august /98



Carlo Penco
penco@unige.it


Frege: Two Theses, Two Senses



Second draft - talk given at Vercelli (1995) Rome (1996) and Leeds (1996)

1. Two Contradictory Claims and a Tension in Frege's "Thought"
From 1891 onwards, the concept of conceptual content defined in Frege's Begriffsschrift splits into three different notions: sense, reference and extension. However, Frege applied the tripartite distinction only to predicates; for names and sentences he used only the distinction between sense and reference. The concept of thought became constantly referred to as the sense of a sentence. The identification of the thought with the sense of a sentence hides a tension in Frege's conception of thought. This tension is manifested by his simulataneously holding two different claims which at some point apparently clash. Frege held that a thought can be expressed by different sentences yet at the same time, he held that a sentence is a picture of the thought it expresses. What's wrong with that position? Why couldn't we simply think of sentences as different ways to picture one thought? An extreme interpretation of this idea - that a sentence is a picture of a thought - implies that there is a strict correspondence between the elements of the thought and the elements of the sentence. Such a view suggests that there must be one - and only one - analysis of a thought which is mirrored by a unique sentence; this is contrary to the idea that many different sentences can express the same thought. Therefore we reach here a contradiction which can be expressed as:

[1] Structurally different sentences can express the same thought.
[2] The structure of a sentence reflects the structure of the thought it expresses.

Can the same notion of thought be used to support both claims? I suggest that Frege uses the term "thought" to refer to two different concepts. First, Frege was striving towards the clarification of sense as truth condition (as it has been developed by Wittgenstein and Carnap after him) and, at the same time, he was blocked in isolating that notion clearly because of a stronger conception of sense required by the internal needs of his philosophy. The second conception should take care of the epistemic aspects not explainable by the simpler relation of logical equivalence. I will try to develop this intuitive and traditional line of interpretation,1 against the more sophisticated attempts to make Frege coherent at prices which I think too high to pay.

2. Some Previous Attempts
A justification of Frege's simultaneous holding of the two theses can be found in Dummett's claim that Frege used two kinds of analysis.2 The first is used to show how a sentence can be analyzed or decomposed in different ways, sorting different internal patterns (i.e. different choices regarding what counts as function and what as argument).3 The second is used to show that a sentence is the expression of a unique set of building blocks. This last thesis seems, however, to hold only for formalized language,4 while the first is applied often also to sentences in languages which have not yet been framed inside a formal semantic theory.5
Dummet's solution of the apparent contradiction can therefore be summarized as follows. Thesis [1] is needed to explain the way we reach new concepts through the discovery of unitary patterns in different sentences. Once we have reached the clarity of a logical language, where everything is explicit and the distinction in function and argument is clearly expressed, then for any sentence in our language there will correspond one -and only one- determinate thought, and consequently, thesis [2] firmly holds. We might call this last claim the thesis of "logical isomorphism." It has a certain appeal even with respect to the Fregean idea of revealing with logical notation the real structure of the thought. Even if basically correct, however, this solution has some apparent disadvantages.
On the one hand, it reduces the thesis of isomorphism of thought and language to a tautology: for if some sentence is not considered isomorphic with the thought it expresses, then it is just simply a sentence which does not convey the thought in its most fundamental form. And in such circumstances, it is unclear how to decide which is the most fundamental form of the thought (see Beaney 1996 242), unless we accept that (some) standard logical notation is exactly what is needed.
On the other hand, even isomorphism intended in this way (as logical notation) is contradicted by other examples given by Frege: pairs of sentences like "A -> B" and "not (A and not B)" or "A" and "not(not A)" or "A and B" and "B and A" express the same thought. Yet they are sentences expressed or expressible in two different ways in his logical formalism.6 Beyond that, Dummett's solution is compelled to make Frege too often wrong or guilty of changing his mind on basic ideas. I will give two examples: € One of the main points of contrast among interpreters is what to do about the idea that each of the following sentence in the "Grundlagen pairs" express the same sense:

A1 a is parallel to b.
A2 The direction of a = the direction of b.
B1 There are as many Fs as Gs.
B2 The number of Fs is the same as the number of Gs.

To these we may add the correspondent Axion V of Grundgesetze, which is the pair B1/B2 in a more technical jargon:

B1' For every a f(a) = g(a)
B2' The value range of f = the value range of g

Dummett finds it "very difficult to reconcile" the idea that these pairs express the same sense with Frege's ideas expressed elsewhere.7 Eventually he claims that Frege was wrong in accepting the thesis that each sentence in the "Grundlagen pairs" express the same sense, and thet Frege had "one of his tacit changes of mind" expecially regarding Axiom V. Hence Dummett claims that Frege did not accept anymore the idea that the two sides of Axiom V express the same sense, as he said in 1891, just two years before the publication of Grundgesetze. The rationale given is the transparency principle clearly expressed by Frege only in 1906 in an unpublished paper.8 However, Dummett claims that Frege should have been wrong in a letter he wrote to Husserl in that same year about the equivalence of sentences (see the following point).
€ Another point of contrast is how to interpret some of Frege's statements about sense identity. Dummett labels "an aberration" the idea sustained by Frege in a letter to Husserl that.two sentences express the same thought when we can derive a contradiction from the supposition that one is false and the other is true. Dummett correctly suggests that this criterion "involves that two analytically equivalent sentences express the same thought, a view irreconciliable with Frege's ideas about sense as stated in other writings."9 This criterion does however hint at a definition of thought which is consistent with all the passages Dummett claims Frege was wrong or changed his mind. I therefore suggest that the appearance of "aberration" may depend on a too strong emphasis on the notion of sense as described by Frege in Sinn und Bedeutung. The feeling of aberration may disappear if we take into account a hidden tension between two different conceptions of sense which are present, even if not acknowledged, in Frege's work (and not only in his private letters).
Dummett almost never considers the possibility of an inner tension in Frege's conception of thought; the only times he does so is to criticize Currie's attempt to discern two distinct theories or conceptions of sense in Frege's writings. Currie distinguishes between a notion related to the information conveyed by a sentence and a notion used to justify the replacement of an intuitive notion by a precise one, as in the analytic definition of arithmetical notions used in the "Grundlagen pairs". Dummett claims that the justification given by Currie is not plausible because "it is hard to see how there could be any acceptable concept of sense according to which an imprecise expression could bear the very same sense of a precise one."10 However, a distinction similar to the one held by Currie can be sustained on other grounds, both theoretical and textual, and could clarify Frege's statements about the identity of sense between the Grundlagen pairs as well as help to solve his apparent contradictions. This is the project of my paper.
Before going into the details, I we should review whether there is some viable alternative to Dummett's solution. Some of the most interesting alternative solutions11 rely on a sharp divide between epistemological and non-epistemological points of view.
In Currie 1985, Thesis [1] is maintained as the fundamental thesis of Frege's theory, as an ontological thesis on the thought: i.e. that the thought is an independent object which can be expressed in different ways. The two sides of Axiom V are two ways of expressing the same thought, "and no language would be ideal in which that principle could be not expressed" (294). On the other hand, thesis [2] and the idea that a thought is build on its constituents which correspond, by and large, to the parts of the sentence cannot be considered an ontological claim, but only an epistemological one: to understand a thought we need to have some sentence whose structure expresses the structure of the thought.
The distinction between the epistemological and nonepistemological12 points of view has an immediate merit. It helps in solving some of the problems about indirect contexts by establishing an intuitive difference between two ways of reporting beliefs (as "holding as true"). We should distinguish between "thought expressed by a sentence" and "thought as expressed by a sentence", hence, we should distinguish between: 13

a) s holds as true the thought as expressed by p
b) s holds as true the thought expressed by p

Taken at face value, these two ways of reporting beliefs may be useful. We might say that if s believes the thought expressed by A -> B she therefore believes the thought expressed by not (A and not B). However - let us imagine that she is a beginner in a logic course: we cannot then say that if she believes the thought as expressed by A -> B she therefore believes the thought as expressed by not (A and not B).
Another apparent (but, as we will see soon, dubious) merit of the distinction is to give an account of the Fregean principle that the senses of the parts of a sentence are parts of the thought expressed. Currie claims that the principle implies a contradiction with the other Fregean tenets only if intended as an ontological claim. Currie's main criticism to Dummett is then the following. Given that "A" has the same sense that "A and A", we should infer from the principle the counterintuitive conclusion that the thought expressed by "A" is a proper part of itself. Strangely enough, Currie does not apply to this problem his distinction between the two different conceptions of thoughts. Why we well might ask? I suggest it is because his notion of "strong sense" is too specifically linked with a particular problem14 and, therefore, forbids the construction of a simpler solution. The simpler solution, still relying on the ambiguity of the notion of thought in Frege, is that the two sentences express the same thought-as-truth-condition. There is nothing wrong in saying that the truth condition of "A" is a proper part of the truth condition of "A and A".
This is not the only flaw in Currie's attempt. The main problem is that this line of thought brings about a very counter-intuitive interpretation of Frege. If further pursued without other restrictions, the distinction between epistemological and nonepistemological readings of thought brings about a conclusion difficult to avoid and difficult to accept. Thoughts per se, being compatible with different analyses, do not possess a unique inner composition, and eventually are without a definite structure. This conclusion, which I strongly disagree with, is explicitly shared by Garavaso 1991 and Bell 1996. Bell suggests that the best way to render Frege coherent is to make him unaware of the dilemma because he used the two claims as pertaining to different problems: [1] concerns "the nature of thoughts and their relation to the language in which we express them", while [2] concerns "the senses of the sentences and the nature of linguistic understanding."15 The main argument given by Bell is that Frege himself used two distinct models to account for the structure of thoughts: the function/argument model and the part/whole model. The part/whole model is fundamentally linked to thesis [2] and to the idea of sense, and of hysomorphism between the structure of linguistic meaning and the structure of the sentences; the function/argument model, linked to thesis [1], implies that a thought can have different analyses in function and argument. Therefore - Bell claims - these analysis in function and argument do not reveal the intrinsic structure of the thought. The price to be paid for recovering the lost harmony of the two Fregean theses is that "we are now compelled to deny that thoughts have a determinate intrinsic structure."
This conclusion involves a split between conceptual content and linguistic meaning, where conceptual content is the unstructured thought and linguistic meaning is the structured sense of a linguistic expression. This solution is reminiscent of the one given by Wagner 1983 who, following Sluga, speaks of Fregean "contents" as "unstructured bearers of truth values". Fregean contents are prior to "propositions" which are "structures which the mind formulates by way of representing contents to itself." From this point of view, Fregean contents inherit the Kantian idea of the mind which imposes form to a realm of formless things. It is however hard to see what we gain in splitting the notion of thought into objective unstructured content and propositional structured content. Actually this conclusion faces at least three strong difficulties:
To summarize, I accept Dummett's criticism of Wagner about thought as an unstructured content (an idea which is shared also by Sluga, Garavaso and Bell). I also I accept, however, contrary to Dummett, the idea that there is a hidden tension in Frege's conception of sense dealing with different problems. I disagree with the specific solution given by Currie and by Bell. The first isolate too narrow an interpretation and concern for a strong conception of thought, and the second cuts too neatly between sense and thought, tranforming the first into linguistic meaning and the second into an unstructured element of the mind. Therefore I suggest another, more traditional kind of distinction, one which is coherent with Frege's texts and also with the history of philosophical thought after Frege. I will begin with the textual evidence (par.3) , then I will try to show how Frege was partly unaware of two really contrasting uses of "sense" and "thought" (par.4).

3. Criteria of Identity
As Dummett 1981 suggests, "We must scrutinize carefully the comparatively rare cases in which Frege positively asserts that distinct sentences express the same thought." The few instances occurr mostly in the scattered definitions of a criterion of identity, as well as in a few other passages. Frege gave different criteria of identity for thoughts, at least four:

(1) criterion based on inferential potential (general substitutability)
(2) criterion based on immediate recognition
(3) criterion based on logical equivalence
(4) criterion based on substitutability in indirect contexts

(1) Inferential potential (sense as inferential content) - This is the basic definition of sense-identity in the Begriffsschrift (par.3), a definition never rejected: two sentences in active and passive form have a "slight difference in sense" but mostly give preponderant "agreement in sense." Frege speaks of "conceptual content" as "the part of the content which is the same in both." Two judgments have the same conceptual content if "the conclusions that can be drawn from one when combined with certain others also always follow from the second when combined with the same judgments." What is in common is their substitutability in inferences, or their inferential power, or the ability to preserve the same consequences. The idea of sense as inferential potential is the main core of a definition of sense, or inferential content, as based on substitutability, as Brandom 1994 has abundantly shown.
The definition, however, has been given before the distinction is made between sense and reference and could be used for both. Beaney (1996, ch.2.5) speaks of veritable content (reference or truth value) and logical content; the criterion could be clarified saying that (a) two sentences have the same veritable content if they are materially equivalent and (b) two sentences have the same logical content if they are logically equivalent (provably materially equivalent).
When used for the notion of sense, this basic definition may be considered to be a source or a possible anticipation of sense as a truth condition. Marconi 1991 points out that, if inferential potential is defined with respect to some logic L and L is complete with respect to some semantic S, then sense-as-inferential-potential is the same as sense-as-truth-conditions, where truth conditions are given in terms of S.
There is, however, some problem about the "slight differences in sense". Depending on which collateral judgements and peculiar interests we take into account , the "slight difference in sense" of which Frege spoke about could become relevant for the deduction.18 In that case, if we still wanted to identify conceptual content with logical equivalence, we should at least relativize logical equivalence to contexts of possible collateral judgements; alternatively, we could use the criterion as defining a concept of equivalence more refined than that of logical equivalence. The general criterion stated in the Begriffsschrift should therefore be considered as a programmatic one, which can have different levels of application and refinement.

(2) Intuitive recognizability (transparency of sense) - A different criterion is the following: two sentences express the same thought if you cannot understand a thought as expressed by one sentence without recognizing that it is the same as the thought expressed by another sentence.
The criterion is explicitly stated in A Brief Survey of my Logical Doctrine (1906, p.213) where Frege says that two sentences A and B have the same content or are equivalent when "anyone who recognizes the content of A as true must straight away also recognize that of B as true, and conversely, anyone who recognizes the content of B must immediately recognize that of A." This criterion is based on the assumption that "there is no difficulty in grasping the content of A or B." It is therefore a conditional principle which could be expressed as: "If somebody grasps the content of two expressions, therefore she recognizes whether they express the same thought." In this survey, Frege repeats his standard idea that the thought is the part of the content which is not affected by poetic aura (tone, coloring). This principle was ultimately reaffirmed in his latest writings (e.g. Gedankegefüge) when Frege speaks of immediate recognition of sense identity of sentences like "A" and "not(notA)" or "A and B" and "B and A".
This criterion may explain the claims of identity of content of the Grundlagen pairs. In Grundgesetze, Frege warns that a dispute might break out over Axiom V because the two sides of the Axiom did not satisfy completely the requirement of intuitive recognizability. Dummett takes this remark as grounds for claiming that Frege did not consider anymore the two sides of the axiom as having the same sense, or expressing the same thought. However, the fact that the two sides of axiom V didn't have the same sense is not the problem here. They should have possessed the same sense if they worked.

(3) Logical equivalence: towards sense as truth condition In paragraph 32 of Grundgesetze entitled "Every Sentence of Begriffsschrift Expresses a Thought" Frege says (i) that by stipulation it is determined under what conditions a sentence refers to the True; and (ii) that the sense of a sentence, the thought, "is the thought that these conditions are fulfilled." This passage has been perceived to be the forerunner to the concept of sense as truth condition developed by Wittgenstein and Carnap. But if sense is intended as truth condition, sameness of sense is to be identified with logical equivalence. Actually Frege almost gave a definition of sameness of thought as logical equivalence in the first of two letters to Husserl in 1906. After having said that his notation does not represent mental processes, he defines "thought" as the content which is shared by "equipollent sentences," disregarding the "colouring" or "intonation" (what elsewhere he calls "tone," heir of what in the Begriffshrift are called "slight differences in sense"). Then, after having hinted at a possible canonical form of a system of equipollent propositions, he poses the question whether "A -> B" and "not (A and not B)" are equipollent. Frege displays the truth table of the conditional, then he shows that the negation of "A -> B" amounts to "A andnot B"; therefore he concludes that the two sentence are equipollent. Equipollence is here logical equivalence. Given that equipollent sentences have been defined as sentences with the same thought, we may conclude that here Frege defines thought as truth condition, and that he uses logical equivalence as the criterion for identity of thoughts. The same conclusion can be drawn from the second letter, as Dummett regrettably remarks, suggesting that we forget this idea as a slip of the tongue in Frege's writings.19 However, the extension of the elucidations given by Frege prevents us for rapidly dismissing this criterion which hints at a definition of sense which can be called "semantic".
The criterion of identity of thoughts as logical equivalence is consistent with and is a possible explanation for the criterion of inferential potential hinted at in the Begriffschrift. Logical equivalence is also compatible with the concept of "sameness of sense" exhibited by the sentences of the Grundlagen pairs (our recognition of the identity of content in the Grundlagen pairs can be seen as recognition of their logical equivalence) and with what is said in Gedankengefüge (where Frege speaks of identity of thoughts comparing logically equivalent formulas with different logical operators).

(4) Substitutability in indirect speech - Identity of objects is given by truth preserving substitutability of coreferring terms. A counterexample to general truth preserving substitutability is given by indirect speech. To preserve the general criterion for identity of objects, Frege has to define sense as what is referred to in indirect speech. However Frege gives no example of substitutivity of identical senses in indirect speech, but only counterexamples to substitutability such as:
from: s believes that the morning star is a planet
you cannot derive: s believes that the evening star is a planet

The counterexamples bring to the intuitive criterion of difference of sense (or thought), "If it is possible to understand two sentences and coherently believe what one expresses while not believing what the other expresses, then those sentences express different senses (different thoughts)."20 The main novelty of this criterion is that it links expressly the definition of sense to the cognitive capacities of the speakers: therefore this notion of sense can be called "epistemic".21
Even if never formulated by Frege it seems consistent with his view to formulate a criterion of identity of sense based on substitutability in indirect contexts: two sentences express the same sense if they are substitutable in indirect contexts salva veritate.
The discussion of indirect speech aligns with the epistemological worries for which Frege wanted the notion of sense, the fruitfulness of mathematical truths. The example of Hesperus and Phosphorus is, from this point of view, a shorthand to show how numerical equations are not boring examples of the principle of identity but rather give new knowledge. On the other hand, the principle of substitutivity in indirect speech could be interpreted as a case against any attribution of sense identity of the Grundlagen pairs or of pairs of logically equivalent formal sentences (if the sentences are complex enough that their logical equivalence is easily missed by a speaker who can be said to understand both).22 The criterion of substitutability in indirect speech is therefore certainly more fine-grained than the other criteria hinted at in Frege's writings.

Relationships Amongs the Criteria

These criteria are not jointly consistent and each of them has its own difficulties. We have seen that the first criterion is vague enough to give rise to different interpretations. I will describe in more detail some of the difficulties with the other criteria.
Contrary to common opinion, the second criterion of immediate recognizability does not conflict per se with the conception of thought as truth condition if we take into account the restriction given in (2) that we have no difficulty in grasping the senses. In fact, we may recognize immediately two sentences as logical equivalent if we grasp their respective truth conditions. This interpretation also fits the examples given by Frege when speaking about the composition of thoughts. Why do we immediately grasp the identity of the thoughts "A&B" and "B&A"? An answer could be that it is easy for us to grasp their truth conditions, therefore it is easy to see that the two sentences express the same truth condition and therefore the same sense.
However, speaking of sense as linked to immediate recognition (2), we are in the empirical realm: people often do not know, are unaware or find it difficult to realize completely the sense of an expression. Frege himself refers often to this problem: even mathematicians have difficulties in acknowledging the sense of some complex mathematical operation or function. This point poses a problem about transparency of senses different from the one given by de-re senses.23 If we admit we beyond our normal grasping of senses, we are not able to grasp them fully, how can we recognize sense identity? If it is so easy for a speaker to have difficulty grasping fully the sense of some expression, how can we say that the immediate recognizability is a suitable criterion for identity of sense? We could overcome this problem if we applied the intuitive recognizability to ideal speakers, speaking of a sense being immediately evident to an ideal mind, to "the mind" (not to minds).24 This last solution fits with Frege's main attitude towards psychological problems; we avoid the risk of giving too much emphasis to psychological questions.
However the "ideal mind recognizability" has some disadvantages. Some examples of Frege apparently rely on the human ability to make immediate substitutions, like in the cases of "A and B" and "B and A". Here it seems that Frege wanted to make us think of sense recognition as linked to the most elementary patterns of substitutions we are able to do in a chain of reasoning. Besides, it is not a viable criterion unless the ideal recognition can be expressed by a computational procedure which humans perhaps cannot perform, but which an ideal mind - and maybe a computer - can perform.We have to know which kinds of computation we should perform if we (or the ideal mind) could make the appropriate substitutions, which are the outcome of immediate recognition. We are then back to the problem of the structure of substitutability.
The criterion of substitutability in indirect speech (4) seems to be a specification of the substitution strategy which lies at the heart of the general definition (1). It is, however, not easy to make it match the remaining two other criteria. We cannot use (4) together with the conception of sense identity as logical equivalence (3): we would reach the unwanted conclusion of the speaker's logical omniscience - a problem which has given so much worry to the philosophical community after Frege. If we identify sense identity with logical equivalence and, at the same time, we allow substitution of logically equivalent sentences in indirect contexts, we fall into the standard argument: if s knows that 2+2=4 and 2+2=4 is logically equivalent to any other mathematical or logical truth, then s knows every mathematical or logical truth. Hence, we would have to claim that every speaker who knows or believes a logical or mathematical truth also knows or believes all logical or mathematical truths. Might we conclude again that Frege's logical systems represent God's viewpoint?
Ideal or God's mind does not suffice to solve the problem because the criterion of sameness of sense as logical equivalence apparently clashes with an other relevant point. From the point of view of Frege's logicism, true mathematical equations are logically equivalent. However true mathematical equations, even "22=4" and "2+2=4", have different senses. The passages in which Frege says they have different senses are so abundant that we feel almost compelled to reject the logical equivalence criterion as generally acceptable (and certainly they justify Dummett's reaction against it).
We should then adhere more strictly to the criterion of substitutivity in indirect context. However, if we want to make this criterion more precise, we have more than one difficulty. Two sentences could be said to have the same sense if their subsentential parts have the same sense. Which is the criterion of sameness of sense of subsentential parts? Dummett suggests "that there probably is no sharp criterion for sameness of sense short of the rather boring notion of intensional isomorphism."25 Whether boring or not, even intensional isomorphism has its flaws when propositional attitudes are concerned, as Mates' puzzle shows. Mates' puzzle could, however, be defeated by the application of a Fregean (conditional) Transparency Principle: if we grasp the senses of two expressions, we always recognize whether these expressions have the same sense. It is apparent that preceding failures of sense recognition, we can have failures in substitutability; but we may not be interested in these kinds of failures.26 Therefore, the criterion of substitutability in indirect speech could still be used as a viable criterion of sense identity (or intensional isomorphism), given a presupposed notion of sense recognition (or the ability to grasp the sense). In this respect, the criterion of substitutability is similar to the criterion of immediate recognition: both depend on the concept of sense understanding.
Dummett claims that the problem of sense understanding is the main problem in Frege, and that we should set aside the problem of synonymy to concentrate on the problem of grasping the sense. If we concentrate on the problem of sense understanding however, it seems really difficult to give an objective representation of its structure, unless it is in terms of one's ability to make the right substitutions. We end up running in a circle: to have a notion of grasping the sense, we need a notion of correct substitutions. But, as we have already seen, to have a viable notion of substitution, we need a notion of grasping the sense.
This circle could be broken in two different ways: the first is to follow a Wittgensteinian strategy, defining grasping the sense as the ability to follow rules, without an explicit acknowledgement either of intuition or of substitutivity.27 The second is to give careful attention to the degrees and contexts of the substitutability . We might think of the criterion of substitutability as a criterion which gives degrees of the sameness of sense, defined as substitutability in kinds of contexts. We should be content with a criterion which permits us to indefinitely specify more and more refined conceptions of sense-identity. In fact, "perfect synonymy as substitutability in every context does not exist," and we have before us cases which range from ideal perfect substitutability and occasional substitutability. We might therefore conclude, as Beaney suggests, that we should consider"as many notions of meaning...as there are distinguishable types of contexts in which substitutions of linguistic expressions occur."28
Is this conclusion warranted? Is it useful? While it is difficult to disagree on the importance of the relation between sense and substitutability in contexts, the proliferation of senses which this answer suggests faces at least two problems:

1. It makes empty any attempt to look for a central notion of sense which could account for compositionality.
2. It does not avoid the necessity of distinguishing between different kinds of sense within each context.

In fact, even on the assumption that senses are context-dependent entities, we still need to distinguish between the two main aspects hinted at by Frege in his attempt to give criteria of sense identity: the semantic one and the epistemic one. Brandom 1986 suggested that, after the distinction is made between the two aspects of sense derived by the emergence of Kripke's and Putnam's analyses, the most urgent problem is the investigation of the interrelation between these two kinds of senses. The investigations which have been pursued thus far, as developed in dual theories of meaning, have separated the two aspect of sense into two separate components, one dealing with the world and the other dealing with the mind. Probably, as Putnam said, no unique concept may account both for the task of fixing the reference and giving a synonym. We are not bound, however, to have two separate concepts, heirs of the Cartesian divide;29 we might find in the tensions under which Frege compressed his conception of sense a possible unifying answer. To answer Brandom's suggestion in a Fregean setting means to solve the problem of understanding the internal link between sense as truth condition and sense as epistemic content. Once we have clarifyed the connection between these two levels of sense, we might develop further analyses towards new contextual restrictions to the application of the principle of compositionality.

4. Constant Oscillation Between Different Concerns
Frege oscillates between different criteria of sense as a result of the different purposes and concerns for which he wants the notion of sense. However, speaking of semantic vs. epistemic content does not amount to saying that "semantic" content does not regard cognition. We have two different concerns regarding cognition, linked to two distinctions:

1) the distinction of cognitive vs. emotive (what Frege calls "tone" "coloring" and so on); and
2) the distinction of cognitive value vs. semantic value.

If we want to look for hints about the two different notions of sense in Frege, the first thing we must do is follow these different two concerns. Thesis [1] or the claim that structurally different sentences may express the same thought is consistent with the idea of sense as truth condition and with the criteria of identity of thought based on logical equivalence. The context in which this line of thought is created is most often the discussion about the distinction between sense and tone, and, in particular, the idea that different sentences in natural language may have the same logical consequences. Formal languages can express in a single formula different equivalent sentences of natural language. To say that the two expressions in natural and formal language have the same sense is different than saying that the sense is imprecisely contained in the natural language expression and fully expressed in a formal language. Dummett would probably reject the first of the two formulations. However both formulations admit an interpretation in terms of sense identity as logical equivalence. Using an example by Beaney, we may say that no expert knowing that NaCl+H2O = Na+Cl+H2O will reject the truth of the natural language sentence "salt dissolves in water" and vice versa. Following the Fregean definition of identity of thought given in the second 1906 letter to Husserl, and discarded by Dummett, we may say that the two expressions express the same thought.
The step from this point to the treatment of different expressions in formal language is given in the first 1906 letter to Husserl where Frege says that we may find some canonical or "normal" formula in formal language which could give in a single expression a set of equivalent logical formulas. Frege speaks of the pragmatic utility of having different equivalent sentences of a formal language: some one formulation may be more useful than another for helping people in deduction. Different expressions, both in natural and in formal language, may express the same thought. This thought has an inner structure, which may be represented by the class of logically equivalent sentences or by what has been called later truth condition (Wittgenstein) or intension (Carnap). This assessment of sense identity as logical equivalence, far from being an "aberration" as Dummett suggested, is not only consistent with Frege's work, but also with the tradition following Frege.
Certainly Wittgenstein, who prided himself on being able to recite by heart entire sections of Frege's writings, didn't miss the passage in Grundgesetze par.32, when Frege says that the sense of a sentence is the thought that the truth conditions are fulfilled and that to know the sense you have to know the truth conditions which have to be fulfilled. If Wittgenstein was the first to define explicitly sense as truth condition, Carnap, who followed Frege's lectures in Jena, developed the idea that "cognitive meaning" is truth conditional meaning, or intension.30 The first development of Frege's ideas was on an aspect of his thought which was certainly well roodted in his writings, and could not be made completely explicit because of the contrast with another, more fine-grained definition of sense.
In the early period of logic and philosophy of language, ideas grew interconnected such that it now requires time and caution to disentangle different contributions. It is tempting to think that the tendency to reason in terms of the isomorphism between thought and language is a late influence from his former pupil Wittgenstein. Frege read the Tractatus during World War I, before writing the essay Gedankegefuge(1923), where he states his major proposition on this idea.31 But strict correlation between linguistic expression and sense once again matches very well with former analyses on the role of language and on the difference between the thoughts expressed by different mathematical propositions. His "building block" theory of the composition of senses ante-dates his reading of the Tractatus and we may easily see that most of Frege's suggestions on this aspect are scattered throughout all his writings.
Thesis [2], or the claim that to any component in the sentence there is a correspondent component in the thought is coherent with the idea of sense as epistemic value and with the stricter criterion of substitutability in indirect speech. Here, for instance, "A -> B" and " not (A and not B)" have different cognitive values. A speaker may believe that "s knows that "A -> B" and disbelieve " not (A and not B)". Given the intuitive criterion of difference of thoughts, the two sentences have different senses. This is contrary to the idea that, being logically equivalent, the two sentences should express the same thought. However the context of discussion which leads towards the idea of thought equivalence as logical equivalence never encounter the problem of the cognitive value of identity statements. This problem is normally discussed inside a clarification of the distinction between sense and reference and the justification of informativeness of analytic truths. When Frege says that two sentences with the same truth value may express different thoughts, i.e. different senses, he most often raises the problem of the change in sense provoked by substitutions of co-referential elements in a sentence. When he speaks of identity of thoughts, he is almost always concerned with the other concerns we have discussed above. The two lines of thought which bring about two different aspects of the sense of a sentence are therefore typically given in different contexts - even if in the same paper - and they don't clash with one another explicitly, because of the inchoative characterization of sense (and therefore thought) as truth condition.
The differentiation between semantic and epistemic conceptions of sense does not need to be reduced to a difference of ontological vs. epistemological points of view. The epistemic conception of sense reveals an intrinsic aspect of semantic thought: the different ways in which it can be given. "Gedanke" is literally "what is thought", but, following Wittgenstein and McDowell, we may speak of the "Thinkable." We may say that it is essential to the thought to be thinkable in different ways. We might devise canonical forms under which to express a class of logically equivalent expressions. Pragmatic aspects press us to devise and use different formulations; but these pragmatic aspects rely on an intrinsic aspect of the structure thought. We cannot speak of a thought but as something which can have different ways of being given to us, all relying on the basic structure expressed by the truth condition. These ways of structuring are the ones we use to get at the truth condition, when possible; they may be intended as the accessibility conditions of thoughts. From Frege's point of view, they do not depend on human beings, but are intrinsic to the thought.
This interpretation is matched by an ambivalence in the usage of the term "content" in Frege's early writings. Frege suggested that the content is something which can be "given in different ways." This has often been interpreted as meaning that the True can be given in different ways; but also that the Thought is thinkable in different ways. The problem is that, using only the terminology of "sense of a sentence" for speaking of thought, Frege has no way to express this ambivalent aspect of the notion of "conceptual content."
However, after the identification of the Thought with the sense of a sentence in Sinn und Bedeutung, we may find a sign of the old ambivalence regarding the term "content" in the choice Frege normally makes of using respectively the term "sense" or the term "thought". On the one hand, the remarks on the epistemic aspect of sense are almost always given inside a discussion of differences of sense, contrasted with identity of reference. On the other hand, treating the problem of criteria of identity, Frege speaks always in terms of identity of thoughts. This could make us think that, when speaking of identity of thoughts, he is referring mainly to what is expressed by logically equivalent sentences (and we have seen that, up to a point, the criterion of logical equivalence is consistent with the criterion of immediate recognizability).

Indexicals

Is this impression about Frege's terminology consistent also with what Frege says about indexicals? This point is important, because it is one of the few passages where he does apply his criteria of identity to natural language. In Der Gedanke Frege says that the two sentences "yesteday it was fine" and "today it is fine" spoken on different occasions may express the same thought. If we adhere to our intuitive split of terminology between "different senses" and "same thought" we should say that Frege is referring here to two sentences as expressing the same truth condition, or semantic sense. However it is possible to imagine situations in which a speaker may disbelieve "yesterday is fine" said on the day after the one he said (believing it true) "today is fine."
Imagine this situation: on Fred's birthday it is raining; the day after it is sunny and Fred says "eventually it is fine today!". He is so happy that he works day and night without realizing the time passing by. A day later, if asked, he refuses to assent to "yesterday was fine." Following the principle of intuitive difference of thoughts we should say that these two sentences express different thoughts, because Fred may rationally believe that his occurrence of "today is fine" said that day was true, while he believes that "yesterday was fine" said the day later is false. Shall we run into a contradiction with the Fregean claim that the two sentences should express the same thought? The contradiction is avoided if we think in terms of difference of epistemic senses and identity of semantic senses. "Yesterday is fine" and "today is fine", said in the relevant circumstances, are two different ways to express the same thought. The situation they refer to is the same (let us remember that for Frege "a fact is a true thought"); but we need to realize their epistemic difference, due to our epistemic limitations as human reasoners.
An objection could be the following: in disbelieving "yesterday is fine", the speaker is not referring to the same day he was referring to while saying "today is fine"; therefore, he has not the same de-re sense, he has not the same "dynamic" thought (Evans 1981). We should say that the speaker expresses two different thoughts: a true thought on a certain day ("today is fine"), and a false thought on that same day ("yesterday was not fine"). However Fred might also tell us: "Yesterday was not fine; I remember it well: it was my birthday!" He is wrong to say that yesterday was not fine, but what he intends to say is true, and he is referring to another day in a way similar enough to typical cases of speaker's reference. We certainly understand him as asserting something true about two days ago. We have to give an account of this shift of reference. What shall we say then?
Either he does not understand the de-re sense of his utterance - and says something false - or he gives another sense to his words, and says something true. Are these two ways of treating his belief radically alternative? Evans said that Perry's treatment of demonstratives was a "notational variant of Frege's position". Perry answered that Evan's treatment was a variant of his.32 More similar to Perry, here "semantic" thought would be an equivalent class of (epistemic) senses. The distinction between two aspects of thought is well-suited to treat our epistemic limitations and failures in grasping and expressing different ways a thought can be expressed.

Summarizing:
the oscillation between criteria of identity and difference of senses reflects the internal tension of the two different conceptions of sense whose contrast Frege never became aware of; but there were reasons why he was unaware of the possible contradictions to his claims. First of all he treated the two conceptions of sense in different contexts and, second, he relied on a previous intuition about the different ways to express the same "content". I have tried to give here a hint at the way in which his discussion of sense is encapsulated into different contexts and concerns, such that he could not recognize the possible contradiction which could have arisen if he wanted to keep a univocal notion of sense to do all the work needed in his Begriffsschrift. I will now give some further motivation for Frege's inability to realize the tension and the possible contradiction of his claims, suggesting a way in which his system could have developed such a distinction with a little effort.

5. Why Frege Didn't Get It Right: Hints Toward a Reconstruction of Fregean Thought

A criterion of identity between thoughts which is more fine-grained than logical equivalence is not easy to give. In his first 1906 letter to Husserl, after having defined logical equivalence (equipollence) as the criterion of identity of thoughts, Frege hints at the problem of a more restricted idea of equivalence: teh problem of congruence between thoughts.33 But he says that it not possible "to draw a clearly and recognizable line between merely equipollent and congruent propositions. Even sentences which appear congruent when presented in print can be pronounced with a different intonation and are not therefore equivalent in every respect" [WB 67]. How may we interpret the idea of congruent sentences, sentences "equivalent in every respect", or sentences which express exactly the same thought? Shall we look for something more fine-grained than logical equivalence? Or are logically equivalent expressions also congruent? Frege raises some skeptical doubt: "this could be debated for a hundred years or more. At least I do not see what criterion would allow us to decide this question objectively". Maybe this is a reason why he never stated any precise criterion of identity for his epistemic conception of sense, but suggested only an intuitive criterion of difference.
The problem, however, has been debated almost a hundred years after his letter to Husserl. Attempts have been made to recover this duality of the conception of sense, in an effort to devise some criterion of identity of thoughts (propositions, intensions) which is stricter than logical equivalence. The distinctions between intension and intensional structure (Carnap), between equivalence and strong equivalence (Barwise and Perry), between content and character (Kaplan), between structured propositions and modes of presentation (Shiffer), and between truth conditional content and representational content (Kamp) can be interpreted as variations on this theme.34
Evans 1982, McDowell 1984, and Recanati 1993 have already suggested that direct reference theories could be considered variants of the Fregean theory or at least that their difference is more apparent than substantive. A deeper continuity in the recent history of philosophy of language could be better understood by realizing how these attempts to characterize a multiplicity of levels of meaning are dealing with and are explicilty expressing Frege's hidden ambiguity on the notion of thought as sense of a sentence. We are still searching for a unifying theory which could clarify the connection between the semantic and the epistemic aspects of the Fregean notion of thought.
Why did't Frege realize that his conception of thought as sense of a sentence was oscillating between a general structure (common to many logically equivalent sentences) and a more fine-grained structure which made these sentences different from another? Besides the general argument given in the previous paragraph, I suggest two further reasons:

(i) The antipsychologism problem - Frege would have probably been reluctant to develop an explicit epistemic notion of sense because of its possible psychologistic developments which could have come to collide with his anti-psychologistic tenets. In fact, in a proper definition of epistemic sense we should take into account the sociological and psychological limitations of a speaker's mind. As noted before Frege eventually wanted to give a logical theory of "the" mind, not a psychological theory of minds.35 Frege would not like to give a too strict connection between his conception of sense and the psychological processes of the speaker; for that reason he sustained that "grasping" a sense is a mysterious process where the subjective comes in touch with the objective. Furthermore he claimed that "a property of a thought will be called inessential if it consists in, of follows from, the fact that this thought is grasped by a thinker."36 Thoughts, although they can be grasped by the minds of single speakers, are completely autonomous of such mental processes; therefore, their definition must be independent of the different ways that speakers use to succeed in grasping them.
But is it really necessary to get involved in the working of actual mental processes in order to define epistemic senses? We may speak just of the different possible ways a thought can be given in principle, or the different computational ways of giving the same mathematical proposition. This was the way Frege used to explain the difference between sense and reference in his letters to Peano and Russell. There is a cognitive value in the fact that different computational structures such as "7=7" and "52 *2114/753=7" give the same Truth Value (and, by the way, the same truth condition). But these computational structures do not depend on the mental processes of human beings (if we were not Platonist and we thought that we invented these structures we couuld just say that these structures do not depend any more on the mental processes of human beings).

(ii) The choice of truth value as Bedeutung of sentences - The definition of Bedeutung as truth value, although a good step in the formulation of logical extensional language, prevented Frege from seeing the possibility of developing and clarifying the ambivalence of his concept of content which gave rise to the tensions between semantic and epistemic sense.
In an 1891 letter to Husserl, Frege uses the tripartite distinction of sense, reference and extension with respect to predicates. Many reasons compelled him to identify reference and extension when speaking of sentences, not the least of which is the German terminology of "Bedeutung" intended after 1891 as "truth value". Gabriel 1984 analyses the ambiguity of the conception of "value" in Fregean writings. The term "value" comes both from mathematics and from value theory in nineteenth century philosophy.37 Overlapping the two tradition Frege did not make a proper distinction between Bedeutung as extension and Bedeutung as meaning. Intended as (mathematical) value of a characteristic function, the Bedeutung can be easily interpreted as extension, as the objects 1 or 0, or as the True or the False. But Bedeutung as the value of significance38 should be accounted for in a more complex way. As many commentators suggest, the definition of the Bedeutung of a sentence as its truth condition (or as the state of affairs) is not contradictory with Frege's argument for defining the Bedeutung of a sentence as its truth value39. As Beaney 1994 suggests (p.233) "in restricting "Bedeutung" purely to truth value, the notion of "Sinn" was given too much work to do." This suggests that if Frege had used the distinction between Bedeutung and Extension also for sentences, he could have given a better account of his theory of sense.

After this discussion, we could ask which criteria should hold for a Fregean theory of though which allows a thought to be considered together with its objective ways of being thinkable. The most Basic Criteria40 for a Fregean Representation of Thought, following the previous discussion, could be summarized as:
1) Thought must be represented as a class of equivalent expressions; the different expressions represent different ways in which the same truth condition is given. They may also represent our epistemic accessibility to the Thought.
2) These different ways of getting at a unique structure must be intended as intrinsic to Thought, and not dependent on our psychology. However, when expressed in a language, they represent our explicit representation of the working of the Thought.
3) The semantic and epistemic aspects of Thought must comply with compositionality. However, contextual restrictions to compositionality can be given (as in indirect speech).

Is it possible to generalize the tripartite division of sense, reference and extension Frege made for predicates, so that we could adhere to these criteria? If Frege had also pursued a distinction of this kind for sentences and singular terms he could have found a natural solution to his concerns. If truth values are the extensions and truth conditions the referents of sentences, (epistemic) senses could be represented by the different procedures with which each formula is given a truth condition. Even logical truths, which - being always true - have the same truth conditions, should have been recognized as having different (epistemic) senses (the difference being on the complexity of the formula).
In this way, we might attain a rational reconstruction of the tensions in Frege's logic; accepting, for sake of simplicity, the modern terminology of intension, considered as function from possible words to extensions, we might sketch the development of the tripartite Fregean schema in the following way:
epistemic sense (sense) procedures associated with the intension
semantic sense (Bedeutung) intension
extension extension

Here we may compare Frege's terminology, so conflated with overlapping ideas, with some correspondent concept in our contemporary terminology. It is worth noting that the idea that intension corresponds to the Fregean reference and not to the Fregean sense (a hint derived from Carnap) is taken explicitly by Cresswell 198541. Abandoning Fregean terminology we may say that a representation of a truth condition (intension as a function from possible worlds to truth values) can be given together with procedures attached to the function; the different procedures which compute the function can be considered an explication of what Frege used to call "sense" in its epistemic aspect.
An example of a possible development on these lines can be found in the attempts to build a bridge between model theoretical semantics and procedural semantics in artificial intelligence. It might be objected that in representing epistemic senses as (sets of) procedures we simply give an explication of linguistic meaning, not of sense. However this objection is ruled out by the perspectives offered by intelligent systems, where we may give procedures, linked to perceptual devices, to pick out objects in a (restricted) environment. Regarding the restrictions given to a Fregean theory of thought, beyond the possibility of distinguishing clearly truth conditions and other kinds of computational procedures, these attempts respect the requirement of the compositionality principle. A discussion may arise about the antipsychologistic requirement; however procedures used in intelligent systems could be interpreted as representations not of subsymbolic mental processes, but as of the laws of symbolic thought.42 After the contrast between connectionism and symbolic A.I. we are beginning to face the contrast between a computational theory of mind and a computational theory of thought.
From the point of view of a computational theory of thought, we may say that truth conditions and the way to get them are both part of the objective structure of the Thought - the thought is not an unstructured content, but something which intrinsically comes with its own different ways. Thoughts, or thinkables, are to be studied at different levels of complexity: intensions are the most unifying structures, representing the basic semantic stuff; procedures attached to intensions are the ways to make intensions realized in different structures of thought. Frege's tensions could be overcome by defining Thought as a multi-level structure: both as intension and as procedure, as semantic and objective truth condition and as procedural objective ways to determine truth conditions.
Being that different sentences can provide a representation of the same truth condition, a representation of the thought is non only what is thought but also how it is given. It belongs to the thought to be thinkable in different ways; we cannot separate in to two realms an unstructured thought and a structured linguistic meaning: the thought has its own general structure (intensions) which are the sources of all possible objective articulations, a subset of which are conventional linguistic meanings.

APPENDIX


Following the discussion given in par. 4 I give here a short summary of quotations consistent on one hand with a semantic and on the other with a cognitive notion of sense. These quotations given here as not self-subsistent evidence of the two different trends in Frege's thought; they are a reminder of the passages quoted in the text and not always properly referred to, and a remainder to the arguments given in the paper.

Some Relevant passages consistent with Thesis [1]:a same thought may be expressed by different sentences: towards Sense as Truth Condition

1879 Begriffsschrift ß 3 on the irrelevance to logic of the of the subject/predicate distinction: there are "little difference in sense" which affect the tone, but not content (= inferential potential). ß 9 on decomposition of the same conceptual content in different formulae;

1884: Die Grundlagen der Arithmetik: "The sentence 'line a is parallel to line b' is to mean the same as 'the direction of line a is equal to the direction of line b'" (par.65,p.76)

1892 Begriff und Gegenstand again on the irrelevance to logic of the subject/predicate distinction. Example with difference between "there is one à2" and "the concept à2 is realized": "we must never forget that different sentences may express the same thought" (p.49)

1891 Funktion und Begriff: the two sides of what will be Axiom V express "the same sense, but in a different way" (p.11). Example given with "x2-4x=x(x-4)" and "e(e2-4e) = a(a(a-4))"

1893Grundgesetze , ß32: the sense of a sentence, the thought, "is the thought that these conditions are fulfilled". ß on the equivalence in sense of the two sides of Axiom V:

1897 Logik : "the only essential thing for us is that a difference of thought does not correspond to every difference in the words used" (141); again on active and passive as pertaining to the tone and not to the thought: "The sentences 'M gave the document A to N' and 'Document A was given to N by M'..express exactly the same thought". (ibid.)

1903 On the Foundation of Geometry (281) : Again on the difference of the "linguistic point of view" and the "logical point of view" in respect of subject/predicate distinction. We may decompose "8=23" in different ways ("8" and "...is the third power of two"; or: "2" and "...is something whose third power is 8").

1906 Letter to Husserl on "normal sentence" which express the set of logically equivalent sentences; on the logical equivalence between two formula of the logical writing: "equipollent sentences have something n common in their content, and this is what I call the thought they express" (p.102) example of equipollent propositions: "A->B" and "- (A & -B)" (103-104).

1906 Einlaitung in die Logik : on natural language expressing the same thought in different ways and on the different decompositions of logical writing in function and argument;

1919Die Verneinung : two sentences may express the same thought but with difference force (assertion and question);:

1923Logische Allgemeinheit : different expressions belong the coloring of the thought; we need a unique formula to avoid the idea that they are difference in thought.

1923Gedankegefuge: on the equivalence of different compositions of thoughts; there are examples ("A&B" and "B&A"; "not(notA)" and "A") of case where "two linguistically different expressions correspond to the same sense. This divergence of expressive symbol and expressed thought is an inevitable consequence of the difference between spatiotemporal phenomena and the world of thoughts" (59)

1924Erkenntinsquelle der Mathematik : "A sentence, as expression of the thought, is to be distinguished from the thought. It is possible to express one and the same thought in different ways"

Some relevant passages consistent with thesis [2]: to each difference in a sentence there must correspond a difference in thought.: towards Sense as cognitive value .

1891Funktion und Begriff : "24=42 and 4x4=42 have the same reference but not the same sense (i.e. in this case they do not contain the same thought)." (14). Anticipation of the example of "the Morning Star" and "the Evening Star".

1892Uber Sinn und Bedeutung : The well known argument with the analysis of substitutivity on the example of Morning and Evening Star.

1893 Grundgesetze : 2=4 and 2+2=4 "do not have the same sense" (the sense of a name of truth value is a "thought") (ß2):

1897 Letter to Peano : the sense of "5+2" is different from the sense "4+3"; therefore the sense of "22+3>2+3" is different from the sense of "5+2>5";

1904 letter to Russell : two sentences such as "7=7" and "52 *2114/753=7" "do not have the same value for our knowledge" even if "52 *2114/753=7" denotes the same as 4'7,4'. We conceive the thought as sense of a sentence and therefore we say that a sentence express a thought.

1906 Einleitung in die Logik : as a proper name is part of a sentence, its sense is part of the thought. As thought is the sense of an entire sentence, part of a thought is sense of a part of a sentence.

1910 Letter to Jourdain : the sense of the sentence "Ateb is high 5000 meters" is different from the sense of "Afla is high 5000 meters". Argument of SuB explained: strict relation between linguistic expressions and senses.

1913 Begriffsschrift II (Carnap's notes): "The reference of a part are not parts of the reference of the sentences. But: the sense of a part of a sentence is a part of the sense of the sentence"

1914 Logik in der Mathematik: The "content of thought' of "137+469=606" is different from the content of "606=606", because the first sentence "extends our knowledge". Similar examples are given from mathematics and natural language (Hesperus and Phosphorus). Thoughts are constituted by blocks corresponding to groups of sounds composing the sentence.

1918 Der Gedanke: Two sentences with the same truth value but with different proper names express different thoughts, because the speaker might not recognize the identity between the expressions ("I have been wounded" and "dr.Lauben has been wounded".

1919 Negation: "The world of thoughts has a model in the world of sentences, expressions, words, signs. To the structure of the thought there corresponds the compounding of words into sentence" [148]

1919 Aufzeichnungen fur L. Darmstaedter other examples of substutitivity of coreferential expressions which do not preserve truth in indirect speech.

1919 Die Verneinung: ":The world of thoughts has a model in the world of sentences, expressions, words, signs. To the structure of the thought there corresponds the compounding of words into a sentence, and here the order is in general not indifferent" (148)

1923 Gedankegefuge the "locus classicus": We are able "to distinguish parts in the thought corresponding to the parts of a sentence, so that the structure of the sentence serves as a picture ("Bild") of the structure of the thought." (390)


Bibliography