1. Sense as Cognitive Value

The account of sense as cognitive value is an interpretation and generalization of the theoretical significance of Frege's puzzle about identity statements. This is well-trodden territory that I will not be pausing to survey. Instead, my aim in this section is to briefly explain the theoretical significance of the puzzle in a relatively novel but intuitive way. I assume basic familiarity with the puzzle. I also assume that Frege's primary focus is thought and only secondarily language.

The theoretical significance of Frege's puzzle is to bring to light the notion of the cognitive value of a concept.Footnote ³ What does that mean?

The cognitive value of a concept is the contribution that grasping or understanding the concept makes to a thinker's epistemic perspective – what she knows. In a helpful but essentially incomplete slogan, if x is a concept of x, then the cognitive value of x is to make possible thinking of x as x. Thinking of x as x is to employ a particular way of thinking of x or to have a particular mode of presentation of x. So, to connect with Frege's specific version of the puzzle, unlike the thought a = a, the thought a = b ‘often contains[s] very valuable extensions of our knowledge’. These thoughts contain concepts with distinct cognitive values that, hence, are distinct concepts. Thinking of a/b as a is distinct from thinking of a/b as b. The cognitive value of these concepts is to provide these different ways of thinking of a/b.

The version of the puzzle Frege works with here focuses on how differences of cognitive value make for ‘valuable extensions of our knowledge’. The difference between concept a and concept b shows how knowing a = b extends knowledge beyond knowing a = a. Call this focus on cases of differences in cognitive value for the individuation of senses the Hesperus/Phosphorus model for individuating senses, or the HP model for short. The account of sense as cognitive value emphasizes in addition the importance of how the sameness of cognitive value can make for the extension of knowledge – what we can call the Hesperus/Hesperus model for individuating senses, or the HH model for short.

The HP model and the HH model are not in competition, but instead describe complementary functions of a principle of individuation for senses: to make for one sense and not two or to make for two senses and not one. The problem, however, is that there is a tendency to apply the HP model to explain why senses are different when what is called for is some explanation for why senses are to be identified. The account of sense as cognitive value corrects this tendency to overextend the application of the HP model for individuating senses and thereby corrects a tendency to error in individuating senses in tricky cases. Why is there such a tendency? The short answer is that the explanation of the general notion of sense has been driven by thinking about singular senses, and in thinking about singular senses, by excessively internalist and individualist intuitions. By thinking about sense in terms of a more general notion of cognitive value that not only uses both the HP model and the HH model, but also interprets them in terms of cognitive value and the extension of knowledge, two deficiencies in thinking about sense are overcome. Let me explain with a first application to Frege's specific version of the puzzle.

Concepts a and b differ in cognitive value. Although this difference grounds one extension of knowledge, it poses an obstacle to another. For example, from the thoughts a is F and b is G one cannot infer the thought Something is both F and G. No such obstacle is present for the inference from the thoughts a is F and a is G to the thought Something is both F and G. What differentiates the two inferences?

The inferences do not differ in the referents of the concepts the thoughts involved contain; these are the same. Nor do the inferences differ in the presence of the different linguistic expressions ‘a’ and ‘b’; the inference is thought-theoretic and involves concepts and thoughts, not linguistic expressions.Footnote ⁴ A hint as to what differentiates the two inferences comes from determining how the obstacle in the first inference is to be overcome. Plainly, what is required is the identity thought a = b. But this cannot be the answer to what differentiates the inferences for it just brings up the question again. What differentiates the first inference from the second and the first supplemented with the identity thought?

We should not be looking for some hidden property that differentiates the inferences; the answer is out in the open. The answer is that in the first inference there is not, but in the second inference and first inference supplemented with the identity premise there is, an understanding-based knowledge of co-reference allowing for the immediate extension of knowledge. Footnote ⁵ This is constitutive of the identity of concept a and concept a and of the distinctness of concept a from concept b. Sameness of concept or sense is constituted by understanding-based knowledge of co-reference that allows for the immediate extension of knowledge, in this case of the immediate extension of knowledge afforded by deductively valid inference from premises. This is

Case 1: The immediate extension of knowledge through discursive justification.

Case 1 is our first example of deploying the HH model and finding an understanding-based knowledge of co-reference making for the possibility of an immediate extension of knowledge. This is a constitutive account of the sameness of sense present in the examples.

Once one sees how the HH model works here, one can begin to recognize it as one example of a more general semantic/epistemic phenomenon. Moreover, one begins to see how the individuation supported by the HH model conflicts with individuations that, almost as a reflex, incorrectly invoke the HP model. The account of sense as cognitive value guides intuitions about individuation by construing senses in their role in contributing to objective knowledge. Here are some briefly articulated and explained examples:Footnote ⁶

Case 2: The immediate extension of knowledge through perceptual demonstrative tracking

In perceptually demonstratively tracking an object, a thinker receives a continuous stream of information that is conceptualized as being abouta single object through time. This allows a thinker to gain knowledge about the object over that period of time without having to establish in addition that the same object is in question over the period of time. Footnote ⁷

Case 3: The immediate extension of knowledge through joint attention

Interlocutors’ demonstrative-involving utterances are mutually understood as being aboutthe object to which they are jointly attending. This allows a thinker to give and acquire knowledge about an object without having to establish in addition that one's interlocutor is talking about the same object.

According to the account of sense as cognitive value, perceptual demonstrative tracking and joint attention involve a sameness of demonstrative concepts or senses across times and spatial viewpoints because of the possibility for the immediate extension of knowledge that the understanding-based knowledge of co-reference that is present in tracking and joint attention affords. Senses are identified and not distinguished in such cases despite the different spatiotemporal perspectives involved in thinking about a tracked object over time and in jointly attending to an object. It might be tempting to think of these different spatiotemporal perspectives as constituting distinct modes of presentation or ways of thinking of the relevant objects. To think this is to apply the HP model. But the account of sense in terms of cognitive value and an application of the HH model shows why and how that temptation should be resisted.Footnote ⁸

Case 4: The immediate extension of knowledge through testimony

Parties to a testimonial exchange mutually understand the testimony as being aboutthe object to which the testifier refers. This allows a thinker to give and acquire knowledge about an object from testimony without having to establish in addition that the object to which the testifier refers is the object of which the recipient comes to think. Footnote ⁹

According to the account of sense as cognitive value, both testifier and recipient express and comprehend the same thoughts in a testimonial exchange. This is so despite wide discrepancies in their individual beliefs about the object in question, in the limiting case discrepancies that make it appropriate to describe the testimonial exchange as one in which the recipient acquires conceptual competence with the relevant concepts. It might be tempting to think of these extreme discrepancies in belief as constituting distinct modes of presentation or ways of thinking of the relevant objects, but the account of sense in terms of cognitive value shows how and why this temptation should be resisted.

What I want to do now is to try to fit the concept of truth into this pattern and apply this account of sense as cognitive value to the concept of truth. Up to this point, the account of sense as cognitive value has helped to correct for excessively internalist or individualist intuitions in individuation. But what is of particular interest in what follows is that fitting the concept of truth into this pattern shows a kind of cognitive value that is not explained as the cognitive value of singular concepts or even of ordinary predicate concepts – of providing a way of thinking about an object or a property. The concept of truth is not explained as a mode of presentation or way of thinking of some thing. To reflectively understand the concept of truth, one needs to ask a more general question about the cognitive value of the concept of truth.

2. The Cognitive Value of the Concept of Truth

I begin with a distinction. There are broadly speaking two kinds of truth attributions to thoughts. First, there are truth attributions that refer to thoughts using that-clauses or ‘the proposition that’ followed by a sentence, for example, ‘that I smell the scent of violets is true’ or ‘the proposition that I smell the scent of violets is true’.Footnote ¹⁰ Second, there are truth attributions that do not refer to a proposition in this highly explicit way, but either demonstrate, name, describe, or generalize over, propositions to which truth is attributed. For example ‘That is true’ (demonstrating some proposition), ‘Axiom 2 is true’, ‘Jane's first premise is true’ and ‘Everything Sangeet says is true’ are all truth attributions of the second sort. Call the first kind of truth attribution explicit, and the second, inexplicit or blind.Footnote ¹¹

Frege famously seemed to have held a redundancy view about explicit truth attributions. He wrote:

Two things are of note about the view Frege expresses here. First, the redundancy of truth described here seems pretty straightforwardly to imply one extreme position on the cognitive value of the concept of truth. Since ‘nothing is added to the thought by my ascribing to it the property of truth’, everything one can think with explicit truth attributions one can already think without them, and this suggests that the concept of truth makes no cognitive difference and hence is without cognitive value. Second, what is redundant here is the contribution of the concept of truth in explicit truth attributions; what Frege says here makes no commitments about the cognitive value of the concept of truth in blind attributions. It is consistent with Frege's position that the concept of truth occurs non-redundantly in blind attributions.Footnote ¹² So, for Frege, although explicit truth attributions are without cognitive value, truth attributions in general need not be.

So Frege need not accept a general redundancy claim. But is Frege right that explicit truth attributions are redundant, that they are without cognitive value? Upon reflection, and with the aid of the account of sense as cognitive value, this can come to look like a rather shocking claim. If explicit truth attributions are of no cognitive value, then nothing epistemic should get lost were we unable to understand explicit truth attributions. But is it really right that nothing epistemic would be lost if we were unable to understand explicit truth attributions?

Blind attributions demonstrate, name, describe or generalize over thoughts, and so are in some generic sense, about thoughts. But explicit attributions too involve reference to thoughts, indeed, a kind of reference that makes explicit attributions especially explicit about the identity of the thought to which truth is attributed. But if the attribution and the thought to which the attribution is made are about different objects – the first about a thought, the second about, say, the scent of violets – how could the truth attribution be cognitively equivalent to the thought to which truth is attributed? They involve ways of thinking about different objects and properties. This is not only implausible, but perhaps even precluded by the Fregean principle that sense determines reference. Does this torpedo Frege's redundancy view?

No. The limited kind of redundancy that Frege espouses can absorb this point. Even if explicit truth attributions make reference to propositions, they still they have an in-built redundancy. Why? The contrast with blind truth attributions is paramount here. Blind truth attributions are of cognitive value because we may know a blind truth attribution, for example, Whatever Sangeet thinks is true, without knowing what Sangeet thinks or even being able to think the thoughts that she thinks. But we cannot think an explicit truth attribution, like that I smell the scent of violets is true, without knowing which thought is true or without being able to think the thought to which truth is attributed. This is because in understanding the truth attribution, one not only thinks of but also with the thought to which truth is attributed. This partially constitutive feature of the explicit way of thinking of thoughts involved in explicit truth attributions elaborates the sense in which this way of thinking of thoughts is especially explicit as to the identity of the thought that it is about.Footnote ¹³

So the limited kind of kind of redundancy that Frege espouses here is consistent with reference to thoughts in a truth attribution. The redundancy is grounded in the identity in explicit truth attributions between the thought to which truth is attributed and a thought that one must think in order to understand the explicit way of thinking the explicit truth attributions uses. The redundancy is based in something that falls short of a sameness of concepts (because the concept of a thought cannot be identical to the thought to which the concept refers) but that nevertheless is a kind of inter-level cognitive sameness in explicit truth attributions – in the way of thinking of a thought that requires thinking with that very thought. This cognitive sameness is really what is behind the charge of redundancy. It is in fact the HP model in action, for the way that the charge of redundancy comes about is by thinking that the explicit truth attribution is an inter-level a = a type case and not an a = b type case. Thinking that I smell the scent of violets is true is just an inter-levelly adjusted way of thinking I smell the scent of violets. The explicit truth attribution is, apart from the difference in level, without cognitive value.

But does this explanation rely on an incorrect application of the HP model? Is this a case for the HP model to explain why explicit truth attributions are like a = a cases and and not a = b cases and hence are not of cognitive value? Or is it really a case for the HH model to explain how an inter-level cognitive sameness is being exploited for cognitive value? Could Frege's redundancy view be based in some such confusion? More constructively, the key question here is: might not the cognitive value of the concept of truth in explicit truth attributions consist precisely in exploiting the understanding-based knowledge of the inter-level cognitive sameness that explicit truth attributions involve? Would something of cognitive value be lost if we could not understand explicit truth attributions in which the concept of truth combines semantically with these explicit ways of thinking of a thought?

The answer is that yes, something of cognitive value would be lost. We would no longer be able to engage in critical reflective thinking. Understanding explicit truth attribution is partially constitutive of critical reflective thinking. The cognitive value of the concept of truth in explicit truth attributions is to semantically combine with such explicit ways of thinking of thoughts to make critical reflective thinking possible. Briefly articulated:

Case 5: The immediate extension of knowledge in critical reflective thinking

Critical reflective thinking is second-order thinking about one's first-order thinking that constituitvely involves conceptualizations of the thoughts involved in first-order thinking by thinking with the very thoughts conceptualized, and measuring these thoughts against the standard of truth. This makes the kind of epistemic advance afforded in critical reflective thinking possible.

Explaining Case 5 in full is beyond the scope of this paper. In the next section I focus on two key issues: first, just what critical reflective thinking is; and second, how critical reflective thinking constitutively involves the understanding of explicit truth attributions.

3. The Cognitive Value of Explicit Truth Attributions in Critical Reflective Thinking

What is critical reflective thinking? Critical reflective thinking is an epistemic resource. It is a resource for improving one's knowledge by attaining clarity on just what thought it is one's evidence supports and how. What makes critical reflective thinking critical is that the evaluation of one's epistemic resources is carried out while making use of the very epistemic resources one is trying to evaluate. This is borne not of epistemic perversity, but of epistemic necessity, because critical reflective thinking evaluates the most basic or central epistemic resources,Footnote ¹⁴ including the most basic or central norms or rules operative in one's thinking. Critical reflective thinking does not take these basic or central norms or rules as given and aim to get thinking into conformity with them. That would be just a matter of taking special care in sticking to the rules. Critical reflective thinking genuinely evaluates basic or central norms and rules.

I think that with even this bare-bones account of critical reflective thinking we can begin to see how critical reflective thinking is such as to constitutively involve the understanding of explicit truth attributions. I explain by explaining, first, why explicit ways of thinking thoughts are constitutively involved, and second, by explaining why the concept of truth is constitutively involved.

To explain why explicit ways of thinking thoughts are constitutively involved in critical reflective thinking, I want to work with a particular example of critical reflective thinking: conceptual analysis. Conceptual analysis is an epistemic resource for establishing and improving the quality of one's knowledge by attaining clarity in one's understanding of the concepts and thoughts with which one thinks. As a method, conceptual analysis makes use of a rational back and forth between intuitions about cases and explicitly formulated analyses of concepts and thoughts. If conceptual analysis is to be an example of critical reflective thinking then two things must be true of it. First, conceptual analysis must be an epistemic resource. And it is.Footnote ¹⁵ Attaining clarity over concepts is an epistemic resource for purposes of critical reflective justification of first-order beliefs. Consider, for example, an analysis of the concept of a priori knowledge that clarifies that the relevant independence from experience in a priori knowledge is independence with respect to justification and not from experience that enables grasp of a thought. Such an analysis can contribute to a critical reflective justification for believing that arithmetic is a priori even if one needs experience to come to grasp arithmetic thoughts.Footnote ¹⁶ Second, it must be the case that in analysis there is an attempt to evaluate one's understanding while making use of the very understanding that one is trying to evaluate. And there is. Conceptual analysis is done from the inside using the very concept in one's intuitions that one is evaluating and for which one is formulating explicit analyses.

So what is the role of explicit truth attributions in conceptual analysis? I break this up into two questions: one about the role of explicit ways of thinking of thoughts, and one about the role of the concept of truth.

What is the role of explicit ways of thinking of thoughts? It is likely clear that the rational back and forth between intuitions about cases and putative analyses in conceptual analysis requires being able to think with the concept being analyzed in one's intuitions and being able to think about the concept in the formulation of analyses. But it is likely not clear that what is required is not just this, but a way of thinking about the concept under analysis that requires an understanding-based knowledge of the cognitive sameness between the concept being thought about and that is under analysis and the concept that is being thought with in one's intuitions about examples. The rational back and forth in conceptual analysis requires this understanding-based knowledge of inter-level cognitive sameness because conceptual analysis does not require that it be in addition established that the concept being thought about in the analysis is one and the same concept as that with which one is thinking in one's intuitions before analyses and intuitive judgments can be brought to rationally bear on each other. Conceptual analysis makes use of a way of thinking about concepts that requires being able at the same time to think with those concepts. But these ways of thinking are explicit ways of thinking of concepts and thoughts. So critical reflective thinking, or at least the kind present in conceptual analysis, constitutively involves explicit ways of thinking about thoughts and concepts.

What is the role of the concept of truth? What does attaining clarity over thoughts have to do with the concept of truth? Achieving clarity is a matter of getting the truth conditions right. Why? The quick answer is that getting the truth conditions right is essential in cases where one's most basic standards are under challenge. Justification in the face of challenges to the most basic standards cannot unproblematically assume the correctness of those standards, and must include some notion of evaluating the most basic standards themselves. But against what are the most basic standards evaluated? The idea is that they are measured against the standard of truth. On this view, the concept of truth is essential to critical reflective thinking because it invokes the standard of standards, and critical reflective thinking needs, because of its critical nature, such a standard.Footnote ¹⁷

More explicitly: Achieving clarity over concepts and thoughts is an epistemic resource, and functions in critical reflective justification of first-order beliefs. To know the conditions under which a thought is not true but instead is F will not interact with knowledge of the obtaining of those conditions to critically reflectively justify believing some thought because it will not critically reflectively justify believing that the thought is true. For example, suppose that we choose F to be the concept of being recommended for belief by our best standards. Then

1. (1) that X is a priori knowledge that p is recommended for belief by our best standards iff X is knowledge that p that is justificationally independent of experience [analysis of a priori knowledge]

together with

1. (2) that X is knowledge that is justificationally independent of experience [assumption]

entail

1. (3) that X is a priori knowledge that p is recommended for belief by our best standards,

and knowledge of this entailment (including its premises) should give critical reflective justification for the belief that X is a priori knowledge that p. But it does not because it does not give justification in the case that our best standards are under challenge, which is exactly the case in which critical reflective justification is required. Contrast the case where F = the concept of truth. Then

1. (1T) that X is a priori knowledge that p is true iff X is knowledge that p that is justificationally independent of experience [analysis of a priori knowledge]

together with

1. (2T) X is knowledge that is justificationally independent of experience [assumption]

entail

1. (3T) that X is a priori knowledge that p is true

and knowledge of this entailment (including its premises) does give critical reflective justification for the belief that X is a priori knowledge that p, even in the case where one's best standards are under challenge.Footnote ¹⁸

To believe with critical reflective justification is to believe on the basis of one's clearest understanding that what one believes, explicitly specified, is true. It is to think with an explicit truth attribution. So I conclude that explicit truth attributions play an essential role in conceptual analysis and critical reflective thinking, and that the cognitive value of the concept of truth is to combine semantically with the explicit ways of thinking of thoughts to make critical reflective thinking possible. This is an account of the cognitive value of the concept of truth that does not think of its cognitive value in terms providing a way of thinking about some thing. Its cognitive value springs from a broader role it plays in knowledge.