Frege, the self-consciousness of judgement, and the indefinability of truth

ABSTRACT

Frege characterizes judgement as the acknowledgement of the truth of a thought, appearing thereby to rule out false judgement. First in this paper I explain Frege’s characterization so that it does not have this consequence. Frege is not saying that for a subject S to judge that p is for S to acknowledge the truth of the thought that p. Rather, he is articulating judgement’s nature within self-consciousness. From within, to judge means to acknowledge a truth. Second, I suggest that this articulation is centrally operative in Frege’s argument for the indefinability of truth. As Frege argues, it follows from judgement’s self-consciousness that truth is indefinable.

KEYWORDS:

• Frege
• judgement
• indefinability of truth
• inference
• self-consciousness

1.

“By Judgment, I understand the acknowledgment of the truth of a thought” (Frege, Basic Laws of Arithmetic, 9). This characterization is found throughout Frege’s work from 1891,¹ and there is no reason to suppose that the conception of judgement it represents was not operable before that date (just replace the word ‘thought’ with the words ‘judgeable content’). As here in Basic Laws of Arithmetic, it commonly appears as an introductory explanation of what Frege means by judgement: Frege seems to think that once given the phrase ‘acknowledgement of the truth of a thought’, his reader will recognize straightforwardly enough the act it articulates. In fact, however, Frege’s characterization has occasioned a good deal of perplexity, and it is not hard to see why. Acknowledging (recognizing, anerkennen) the truth of a thought seems to mean coming to know a thought’s truth, but judgement surely does not entail knowledge.² And even if this matter of knowledge is elided, the characterization would, in any case, appear to rule out false judgement. A subject cannot recognize the truth of something that is not true.

Judgement plays a central role within Frege’s philosophy, and the evident puzzle of his ubiquitous characterization has given rise to a debate in the secondary literature. Participants in this debate fall broadly into two camps. First, there are commentators who bite the bullet, embracing implications of knowledge and factivity. Anscombe, for example, wrote that “being asserted (in this logical sense) is, for both Russell and Frege, something that cannot possibly attach to a proposition unless it is true” (Introduction to Wittgenstein’s Tractatus, 114). Thomas Ricketts writes that for Frege, “to make a judgement is to acquire a piece of knowledge” (“Logic and Truth in Frege”, 131). And Mark Textor has held that “only if a thought is a mode of presentation of the True can its truth be acknowledged” (“Frege on Judging as Acknowledging the Truth”, 641). (False judgements, Textor suggests, are to be understood as failed attempts at judgement (“Frege on Judging as Acknowledging the Truth”, 642).) Commentators in the second camp baulk at this embrace. Dummett, for example, maintains that such “absurdities” as that judgement and assertion cannot be false should not be ascribed to Frege (The Interpretation of Frege’s Philosophy, 5; see also Frege: Philosophy of Language, 312–14). Frege’s characterization, he implies, is simply clumsy, or at least theoretically unimportant. Michael Kremer agrees with Dummett that Fregean judgement can be false, but rather than setting Frege’s characterization aside, he gives it a disarming reading: “The linguistic norms of nineteenth century philosophical German”, Kremer holds, permit an understanding of Frege’s verb ‘anerkennen’ on which it is non-factive (“Judgment and Truth in Frege”, 557). Frege is characterizing judgement not as knowing-true but simply as ‘holding-true’ (“Judgment and Truth in Frege”, 567, 575).

As Kremer notes, there are occasional passages in which Frege appears to countenance false judgement.³ But the principle argument in favour of the Dummett-Kremer view is more global: Frege’s work is simply not illuminated philosophically by the ascription of a position that someone judges only if they know. Balanced against this general consideration, on the other hand, is not just Frege’s characterization itself, but also certain related discussions of inference. To infer, for Frege, is to make a judgement. Indeed, it is to make a judgement on the basis of prior judgements, so that “before acknowledging its truth, one cannot use a thought as a premise of an inference” (CP, 402). And from here Frege appears clearly to infer that inference is made only from truth. For example:

From false premises nothing at all can be concluded. A mere thought, which is not recognized as true, cannot be a premise. Only after a thought has been recognized by me as true, can it be a premise for me.

(PMC, 182)

A premise is something judged – that is, recognized as true – and so a premise must be something true.

There is, then, a genuine difficulty of interpretation. How can we agree with Dummett that Fregean judgement is fallible, whilst taking Frege’s characterization seriously as aligning judgement with knowledge? How can we agree that a judgement may be false whilst allowing that because a premise is something judged, no inference is possible from falsity? Solving this difficulty is the first ambition of this paper. The second ambition is to set out from there an interpretation of Frege’s famous argument for the indefinability of truth. Various authors have suggested that this argument draws on Frege’s conception of judgement. I shall agree. Indeed, I shall suggest that a proper understanding of what Frege means in calling judgement the recognition of a truth provides for a reading of the argument which is both exegetically sound and philosophically compelling.

2.

It is central to this paper that Fregean judgement is a self-conscious act. Indeed, my proposal for Frege’s characterization will be that it articulates judgement’s nature within self-consciousness. Frege is not specifying what judgement is from without. He is not saying that for a subject S to judge that p is for S to acknowledge the truth of the thought that p. That would render judgement infallible. Rather, Frege is specifying what judgement is from within. From within, to judge means to acknowledge a truth.

Understanding this proposal will require, first, an indication of the general idea of a self-conscious act. And for this we shall need to look beyond Frege. Let’s begin, then, by considering some remarks instead of Sebastian Rödl. Rödl writes of intentional bodily action:

My knowing first-personally that I am doing such-and-such is the same reality as my doing it.

(Self-consciousness, ix)

Where the subject writes a letter, or looks for an apple, she therein understands or knows herself to be writing a letter, or looking for an apple. Her self-understanding as acting is not something additional to her acting; rather, it is her acting. This identity defines the general idea of a self-conscious act. And it has application, Rödl holds, beyond intentional bodily action. In particular, it applies also to judgement:

In judging that things are so, I understand myself to do that: judge that things are so. I understand that in judging. I do not, on the one hand, judge that things are so, and, on the other hand, think that I do. My judging something and my comprehending myself to judge it are one act of the mind.

(“Self-consciousness, Negation, and Disagreement”, 215)

In judging that p, the subject self-understands as so judging. And this means: the subject’s judging that p is her self-understanding as so judging.

This idea of a self-conscious act has been adopted and developed by various authors.⁴ Clearly, though, it will be difficult to understand. And whilst a paper on Frege cannot aim for a sustained elaboration, a certain comment will be helpful to clarify the idea’s basic shape, and with that to defuse a couple of natural objections.

For a self-conscious act φ, we’re saying, to φ means to self-comprehendingly φ. The subject’s φ-ing is her self-comprehension as φ-ing. To say this is not, however, to make an identification. The proposed identity of acting and self-understanding, someone might object, is obviously unworkable, for it is as plain as day that whatever is meant by the subject’s self-understanding as looking for an apple – perhaps we mean that she makes a first-personal judgement, or that she enjoys a certain self-awareness – this will be something different from her looking. Looking for something is patently different from making a judgement. The answer to this natural objection is that the subject’s looking is indeed not a judgement, but this is not what is being proposed. Indeed, the looking is not being identified with any separately understood act of self-comprehension. (The idea is precisely not this: You know what looking is, right? And you know what it is to self-understand as looking? Well here’s something interesting you probably didn’t know: if someone is looking, then their looking is the same thing as their self-understanding as looking! (This is not Hesperus and Phosphorus)). It belongs to the proposal, rather, that the self-understanding in question is theoretically proper to self-consciousness, and explicable only in hand with that idea. A self-conscious act is fundamentally self-conscious, where this means it is understood theoretically only as such.⁵ And equally, the subject’s self-understanding in acting is fundamentally just that: the self-understanding of a self-conscious act. Such a comprehension has no articulation separate from its identity with the self-conscious act.⁶

This first natural objection relates also to a second. If mental acts are in general self-conscious, someone might wonder, does this not mean that the subject’s self-understanding will be self-conscious? So where the subject φs, will she not self-understand as self-understanding as φ-ing as well as self-understanding as φ-ing – and so on into a regress? This objection misunderstands again the proposal’s basic form. The idea of self-consciousness is not the idea of a higher order act directed on a lower order looking (say), so that we can ask whether the directed, higher order act is not also self-conscious, and then worry about a regress up the orders. (In particular, the self-understanding as looking is not a judgement about a looking.) Rather, there is a single, unitary act and with that no grip for a regress. The answer to the question posed is, therefore, that no, the subject does not ‘self-understand as self-understanding as φ-ing’ as well as self-understanding as φ-ing. Rather, to say the subject self-understands as self-understanding as φ-ing will, if it means anything at all, mean simply that she self-understands as φ-ing.⁷

3.

Let’s return now to Frege. And let’s consider with Frege some comments by Maria van der Schaar. Van der Schaar argues at length that Frege’s concern with judgement is centrally a concern with judgement “from a first-person point of view” (“Frege on Judgment and the Judging Agent”, 238). In this context, she considers Frege’s characterization of judgement as the recognition of the truth of a thought. She writes:

The distinction between first- and third-person perspective may be used to clarify the lack of conceptual distinction in these places between judgement and knowledge. When we look at judgement from a third-person point of view, there is a conceptual difference between, on the one hand, judgement or belief, and, on the other hand, knowledge, but from a first-person point of view one takes one’s judgement to be true and justified, that is, to be knowledge.

(“Frege on Judgment and the Judging Agent”, 243)

Van der Schaar makes here a pair of closely connected suggestions. First, she claims that whilst from a third-person point of view there is a conceptual difference between judgement and knowledge, there is no such difference from a first-person point of view. And second, she holds that “from a first-person point of view one takes one’s judgment  … to be knowledge” (“Frege on Judgment and the Judging Agent”, 243). The claim of no conceptual difference is in effect, I think, Frege’s characterization. But to understand it, we shall need first to understand van der Schaar’s other claim, her claim that the subject takes her judgement to be knowledge. And for this we need to consider judgement’s self-consciousness.

Rödl holds judgement to be a self-conscious act, writing that “my judging something and my comprehending myself to judge it are one act of the mind” (“Self-consciousness, Negation, and Disagreement”, 215). But there is more to be explained of judgement’s self-consciousness than is explicit in this sentence. Consider Irad Kimhi’s reaction to an argument of Peter Geach. What Geach’s argument shows, Kimhi writes:

is that there is no gap between one’s judging something (p) and one’s assessment of the same judgment as true (“I am truly judging p”). The transition from a judgment to a truth-assessment of that judgment is not based on a recognition of any new fact. A proper philosophical account of this matter must allow us to say that the assessment of one’s judgment as true is internal to the very act of judging.

(Thinking and Being, 7)

And Rödl, again, writes:

A judgment represents itself as correct; it represents itself as conforming to the measure by which, as judgment, it is subject. When we say that a judgment represents itself as correct, we mean that a judgment and its representation as correct are one act: the representation of the judgment as correct is not a second order representation, whose object is the judgment; rather it is the judgment itself. We may – and will – express this by saying that a judgment not only is true but refers itself to the truth.

(Categories of the Temporal, 60)

There is no gap between the subject’s judging that p and the representation of her judgement as correct. There is no gap, that is, between the subject’s judging that p and her self-understanding as judging truly that p. In judging, the subject self-understands not as ‘merely judging’, but as judging correctly – that is as judging truly.

The idea of a self-understanding as acting correctly is not peculiar to judgement. There are other self-conscious acts which carry an internal measure of correctness, and with that the distinctive form of self-consciousness here in view. In reading a text out loud, for example, the subject self-understands as reading correctly, that is as reading faithfully. In calculating a sum, the subject self-understands as calculating correctly. In (deductively) inferring, the subject self-understands as inferring correctly, that is as inferring validly. And in judging, the subject self-understands as judging correctly, that is as judging truly. Accepting this general form of self-consciousness, we may, I however think, take a step beyond Rödl and Kimhi in the case of judgement. Rödl suggests that judgement’s internal measure of correctness is truth. But the perfection of judgement is not mere true judgement, but knowledge. And so the judging subject’s self-understanding as judging correctly is not a self-understanding as ‘merely judging truly’, but a self-understanding as knowing. The judging subject does, as Rödl asserts, self-understand as judging. And she does, as Kimhi and Rödl both assert, self-understand as judging truly. Fundamentally, though, the judging subject self-understands as knowing.

Van der Schaar writes that “from a first-person point of view one takes one’s judgement  … to be knowledge” (“Frege on Judgment and the Judging Agent”, 243). This is not the claim that the subject makes a second-order assessment of her judgement as a piece of knowledge, or is liable to make such an assessment. The claim is not that as and when the subject brings her judgement into view, she will rate that judgement as knowledge (good work me!). Rather, the subject takes her judgement to be knowledge in the sense that her judgement that p is a self-understanding as knowing that p. In judging that p, the subject self-understands as knowing that p. And from here we may move to an understanding also of van der Schaar’s first point, her claim of a lack of conceptual difference from the first-person point of view between judgement and knowledge. The judging subject, we have said, self-understands as judging, as judging truly, and as knowing. This does not mean, however, that she has three different self-understandings, of increasing strength. It means, rather, that from within, to judge is to judge truly, or again to judge is to know. The subject’s self-understanding as judging is a self-understanding as knowing.

Within self-consciousness, the act of judgement is the act of knowledge: it is the act of recognizing a truth.⁸ And this is my suggestion for Frege’s characterization: he is articulating the nature of judgement within self-consciousness. Frege is not identifying judgement by specifying what it is from without. He is not saying that to think of a person as judging is to think of them as recognizing the truth of a thought. Rather, he is identifying judgement by specifying what it is from within. To self-understand as judging is to self-understand as recognizing the truth of a thought. To judge that p is to recognize the truth of the thought that p.

4.

We considered above a difficulty of how Frege’s characterization could be what it seems to be, namely an articulation of judgement as knowledge, without its rendering judgement infallible. The current proposal solves this difficulty. From within, judgement is knowledge, but this does not rule out that someone may judge falsely, for what from within is a knowing may from without be a false belief. The proposal remains nonetheless underdeveloped, both systematically and exegetically. Systematically, the matter of self-consciousness, and more particularly the identity within self-consciousness of judgement and knowledge, has obviously not been given full elaboration. But this is a paper on Frege, so I shall leave that task to one side in favour of an attempt at exegetical progress. In section 1 we briefly considered certain comments on inference, and, in what follows, I shall revisit Frege's thinking here. Primarily, though, I want to use our understanding of Frege’s characterization to arrive at an interpretation of his famous argument for the indefinability of truth. Before addressing either of these two matters, however, we shall need first of all to consider a claim in Frege that every judgement is at once a judgement of truth.

5.

Frege frequently speaks of subjects as ‘holding thoughts true’ (fürwahrhalten), and apparently understands judgement as such an act. (So he writes in “On Sense and Meaning” that the True and the False “are recognised, if only implicitly, by everybody who judges at all, who holds something true” (CP, 163).⁹) Similarly, assertion is described as ‘putting a thought forward as true’ (als wahr hingestellen) (see e.g. PMC, 20). These expressions are not typically intended to give the reader pause, and consonant with this we might look to read them in a theoretically anodyne manner. Specifically, the ‘true’ in ‘holding a thought true’ (or the ‘as true’ in ‘putting a thought forward as true’) might be taken to attach to the verb, and to do so as a merely periphrastic expansion. Holding the thought that p true means holding-true the thought that p, which means holding-true that p, which means – simply – holding that p. (Putting the thought that p forward as true means putting-forward-as-true the thought that p, which means putting-forward-as-true that p, which means – simply – putting forward that p.)

In certain places, however, Frege connects truth with judgement and assertion in a manner on which he clearly does intend his reader to pause, and which cannot be given an anodyne reading. So he writes in “Thoughts” that “we cannot recognise a property of a thing without at the same time finding the thought this thing has this property to be true” (CP, 354). And in the second “Logic” manuscript we find:

What, in the first place, distinguishes [truth] from all other predicates is that predicating it is always included in predicating anything whatever. If I assert that the sum of 2 and 3 is 5, then I thereby assert that it is true that 2 and 3 make 5.

(PW, 129)

Recognizing or asserting a certain thought, Frege says, means recognizing or asserting that thought to be true. Here the ‘true’ is explicitly attached not to the verb, not to the recognizing or asserting, but to the verb’s object, the thought recognized or asserted. Recognizing or asserting that p means recognizing or asserting that it is true that p.

But why should this be so? Why does taking Jack to be tall mean, or include, taking the thought that Jack is tall to be true? Why does asserting that Jill is happy mean, or include, asserting that it is true that Jill is happy?

A straightforward answer to this question appeals to a well-known Fregean doctrine of thoughts and truth. “The sentence ‘I smell the scent of violets’”, Frege writes, “has just the same content as the sentence ‘It is true that I smell the scent of violets’” (CP, 354). Or again, “if I assert ‘It is true that sea-water is salt’ I assert the same thing as if I assert ‘Sea-water is salt’” (PW, 251). In general, the thought that it is true that p is the same thought, Frege holds, as the thought that p. Let’s call this doctrine ‘truth-identity’. And it is truth-identity, someone might propose, that explains why for Frege asserting or judging or holding that p includes asserting or judging or holding that it is true that p. Judging that p includes judging that it is true that p, because that p and that it is true that p are the very same thing to judge. Judging the one includes judging the other because the one is the other.

Straightforward as this answer may be, it does not provide a plausible reading of the passages cited. One way to be suspicious of it is to note that the explanation it offers of why recognizing or asserting that p includes recognizing or asserting that it is true that p is indifferent to the fact that we are talking here of recognising and asserting. In exactly the same way that holding that p means holding that it is true that p, so supposing or hoping that p will mean supposing or hoping that it is true that p. And this does not seem faithful to Frege’s intentions. The impression had in reading these passages is that Frege is making a point about the specific propositional acts he mentions (these are acts of commitment), rather than a point whose substance regards only the fact that they are propositional acts. And this impression is not without foundation. There is no mention of truth-identity in the vicinity of the “Logic” passage: Frege apparently expects his reader to recognize that the assertion that p includes the assertion that it is true that p independently of any recognition they may have of truth-identity. And whilst Frege does in “Thoughts” mention truth-identity alongside his claim of finding a thought to be true, he does so in the following way:

[W]e cannot recognize a property of a thing without at the same time finding the thought this thing has this property to be true. So with every property of a thing is joined a property of a thought, namely, that of truth. It is also worthy of notice that the sentence “I smell the scent of violets” has just the same content as the sentence “it is true that I smell the scent of violets”.

(CP, 354)

Here, Frege’s claim of recognition and finding is explicitly not justified by reference to truth-identity. On the contrary, Frege presents truth-identity as something explanatorily separate: this, he says, is something also worthy of notice.¹⁰

So how else might we explain Frege’s position? Why, if not because of truth-identity, does judging that p mean holding the thought that p to be true? The answer I want to propose is that this is a more or less straightforward consequence of judgement’s self-consciousness. In judging, we have said, the subject self-understands as judging correctly; and so in judging, it follows, the subject holds what she judges to be true. Let’s spell this implication out. In judging that p the subject self-understands as knowing that p, that is, as judging truly that p. It is a condition, however, on self-understanding as judging truly that the subject understand what she judges to be true. Judging truly means for Frege judging a truth, and so taking oneself to judge truly that p means taking that p to be true. And together these deliver the result. They deliver that the subject judges that p only if she takes that p to be true. In judging, the subject understands what she judges to be true.

6.

The claim that the subject self-understands as judging truly that p only if she holds that p to be true needs elaboration. In particular, there is a question of the sense here of ‘holding’. A full response to this question would again pull us away from Frege into an account of self-consciousness. But in short, the thought will be that in this condition ‘holding’ speaks generally of an act for which truth is an internal measure of correctness. Self-understanding is a species of such holding. If the subject self-understands as acting in a certain way when she is not so acting, then her self-understanding is false and as such is mistaken. And it is because self-understanding is a species of holding that the subject self-understands as judging truly that p only if she holds that p to be true. Judging truly means for Frege judging a truth. So, much as hoping or supposing Jack to judge truly that p means hoping or supposing that p to be true, and much as judging Jack to judge truly that p means judging that p to be true, so holding oneself to judge truly that p means holding that p to be true.

There are points in Frege’s work where the current result – viz. that because the subject’s self-understanding in judgement is as judging correctly, she judges that p only if she takes that p to be true – breaks the surface and finds explicit voice, in particular the passages considered above from “Logic” and “Thoughts”. But it also lurks beneath the surface in various other places, motivating and explaining more explicitly expressed views. One such place is Frege’s discussions of inference. Another is his argument for the indefinability of truth. Let’s now consider these in turn.

As we have seen, Frege asserts that no inference is possible from something false. And he appears to explain this by reference to the fact that the premise of an inference is something judged – that is, something recognized as true. So Frege appears to detach being true from being recognized as true. Insofar as this appearance is right, Kremer’s view will be wrong that Frege’s phrase ‘recognising the truth of a thought’ means no more than ‘holding a thought true’. On the other hand, the discussions of inference where this detachment is apparent do not provide unequivocal support either for the opposing view of Ricketts and Textor that a person judges that p only if p. For whilst this view immediately explains Frege’s repeated rejection of inference from falsity, it leaves us somewhat surprised at another of the passages’ recurring features. Frege writes:

From false premises nothing at all can be concluded. A mere thought, which is not recognized as true, cannot be a premise. Only after a thought has been recognized by me as true, can it be a premise for me. Mere hypotheses cannot be used as premises.

(PMC, 182)

[W]e can draw no conclusion from something false. But it might perhaps be asked, can we not, all the same, draw consequences from a sentence which may be false, in order to see what we should get if it were true?

(PW, 244)

Only true thoughts can be premises of inferences.  … But, one might perhaps object surely one can make deductions from certain thoughts purely hypothetically without judging the truth of the latter.

(CP, 335)

In each of these passages, the rejection of inference from falsity is directly connected to a rejection of inference from a hypothesis. This second rejection is not in itself surprising. Inference as Frege conceives it is a movement between judgements: “an inference  … is the pronouncement of a judgment made in accordance with logical laws on the basis of previously passed judgments” (CP, 318). Hypothetical reasoning, it follows, must be understood other than as inference from a hypothesis. And nor is it surprising that Frege considers hypothetical reasoning as a potential counterexample to the claim that inference is made only from truth: a hypothesis may, of course, be false. What will rather be surprising from the perspective of Ricketts and Textor is Frege’s repeated treatment of hypothetical reasoning as the potential counterexample to his rejection of inference from falsity. Why is that the natural objection – indeed the only objection – for an interlocutor to raise? What about the more glaring case of someone who (as we should say) falsely believes that p and then (as we should say) reasons from that false belief to the thought that q?

Unlike both Kremer and Ricketts and Textor, we are in a position to provide a seamless reading of Frege’s discussions of inference. Frege insists quite rightly that because judgement is the recognition of truth, inference is made only from truth. But when he moves then to consider suppositional reasoning, he is not passing over the possibility of someone’s reasoning from a false belief, for Frege’s comments in these passages are not claims as to what someone – a person – can or cannot do.

The premise of an inference is something judged. In judging the subject understands herself to judge truly. And in self-understanding as judging truly, the subject understands what she judges to be true. So, inference is made from truth. (“Of course we cannot infer anything from a false thought” (CP, 375) – of course!) The detachment of the truth of a thought from the recognition of its truth, this is to say, is a detachment within self-consciousness. Frege is not describing inference from without. In particular, he is not saying that to think of someone as inferring is to think of them as making a judgement on the basis of a true premise. Rather, he is describing inference from within. To self-understand as inferring is to self-understand as recognizing a truth on the basis of previously recognized truths. Against this we might raise a worry that inference may be made from a supposition, and so from something which is not recognized as true. But it betrays a misunderstanding of the basic nature of Frege’s theorizing to raise as an objection that someone can surely reason from falsehood. Of course someone – a subject – can infer from falsehood. But Frege is not telling us what it is for a subject to infer, he is telling us what it is for the subject to infer.

7.

This same point applies to Frege’s characterization of inference as “a judgment made in accordance with logical laws on the basis of previously passed judgment” (CP, 318, italics added). This characterization, someone might object, bizarrely and quite mistakenly rules out invalid inference, just as the characterization of judgement bizarrely and quite mistakenly rules out false judgement. But again, Frege is specifying inference’s nature for the subject, and for the subject inference is correct inference, just as judgement is for the subject correct judgement. That’s enough now, however, on inference; let’s move on to truth’s indefinability.

Frege’s assertion in the “Logic” manuscript that predicating truth is included in all predication immediately follows in the same paragraph an early version of Frege’s argument for the indefinability of truth. And following his example of asserting the sum of 2 and 3 to be 5, Frege gives as a second example that “I assert that it is true that my idea of Cologne Cathedral agrees with reality, if I assert that it agrees with reality” (PW, 129). I want to suggest that this colocation and choice of example is no coincidence: Frege’s indefinability argument centrally involves the understanding of judgement and truth on display in these sentences.

Let’s consider the later statement of the argument given in “Thoughts”. Here Frege asks regarding a definition of truth as correspondence:

[I]n that case what ought we to do so as to decide whether something is true? We should have to inquire whether it is true that an idea and a reality, say, correspond in the specified respect. And then we should be confronted by a question of the same kind, and the game could begin again. So the attempted explanation of truth as correspondence breaks down. And any other attempt to define truth also breaks down. For in a definition certain characteristics would have to be specified. And in application to any particular case the question would always arise whether it were true that the characteristics were present. So we should be going round in a circle. So it seems likely that the content of the word ‘true’ is sui generis and indefinable.

(CP, 353)

This argument has been given significantly divergent interpretations. Nonetheless, it has a pretty clear first-pass reading, as follows. Suppose truth were definable. Then to decide whether something is true, we should need to decide whether it meets the characteristics specified by the definition. In deciding that, however, “the question would always arise whether it were true that the characteristics were present” (CP, 353). And so the question of truth would repeat. Or more specifically with truth as correspondence to reality, Frege is arguing as follows. Suppose truth were defined as correspondence to reality. Then to decide whether the thought that p is true, we should indeed need to decide whether the thought that p corresponds to reality. In deciding whether the thought that p corresponds to reality, however, we should need to decide whether it is true that the thought that p corresponds to reality. And so the question of truth would repeat.

According to this proto-reading, Frege’s argument involves the premise that deciding whether a thought corresponds to reality means (or involves, or requires) deciding whether it is true that the thought corresponds to reality. Within this premise, however, the content of what is decided is surely immaterial. So the general view is apparently operative that that deciding whether p means (or involves, or requires) deciding whether it is true that p. Perhaps the claim is conditional: if truth were correspondence to reality, then deciding whether p would mean deciding whether it is true that p. Or perhaps it is not. Either way, however, any development of the proto-reading will need to explain this striking premise. Indeed, doing so would appear the major exegetical and philosophical task. So Ricketts writes:

The regress argument assumes that if truth is characterized as correspondence, then the judgment that p requires the  … judgment that p corresponds to Reality, i.e, that it is true that p. Here is the tendentious linchpin of the argument. To many contemporary ears, this assumption will sound gratuitous.

(“Logic and Truth in Frege”, 130)

And Kremer:

The fundamental question is why, on the correspondence theory, judging that p will require judging that the thought that p is true.

(“Judgment and Truth in Frege”, 554)

We are in a position to answer this fundamental question. Frege holds unconditionally that judging that p requires holding the thought that p to be true. And he does so as a consequence of judgement’s self-consciousness. In judging that p, the subject self-understands as acting correctly, and so as judging truly that p. And in self-understanding as judging truly that p, the subject understands that p to be true. So where the subject judges that p, she therein comprehends what she judges, that p, to be a truth.

Frege’s argument against the correspondence theorist may thus be given as follows. Suppose truth were defined as correspondence to reality. Then deploying this definition to decide truth in the case of the thought that p will mean judging the thought that p to correspond to reality. By the self-consciousness of judgement, however, doing this will involve holding it to be true that the thought that p corresponds to reality. (In judging the subject self-understands as judging truly, and so holds what she judges to be true.) But definitions for Frege carry an identity of sense between definiens and definiendum.¹¹ So where truth is defined as correspondence to reality, holding it to be true that the thought that p corresponds to reality means holding the thought that the thought that p corresponds to reality to correspond to reality. And so the correspondence theorist faces a regress. Holding a certain thought to correspond to reality requires holding it to correspond to reality that that thought corresponds to reality, and so on.

8.

This is a relatively simple argument once the result is in place that holding something means holding it to be true. Two points are nonetheless worth highlighting. First, the issue here is not as some have thought one of a precondition. It is not that in order to decide whether p the subject must first decide whether it is true that p.¹² Nor is it that if the correspondence theory were true, then in order to decide whether p the subject would have first to decide whether it is true that p.¹³ The difficulty stems, rather, from Frege’s claim, explicit in texts we have cited, that deciding whether p includes deciding whether it is true that p, that the subject does not recognize that p without therein recognizing the thought that p to be true.

The second point to highlight, one which Frege isn’t explicit about, is that this is a problem for the correspondence theorist because the thought that p and the thought that the thought that p corresponds to reality will for them be distinct thoughts. If ‘corresponds to reality’ is to signify something substantial by which truth may be defined, then the sentence ‘The thought that Jack is tall corresponds to reality’ must express something other simply than that Jack is tall. And so by Frege’s argument, it is a consequence of the correspondence theory that maintaining one thing will mean maintaining also something else – and so, by repeat, it will mean maintaining an infinity of distinct things.

This second point brings attention back to Frege’s identification of the thought that p and the thought that it is true that p: truth-identity, as we called it. Frege does not mention truth-identity in the immediate vicinity of his indefinability argument, whether in “Logic” or “Thoughts”. And nor as I argued is it what justifies the argument’s centrally operative assumption that every assessment is at once an assessment of truth. This assumption does not arrive in the same way as the claim that every hope is at once a hope of truth – that is, merely as a consequence of truth-identity. If it did, Frege’s argument would be both question begging and absurdly prolix: question begging because the truth-definer has no reason to accept a premise of truth-identity, and absurdly prolix because Frege’s discussion of deciding and inquiring would be entirely unnecessary.¹⁴ Frege starts the argument, let’s underline again, not with a thesis about truth, namely truth-identity, but with a certain conception of judgement, its conception as the recognition of the truth of a thought.

Still, truth-identity is, we can see, a condition of the coherence of Fregean judgement, for without it Frege would face essentially the same difficulty as the correspondence theorist. Without truth-identity, a conception of propositional commitment under which judging that p means holding it to be true that p will be a conception under which thinking one thing includes always thinking something else. Recognizing this, it is natural to ask what sort of a condition truth-identity is here. Is truth theoretically prior to judgement for Frege, so that his commitment to truth-identity is independent of his understanding of judgement, a theoretically prior condition of the coherence of that understanding? Or is truth-identity to be explained through Frege’s conception of judgement, so that truth and judgement are theoretically coeval?

I cannot justify here an answer to this large question. At a gesture, however, my reading of Frege would be that truth-identity is explained independently of judgement by reference to the pride of place Frege assigns in his theorizing to the content of the word ‘true’ (PW, 253). More generally, truth is, I think, prior in Frege to judgement and assertion.¹⁵ It follows from this that we should not look to understand Frege’s stated views on truth – for example, truth-identity, the simplicity of truth (PW, 129), the view that truth is not a property “in the ordinary sense” (CP, 354) – by reference to the argument we have been considering for truth’s indefinability, for this argument makes essential reference to the nature of propositional commitment. Frege’s indefinability argument, whilst of considerable systematic interest, is nonetheless peripheral to his own theorizing. The argument demonstrates well enough that truth is indefinable, but it does not illuminate the theoretical basis of Frege’s views on truth – including its indefinability.

9.

Is Frege’s argument compelling? Well, it surely is not psychologically compelling, in that the correspondence theorist will no doubt merrily reject Frege’s conception of judgement as the recognition of a truth. And indeed no correspondence theorist has ever, as far as I am aware, been impressed by Frege’s argument. (I’m not expecting my interpretation to change that.) But it is compelling, I think, in the only sense in which any argument is ever compelling in philosophy, namely that it provides a non-trivial way if not of explaining the truth of its conclusion, then at least of recognizing that truth. Frege shows us that if truth were definable, the subject would not judge thinking her act correct. Or again, he shows us that if truth were definable, then judgement could not be what it is, the acknowledgement of a truth.

Let’s close with some remarks on truth as the goal of judgement. In Section 3, we placed judgement in the context of various self-conscious acts for which in acting the subject self-understands as acting correctly. As in judging the subject self-understands as knowing, so in reading the subject self-understands as reading faithfully, in calculating the subject self-understands as calculating correctly, and so on. Part of the point of this was to suggest, implicitly, that what we have here with Frege’s articulation of judgement’s self-consciousness is an articulation of the sense in which judgement aims at knowledge, and so at truth, the sense in which the judging subject aims to judge truly. Reading aims at fidelity, inference at validity, calculation at correct calculation etc. And the sense in which this is so is given by their form of self-consciousness. Reading aims at fidelity in the sense that in reading, the subject self-understands as reading faithfully: this is how the act’s condition of correctness figures in the mind of the acting subject. And judgement aims at knowledge in the sense that in judging, the subject self-understands as knowing.

That what has been set out in this paper is inter alia an understanding of truth as the goal of judgement,¹⁶ makes evident a substantial commonality between the current interpretation of Frege’s indefinability argument and that of Ricketts. Ricketts asks, “Why, on the correspondence theory, must one inquire whether the thought that Socrates is mortal corresponds to Reality in order to determine whether Socrates is mortal?” (“Objectivity and Objecthood: Frege’s Metaphysics of Judgment”, 78). His answer issues from the following thought:

We cannot take someone to be making assertions in complete disregard for the correctness of what he asserts; such a person would be understood to be merely play-acting or perhaps merely mouthing words.

(“Objectivity and Objecthood: Frege’s Metaphysics of Judgment”, 78)

Ricketts continues:

To take truth to be definable forces a particular construal of this talk of standards of correctness. For to have a definition of truth is to have a general description of the conditions that have to be satisfied for the judgment to be correct. So if truth is definable, then any person who makes a judgment must have ascertained, or taken himself to have ascertained, whether these conditions, applied to the thought under consideration, are satisfied. If I judge that Socrates is mortal then I must have determined that the thought that Socrates is mortal corresponds with Reality. But to ascertain that some condition holds is to make a judgment. Given the definition of truth, a person cannot have judged that the thought that Socrates is mortal corresponds with Reality unless he has judged that the content of this second judgment corresponds with Reality. On the correspondence theory then, a person is never in a position to make a judgment, for no one is ever in a position to have satisfied, or even think of himself as having satisfied, the standards for judgment that would ipso facto be provided by its definition of truth.

(“Objectivity and Objecthood: Frege’s Metaphysics of Judgment”, 78)

Aside from a quibble about whether judging a thought to be true appears as a precondition for the truth-definer on judging that thought, this is essentially my view. (Ricketts is clearly holding here that if truth were definable, judging that p would require the subject to have already judged something else.) If truth were correspondence to reality, Ricketts proposes, judgement’s regard for its correctness would mean that judging that p entails judging that the thought that p corresponds to reality. Ricketts does not, however, surround this proposal with a general, Fregean account of judgement’s intrinsic regard for truth. And so he does not explain by means of a derivation from such an account why, if truth were correspondence to reality, judging one thing would require holding also something else. I have sought above to supply this absent material.

The second thing achieved by bringing into clearer view that what is at issue here is the subject’s regard for the correctness of her act is to reveal as inept a certain possible objection to Frege’s argument. We made above an inference from the subject’s self-understanding as judging correctly to her self-understanding as judging truly. Or again we inferred, from the subject’s taking what she judges to be true and the supposition that truth is correspondence to reality, that the subject takes what she judges to correspond to reality. These moves were made with only minimal pause, but might not the nature of judgement’s correctness, or truth, be opaque at least in judging to the judging subject? Might not truth be correspondence to reality without it following that the subject who judges thinking what she judges to be true thereby judges thinking what she judges to correspond to reality?

One reply to this objection would be to mount a defence of Frege’s general position that definitions carry an identity of sense between definiendum and definiens. But that would be a large and distracting task. The simpler response is to point out that the validity of our moves here is implicit in the fact that what is offered is an understanding of the subject’s aiming at truth. Our account can spell out the sense in which the subject aims at correct action only because her self-understanding as judging correctly is a self-understanding as judging truly. One does not aim in acting to act correctly unless one knows in so acting what such correctness is. (The reading subject’s self-understanding in reading is: ‘I read correctly – that is, faithfully’.) Similarly, if the subject aims in judging to judge truly, and if truth is correspondence to fact, then the subject must aim in judging to judge what corresponds to fact. (In general, one does not aim at something unless one knows in so aiming what it is to meet that aim, aiming to achieve that.) And the general nature of definitions to one side, this is enough to give the result that if truth were definable, the subject would judge only if she holds what she judges to bear the characteristics specified by the definition.

Acknowledgements

This work is indebted to my colleagues Adrian Haddock and Peter Sullivan. Thanks are due also to two referees and an associate editor at BJHP for their considerable help in improving the paper.

Notes

1 See for example the first “Logic” manuscript (between 1879 and 1891) (PW, 2); “On Sense and Meaning” (1892) (CP, 164 n.10); Basic Laws of Arithmetic (1893) (§5); the second “Logic” manuscript (1897) (PW, 139); “On Euclidean Geometry” (1899–1906) (PW, 168); “Introduction to Logic” (1906) (PW, 185); “A Brief Survey of my Logical Doctrines” (1906) (PW, 198); “My Basic Logical Insights” (1915) (PW, 251); “Thoughts” (1918) (CP, 356); “Notes for Ludwig Darmstaedter” (1919) (PW, 253); and “Sources of Knowledge in Mathematics and the Mathematical Natural Sciences” (1924/5) (PW, 267).

2 Indeed, Frege occasionally interchanges talk of acknowledging a thought as true (anerkennen als wahr) with talk of knowing a thought to be true (wissen, dass er wahr ist). See for example PMC, 20.

3 See Kremer, “Judgment and Truth in Frege”, 574.

4 Besides Rödl see for example Kern, Sources of Knowledge, Kimhi, Thinking and Being, and McDowell, “Perceptual Experience and Empirical Rationality”.

5 The philosophical articulation of intentional bodily action, say, should explain it as a species of comprehension; for this see Anscombe, Intention.

6 The idiosyncratic language of ‘self-understanding’ is intended to underline that what we are speaking of is not separately comprehensible as, say, a first-personal judgement or self-awareness.

7 Consider here Kant’s “I think [which] must be able to accompany all my representations” (Critique of Pure Reason, B 132). This is the ‘I think’ of self-conscious representation. And as Kant insists, this ‘I think’ “cannot be accompanied by any further representation” (Critique of Pure Reason, B 132). There is, this is to say, no ‘I think I think’ further to the ‘I think’.

8 Compare Rödl on judgement as correct judgement: “It is easy to see why understanding oneself to judge, or assert, is taking oneself to judge, or assert, correctly: the concept of judgement, or assertion, is the concept of correct judgement, or assertion. She who judges that things are so judges with the concept of judgement, and this is to say, with the concept of correct judgement” (“Self-consciousness, Negation, and Disagreement”, 216).

9 I follow here Kremer’s manifestly correct translation (“Judgment and Truth in Frege”, 572). See §6 of Kremer’s paper for further evidence of Frege thinking of judgement as (a species of) holding-true.

10 This leaves a nice question of how else to understand their proximity. One possibility is that these points are little more than a list of interesting stuff in a context of Frege’s introducing his reader to the idea of thoughts as imperceptible senses of sentences, things for which the question of truth arises. More likely, I think, Frege is inviting his reader to notice truth-identity in order to forestall an obvious concern with the recognition claim that it generates a regress. If recognizing a property of a thing means at the same time recognizing a thought to be true, then it must mean also recognizing the thought that that thought is true to be true, and so on. But we’ll come to this regress below.

11 See, for example, “The definiendum acquires its sense only from the definiens. This sense is built up out of the senses of the parts of the definiens” (PW, 208). So “if the definiens occurs in a sentence and we replace it by the definiendum, this does not affect the thought at all” (PW, 208).

12 See Dummett, Frege: Philosophy of Language, 443.

13 This is Ricketts’ position. To avoid distraction, I removed the word ‘prior’ when citing his claim that “the regress argument assumes that if truth is characterized as correspondence, then the judgment that p requires the prior judgment that p corresponds to Reality, i.e, that it is true that p” (“Logic and Truth in Frege”, 130).

14 Wolfgang Künne offers an interpretation of Frege’s argument on which it deploys truth-identity as a premise (Conceptions of Truth, 129–33). It is surely better to admit interpretative defeat than to cast Frege’s argument as trivially question-begging.

15 That truth is prior to judgement for Frege is visible, I would suggest, in his repeated stance that the normative laws of judgement are consequent upon the descriptive laws of truth (see e.g. CP, 351). More interestingly, the priority is I think dictated by Frege’s “separation of the act [of judgment and assertion] from its subject matter” (PW, 142), a separation embodied in the use of his assertion sign. Wittgenstein’s Tractarian criticisms of this use (Tractatus Logico-Philosophicus, e.g. §§4.063, 4.064, 4.442) issue from his contrary view that truth is not understood other than as correctness in thinking and saying. For an opposing interpretation of Frege see Ricketts: “Truth is the goal of judging, and judgment is the recognition of truth. We have no grasp on the one apart from a grasp on the other” (“Logic and Truth in Frege”, 130–1).

16 See PW pp. 2 and 128 for talk of truth as a goal.