The epistemology of “On Sense and Reference”

Abstract

This paper sheds light on an epistemological dimension of Frege’s “On Sense and Reference.” Under my suggested reading of it, one of its aims is to suggest a picture about propositional knowledge and its production. According to this picture, judgment, which produces propositional knowledge, is identification of the truth-value True with the reference of a given sentence. The propositional knowledge that p, produced by the judgment that p, consists in the knowledge of the identity between the True and the reference of “p.” Judgment as such is a primitive kind of identification. It produces non-propositional knowledge of the identity of the True to which propositional knowledge is reduced.

1 Toward an epistemological reading of “On Sense and Reference”

Many scholars take “On Sense and Reference” (1892b) to be dedicated to a theory of meaning—or something that can be developed into such a theory.¹ This semantic interpretation is undeniable. The paper presents a conception of meaning that divides it into the level of sense and that of reference and puts forward crucial semantic claims such as the compositionality thesis. But the semantic interpretation is not entirely correct. “On Sense and Reference” is also dedicated to epistemology. By “epistemology,” I do not refer to the puzzle about identity statements, which Frege addresses at the beginning of the paper. “On Sense and Reference” has a larger epistemological project of which the puzzle constitutes a part. In a nutshell, “On Sense and Reference” develops a picture of propositional knowledge and its production. It elucidates the act of judging—which produces propositional knowledge—as that of identifying the truth-value True and propositional knowledge as knowledge of the identity of the True.

We can find a motivation for developing such a new reading in “On Sense and Reference” itself: a good chunk of the paper is dedicated to the relationship among truth-value, judgment, and knowledge, and this relationship seems to embody substantive epistemology. Let me first point out that Frege argues that truth-values, which are the references of sentences, are objects:

Every declarative sentence concerned with the reference of its words is therefore to be regraded as a proper name, and its reference, if it has one, is either the True or the False. (1892b, 63, italics mine).²

Scholars such as Gabriel (1984) maintain that this claim is not to be regarded as a philosophical thesis because Frege writes:

The designation of the truth-values as objects may appear to be an arbitrary fancy or perhaps a mere play upon words from which no profound consequences could be drawn. (1892b, 63–4).

However, Frege’s point is that taking truth-values to be objects is not an arbitrary fancy though it may appear to be so.³ The above statement is followed by his philosophical argument that the True is an object, which we will see later. Also, Frege dedicates the remainder of the paper after the argument to examining the “supposition that the truth-value of a sentence [that is a proper name] is its reference” (1892b, 65).⁴

Frege draws epistemological consequences from his claim that truth-values are sentential references. These consequences concern judgment and propositional knowledge. Frege often elucidates judging as acknowledging the truth of a thought, i.e., the sense of a sentence (Frege, 1892b, 64n; 1893, §5; 1897, 139; 1918a, 329). In “On Sense and Reference,” he provides a different elucidation of judgment in terms of thoughts and truth-values:

But so much should already be clear, that in every judgment, no matter how trivial, the step from the level of thoughts to the level of reference (the objective) has already been taken. (1892b, 63).

Because judging is advancing to truth-values, a judging subject recognizes them.

These two objects [i.e., the True and the False] are recognized, if only implicitly, by everybody who judges something to be true—and so even by a sceptic. (1892b, 63).

Also, Frege elucidates propositional knowledge, which is produced by judgment, in terms of the relationship between a thought and its truth-value.⁵

If now the truth-value of a sentence is its reference, then on the one hand all true sentences have the same reference and so, on the other hand, do all false sentences. From this we see that in the reference of the sentence all that is specific is obliterated. We can never be concerned with the reference of a sentence; but again the mere thought alone yields no knowledge, but only thought together with its reference, i.e., its truth-value. Judgments can be regarded as advances from a thought to a truth-value. (1892b, 66).

Thus, as I have said, a considerable part of “On Sense and Reference” is dedicated to relating truth-value, judgment, and propositional knowledge. All these claims are epistemological claims, which seem to have substantive implications about knowledge and its production.

If the aim of “On Sense and Reference” is just to provide a conception of meaning or address the puzzle about identity statements, all these claims are at most unnecessary side comments. A paper can have dispensable, peripheral, parts. However, it is a natural move to think about the possibility that those claims about truth-value, judgment, and knowledge are central to the project of the paper—to think about how the paper reads if we take them to be the main claims of the paper. This is more so—given that Frege repeats these points at the end of the paper where he recaps its major points.

Let us return to our starting point.

When we found ‘a$=$a’ and ‘a$=$b’ to have different cognitive values, the explanation is that for the purpose of knowledge, the sense of the sentence, viz, the thought expressed by it, is no less relevant than its reference, i.e., its truth-value. (1892b, 78).

This suggests the possibility that those claims about truth-value, judgment, and knowledge rather play an important role in the paper’s project.

My reading of “On Sense and Reference” is based on this motivation. I argue that one of the aims of “On Sense and Reference” is to elucidate the nature of judging and propositional knowledge by appealing to the distinction between sense and reference. What plays a central role in this elucidation is the act of identification, i.e., the act of producing knowledge of identity, which Frege elucidates in terms of sense and reference at the beginning of the paper. Kremer (2010) and Weiner (2020) have developed interpretations of “On Sense and Reference” that take the identity relationship to be the central issue of the paper. They both argue that the paper is an attempt to solve the difficulties with Frege’s early conception of identity in Begriffsschrift (1879). I agree. However, “On Sense and Reference” is not only about identity but also about identification qua epistemic action. As we will see ($\mathrm{\S }2$), Frege understands the act of identifying an object ${\mathrm{N}}_{1}$ with ${\mathrm{N}}_{2}$ as that of deciding that the sense of “${\mathrm{N}}_{1}$” belongs to ${\mathrm{N}}_{2}$ (or that the sense of “${\mathrm{N}}_{2}$” belongs to ${\mathrm{N}}_{1}$). My main argument ($\mathrm{\S }3$) is that a crucial aim of “On Sense and Reference” is to establish that judging that p is identifying the True with the reference of “p” and that the propositional knowledge that p produced by the judgment that p is the knowledge of the identity between the True and the reference of “p.” In this reading, the above passages of “On Sense and Reference” turn out to play a critical role in the paper. Furthermore, this reading eventually leads to a new, arguably Fregean, epistemology ($\mathrm{\S }4$).

2 Knowledge of identity

“On Sense and Reference” starts with the famous puzzle about identity sentences. Assuming that we know that “a” has a reference, we can know that “a = a” is true merely by inspection. It is trivial knowledge. But “a = b” is different. Assuming it to be true, we cannot know that it is true merely by inspection. It is not trivial knowledge at all in many cases, e.g., the knowledge that the Morning Star is the Evening Star. So, “a = a” and “a = b” are different with respect to their cognitive value. Frege explains this difference in cognitive value by appealing to the distinction between sense and reference. If “a = b” is true, then the reference of “a” is surely identical with that of “b.” However, the sense of “a” can still differ from that of “b.” The difference between their senses yields the difference in cognitive value between “a = b” and “a = b”⁶

This orthodox interpretation is on the right lines. But there is more to be said. For one, Frege needs to explain why we cannot know that “a = b” is true merely by inspection. In his letter to Russell, Frege writes:

The words ‘morning star’ and ‘evening star’ designate the same planet, Venus; but to recognize this, a special act of recognition is required; it cannot be simply inferred from the principle of identity. Wherever the coincidence of reference is not self-evident, we have a difference in sense. (Frege, 1980, 152).

If an identity is not self-evident, i.e., requires a special act of recognition for capturing the identity, that is because of a difference in sense. Then, Frege needs to explain why a difference in sense makes special epistemic effort necessary for recognizing an identity.

There is more. Frege writes:

What is intended to be said by $a=b$ seems to be that the signs or names ‘a’ and ‘b’ designate the same thing, so that those signs themselves would be under discussion; a relation between them would be asserted. $\cdots$ But this is arbitrary. Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something. In that case, the sentence a = b would no longer refer to the subject matter $\cdots$; we would express no proper knowledge by its means. (1892b, 56–7).

Frege turns down the suggestion that “a = b” expresses the relation between two signs, because if that is correct, the knowledge that a is identical with b is just the knowledge of an arbitrary stipulation and thus it is not proper knowledge. The arbitrariness issue is supposed to be solved by the sense-reference distinction. Surely, the relationship between a name’s sense and its reference is not arbitrary. However, we need to hear about how the non-arbitrariness of this relationship contributes to establishing that knowledge of identity is proper knowledge.⁷

Though often neglected, Frege does have answers to these questions. First, I explain his answer to the question of why inspection is often insufficient for knowing that a is b. Frege writes:

The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs to; but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge we never attain. (1892b, 57–8).

Say that the sense of “a” is given to us. If the sense of “a”, or simply $\langle$a$\rangle$, alone lets us know whether it belongs to an object o, we should be able to say whether $\langle$a$\rangle$ belongs to $o$ when it is given to us. However, Frege says, we never have the ability to say immediately whether any given sense belongs to it. So, the sense alone does not let us know whether it belongs to o. The sense of a proper name thus does not contain information about whether it belongs to an object. One might think that the sense of a proper name “a” lets us know whether it belongs to the reference of “a”, i.e., whether “a” has a reference. However, that is not the case. Frege writes:

The words ‘the celestial body most distant from the Earth’ have a sense. But it is very doubtful if they also have a reference. $\cdots$ In grasping a sense, one is not certainly assured of a reference. (1892b, 58).

Thus, the sense of a proper name alone does not necessarily let us know if the name has a reference.

Say we grasp $\langle$a$\rangle$ and know that “a” has a reference. Then, there is nothing else we need in order to know that “a$=$a” is true. Inspection is sufficient for realizing that $\langle$a$\rangle$ belongs to the reference of “a.” However, to know that “a$=$ b” is true, we need more. Assuming that we already grasp $\langle$b$\rangle$, we need to know that “b” has a reference, and that $\langle$a$\rangle$ belongs to the reference of “b.” We cannot achieve these tasks merely by inspection in many cases. That is because the sense of a name does not contain the information about whether it belongs to a certain object. So, figuring out whether a sense belongs to an object takes epistemic effort to go beyond the knowledge of the sense in many cases. That is why it takes empirical research to know that the Evening Star is the Morning Star, or a mathematical proof or testimony to know that 2 + 2 is 4.

Explaining why inspection is often insufficient for achieving the knowledge that a is b, Frege seems to be elucidating what it takes to achieve the knowledge that a is b, namely, to identify a with b: we identify a with b by “saying” or deciding that $\langle$a$\rangle$ belongs to b or that $\langle$b$\rangle$ belongs to a. If identifying is deciding that a sense belongs to an object, the arbitrariness issue is indeed solved: knowledge of identity can only be achieved by figuring out the relationship between a name’s sense and an object, and the relationship is not arbitrary at all. Our knowledge of identity is proper knowledge.

For Frege, the act of identifying is deciding that a sense belongs to an object. However, I am not suggesting that “deciding that $\langle$a$\rangle$ belongs to b” is to be understood as a definitive description of identifying a with b. A sense does not “belong to” an object. This is merely a metaphor. All I am trying to say here is that, in his solution to the puzzle about identity statements, Frege suggests an understanding of identifying as relating a sense to an object somehow. What is important is that Frege applies this understanding of identification to judgment. I turn to this point in the next section.

3 Judgment qua identification in “On Sense and Reference”

Frege elucidates judgment in terms of sense and reference:

But so much should already be clear, that in every judgment, no matter how trivial, the step from the level of thoughts to the level of reference (the objective) has already been taken. (1892b, 63).

Judging that p is taking a step from $\langle$p$\rangle$ to a truth-value. As we will see soon, it is taking a step to the True.⁸ What is important is that this metaphorical elucidation clearly points to an act of relating a thought—a sentential sense—to a truth-value—a sentential reference. Given that Frege understands identifying as relating a sense to a reference, this metaphor seems to point to the act of identifying a truth-value with the reference of “p”, or simply $|$p$|$, which we can also describe as deciding that $\langle$p$\rangle$ belongs to a truth-value.

There is further evidence that the metaphorical elucidation “taking a step” points to the act of identification. First, taking a step from the sense of a name to the reference of it is an act we can perform with non-sentential names. Frege writes:

The sentence ‘Odysseus was set ashore at Ithaca while sound asleep’ obviously has a sense. $\cdots$ Whoever does not admit the name ‘Odysseus’ has reference can neither apply nor withhold the predicate. But in that case it would be superfluous to advance to the reference of the name. (1892b, 62, italics mine).

Therefore, we can take a step from the sense of a non-sentential name to the reference of it. Frege makes this point clear, also in “Comments on Sense and Reference”:

[The intensionalist logicians] forget that logic is not concerned with how thoughts, regardless of truth-value, follow from thoughts, that the step from thought to truth-value—more generally, the step from sense to reference—has to be taken. (1892a, 122, italics mine).

In the above passage about “Odysseus,” Frege states that if one does not admit the name has reference, there is no reason to take a step from its sense to its reference. We can say exactly the same thing about (i) acknowledging the existence of the reference of a name “a” and (ii) identifying a with a known object: if we do not acknowledge the existence of the reference of “a”, there is no reason to identify a with a known object. So, taking a step from a name’s sense to its reference is identifying the name’s reference with a known object.

Therefore, the metaphor “taking a step from a thought to its truth-value” seems to put forward the idea that judging is identifying. In fact, Frege does believe that judging that p is identifying the True with $|$p$|$. In “Comments on Sense and Reference”, Frege writes:

$\cdots$[I]f we complete the name of a concept with a proper name, we obtain a sentence whose sense is a thought, and this sentence has a truth-value as its reference. To acknowledge this reference as that of the True (as the True) is to judge that the object which is taken as the argument falls under the concept. (1892a, 119, italics mine).

Frege is talking about sentences like “2 is prime”—those sentences that state that an object falls under a concept. So, he is saying that to judge that 2 is prime is to identify the True with $|$2 is prime$|$. This idea is also found in Frege’s elucidation of asserting, a verbal counterpart of judging. In Begriffsschrift, to put the sign “├” in front of p is to assert that p. Now, Frege writes:

By writing

$$2 + 3 = 5$$

we assert that 2 + 3 equals 5. Thus here we are not just writing down a truth-value, as in

$$2 + 3 = 5$$

but also at the same time saying that it is the True. (1891, 34, italics mine)

In Begriffsschrift, we assert that p by identifying the True with $|$p$|$.⁹ That is how Begriffsschrift “represents a judgment” (Frege, 1893, §5).

We can see a clear connection between “On Sense and Reference” and Frege’s notion of judgment. For him, judging is the “logically primitive activity” (1880, 15), which is “essential” (1980, 79) to logic.¹⁰ Thus, logic under his conception demands the notion of judging to be clarified. Given that Frege takes judging to be identifying, this clarification requires the notion of identification to be clarified. “On Sense and Reference” is dedicated to clarifying the nature of identification. As we have seen, Frege roughly understands identifying as relating a sense to a reference. He is applying this understanding of identification to the act of judgment by way of the metaphor “taking a step from a thought to its truth-value.”

Furthermore, we can understand why Frege needs to argue that the True qua a sentential reference is an object. If Frege takes judgment to be identification of the True, it is critical for him to establish that the True is something that can be identified, namely, that it is an object. It is not a superficial or technical claim but a linchpin for his conception of judgment. That is why Frege defends the claim by the following argument:

One might be tempted to regard the relation of the thought to the True not as that of sense to reference, but rather as that of subject to predicate. One can, indeed, say: ‘The thought, that 5 is a prime number, is true.’ But $\cdots$ nothing more has been said than in the simple sentence ‘5 is a prime number.’ The truth claim arises in each case from the form of the declarative sentence, and when the latter lacks its usual force, e.g., in the mouth of an actor upon the stage, even the sentence ‘The thought that 5 is a prime number is true’ contains only a thought, and indeed the same thought as the simple ‘5 is a prime number.’ It follows that the relationship of the thought to the True may not be compared with that of subject to predicate. (1892b, 64).¹¹

Frege needs to resist the claim that the True is a property of thoughts—which in fact seems to be way more intuitive—because if that is true, his conception of judgment qua identification of the True cannot be sustained. The True ought to be an object.

However, there is more to be told about the relationship between judgment and identification. Elucidating judging as relating a thought to the True, Frege is using the metaphor “taking a step.” Relating a sense to a reference—deciding that a sense belongs to a reference—is a vague notion so that it cannot constitute a definition of identification. To apply this vague notion to judgment, Frege is using such a cryptic metaphor. A due question is why Frege has to use a metaphor in order to apply this notion of relating a sense to a reference, which is already vague, to judgment.

There is a reason why Frege has to use such a metaphor: judging qua identifying should not be making an identity judgment. Say that to identify a with b is always to judge that a is b. To judge that p is to identify the True with $|$p$|$. By our assumption, to judge that p is then to judge that $|$p$|$ is the True. Then, a regress starts: to judge that p is to judge that $||$p$|$ is the True$|$ is the True. This regress will never stop.¹² To avoid this regress, Frege should deny the assumption that to identify a with b is always to judge that a is b. In particular, Frege should say that to identify the True with $|$p$|$ is not to judge that $|$p$|$ is the True. Judgment should be non-judgmental identification.

Keeping this in mind, let us ask in what the act of deciding that a sense belongs to a reference consists. A quick but tempting answer is to say that it is to judge that a sense belongs to a reference. Surely, such a judgment must be possible. However, judging that p, qua deciding that $\langle$p$\rangle$ belongs to the True, should not be judging that $\langle$p$\rangle$ belongs to the True. Otherwise, we will have an infinite regress once again: to judge that p is to judge that $\langle$p$\rangle$ belongs to the True, which is to judge that $\langle \langle$p$\rangle$ belongs to the True$\rangle$ belongs to the True. So, judging must be deciding non-judgmentally that $\langle$p$\rangle$ belongs to the True. However, such a non-judgmental way of relating a sense to a reference is a primitive kind of identification that can only be indicated by a metaphorical elucidation such as “taking a step from a sense to a reference.” So, judgment constituted by this kind of identification is also a primitive notion that can only be elucidated with a metaphor:

Judgments can be regarded as advances from a thought to a truth-value. Naturally this cannot be a definition. Judgment is one of a kind and incomparable. (1892b, 65).

One might object that my interpretation makes judgment reduced to identification, which goes against Frege’s claim that judgment is one of a kind. But it is not my interpretation but Frege himself that makes such a reduction. His Begriffsschrift represents the act of judgment as that of identification of the True; we judge that p by identifying $|$p$|$ with the True in Begriffsschrift. How can he be more explicit about his understanding of judgment as identification? Thus, the given objection must be an objection to Frege himself. Perhaps, “one of a kind” is a very poor choice of word. However, Frege has a reason to make such a comment: it is identification of a unique kind that can only be captured by a metaphor. Judging is a kind of identifying, which is non-judgmentally relating a thought to its truth-value somehow. But that is all he can say about it. Frege believes that judgment qua such identification cannot be fully analyzed.

Judgment produces propositional knowledge. If judging is identifying the True with $|$p$|$, i.e., deciding that $\langle$p$\rangle$ belongs to the True, then we can now explain why Frege elucidates the notion of propositional knowledge in relation to a thought and a truth-value. As we have seen, Frege writes:

[1] If now the truth-value of a sentence is its reference, then on the one hand all true sentences have the same reference and so, on the other hand, do all false sentences. [2] From this we see that in the reference of the sentence all that is specific is obliterated. [3] We can never be concerned with the reference of a sentence; but again the mere thought alone yields no knowledge, but only thought together with its reference, i.e., its truth-value. [4] Judgments can be regarded as advances from a thought to a truth-value. (1892b, 66).

[1] makes it clear that the relationship holding between the True and the reference of a true sentence like “2 + 3 = 5” is the relationship of identity. [2] describes one of the issues that leads to the puzzle about “a$=$a” and “a$=$b”: we cannot find a room for the cognitive value difference between them in the level of reference. The room must be found at the level of sense where only a single aspect of an object is illuminated by an individual sense. The knowledge of the identity between a and b is achieved only when we relate $\langle$a$\rangle$ ($\langle$b$\rangle$) to b (a), i.e., decide that the sense belongs to the object. Frege is applying this point to the True and, say, $|$2 + 3 = 5$|$ in [3]: we need to relate $\langle$2 + 3 = 5$\rangle$ to the True to achieve the knowledge of the identity between the True and $|$2 + 3 = 5$|$. [4] is saying that judgment is the very act that relates the thought to the truth-value True. The connection between propositional knowledge and the sense-reference distinction now seems to be clear. In [3], Frege is arguing that propositional knowledge requires us to be concerned with both a thought and a truth-value. That is because the propositional knowledge that p is the knowledge of the identity between the True and $|$p$|$, and the latter concerns both the level of thought and that of reference. Furthermore, it is because propositional knowledge is knowledge of the identity of the True that judging makes judgers, including sceptics, recognize truth-values.

Thus, if we take “On Sense and Reference” to aim at elucidating the nature of identification and thereby the nature of judgment, we can interpret Frege’s conception of judgment as identification of the True more charitably and make sense of why the paper includes the passages that put forward straightforwardly epistemological points. All these points are compatible with the semantic interpretation of the paper. Frege is arguing that judging is identifying the True through sentences. To make this work, Frege should provide a semantic framework in which all sentences, i.e., the expressions whose senses are potential objects of judgment, turn out to be the names of a truth-value. Thus, he provides such a framework in the paper and examines if that framework can be generalized over different kinds of sentences (1892b, 65). Precisely because Frege has an epistemological aim to establish the point that judgment is identification of the True, he needs to provide such a semantic framework.

The current discussion shows that there is a substantive reason to read “On Sense and Reference” as an epistemological paper, specifically, a paper that elucidates the nature of judging and that of propositional knowledge. The next section rearranges “On Sense and Reference” according to this epistemological reading.

4 The epistemology of “On Sense and Reference”

Frege’s argument that the True is not a property of thoughts explains why he regards judgment as identification of the True. For it is also an argument that truth is not a property. The main premise of the argument is that if “true” refers to a property, $\langle$p$\rangle$ is not identical with $\langle \langle$p$\rangle$ is true$\rangle$. If truth is a property, however, “true” must refer to it. Thus, if $\langle$p$\rangle$ is identical with $\langle \langle$p$\rangle$ is true$\rangle$, truth is not a property. This argument is repeated in “Introduction to Logic” (1906) and “Logic in Mathematics” (1914). In the latter, Frege makes it clear that this argument establishes that truth is not a property:

Showing, as it does, that truth is not a property of sentences or thoughts, as language might lead on to suppose, this consideration confirms that a thought is related to its truth-value as the sense of a sign is to its reference. (1914, 234; italics mine).¹³

Given that judging is acknowledging the truth of a thought for Frege, this means that he cannot take judging to be acknowledging a property of an object. He needs an alternative for understanding judging qua acknowledging the truth of a thought. “On Sense and Reference” is a paper that presents Frege’s alternative conception of judgment as such. This alternative takes truth to be an object, i.e., the truth-value True, and the act of judging that p to be that of identifying the True with $|$p$|$ non-judgmentally. That “On Sense and Reference” aims to provide this alternative is also revealed by the fact that Frege provides an explicit elucidation of judgment as such identification in “Comments on Sense and Reference”—a manuscript clearly written for emphasizing and reinforcing his points in “On Sense and Reference.”¹⁴

If we endorse this interpretation of the aim of “On Sense and Reference”, the paper can be divided into three parts. In the first part, Frege answers why knowledge of identity is proper knowledge that often requires more than inspection. He needs to answer this question, because he should be able to say that the knowledge of the identity between the True and the reference of a sentence is such proper, substantive, knowledge. Frege suggests that to identify a with b is to decide that $\langle$a$\rangle$ ($\langle$b$\rangle$) belongs to b (a)—to relate the former to the latter somehow. We often need more than inspection to have identity knowledge because the sense of a name does not contain information regarding whether it belongs to a certain object. Knowledge of identity is not knowledge of arbitrary stipulations because the relationship between sense and reference is not a matter of stipulation at all.

In the second part, Frege establishes that judging is identifying the True. He first shows that sentences have references and their references are truth-values. Then, as we have seen, he defends the claim that truth-values are objects. At this point, Frege provides his elucidation of judging as taking a step from a thought to its truth-value. To take a step from a thought to its truth-value is to decide that the thought belongs to the True, i.e., to identify the True with the reference of the sentence whose sense is the thought. Frege provides this metaphorical elucidation of judgment in order to emphasize that the kind of identification constitutive of judgment is primitive, i.e., is not reducible to anything including judgment. Lastly, he provides a conception of propositional knowledge that regards it as the knowledge of the identity of the True we achieve by judging.

In the last part, Frege shows that for any sentence “p”, we can say that its reference is a truth-value and thus that to judge that p is always to identify the True with $|$p$|$. To establish this point is important to his project, because his conception of judging is not technical but philosophical. In other words, Frege’s conception of judgment as identification and of propositional knowledge as identity knowledge are his philosophical claims about the nature of judgment and propositional knowledge. So, he ought to examine whether his conception can be generalized over all judgments. As we have seen, Frege comes back to his epistemological points after the examination. If my suggested reading is correct, that is because the whole point of this examination is to support those epistemological points in the end.

Under this epistemological interpretation of “On Sense and Reference”, one of the main theses Frege is defending in it is the following:

(JI) To judge that p is to identify the True with |p| non-judgmentally.¹⁵

Judging that $p$ is deciding that $\langle$p$\rangle$ belongs to the True. But the latter is not judging that the thought belongs to the True. It is a primitive kind of identification that can only be captured by a metaphor such as “taking a step from a thought to its truth-value.” Hence, (JI). The propositional knowledge that p, produced by judging that p, thus consists in the knowledge of the identity between the True and $|$p$|$.

I note three points regarding the epistemology Frege presents in “On Sense and Reference” under this reading. First, the knowledge of the identity between the True and $|$p$|$, produced by judging that p, cannot be the propositional knowledge (p-knowledge) that $|$p$|$ is the True.¹⁶ If the former is the latter, then it follows that we can produce the p-knowledge that p only by producing the p-knowledge that p is the True, which leads to the kind of vicious infinite regress we have repeatedly seen. Thus, the knowledge of the identity between the True and $|$p$|$, produced by judging that p, must be non-p-knowledge. Then, p-knowledge consists in this non-p-knowledge of the identity of the True.

Secondly, the identity judgment that a is b primarily produces the non p-knowledge of the identity between $|$a is b$|$ and the True. Because this non p-knowledge is the p-knowledge of identity that a is b, judging that a is b is identifying a with b. Because judging that a is b is identifying a with b, it is also deciding that $\langle$a$\rangle$ belongs to b. However, this does not mean that we need to decide that $\langle$a$\rangle$ belongs to b in order to judge that a is b. We rather decide that $\langle$a$\rangle$ belongs to b by judging that a is b, i.e., by taking a step from $\langle$a is b$\rangle$ to the True. One question is whether there is an act of deciding that $\langle$a$\rangle$ belongs to b without judging that a is b, namely, an act of identifying a with b non-judgmentally. I believe that Frege has such a non-judgmental identification in mind when he talks about taking a step from the sense of “Odysseus” to the reference of it. But I will leave this issue behind in this paper.

Lastly, we can say that p-knowledge is grounded in our knowledge of the True. Frege writes:

Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge we never attain. (1892b, 57–8).

We have never had the ability to say immediately whether any given thought to belongs to the True. Thus, we do not have comprehensive knowledge of the True. When our knowledge of the True is expanded, we come to have an ability to acquire new p-knowledge, i.e., the knowledge of the identity between the True and the truth-value of thoughts that have not been judged before. In that sense, our p-knowledge is grounded in our knowledge of the True.

Under the suggested epistemological reading of “On Sense and Reference”, Frege provides an entirely new picture of p-knowledge and its production. This picture bases propositional knowledge on the non-propositional knowledge of the identity of the True, which seems to be distinctively objectual knowledge in that it is knowledge about an object that is not reducible to p-knowledge. What he provides is only a picture, not a theory, because he leaves the nature of non-judgmental identification largely underdeveloped. However, it still contains a highly controversial epistemology. It might raise a doubt to describe Frege as such a serious epistemologist. Given that his lifetime project, i.e., the logicist project, concerns the nature of mathematical knowledge, however, it must not be all that surprising that he develops an epistemological picture. He is an epistemologist in the end.

It might be objected that my interpretation of Frege conflicts with his anti-psychologism about logic because if my reading is correct, Frege is highly interested in clarifying the nature of judgment qua mental action.¹⁷ However, as we have seen, Frege is interested in the nature of judging. He clearly refers to the act of judgment by “judgment.” In his letter to Jourdain, Frege writes:

Judging (or recognizing as true) is certainly an inner mental process. (1980, 78).

In a footnote of “Negation” (1918b), he also writes:

We are probably best in accord with ordinary usage if we take a judgment to be an act of judging, as a leap is an act of leaping. $\cdots$ Judging, we may say, is acknowledging the truth of something; what is acknowledged to be true can only be a thought. (1918b, 354n).

Thus, Frege’s initial elucidation of judgment as acknowledgment of the truth of a thought is that of judgment qua mental action. In the same footnote, he even seems to use the point that judgment is mental action in order to point out a problem with Kantian epistemology.

If a judgment is an act, it happens at a certain time and thereafter belongs to the past. With an act there also belongs an agent, and we do not know the act completely if we do not know the agent. In that case, we cannot speak of a synthetic judgment in the usual sense. If we call it a synthetic judgment that through two points only one straight line passes, then we are understanding by ‘judgment’ not an act $\cdots$, but something timelessly true, even if its being true is not acknowledged by any human being. If we call this sort of thing a truth, then it may perhaps be better to say ‘synthetic truth’ instead of ‘synthetic judgment’. If we do nevertheless prefer the expression ‘synthetic judgment’, we must leave out of consideration the sense of the verb ‘to judge’. (1918b, 354n).

The gist is that we cannot take judgments as actions to be synthetic or analytic as Kantian epistemologists do.¹⁸ Frege is emphasizing that a judgment as an act is clearly distinguished from a truth in his logic. Therefore, it is a challenge against Frege himself to reconcile his interest in judgment as action with his anti-psychologism about logic. The issue is already there before my interpretation comes in.

Now, Frege hints at a response to this challenge. Again in his letter to Jourdain, Frege writes:

Judging (or recognizing as true) is certainly an inner mental process; but that something is true is independent of the recognizing subject. If I assert something as true I do not want to talk about myself, about a process in my mind. And in order to understand it one does not need to know who asserted it. (1980, 78–9).

It is completely independent of the recognizing subject that something is true. What we do when we judge or assert is to be committed to something’s being true, not to something’s being recognized as true by us. When we judge that 2 + 2 is equal to 4, we recognize that 2 + 2 is equal to 4, not that we take 2 + 2 to be equal to 4. Thus, judging (asserting) is not thinking (talking) about ourselves. To understand what is judged—that 2 + 2 is equal to 4—we do not need to know the recognizing subject. This explains why Frege has complaints against logical psychologism. To acknowledge something as a logical law under logical psychologism is to acknowledge it as our way of thinking.

The phrase “laws of thought” seduces one to form the opinion that these laws govern thinking in the same way that the laws of nature govern events in the external world. In that case, they can be nothing other than psychological laws; for thinking is a mental process. And if logic had to do with psychological laws, it would be a part of psychology. And thus it is in fact conceived. (1893, xv).

For psychological logicians, logical laws describe our ways of thinking that have a special status. That is what Frege denies. For him, logical laws are first and foremost truths. When we acknowledge something as a logical law, we acknowledge it as a truth—with a special status. What logicians should not forget according to Frege is then that logical laws are judged, i.e., that logicians are committed to their truth, not to their being recognized as true by us. That seems to explain why judgment is essential to logic for Frege.

If that is why Frege takes judgment to be essential to logic, my epistemological reading rather sits well with his anti-psychologism about logic. Frege’s point in “On Sense and Reference” is that judging is advancing to the level of reference—the level he takes to be “objective” (1892b, 64). Specifically, we identify the object of truth—an object in the level of reference and thus completely independent of us—by way of different names of it. When we identify an object, we are not concerned about what the object seems to be to us, but about what the object is. Thus, judgment qua identification is not about ourselves as judgers but about the True. As we have seen, that is why Frege takes judging to be essential to logic.

5 Conclusion

There is clear evidence that Frege in his mature career takes judgment to be identification of the truth-value True. “On Sense and Reference” aims to present and explain his conception of judgment as such identification. In a nutshell, judgment consists in non-judgmental identification of the True, which in turn consists in non-judgmental act of relating a thought to the True. Frege does not fully understand the notion of non-judgmental identification as such. Thus, he elucidates it with a vague metaphor “taking a step from a thought to its truth-value”—leaving the nature of judgment qua such identification largely inexplicable. This interpretation provides an integral understanding of “On Sense and Reference” including the parts that seem unnecessary and peripheral under the semantic reading of the paper. However, it is still entirely compatible with the main idea of the semantic reading that the paper is dedicated to developing a semantic framework. In fact, if my reading is correct, developing such a framework is an indispensable part of his entire project. If the suggested interpretation is correct, “On Sense and Reference” develops an epistemology in which propositional knowledge is reduced to non-propositional identity knowledge that is distinctively objectual knowledge.