss the question whether Tarski’s truth-predicate corresponds to an analysis of the semantic conception of truth that has become involved in what is called “formal semantics.” This does not seem to be the case, in spite of the fact that the technical tools introduced by Tarski in providing his ‘recursive’ truth-predicate have paved the way for such further developments, which on the other hand required the introduction of an undefined notion of truth. (For a valuable discussion of this and related issues see Etchemendy 1988.)
The reason for this—as we have already hinted—is that Tarski wanted to avoid recourse to senses and propositions, while the most natural way of understanding the whole issue (a way which is also accepted by modern formal semantics) is that the sentence “Snow is white” makes a claim which depends on the colour of snow, while the sentence “‘Snow is white’ is true” makes a claim that depends both on the colour of snow and on the meaning of “Snow is white.” This implies that the left and right sides of (T) are not on an equal footing. However, it is for this reason that the biconditional expressed by (T) is informative, that is, that it gives us information about the meaning of the sentence “Snow is white.” The fact that Tarski, in spite of elaborating an ‘eliminative’ truth concept, introduces his equivalence (T) as a touchstone for evaluating the material adequacy of his definition of truth, indicates that he was actually working to some extent with “a hybrid of different pretheoretic conceptions of truth” (Etchemendy 1988, p. 62). In particular, the concept of truth that Tarski tries to analyse retains certain elements of that which is called the propositional conception of truth, which sees truth as a property of extralinguistic entities, independent of the linguistic or semantic features of any particular language (on this point, see again Etchemendy 1988, pp. 62–63).
- 69.
See Tarski (1944), p. 342–343.
- 70.
Categ., 4.2a, 8–10. Other passages in which he speaks of the apóphansis are, for example: De Int., 4, 17a2; 5, 17a22; 6, 17a25; An. Pr., I. 1 24a16. According to Aristotle, the apóphansis is in general the declarative sentence, which may be either an affirmation (katáphasis), or a negation (apóphasis: notice the difference in the orthography). Latin authors translated the Aristotelian term differently, with enunciatio, sententia, propositio, which are the obvious etymological antecedents of our “statement,” “sentence,” and “proposition”; but in general, in the traditional textbooks of logic, one speaks of judgment, and in more recent textbooks one finds “apophantic judgment” in the sense of “predicative judgment.”
- 71.
Here is the complete passage:
This is clear, in the first place, if we define what the true and the false are. To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true; so that he who says of anything that it is, or that it is not, will say either what is true or what is false; but neither what is nor what is not is said to be or not to be. (Metaph. 1011b26–29; transl. by D. Ross.)
This is, by the way, the Aristotelian text which Tarski explicitly quotes in his article of 1944.
- 72.
Let us simply provide additional confirmation by quoting a few lines from the De Interpretatione, where the definition of truth is given through a clear reference to a state of affairs, or to something being the case, rather than to existence. The text is quite compact (but clear), and the translation should not be too literal in order to make it easily understandable in English: “If it is true to say that a thing is white, it must necessarily be white. Again, if it is white, the proposition stating that it is white was true; if it is not white, the proposition to the opposite effect was true. And if it is not white, the man who states that it is, is making a false statement; and if the man who states that it is white is making a false statement, it follows that it is not white. It may therefore be argued that it is necessary that affirmations or denials must be true or false.” (Hermen. 9, 18a40–b4; translated by E. M. Edgehill, W. D. Ross editor). A similar declaration is formulated more synthetically in Metaph., IX, 10, 1051b5.
- 73.
To be more precise, the term “correspondence theory of truth” is rather recent, and was introduced by Russell when, against the doctrine of absolute idealism which claims that “truth consists in coherence,” he wanted to maintain that “truth consists in some form of correspondence between belief and fact.” In this sense, the correspondence theory of truth is a recent doctrine, which was probably defended in its explicit form by a few authors such as Russell, Moore, and the early Wittgenstein. However, it has predecessors in the whole history of Western philosophy, starting with Plato. But if we extend its scope to such a broad spectrum, it becomes almost impossible to characterise it univocally (e.g., it is hard to say whether the Scholastic definition of truth as adequatio intellectus et rei should be qualified as a correspondence theory). For a condensed but excellent account, see Prior (1967).
- 74.
It is not without interest to note that Hegel’s criticism of Kant’s doctrine of the unknowable thing-in-itself was expressed, at least on one occasion, by stressing how this theory would make self-contradictory the very notion of truth. We would accept “the contradiction of a truth, which must be at the same time non-truth, a knowing of what is, which at the same time does not know the thing in itself” (Hegel 1812, 1969 ed., vol. 2, p. 500).
- 75.
This conception was already included in a thesis of Scholastic philosophy, which it is fashionable to discredit as being naively realist and committed to uncontrolled metaphysical enthusiasm. This thesis concerns the identification of the famous ‘transcendentals,’ that is, the identification of those features of reality which were thought to be endowed with such a degree of universality as to be ‘commutable’ with being itself. These transcendentals, as is well known, are unum, verum and bonum. Let us only consider verum (truth), which is of direct relevance to our discourse. Why was it claimed to have the same ‘latitude’ as being itself (ens et verum convertuntur)? Simply because verum was not conceived of as something existing besides ens (note that this would be impossible, because everything existing is ipso facto included in the domain of being), but as being ens itself as far as it bears a relation to thought. This doctrine was sometimes summarised by saying that the sentence ens et verum convertuntur expresses the ‘intelligibility’ of being.
This may be accepted, but it is perhaps more perspicuous to a modern reader if we say that it expresses three fundamental facts: (a) that there is no possible ‘exteriority’ of being with respect to thought (not in the sense that being coincides with thought, but in the sense that one cannot even think of a being as ‘external’ to thought, without including it in thought by this very act); (b) that it is not possible that thought be exterior to being (thought must necessarily be thought of something, otherwise it would be thought of nothing and therefore ‘no thought’ at all—this amounts to a radical rejection of epistemological dualism); (c) that this non-exteriority of thought and being does not imply their ontological identity, but only an intrinsic and necessary relation between them. This was sometimes indicated as ‘the intentional identity of thought and being,’ and we prefer to indicate it with the notion of the relation of referentiality. We can therefore conclude that this third fact may be seen as making explicit that being is the referent of our thinking activity and of the relational nature of truth.
Let us point out a curious fact. We are spontaneously accustomed to saying that truth is the property of a sentence, of a discourse, of thought (to the extent that it is expressed in a discourse). The ancient way of thinking analysed above seems instead to conceive of truth as a universal property of reality, and this can be somewhat puzzling. However, there is little reason to feel puzzled. Truth is neither a property of discourse nor of reality proper, for it is a relation between them—so we might be more inclined to lay stress on one of the poles of the relation rather than the other; but both are necessary. It is a little like preferring to say that X is the father of Y rather than that Y is the child of X. Both sentences express the same relation from two different points of view, and this is why, though having different meanings, they express the same state of affairs, and are true or false under identical circumstances.
- 76.
We shall return to the distinction between the definition and criteria of truth in Sect. 4.6.
- 77.
It is certainly not accidental that in the passages just mentioned (Tarski 1933, p. 153 and 155) the author explicitly wants to contrast his conception with what he calls the utilitarian conception of truth, which we would now call the instrumentalist conception. Moreover, in Kokoszynska (1936) the author, who was a pupil of Tarski, very carefully analyses the differences between the Tarskian approach and the logical positivists’ theory of truth, as it was expressed at that time, especially by Carnap in his Logical Syntax of Language (Carnap 1934). Kokoszynska qualifies the Tarskian view as “The absolute truth concept” (p. 149), and this expression is intended to oppose what she presents as the coherence theory of truth, which was actually implied in the logical positivist effort to eliminate the truth concept:
The efforts to eliminate the truth concept from science proceed mainly in a determinate direction. One tries namely to replace this concept through a syntactic concept. Every coherence theory of truth, i.e., every theory according to which the truth of a sentence consists in its correspondence [Übereinstimmung] with other sentences may—fundamentally—be considered as such an effort. To this it is usually opposed, as a correspondence theory of truth, the theory that truth consist in a correspondence [Übereinstimmung] with reality (op. cit., p. 149).
It is not our aim here to discuss Kokszynska’s paper, which clearly explains why the Tarskian conception of truth can “by no means be reduced to a concept related to the syntax of any language” (p. 153), and at the same time explains why it is not intended to provide criteria for truth (pp. 156–157). We would simply like to call attention to the fact that in his 1944 article Tarski himself makes reference three times (with approval) to this paper of his former pupil. This constitutes an important confirmation of what is already sufficiently clearly expressed in his direct statements, where the acceptance of the ‘classical (i.e. Aristotelian) correspondence theory of truth’ is indicated as the notion he accepts and wants to clarify.
Therefore it is simply fair not to put Tarski against himself, or to charge him with inconsistency or lack of insight, by saying, for example, as Max Black does:
I cannot accept Tarski’s claim that his definition favors the “classical Aristotelian conception of truth.” I regard his view as neutral to this and other philosophical theories of truth (Black 1949, p. 105).
This interpretation of Tarski’s theory has become rather common. Putnam, for example, also maintains that “Tarski’s work is philosophically neutral; that is, it does not vindicate the correspondence theory of truth” (Putnam 1983, p. 83).
The fair way of interpreting Tarski, as we have already discussed in the preceding section, seems therefore to be the following:
-
(a)
the intuitive ‘correspondence’ conception is pre-theoretically accepted;
-
(b)
the effort is made to provide a definition for the use of the concept of truth which will protect it from introducing inconsistencies in the language;
-
(c)
the definition is given in two ways: the first simply by ‘codifying’ the fact that a correct speaker cannot assert a sentence and at the same time say that it is not true; the second by constructing the concept of truth from the concept of satisfaction.
The result is therefore that we can rely upon this conception because it will not introduce inconsistencies if properly applied. Now the problem is whether the intuitive conception receives some kind of additional support or indication of plausibility. This support is not implied by the first ‘extensional’ definition, since the ‘reason why’ a speaker asserts “p” (or the ‘criteria’ for such an assertion) are irrelevant to the fact that this speaker cannot refuse to call “p” true, if he or she asserts it. The second, ‘recursive,’ definition, on the other hand, is closer to the intuitive conception, since the concept of satisfaction, as presented by Tarski himself, clearly expresses a language–world relation, in which, in the last analysis, words are put into correspondence with non-linguistic entities, with objects. This is also demanded by the meaning of the concepts one uses in doing this, such as that of ‘denoting’ in the case of a name or an individual variable, of ‘applying’ in the case of a predicate, or of being ‘fulfilled’ in the case of a sentential function or a sentence. This situation has been explicitly recognised, for example, by Davidson, where he admits that:
The semantic concept of truth as developed by Tarski deserves to be called a correspondence theory because of the part played by the concept of satisfaction; for clearly what has been done is that the property of being true has been explained, and not trivially, in terms of a relation between language and something else (Davidson 1969, p. 758).
For this reason we cannot agree with those who consider Tarski’s efforts as “philosophically irrelevant,” because, to repeat with Black:
The philosophical disputants are concerned about what in general entitles us to say “It is snowing” or “London is a city” and so on. In other words, they are searching for a general property of the designata of true object-sentences (Black 1949, p. 105).
In fact, it is already philosophically relevant to know that we can use the intuitive notion, call it “correspondence theory” or what you will (which was held responsible for contradictions such as the antinomy of the liar) as a legitimate content or sense of our concept of truth, and that we are ‘guided’ by this notion in selecting the definitional starting point for the construction of a formal recursive definition of truth.
However, we must also recognise that it was not within the reach of Tarski’s conceptual approach to give a more satisfactory characterisation of the intuitive or ‘classical’ conception. This is simply because the classical conception was equipped with a theory of knowledge in which intentionality played a central role, while Tarski, in spite of having broken the constraints of a purely syntactic perspective, was still imbued with the empiricist atmosphere of his philosophical environment, and could not make more explicit what it means for a sentence to ‘correspond to a state of affairs.’ His semantics remains, as we have called it, an extensional semantics; and it is not accidental that its precious technical tools could be used for the elaboration of modern ‘formal semantics’ only when they were supplemented with the consideration of meanings, as we have already mentioned in a note in the preceding section.
Something similar also applies to the other great contribution due to Tarski, that is, his characterisation of the notion of logical consequence in terms which are not purely syntactic. Here again, successive ‘model theoretic’ tools, which are usually considered to constitute a coherent development of Tarski’s original view, are rather at variance with this view. They could develop out of Tarski’s techniques only because they were tacitly equipped with meanings they did not actually have in Tarski’s original approach. In our terminology, we should say that they were to be interpreted in the spirit of an intensional semantics (see Agazzi 1976). In a more recent work, John Etchemendy has advanced similar remarks, and supplemented them with a thorough analysis, vindicating the role of a representational semantics which has essentially the same meaning (see Etchemendy 1990). By considering all these elements, one may adopt a more objective attitude towards Tarski than that which is based only on a strictly logical analysis of his papers. For example, most (or perhaps all) of the critical remarks advanced in Field (1972) are correct in themselves, but not equally pertinent as an interpretation of Tarski’s programme, since it must be evaluated historically, that is, by considering what Tarski could express within the framework of the concepts available to him in the 1930s, and not on the basis of clarifications which have come much later.
-
(a)
- 78.
“The drive towards truth” said Frege, “is that which pushes us forward from sense to reference” (Frege 1882, p. 33). We do not maintain that meaning reduces to this (in fact we have already said that, for us, meaning includes both sense and reference). But we can agree to a large extent, for example, with Dummett, when he states that a “grasp of the meaning of a sentence of a language is to be taken as consisting in a knowledge of the conditions for it to be true” (Dummett 1973, p. 460).
- 79.
See the discussion in Prior (1967), p. 228.
- 80.
See Davidson (1969), pp. 752–753, and Keuth (1978), pp. 76–84, for this kind of objection.
- 81.
Davidson (1969), p. 759.
- 82.
Ibid.
- 83.
See Categories, Chap. 2.
- 84.
Let us mention in this connection the articles: Simons (1982) and Mulligan et al. (1984). The second of these papers contains useful references to additional literature. We should like to stress, however, that an analysis of these topics, from both an historical and a critical point of view, had already been offered in Küng (1963), which can therefore be reckoned as the first proposal for the development of an ontology of ‘concrete properties’ in connection with modern semantic analysis.
- 85.
However, these are rediscussed and refined along the lines of the formal ontology opened by Husserl in the third of his Logical Investigations.
- 86.
See Mulligan et al. (1984), p. 294.
- 87.
This is concisely put by Simons as follows: “Many, perhaps all, states, events and processes involve substances, and are thus moments” (Simons 1982, p. 159).
- 88.
Let us consider the example given by our authors:
If ‘This cube is white’ is true, then it is true in virtue of the being white (the whiteness) of this cube, and if no such whiteness exists, then ‘This cube is white’ is false.
Because the whiteness in question here is a particular dependent on the cube, and not a universal whiteness shared by all cubes, its existence does nothing to make sentences about other things’ being white either true or false (Mulligan et al., op. cit., p. 297).
A minor point is that, apparently, there is a small inaccuracy in this statement since, instead of saying “shared by all cubes,” the context obviously required saying “shared by all white objects,” because it is not the fact of being cubic, but the fact of being or not being white, that would matter for the attribution of the moment of whiteness to a substance. This remark, however, draws our attention to a decisive point. Even though we recognise a moment as being particularised to a given substance, we cannot elevate a particularisation to the level of making the moment dependent on that particular substance, not only as to its existence (which is correct, since the substance is its basis), but also as to its essence or quality. This is tantamount to saying that it would be absurd to maintain that a given moment may exist only in a given substance. If we pushed the ‘individualisation’ of moments that far, we would completely trivialise their function, and would be obliged to designate them by proper names. On the contrary, we want to be entitled to say that whiteness has an individuality as a moment, but this in the sense that it is different from redness or blackness, and so on. However, this does not prevent this moment (and in general all moments) from being aptum inesse pluribus, so that even if the whiteness which is in Socrates does not coincide completely with the whiteness of our cube, or with the whiteness of snow, it must be in all these cases an exemplification of whiteness.
But now we have an inevitable consequence. If whiteness is not in itself the whiteness of any particular substance, it follows that it might well not exist in this cube. It might be one of the many moments which are not exemplified by our concrete cube. The contingent fact that this cube and whiteness are combined is the particular state of affairs that makes our sentence true. In this way we could even vindicate the possibility of speaking of facts as truth-makers, a possibility against which many contemporary philosophers would revolt, but which is acceptable to the extent that facts are understood just in this way. However, since the use of the word “fact” is open to many ambiguities, we shall refrain from using it when we specifically speak of truth-makers, or of referents of sentences, using instead the less disputed expression “state of affairs” which, in addition, has for us the technical sense explained.
- 89.
A significant example of this sense is provided in the first pages of Prior (1971).
- 90.
In this way we can maintain that sentences refer to their truth-makers, while in the perspective of the authors we have discussed, truth-makers are not designated by the sentences they make true (p. 303). These authors do not consider this an inconvenience, but we believe that to leave the question of the reference of a linguistic expression (i.e., a sentence) without answer is not a desirable feature of a semantic analysis. For a different but related criticism of this conception, see also Buzzoni (1995), pp. 49–53, where the expression indirect realism is adopted in this connection.
- 91.
We are even prepared to say that the state of affairs exists, since existence is an ‘analogical’ concept; and we can therefore say that for a substance to exist means to have an independent ontological status, that for an attribute it means to be inherent in something else, and that for a state of affairs it means to be the case.
- 92.
This was, in particular, the Marxist conception of knowledge as the “Widerspiegelung” (“mirroring”) of reality; so we can say that Marxism was one of the most paradigmatic expressions of the ‘rough’ correspondence theory of truth. We do not underestimate, however, more refined forms of conceiving mappings, projections, or representations of reality that have been developed by several authors and that we are not going to consider here.
- 93.
See Frege (1918).
- 94.
For a critical examination of this point, see Mulligan et al. (1984).
- 95.
We have already quoted Davidson (1969), and Keuth (1978) for a presentation of this objection.
- 96.
Rescher (1982), pp. 263–266.
- 97.
However, what we have established regarding the plurality of ontologies secured by the recognition of the ‘realist’ purport of the various kinds of criteria of referentiality is by no means elementary or trivial.
- 98.
Let us note that this is why there is such a general agreement about taking empirical evidence to imply what is usually called “ontological commitment” (that is, the existence of something “real” of which this is evidence). As we have already noted, sensory experience is an encountering, one’s ‘meeting’ things, and not simply a formation of images. Both idealists and realists may agree about this “ontological function” of empirical concepts; idealists because, all kinds of reality being for them nothing but intentional, they have no special reason for denying reality (in this sense) to sensory evidence as well; realists because, when distinguishing between intentional reality and concrete reality, they must give at least one criterion for recognising the latter, and no better criterion seems available than that offered by sensory evidence. In conclusion, unless one is ready to claim that nothing exists, or that we know nothing (not in the sense that we do not know anything, but in the sense that what we know is nothing), one should at least admit that the referents of what we could call immediate empirical evidence are real in a full “ontological” sense. Hence, as the attributes which are operationally defined in a science have the characteristics of the immediate empirical evidence, they are referents which are real in this genuine “ontological” sense.
- 99.
Tarski (1944), pp. 361–362.
- 100.
The coherence theory, Rescher says, “is designed to give (or at any rate is best construed as providing) an answer to the problem of a criterion for truth” (p. 10). “The position we shall defend supposes that coherence is not the meaning of truth in the context of factual claims, but its arbiter (to use F. H. Bradley’s well-chosen word).” (Rescher 1973, p. 12).
- 101.
As a matter of fact, this prominence of the correspondence theory as to the determination of the pure meaning of truth has been more or less explicitly recognised by many of the most serious proponents of the coherence theory, as is sufficiently documented in the first two chapters of Rescher’s book.
- 102.
The distinction between definitions and criteria of truth, as we have already said, is not always made in the literature, and even the meaning of “criterion” is not clear. The most usual notion of criterion is that of a sufficient condition (though in the philosophical-linguistic debate on the nature of criteria, they are normally considered to be neither necessary nor sufficient.) For instance, in mathematics we find an explicit definition for the convergence of a series, stating necessary and sufficient conditions for a series’ being convergent. This definition, however, is often of no use for establishing whether a given series is convergent or not, and certain criteria have been found (e.g., Kummer’s criterion). They indicate sufficient conditions for convergence that may be usefully applied in concrete cases, but which are not requested for the convergence of any series whatever. In the case of Rescher’s coherence theory of truth, coherence seems rather to play the role of a necessary but not sufficient condition for truth, since a sentence can be considered as a good candidate for truth only if it is consistent with the system of sentences already admitted as true (necessary condition). But an additional requirement must come into play, i.e., the presence of data among the sentences of this system (see footnote 11).
In the case of the acceptance theory of truth, acceptance seems to play the role of a sufficient condition, not in the sense that it is sufficient to grant that the generally accepted sentence corresponds to the facts, but in the weaker sense that we have no better means for believing that it is true. In the case of the pragmatist definition, practical usefulness plays the role of a necessary and sufficient condition, since truth is displaced from the domain of theoretical to that of practical reason. (In this sense, the definition of truth as correspondence to the facts loses its representational characteristic and is reduced to a pragmatic efficacy in ‘dealing’ with the facts).
An interesting case is that of instrumentalism, a case which is related to the pragmatist view of truth (indeed, this term has been coined by John Dewey) but which has additional features. If it is understood not in the trivial sense currently attached to it (according to which it is equated with relativism and conventionalism) but in the much more refined sense presented, e.g., in Fine (1986), it maintains that what we must require of a (scientific) sentence or theory is that it be reliable for practical as well as for theoretical purposes. Reliability does not entail nor presuppose truth; it simply allows us to ‘dispense with’ truth and, in this sense, constitutes a ‘deflationary’ position according to which reliability is a necessary and sufficient condition not for truth, but for acceptability. The foregoing sketchy reflections indicate that even the notion of “criteria” for truth is still in need of precisions that are not fully developed in the literature.
- 103.
Rescher (1973), p. 27.
- 104.
It is therefore clear that our way of indicating the correspondence between true sentences and facts is completely alien to those characterisations on which many criticisms of the correspondence theory are based, criticisms which unduly attribute to this theory the fallacy of considering language as a copy or mirroring of the world. (We have already discussed this issue; for a few additional references and examples, see Rescher 1973, pp. 8–9).
- 105.
Two points may be useful. The first is that we have said nothing concerning false sentences in order to avoid discussions regarding the ‘bivalence principle,’ which would take us far from our immediate concern without being of decisive help in clarifying our issue. In fact it suffices to say that if (under whatever form or circumstances) we are justified in stating or believing that a sentence is true, then we are implicitly making an assertion or expressing a belief regarding the existence of some referent, unless we are expressing a purely logical truth (a case which remains outside the scope of our considerations).
The case of false sentences splits into two sub-cases. A sentence is false when it has no referent or when it says of its referent(s) something that is not the case. As is well known, some authors consider in the first sub-case the sentence to be neither true nor false. (See the famous example, “The present king of France is bald,” in which one can say that the sentence has no referent because its descriptive term has no referent.) These authors therefore advocate (at least implicitly and perhaps unconsciously) a referential condition not only for truth, but even for falsity. Our conviction—which we shall not explain in full here, but which easily follows from what we maintain in the previous sections of this work—is that a more correct appreciation of the referential nature of truth should lead to considering sentences of this kind to be false, and in that way to favouring the ‘bivalence principle.’ This has to do with the nature of the apophantic discourse, which engages itself in expressing ‘what is the case’ or ‘what is not the case,’ and in which the relation to a referent is already incorporated.
A non-asserted sentence may have a sense, even though it has no referent, either because one of its terms lacks reference, or because some of the properties or relations it expresses do not hold for one or more of its individual referents. Therefore, “The present king of France is bald” belongs to the semantic discourse, until it is not uttered as a claim concerning some existing individual, in which case the non-existence of this individual leaves it meaningful, but makes it false. But also “The present president of the United States is a multiple of 7,” or “Beethoven’s seventh symphony is soluble in water” are sentences that are meaningful but false since, this time, they refer to existing individual objects which, for different intrinsic (in this case, categorial) reasons, cannot possess the property expressed in the sentence. That they have a sense is already granted by the fact that we can understand them; and it is because of this sense we can say that they cannot possibly refer to a state of affairs.
Of course the propositions expressed by these sentences have an intentional reality and, as such, they continue to constitute the ‘denotation’ of the corresponding sentence (according to our terminology) so that, in ‘intentional contexts,’ it may be perfectly meaningful, and even true, to say, for example: “John thinks, believes, imagines… that p,” where p is one of the above sentences.
It is when we proceed to the assertion (apophantic discourse) that the referent is needed; and the asserted proposition is true if and only if the state of affairs to which it refers obtains. This requires: (a) that the referents of its individual terms exist; (b) that they may in principle possess the properties or relations which are attributed to them; and (c) that they are actually related to their attributes in the way expressed by the sentence. Failing to meet just one of these conditions makes the sentence false.
Frege, precisely because he was perfectly aware that reference is one of the basic conditions for truth, never accepted that a sentence could lack a referent; and, since in common language such sentences may actually be constructed, he saw in this fact a confirmation of the necessity of passing to an artificial language (in which no such sentences may be constructed) for elaborating rigorous logical investigations.
- 106.
We are aware that we are here making a jump, since we have said thus far that sentences are true or false, and now we are speaking of theories. Do we mean by this that theories are sentences? We have already said that this is not what we mean; and this will become even clearer in the sequel (see Chap. 6). However, we intend to underscore here the ontological commitment of theories, and this we can do via the following claim: considering that theories (even though they are not just sets of sentences) give rise to sets of sentences, we may say that the objects denoted by the sentences a theory obliges us to state as true must exist, unless the theory is untenable (be it globally, or as far as that particular aspect is concerned). This is related to the fact that, according to what we have said in the preceding note, sentences without referents must be considered false (in the sense that the non-existence of the referent is a sufficient, though not a necessary, condition for falsity).
- 107.
What we have just said is reminiscent of the Aristotelian and ‘classical’ distinction between ‘immediate’ and ‘derived’ truth, and we do not want to deny this affinity, though we do not agree with Rescher, when he qualifies it as a particular ‘theory’ of truth, that is, as the ‘intuitionist’ theory (op. cit., pp. 10–11). In fact, we have shown how ‘immediate’ truth does not come out of any special ‘intuition,’ but is rather the result of the application of intersubjective operational criteria (usually complicated and very artificial). It is also undeniable, in our view, that the immediate truths are, in a way, stable. Even if we prefer not to use Schlick’s emphatic statement: “The problem of the ‘basis’ changes automatically into that of the unshakeable point of contact between knowledge and reality” (quoted in Rescher 1973, p. 11), we must recognise that a protocol cannot be proved wrong by other protocols. In such cases of discrepancy, we should try rather to understand and explain how the ‘wrong’ protocol came about, and to consider the disturbances, the imperfections of the instruments, and other conditions which, while they cannot ‘annihilate’ the protocol, can allow us to disregard it.
A confirmation of the impossibility of dispensing with this ‘injection’ of truth from the outside is also found in Rescher’s coherence theory, where he correctly emphasises the indispensability of introducing data in order that the coherence theory not be reduced to the requirement of a purely internal relation among sentences:
To the criticism why should coherence imply truth, we thus propose to reply: what is at issue here is not mere coherence, but coherence with the data. It is not with bare coherence as such (whatever that would be) but with data-directed coherence that a truth-making capacity enters upon the scene (op. cit., p. 65).
We completely agree with this statement but, on the other hand, we must note that, if data are to function as ‘truth-makers’ (as is appropriately said here), they must possess a legitimacy which transcends coherence. Rescher does not draw this conclusion since for him “[a] datum is a truth-candidate, a proposition to be taken not as true, but as potentially or presumably true” (p. 54). This is, in our opinion, a less satisfactory aspect of his theory, which should instead here exploit the fact (duly acknowledged by Rescher), that there exist several criteria for determining truth. This may be understood in more than one way. The most obvious is that, for example, the criteria for ascertaining historical truth are not the same as those for mathematical truth, or for physical truth. But an additional meaning is also useful. In order to take full advantage of the criteria provided by a coherence theory of truth we have to supplement them with criteria which are closer to the basic ‘meaning’ of truth, such as the operational criteria of referentiality. This is the position we advocate.
- 108.
For example, the coherence theory of truth developed by Rescher adopts a nonclassical logic, precisely because it intends to propose a criterion for truth.
- 109.
Additional considerations concerning the problem of the existence of ‘unobservable’ objects are developed in Agazzi (2000).
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Agazzi, E. (2014). The Ontological Commitment of Science. In: Scientific Objectivity and Its Contexts. Springer, Cham. https://doi.org/10.1007/978-3-319-04660-0_4
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