Frege & Foucault on the Conditions of Thought
Frege posits the existence of sense [Sinn] on the basis of needing to have some entity that can produce an identity within a seeming diversity, and diversity over seeming identities. The former is needed because there exists a diversity between the ideas of different users of language, and language possesses a near infinite ability to vary expression. Frege needs a ‘something’ that different speakers can communally grasp, such that debates concerning the truth and falsity of various propositions have a singular, common ground. The latter is needed because Frege wants to account for the cognitive significance of sentences of the form ‘a = b’, as opposed to sentences of the form ‘a = a’, despite these sentences seemingly saying the same thing if the first is true. I wrote on this latter difference in an article in December.
What I am interested in here is what Frege does next, after he has discovered this entity, ‘sense’. On the back of sense, which was discovered as the mode of presentation of a name, Frege begins thinking about the sense of sentences, making a distinction between the senses of sentences that can be true or false and the senses of sentence that can’t be either (for example, the sentences of literature). It’s this distinction I want to explore here, arguing that Frege ends up in a groundless circle when we ask how to determine this distinction, and that Foucault, in the Archaeology of Knowledge, is unexpectedly covering this same terrain, and providing a solution.
Frege on Thoughts and Representations
To fix the terms, for Frege the term ‘thought’ [Gedanke] is reserved for a sense of a declarative sentence that has as its referent a truth value (Frege, 1918, p.292). This is to say that ‘thoughts’ (and only ‘thoughts’, thus defined) are what partake of truth and falsity. This seems fair enough; the world itself is not something of which we can say it is true or false, and the same with many grammatically, or pragmatically, sound utterances as well (questions, for example). Thus, it seems worthwhile to delimit an object which is the ‘that to which truth and falsity is rightly ascribed’. Frege calls these ‘thoughts’. These ‘thoughts’ are not produced, or formed, by those that would ‘apprehend’ them, but rather exist eternally (the true as much as the false), ambivalent to whether they are entertained, or not, by anybody.
“Thus the thought, for example, which we expressed in the Pythagorean theorem is timelessly true, true independently of whether anyone takes it to be true. It needs no bearer.” (Frege, 1918, p.302)
“When one apprehends or thinks a thought one does not create it but only comes to stand in a certain relation, which is different from seeing a thing or having an idea, to what already existed beforehand.” (ibid, fn)
Opposed to this are the senses of declarative sentences that do not have as their reference a truth value (they do not partake of truth and falsity). For these, he suggests the term ‘representation’ [Bild].
“It would be desirable to have a special term for signs having only a sense. If we name them, say, representations, the words of the actors on the stage would be representations; indeed the actor himself would be a representation” (Frege, 1892a, p.42, fn)
So, when an actor on stage, in character, announces they are “going outside to take a walk” this is a sentence that has a sense which we grasp, but it does not have as its referent the circumstance of its being true (or false). It would be frivolous to say this utterance is false on account of the fact that the actor merely intends to walk off of stage right and wait in the wings. Indeed, the actor/character themselves, insofar as they express a ‘subject’, are a sense without a reference (in the manner that individual names have senses), thus, a representation.
So, the sense of a declarative sentence that has (as its referent) a truth value is called a ‘thought’, and the sense of a declarative sentence, that which we grasp when understanding the sentence, that has no relation to truth or falsity is called a ‘representation’.
Now, what are the conditions to determine this difference? We cannot look to any grammatical or logical differences between the expressions themselves, because they are identical in this regard. Frege argues that the difference devolves upon whether or not the sense of the name of the subject of the sentence has a referent or not (Frege, 1892a, p.42). So, for example, concerning the sentence “Darwin often expressed his homesickness while he sailed on the Beagle” our discussion of whether this is true or not hinges upon the sense of the name ‘Darwin’ possessing a reference, an object to which it refers. If it does (as it seems to do here), then the question of truth and falsity emerges. If, however, the sense of the name does not have a reference, then we are dealing with a ‘representation’; not even false. “The Golden Mountain is in California” is a classic example of such a sentence. Frege wants to avoid as much as he can (though he admits the necessity of sometimes needing to) seeing in declarative sentences a conjunction between an existential assertion (“there is something called the Golden Mountain”) alongside the more apparent predication of the subject (“and it is in California”) because this would make the simple negation of the sentence a disjunction (“either there is no Golden Mountain, or there is but it is not in California.”)(Frege, 1892a, p.47–48). Frege prefers to suspend the whole question of truth and falsity for these sentences whose subjects are referentless orphans, and pin his hopes on a logically perfect language to come, in which no sign would be admitted without first being ‘secured’ a referent (ibid).
Fine. But what, then, are the conditions for determining whether a sign, via its sense, has a referent? How does this ‘securing a referent’ work? If that is what the ‘thought’/’representation’ distinction is to turn on, then we need conditions for now determining which senses (of names) refer to referents, and which don’t. Truthfully, Frege does not seem to pose this question. Perhaps he took it as a given that references were secured in the different sciences already, or that it is the role of these sciences to secure these references. All the same, the question still hovers, whether it is dealt with here in the analysis of propositions and sense, or deferred elsewhere.
There are two possible approaches to this question of how to determine if a name has a referent, given the connections Frege has just established. The first is ‘top down’: we say that those signs have referents that feature in sentences that we can verify are true or false. That is, we take the status of ‘thoughts’ readymade, and determine the referent objects on the basis of them, by breaking them down into their constitutive elements (subject, predicate). Or, alternatively, working ‘bottom up’, we give ourselves the referent objects readymade, such that we can then divide the senses of sentences into thoughts and representations.
As implied by the quick presentation of these two alternatives, neither of them is that attractive. Firstly, to begin with ‘thoughts’, and thus with the condition of truth and falsity, would require us to have a robust set of conditions in place for these philosophically complex, and mysterious, terms. Frege himself actually offers arguments for the impossibility of a coherent theory of ‘truth’ (1918, p.291). In short, we will be sent on a regress when examining a judgment we have determined to be true, in line with our theory of truth, whether or not the conditions of truth specified by our theory are truthfully present, which would amount to a new judgment that would need to be determined whether it was true or not, in line with whatever conditions are specified by our theory, and so on and so on (Frege, 1918, p.291). So, if we say ‘reference is determined by the condition that the referring name enters into sentences that are true or false’ we will fall into a regress. A simple ‘definition’ sentence to secure the reference fails here for the same reason: how to determine if this definitional sentence is true?
But what of the other alternative? Surely it is unproblematic to give ourselves a readymade referent? One may throw their hands up here, and reach for the nearest object, and say “this, this coffee cup”. But we don’t need to even bring in Sorites paradoxes to show that taking the notion of ‘referent’ as given readymade is problematic. For Frege, the Pythagorean theorem is a perfect example of a ‘thought’, thus “the square of the length of the hypotenuse of any right angle triangle” is just as much a referent as this bottle cap I can clasp between my fingers. Frege also interprets what happens when we take a concept (say, ‘three-sidedness’) and further predicate it by placing it in the subject position of a sentence: here is not a case of a concept also being an object (which is theoretically problematic for Frege, who wants to maintain a hard difference between concepts and objects), but, rather, of a name being produced (“the concept/property of three-sidedness”), which then operates as a proxy-object for the concept in question.
“Consequently, one would expect that the Bedeutung [reference] of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or, more precisely, an object must go proxy for it.” (Frege, 1892b, p.185)
So, we can produce objects on the fly (or access a surplus of objects-in-waiting) as proxies which satisfy the referent condition for ‘thoughts’, for example “the point one quarter of the distance between my right elbow and the door”. And yet, Frege wants to hold onto the distinction between thoughts and representations such that we can draw the distinction between, say, the scientific description of a theoretical method of propulsion in a scientific journal, replete with references to as yet merely theoretical particles and forces that have yet to be empirically determined but are so many proxies and placeholders within a theoretical edifice, and a similar description occurring in a work of science fiction, in which, as readers, we naturally suspend the question of truth and falsity and nonetheless comprehend the logic of the description. At this juncture, it now feels preferable to return to our first alternative: the difference consists in that the scientific journal description, as opposed to the science fiction one, takes part in truth and falsity, and thus the objects named within it hope to have referents, and say true things about them, while the science fiction description, not caring to take part in truth or falsity, fabricates its names without any care for whether referents can be given. But this then returns us to the problem of needing the elusive set of conditions for the true and the false. We are sent in a circle.
There is another option, which Frege’s presentation intimates, where we simply posit the distinction based on the intentions of the person who proposes the sentence. However, this is to have things back to front: senses, thoughts, representations, these all precede individual subjects who would intend to do anything with them by grasping them and expressing them in sentences. If senses, and their truth values, are to precede subjects, then this question needs to be resolved prior to any theory of ‘speech acts’, which depends on a manifesting subject. How are these determinations to be made prior to our beginning to speak and think?
Foucault on Statements
It would be unorthodox, but not for that reason unprofitable, nor entirely inaccurate, to read Foucault’s Archaeology of Knowledge as an attempt to step right into this problem and untie the circle. In the course of the book Foucault also identifies the necessity of a ‘sense-like’ extra layer that needs to be added in addition, and anterior, to logical and linguistic analyses to account for the functioning of knowledge. He terms these ‘sense-like’ entities statements [l’énoncé], and the formations they necessarily enter into (or which produce them, this is a reciprocal conditioning) discourse. He also brings this entity into focus by positing identities within seeming multiplicities, and multiplicities over apparent identities. The sorts of identities and multiplicities that are produced, and in what cases, maps well to those that Frege develops under the heading of ‘sense’. Especially so considering, as with Frege, ‘substitutability’ is one of the conditions under which the identity of this entity (sense/statements) is to be determined.
“if the information content and the uses to which it could be put are the same, one can say that it is the same statement in each case” (Foucault, 2002, p.116–117)
Now, the ‘statement’ is first put forward as the “atom of discourse” (Foucault, 2002, p.90), however, this metaphor is quickly abandoned. An atom implies a possible atomization, the taking of a single statement in isolation, and the ambivalent independence of individual statements from all others, which runs counter to even a rudimentary understanding of how texts (as representatives of discourse) function. A sentence is never the last, nor the first, it always suggests another sentence. Foucault holds that an atomization of statements is impossible: statements are defined by their exteriority through and through, they cannot be removed from the discursive context within which they appear (the text, the subject, the conversation, etc) without losing something.
“[A] statement always belongs to a series or a whole, always plays a role among other statements, deriving support from them and distinguishing itself from them: it is always part of a network of statements, in which it has a role, however minimal it may be, to play.” (ibid, p.111)
At times Foucault treats statements just as this term is regularly used, as an assertion among others in the demonstrations of various discourses; however, his characterizations of statements, both in the negative (“not this”) and positive (“is this”) modes illustrate that the statement is not some isolable kernel, but rather exists, or subsists, or inheres, with a pure exteriority between, and on the surface of, the traditional referent of the term ‘statement’, that is, declarative sentences. The term ‘statement’ ends up taking on a significance that is quite foreign to the term’s ordinary use, and becomes a term of art for Foucault, just as ‘thought’ did for Frege.
“The statement is … a function of existence that properly belongs to signs and on the basis of which one may then decide, through analysis or intuition, whether or not they ‘make sense’, according to what rule they follow one another or are juxtaposed, of what they are the sign, and what sort of act is carried out by their formulation (oral or written). Not a thing, nor a place in a structure, but a function that cuts across levels.” (Foucault, 2002, p.97)
Observe here how a number of these functions ascribed to the statement are reminiscent of Fregean senses, not least of all that it is, for Foucault, in virtue of statements that a given string of signs can be determined to ‘make sense’. It is the statement that lets us determine of signs “of what they are the sign”, in a manner akin to Frege’s ‘apprehension of the sense of a name’. Statements, like senses, are not ‘things’, nor ideas, but “a function that cuts across levels” (hence the need, based on this ‘cutting across levels’ for new identities and multiplicities). Some functions ascribed here, though, are original: that statements are that which form the basis upon which we determine the rule for their succession, how one follows the other. This is Foucault’s addition, discovered precisely because he has discovered the ‘statement’ through the analysis of discourse, rather than isolated propositions (like Frege). Also, absent here is Frege’s most central determination of sense: that sense performs a role in mediating words and things, sentences and truth values. For Frege, one cannot stop at the sense, but is always referred to what it correlates to.
Foucault wonders if statements might have their correlates, in a way akin to Frege’s correlating of the sense of a sentence to a truth value, via the correlation of the subject with a referent. Foucault briefly considers this, but it is in his examination of the example “The Golden Mountain is in California” that this possibility is rejected.
Obliquely referencing Frege (through referring to the ‘logicians’), Foucault notes that traditionally this sentence fails to be true or false because of its subject’s lack of a correlate (referent), or, if we interpret it, like Russell, as also making an existential claim, then it is false for this lack. But, it does not for that reason fail to be a statement, because it demonstrably appears in the discourse on logic: as an example of a proposition that fails to be true (at least) because of its subject’s lack of a referent. Within this discourse, it is more or less substitutable with other positive propositions that have the same exemplary function, i.e., “the present king of France is bald”. This is to say that the statement still appears as a crucial, or at least perfectly intelligible and acceptable, element in a discourse that itself takes part in the true and the false (the discussion of logic, sense, and reference), and such statements are demonstrably vital to this discourse. This is not too surprising, Frege noted that these referentless sentences nonetheless possessed a sense (Frege, 1892a), and that the sense of a sentence can be taken as the referent of another sentence (ibid), otherwise we would never be able to productively talk about what we say, or has been said, which we demonstrably can.
However, Foucault does not stop here. He further points out that “the Golden Mountain is in California” only fails to refer when it is taken within a particular discourse, that of geography. So, the logicians have invented a sentence that is indispensable to them for demonstrating a failure of reference, and malfunction of truth, but only if we posit that this sentence appears not within a discourse on logic (where it happily refers to its desired object: the referentless proposition), but in a discourse on geography. Foucault points out that the subject of the sentence could have its referent if it appeared in some novel, and in this way could be accepted as ‘true’, or rejected as ‘false’, insofar as it conflicts or accords with the possibilities prescribed by the novel itself (as a collection of statements).
“Let us suppose in fact that the formulation ‘The golden mountain is in California’ is found not in a geography book, nor in a travel book, but in a novel, or in some fictional context or other, one could still accord it a value of truth or error (according to whether the imaginary world to which it refers does or does not authorize such a geological and geographical fantasy). We must know to what the statement refers, what is its space of correlations, if we are to say whether a proposition has or has not a referent.” (Foucault, 2002, p.101)
For example, think about the endless arguments science fiction fans engage in concerning the wider worlds of Star Wars, or Star Trek. As irrelevant as these debates might seem, they are not senseless, groundless, purely creative or imaginative spontaneous enterprises: these debates have their rules, their criterion for what counts as ‘canon’, and how it is to be mobilized in the demonstration of the truth or falsity of a given proposition. These conditions, as with the conditions of any discourse, are ‘tighter’ than the basic conditions of grammatical or logical rules (though these are obviously also in effect in these debates), even while the subject matter, the possible objects and predicates, that form this science fiction discourse exceeds the description of present empirical possibilities of the world, by adding to it, in a highly regulated way, fictitious and speculative objects.
When Foucault points out the Golden Mountain may be in California within certain discursive practices (i.e., the fantasy novel and its discussion) he thus slides over to Frege’s definition of ‘representation’. Now, our question was how do we determine the difference between ‘thoughts’ and ‘representations’ when this difference apparently hinged upon whether or not a name had a referent. Foucault is here arguing that “the Golden Mountain”, though possessing no empirical-geographical referent, can, depending on where this statement appears, have its referent such that we can discuss the truth and falsity of the predication “is in California”. How does this work?
In finally answering his own question about what the correlate of the statement could be, Foucault writes, specifically in regard to the “Golden Mountain” proposition:
“what might be defined as the correlate of the statement is a group of domains in which such objects may appear and to which such relations may be assigned: it would, for example, be a domain of material objects possessing a certain number of observable physical properties, relations of perceptible size — or, on the contrary, it would be domain of fictitious objects, endowed with arbitrary properties (even if they have a certain constancy and a certain coherence), without any authority of experimental or perceptive verification.” (Foucault, 2002, p.102)
It is the statement that stands between the string of signs (the sentence/s) and a series or group of domains within which (and through which) this sentence is determined to ‘make sense’. This is to say, if I am right in positing at least a loose identity between Fregean senses/thoughts and Foucaultian ‘statements’, that the sense of a sentence (the thought) does not correlate immediately to its truth value, but rather firstly to a domain in which truth values could be allocated; depending upon the regularities or idiosyncrasies of that domain, and its respective ontology (or, more precisely, its rules for the formation of those objects in its ontology).
Foucault’s solution to our problem is, thus, to reverse the relations. The ‘Golden Mountain’ proposition may have (or fail to have) its correlate as determined by the accumulated discourse on geography, but the statement/thought has as its correlate those domains in which it may appear as an object. That is, where can the name ‘Golden Mountain’ appear as possessing any possible reference, real or imaginary, and where is it acceptable to predicate of it its being in California?
“Should we say similarly that a statement refers to nothing if the proposition, to which it lends existence, has no referent? Rather the reverse. We should say not that the absence of a referent brings with it the absence of a correlate for the statement, but that it is the correlate of the statement — that to which it refers, not only what is said, but also what it speaks of, its ‘theme’ — which makes it possible to say whether or not the proposition has a referent: it alone decides this in a definitive way.” (Foucault, 2002, p.101)
However, Foucault takes pains to emphasize that this correlate is not of the same type of the usual ‘correlation’, from one self-identical entity to another. This would introduce a problem, discussed by Frege, but going back at least as far as Berkeley, of the conditions of this correlation if the correlated entities are not to be numerically identical — if they are to be correlated in virtue of some identity within a subset of their properties, which ones? And the fixing and determining of these then re-introduces the regress concerning the theory of truth described above (Frege, 1918, p.291). Foucault circumvents this difficulty in a number of ways, one of which is by arguing that the statement, in referring a proposition to a domain, does not make the referent of the proposition a discourse, a body of texts (or some such positive entity), but rather the statement correlates to that which makes both the proposition and the body of texts possible — that is, further statements. The ‘domain’ that is correlated with the statement is a network of statements itself. Statements refer to statements, creating networks of ‘referentials’, discourses, that provide a condition of intelligibility (alongside, but tighter than, grammatical and logical conditions) to utterances, texts, debates, demonstrations, etc. A sentence is never the first or last, but always suggests other sentences.
Thus, a statement under consideration cannot refer to a thing but rather a set of conditions and functions, rules and regularities. A rule or a function is not a thing, but a relation or process for the translation between series of things. 2x=y, for example, is not an entity, but a rule for relating any members of ‘x’ to members of ‘y’. The statement correlates to, or refers to, or is, a function, rather than a class or set of positive members.
“A statement is not confronted (face to face, as it were) by a correlate — or the absence of a correlate — as a proposition has (or has not) a referent, or as a proper noun designates someone (or no one). It is linked rather to a ‘referential’ [référentiel, lit. “reference frame”] that is made up not of ‘things’, ‘facts’, ‘realities’, or ‘beings’, but of laws of possibility, rules of existence for the objects that are named, designated, or described within it, and for the relations that are affirmed or denied in it… [The statement] defines the possibilities of appearance and delimitation of that which gives meaning to the sentence, a value as truth to the proposition.” (Foucault, 2002, p.103)
In this way, the Fregean ‘thought’ presupposes its own conditions of apprehension. It is not the case that we apprehend the sense of a sentence, then go off, in a simple and unproblematic way, to secure it a referent in order to determine whether it, as a thought, takes part of truth and falsity, or whether it, as a representation, does not. Rather the sentence has sense, is a thought, only insofar as a ‘statement’ has secured its position in a discourse that has its own conditions for the ‘securing’ of referents, and the rules for their predication, and whether or not it refers to a set of functions that would specify (sometimes provisionally, sometimes precisely) how we were to carry out these determinations of reference, and truth and falsity, in the first place.
This is to say there are no ‘representations’ in Frege’s definition of this term, but only ‘thoughts’, true or false, with these terms taking on different significance relative to the positive discourse within which the thought is apprehended (and apprehendable). “A sentence cannot be non-significant; it refers to something, by virtue of the fact that it is a statement.” (Foucault, 2002, p.102). When we apprehend the sense of the sentence, we are immediately thereby situated, positioned, at a vantage within a positive discourse that conditions the rules for securing referents and predicating them, and how these relations would be verified, thus rendering certain propositions acceptable, and others unacceptable by the conditions of allocating truth values within this discourse. Anything less and the sentence would fail to have a sense at all. It is in relation to these rules that we then discover the ‘Golden Mountain’ proposition is unacceptable, but not senseless, within a discourse on geography (though, we should remember the fact that it doesn’t appear there, but is purely a product of the discourse on logic). We may discover this is a perfectly acceptable sentence if we take it in a different sense which amounts to viewing it from the vantage of a different positive discourse, with different rules for how referents are secured, and rules for how they may be predicated, and these relations verified.