Kantian Thoughts. Towards an Alternative to Russellian and Fregean Propositions

Introduction

What are thoughts, or propositions, exactly?^[1] My aim is to develop an answer to this question in relation to the two classical views held in the analytic tradition. These views, which, to this day, constitute the most common on the nature of thoughts, are Russellianism and Fregeanism, while the answer I defend is Kantianism.

In my reconstruction of these views, I consider their founding figures – Moore/Russell, Frege, and Kant – and more recent developments of their views. For my presentation of Kantianism, I use Kant and Analytic Kantianism, broadly construed. From Kant, I focus on the “Analytic of Concepts” in the Critique of Pure Reason, where he provides the essential resources to treat the question of this essay and where his investigation resides on the appropriate level of generality. The introductory sections and Kant’s Metaphysical Deduction, with its tables of logical functions of judgment and categories, supplemented by considerations from the Transcendental Deduction, contain the main components needed to formulate a Kantian view on thoughts.

My essay consists of four sections, where I introduce the question (section 1), present Russellianism and Fregeanism from a developing Kantian perspective (sections 2 and 3), and, finally, present Kantianism more systematically (section 4). I take myself to be reconstructing a progression of views that, although moving backwards in terms of historical origin, moves forward in terms of substantive truth. I move from natural or naïve Russellianism and its difficulties to more sophisticated and promising Fregeanism, which can respond to these difficulties but only at the expense of leaving open serious explanatory gaps of its own. Along the way, I develop Kantianism as incorporating what is promising in Fregeanism while closing the gaps this view left open, and present it more systematically at the end.

1 Asking for the nature of thoughts

My question concerns the nature of thoughts. As is generally true in philosophy, initially, there is some unquestionable phenomenon which is not well enough understood. Take how Stroud describes the origin of philosophical investigations:

There has to be something we think, something we are trying to understand, some puzzling phenomenon or aspect of the world. There must be some “data,” so to speak, to reflect on, or to come to terms with […]. There must be some things we know, or things that are so, or things that we think and cannot deny, that are firmer than anything that philosophical theorizing can undermine.^[2]

What phenomenon leads us to the question about the nature of thoughts? The question arises once we try to gain a philosophical understanding of the phenomenon of our thinking, believing, and speaking the way we do. To reach it, we need to conceive of what it is, exactly, that we think, believe, or say when thinking, believing, or saying something.

We think, believe, or say things^[3] we take to be true or false. We can truly think, believe, or say, e. g., <the Earth orbits the Sun>, or, falsely, <the Sun orbits the Earth>. The thing we think, believe, or say can be identical across these acts: we can think, believe, or say it. Besides believing, we can have other attitudes towards it like entertaining, denying, supposing, etc. If we say it, we can do so through different sentences of the same or different languages, e. g., through ‘the Earth revolves around the Sun’ in English or ‘die Erde dreht sich um die Sonne’ in German. Finally, sentences are true or false if and only if what is said through them is true or false.

Thus:

I want to emphasize two more characteristics of thoughts that will prove important for the dialectic of this essay. The first is closely related to (ii)–(iii) and given, as Sellars puts it, by

the idea that one and the same content can exist in many representings by many minds, which seems to be an implication of the intersubjectivity […] of what we conceptually represent,^[5]

namely,

the fact that different persons, and the same person at different times, can represent the same, even though the representings (as acts) are numerically different.^[6]

Thoughts must not only be able to be the same across different attitudes (ii)^[7] and sentences (iii),^[8] but also across different persons and times. Different persons must be able to think, believe, or say the same things, and to do so at different times. This is implied by the shareability of thoughts. We take ourselves to be able to communicate what we think or believe, mostly through what we say and write – e. g., in science and philosophy –,^[9] and this, in turn, is something we can do only if we can think, believe, or express numerically the same thoughts as others, and can do so at different times. Thus:

What is among the clearest expressions of this can be found in Frege. Take “On Sense and Referent”, where he notes: “[b]y thoughts I do not understand the subjective doing of thinking but its objective content which can be the common property of many”,^[10] distinguishing various acts of thinking from the same thought that can be thought through them. Or: “one will not be able to deny that mankind has a common treasure of thoughts that it transfers from one generation to the next”,^[11] whereby he describes the shareability of thoughts as what implies that they can be the same across persons and times.

Now for the second additional characteristic of thoughts, which is closely related to (i). This essay belongs to the debate about structured propositions,^[12] namely, propositions consisting of various constituents, as the unstructured approach has failed with good reason. A proponent of the view that propositions are functions from possible worlds to truth-values (or, equivalently, sets of possible worlds) individuates, say, necessarily true propositions such that they are true in all possible worlds. In this way, necessarily true propositions are not individuated precisely enough to distinguish what are distinct propositions of this kind – e. g., <2+2=4> and <bodies are bodies> –, yielding the incredible result that all necessarily true propositions are identical. However, we can think, believe, or express all kinds of necessarily true thoughts. In light of this failure, there was a return to structured propositions in Frege and especially Russell,^[13] as their proponents could individuate propositions more precisely exactly by reference to their constituents.

I thus consider propositions as individuated by various constituents forming a true or false unity,^[14] which raises the questions of how to understand the nature of these constituents and their unity within a proposition. Different ways to answer the former question amount to the central difference between Russellianism and Fregeanism, while answering the latter arguably forms the main task for any view on the nature of thoughts. Russell gives a classical formulation of this problem of the unity of the proposition in Principles of Mathematics:

Consider, for example, the proposition “A differs from B”. The constituents of this proposition, if we analyse it, appear to be only A, difference, B. Yet these constituents, thus placed side by side, do not reconstitute the proposition. […] A proposition, in fact, is essentially a unity, and when analysis has destroyed the unity, no enumeration of constituents will restore the proposition.^[15]

It is this essential unity of their constituents that distinguishes thoughts from mere aggregates like lists and – as can be added to Russell’s description – amounts to thoughts’ representing things as being some way, or predicating something of something, so that they are true or false in the first place. E. g., <the Earth orbits the Sun> is distinguished from a list containing <Earth>, <Sun>, and <orbiting> exactly by a unity where, say, <orbiting the Sun> is predicated of <Earth>.^[16] Thus:

Here is how Stroud puts this: “A list or collection of objects is not a thought that something or other is so.”^[17] Both Stroud’s remark and my talk of representation involve a distinction between thinking, believing, or expressing a thought and the way things are. If and only if things are the way they are thought, believed, or said to be, then the thought is true; otherwise, it is false. Thoughts possess objectivity, or objective purport: they are about things and true or false of them depending on how these things, as objects of our thoughts, in fact are.

In the third Critique, Kant connects the shareability (iv) and objectivity (v) of thoughts such that only what is objective can be communicated:

[N]othing can be generally communicated but cognition and representation insofar as it belongs to cognition. Since only insofar is the latter objective and has a common point of reference with which everyone’s power of representation is compelled to agree. […] [C]ognition, as determination of the object with which given representations (in whatever subject it may be) should agree, is the only kind of representation which holds for everyone.^[18]

Thoughts can only be communicated in virtue of their representational relation to objects, as objects of representations are their common points of reference. Cognitive acts, as exercised by persons, are singular and concrete occurrences happening at times. They are token-acts. What is common between token-acts such that what we think, believe, or say can be shared will have something to do with the objects of our acts and our relations to them through these acts.

To play this role as common points of reference and allow communication, these objects must be objective, namely, independent of subjects and acts of cognition.^[19] We think, believe, or say things we take to be true or false independently of us and of our acts of thinking, believing, or saying them. What can be communicated, Kant writes in a letter, is “referred to something that is valid for everyone, which is distinguished from subjects, i. e., to an object.”^[20] In thoughts, or judgments, as Kant mostly calls them, we purport to represent what is so “in the object, i. e., regardless of any difference in the state of the subject”.^[21]

The connection between shareability (iv) and objectivity (v) establishes the proper focus for any view on thoughts, namely, on acts of thinking, believing, and saying as cognitive acts in relation to empirical objects. If thoughts are true or false of objects, the topic is cognition; and if these objects are independent of subjects and acts of cognition they will, typically, be empirical and we know about them through sense perception.

I accordingly focus on thoughts de re, not de dicto or de se; empirical, not mathematical or logical; and simple or non-compound where, typically, properties are predicated of objects. At the same time, I confine myself mainly to metaphysical and semantical issues concerning the representational or referential nature of thoughts.

2 Overcome from a Kantian perspective: Russellianism

In “The Nature of Judgment”, Moore puts his view as follows: “A proposition is composed not of words, nor yet of thoughts [=acts of thinking], but of […] possible objects of thought”, which “may come into relation with a thinker”.^[22] Russell, too, describes what “may occur in any true or false proposition” as “an object of thought”.^[23]

For Moore and Russell, constituents of propositions are objects and properties, i. e., referents of cognitive token-acts relating to objects or properties, say, through predicates.^[24] Russellian propositions are facts constituted of such objects and properties, namely, referents of cognitive token-acts truly or falsely relating to objects and properties, or facts, say, through sentences.

By contrast to a list of constituents A, difference, B, the proposition <A differs from B> is such that, as Russell remarks, “[t]he difference which occurs in the proposition actually relates A and B”,^[25] which makes it nothing other than the fact that, actually, A differs from B.^[26] Thus:

Russellianism: Thoughts are facts. Thoughts consist of objects and properties we can relate to through token-acts of cognition so that thoughts, as constituted of such objects and properties, are facts we can truly or falsely think, believe, or express through token-acts of cognition.

Russellianism can be described as naïve or natural response to the requirements that thoughts can be the same across different attitudes (ii), sentences (iii), persons and times (iv), as implied by the shareability of thoughts.^[27] To have this ability, different persons must be able to think the same things, and to do so at different times.

For Russellianism, the same in all these contexts are objects and properties, or facts, that can be thought, believed, or expressed through cognitive acts. We can think the same thing across different attitudes, sentences, persons, and times because in all these contexts we relate to the same objects and properties, or facts. We can think, believe, or say the same thing: <the Earth orbits the Sun>, by relating to the same objects and properties, or facts: to Earth, Sun, and the relation of orbiting where the Earth orbits the Sun, or, equivalently, to the fact that the Earth orbits the Sun.

Russellianism uses two explanatory levels:

acts;

referents.

Hereby, things are admitted that are part of an ordinary understanding of our thinking, believing, and speaking anyway, namely, cognitive acts as exercised by persons and the objects, properties, or facts, they relate to.

This illustrates truth (arrow=true relation):

Regarding true thoughts, what can be thought, believed, or expressed through cognitive acts are objects and properties, or facts. Such acts are true because the thoughts they relate to are, meaning the objects and properties, or facts, related to actually exist. By collapsing thoughts into facts, Russellianism collapses the truth of thoughts into the existence of facts.^[28] Russellian propositions are about their referents by containing them as constituents.

Russellianism implies that cognitive acts are the acts they are by relating to their referents. Referents individuate acts. To use a distinction given by Sellars, this is a variety of

the idea that intellectual acts differ not in their intrinsic character as acts, but by virtue of being directly related to different relata. Thus the thought [=act of thinking] of X differs from the thought [=act of thinking] of Y not qua act of thought, but qua related to X as opposed to Y.^[29]

The idea is that cognitive acts are individuated extrinsically through their relation to something other and independent. The specific form this takes depends on what are construed as these independent relata. In Russellianism, they consist of objects and properties, or facts. More precisely, individuated are act-types: A cognitive token-act is of a certain type by having certain objects and properties, or facts, for its referents. For instance, a token-act of thinking, believing, or saying <the Earth orbits the Sun> is of that type by relating to Earth, Sun, and the relation of orbiting where the Earth orbits the Sun, or, equivalently, to the fact that the Earth orbits the Sun. Such a token-act of cognition is in turn individuated through, additionally, its exercise, actual or possible, by a person, at a location in space and time, and in contextually relevant relations to objects and properties, or facts.

Prima facie, that what can be thought, believed, or expressed through cognitive acts are objects and properties, or facts, seems appropriate for true thoughts. But already in illustrating falsity, difficulties emerge (arrow=false relation):

Regarding false thoughts, there is nothing thought, believed, or said. If a thought is false, there is no fact thought, believed, or expressed, so that Russellianism forces us, as Russell himself later criticized, “to admit that when we judge falsely there is nothing that we are judging”.^[30] But this view cannot be right even on its own terms, since there would be nothing by which these acts are the acts they are. After all, referents individuate acts. This yields one of two incredible results:

Either there can be no falsity since a thought can only be thought, believed, or expressed if there is the appropriate fact for it. However, we can think, believe, or say false things.

Or, if there can be falsity in some sense after all, there is only one kind of it in that every false thought is just empty. However, again, we can think, believe, or say all kinds of false things. To think, believe, or say <2+2=5> or <bodies are points> are different ways of getting things wrong.

The inability to do justice to the possibility of false thoughts is a fatal flaw of Russellianism as originally conceived. Thoughts cannot be identified with objects and properties, or facts, cognitive acts relate to.

In this respect, a more recent variety of Russellianism developed by (early) Scott Soames, among others, fares better.^[31] It says that propositions are not facts constituted of objects and properties related to in cognition, but rather n-tuples (ordered sequences) of such objects and properties, e. g., <the Earth orbits the Sun> is, say, {Earth, orbiting, Sun}. Regarding both truth and falsity, thoughts are n-tuples of objects and properties thought, believed, or expressed through cognitive acts. They differ in that for a true thought there is, additionally, the fact constituted of the objects and properties, while for a false thought there is no such fact.

This illustrates truth and falsity (line=relation of thinking/believing/expressing thoughts; arrow=true/false relation):

Even if the objects and properties thought, believed, or expressed through cognitive acts do not constitute the appropriate facts, as with false thoughts, there are still the same n-tuples of these objects and properties (if they exist). Cognitive acts are of the type they are and truly or falsely represent the objects and properties they do by relating to such n-tuples, which, in turn, truly or falsely represent these objects and properties on their own.

While this modified Russellianism indeed allows for falsity, the presentation above points to even more fundamental difficulties:

First, formal constructions like n-tuples are not the kind of thing truly or falsely representing objects and properties, or predicating properties of objects. Just like lists, n-tuples typically do not represent anything, or do not predicate anything of anything, so that there is no reason to suppose that those n-tuples that are supposed to be propositions do. As Soames himself recently put it:

The problem is that it is hard to see how any formal structure of […] any […] sort could be that proposition [that A is different from B]. […] [T]here is nothing in any abstract structure we might construct, or explicitly specify, which, by its very nature, indicates that anything is predicated of anything.^[32]

Once this difficulty is recognized, it can be seen to spread to Russellianism as originally conceived: referents of cognition typically do not represent anything either. We can, of course, interpret referents or n-tuples of objects and properties in this way and use them as representations, but then they do not truly or falsely represent on their own, but only through acts of interpretation that will themselves need to be related to propositions that truly or falsely represent, setting off a regress.^[33]

Second, for any proposition there are various candidate n-tuples that could be identified with that proposition – for <the Earth orbits the Sun>, say: {Earth, orbiting, Sun}, {Sun, orbiting, Earth}, {orbiting, Sun, Earth}, etc. – but no principled way of deciding which one it really is.^[34] Consequently, this variety is not even able to individuate true propositions, whereas Russellianism as originally conceived does this straightforwardly by reference to the objects and properties, or facts, they are identified with.

Moreover, and generally, Russellianism in either variety cannot appropriately describe acts which cannot sufficiently be characterized by reference to objects and properties, or n-tuples thereof, thought, believed, or expressed through such acts. Besides acts of thinking, believing, or expressing false thoughts this holds for

1. act-types without referents like uses of empty names (‘Odysseus’);

2. distinct act-types sharing the same referent like uses of co-referential names (‘Morning Star’/’Evening Star’).

In Russellianism, neither can be properly individuated. Thus, assuming propositions are constituted of objects and properties, or n-tuples thereof,

1. for a proposition like <Odysseus returns> there simply is no proposition if there is no referent (Odysseus);

2. for pairs of propositions like <the Morning Star is the Evening Star> and <the Morning Star is the Morning Star> these are the same proposition if the referent is the same (Venus).

However, we do think, believe, or say something if we think, believe, or say <Odysseus returns>, as we do think, believe, or say different things if we truly think, believe, or say, informatively, <the Morning Star is the Evening Star> (a=b) rather than, trivially, <the Morning Star is the Morning Star> (a=a).

The difficulties for Russellianism are due to admitting only two explanatory levels, namely, acts and referents. This compels a transition to Kantianism and Fregeanism, which, by adding a level of contents, can do justice to the acts Russellianism is unable to capture. What we think, believe, or express on these views in false, empty, and co-referential thoughts are representational contents. In closing this section, I begin to sketch how Kant’s notion of content can be understood as responding to the possibility of falsity, while, in the next, I introduce Frege’s view as responding to the possibility of co-referential thoughts. Then I relate it to Kantianism.

By contrast to Russellianism as originally conceived, take how Kant describes false judgments: “a cognition is false if it does not agree with the object it is referred to, although it does contain something [=its content] that could well hold of other objects.”^[35] If truth consists in “the agreement of the cognition with its object”,^[36] what makes a judgment false is that it does not so agree with its object. But even if its object cannot individuate the cognition as Russellianism requires, there is still something about it that makes it the cognition it is – it could be true of other objects, after all –, namely, its content. Kant’s description of falsity reveals a third explanatory level and provides good reason to introduce it.

Accordingly, introducing the “Analytic of Concepts” Kant distinguishes from act and object, additionally, the representational content of the act characterized as its representational relation to the object:

1. content of cognition, i. e., […] its relation to the object;^[37]

2. content of cognition (relation to its object);^[38]

3. [cognition’s] content […], i. e., […] relation to some object […].^[39]

Once such a distinction between act, object, and content is recognized,^[40] the possibility of falsity falls into place. If an act’s content is construed as independent of the represented object’s existence and it being the way it is represented to be, an act can, in virtue of its content, represent an object even when there is no such thing.

3 Advanced from a Kantian perspective: Fregeanism

In a letter to Frege, Russell writes:

[I]n the proposition ‘Mont Blanc is more than 4,000 meters high’ […] we assert the object of the thought, and this is […] a certain complex […] in which Mont Blanc itself is a component part.^[41]

With this statement of Russellianism, Russell replies to a letter where Frege had elaborated:

[…] Mont Blanc […] is not itself a constituent of the thought that Mont Blanc is more than 4,000 metres high. […] The sense of the word ‘moon’ is a constituent of the thought that the moon is smaller than the earth. The moon itself (i. e., the referent of the word ‘moon’) is not part of the sense of the word ‘moon’ […].^[42]

For Frege, constituents of propositions are senses of cognitive token-acts representing objects or properties, say, through predicates.^[43] Fregean propositions are senses constituted of such senses representing objects and properties, namely, senses of cognitive token-acts truly or falsely representing objects and properties, or facts, say, through sentences.^[44]

In “On Sense and Referent”, Frege distinguishes from the referent of a sign and the sign itself, considered as possessing a certain (perceptual) “shape”,^[45] the sense of a sign, considered “as a sign”,^[46] i. e., in the “way in which it signifies something”.^[47] Fregean senses are ways of representing referents through cognitive acts, or their representational contents. One can

think of there being connected with a sign (name, combination of words, written mark), besides that which is signified, […] the referent [Bedeutung] of the sign, also […] the sense of the sign, wherein the mode of presentation [Art des Gegebenseins] is contained.^[48]

Senses are perspectival in that they contain a specific way in which the referent is represented by and presented to the thinker. They are abstract in that they can be the same across persons and times (iv). By being independent of token-acts through which they are thought, believed, or expressed, and of minds generally,^[49] senses are shareable among thinkers.^[50] Finally, they are independent of the existence of objects and properties that can be represented, so that, by contrast to Russellianism, cognitive acts can have contents even without referents.^[51] Thus:

Fregeanism: Thoughts are contents. Thoughts consist of abstract contents (singular or general) by means of which we can represent objects or properties through token-acts of cognition so that thoughts, as constituted of such contents, are abstract (propositional) contents by means of which we can truly or falsely think, believe, or express objects and properties, or facts, through token-acts of cognition.

Fregeanism can be motivated in response to difficulties of Russellianism. As Stephen Schiffer puts it:

Think of the Fregean as a theorist who began as a Russellian, encountered problems with her position, and then developed Fregeanism as the antidote to those problems.^[52]

This, in fact, happened to Frege. He says himself that once he had held identity to be “a relation between names or signs for objects”.^[53] Frege had tried to capture this difference by taking the informative claim ‘a=b’ to be about the signs ‘a’ and ‘b’ and as saying that they are different signs for the same object. But then he notices: this relation of identity “would hold between the names or signs only insofar as they named or signified something”, where this “connection of each of the two signs with the same signified object” is “arbitrary”^[54] and can express no cognition of the object. If sign-types are individuated through their referents, as in Russellianism, there can be no difference between informatively and trivially true claims of identity. Thus, if one sign for an object differs from another for that same object only through its (perceptual) “shape”^[55] – ‘a’/’b’ – and not “as a sign”^[56], i. e., in the “way in which it signifies something”,^[57] the difference between such identity claims is lost. But if one introduces, besides the referent and the sign itself, the sense of the sign, this difference can be captured as follows: while ‘a’ and ‘b’ in an expression of the thought <a=b> relate to the same referent, they do so in different ways. Consequently, informatively true thoughts of the form a=b can be seen to differ from thoughts of the form a=a and considered cognitions of their objects.

Frege’s notion of sense as the way in which signs signify their referents forms a counterpart to Kant’s notion of content in terms of the representational relation cognitive acts have to their objects.^[58]

Both Kantianism and Fregeanism can respond to the requirements that thoughts can be the same across different attitudes (ii), sentences (iii), persons and times (iv), as implied by the shareability of thoughts.^[59] To have this ability, different persons must be able to think the same things, and to do so at different times.

For Kantianism and Fregeanism, the same in all these contexts are contents that can be thought, believed, or expressed. We can think the same thing across different attitudes, sentences, persons, and times because in all these contexts we relate to the same representational content. We can think, believe, or say the same thing: <the Earth orbits the Sun>, by relating to the same content: <the Earth orbits the Sun>.^[60] Correspondingly, representational contents are what is thought, believed, or expressed in false thoughts like <the Sun orbits the Earth>, in empty thoughts like <Odysseus returns>, and in co-referential thoughts like <the Morning Star is the Evening Star>. Introducing contents, if convincing, straightforwardly solves the difficulties confronting Russellianism.

This is essentially due to using three explanatory levels:

acts;

referents;

contents.

Alongside things that are admitted as part of an ordinary understanding of our thinking, believing, and speaking anyway, namely, cognitive acts as exercised by persons and the objects and properties, or facts, they relate to, additionally, Fregean senses or Kantian contents are introduced for explanatory reasons. How these representational contents are introduced and how well they can be explained amounts to the main differences between Kantianism and Fregeanism. I begin with Fregeanism.

This illustrates truth and falsity (line=relation of thinking/believing/expressing thoughts; arrow=true/false relation):^[61]

Regarding true and false thoughts, what can be thought, believed, or expressed through cognitive acts are representational contents. Such acts are true or false because the thoughts they relate to are, meaning they relate to true or false representational contents.

Fregeanism implies that cognitive acts are the acts they are by relating to their contents. Contents individuate acts. To again use the distinction given by Sellars: Cognitive acts are individuated extrinsically through their relation to something other and independent. The specific form this takes depends on what are construed as these independent relata. In Fregeanism, they consist of contents. More precisely, individuated are act-types: A cognitive token-act is of a certain type by having a certain content.^[62] For instance, a token-act of thinking, believing, or saying <the Earth orbits the Sun> is of that type by relating to the content <the Earth orbits the Sun>. Here, too, such a token-act of cognition is individuated through, additionally, its exercise, actual or possible, by a person, at a location in space and time, and in contextually relevant relations to objects and properties, or facts.

Fregeanism has an enormous explanatory advantage over Russellianism: it can distinguish acts which cannot sufficiently be characterized by reference to objects and properties, or n-tuples thereof, thought, believed, or expressed through acts of thinking, believing, or expressing, say, false, empty, or co-referential thoughts. But this advance depends on introducing independent representational contents for explanatory reasons, the explanation of which in turn proves difficult. I am specifically thinking of three explanatory gaps:

1. Existence. Supposedly, Fregean thoughts are independent of cognitive acts exercised by persons and of objects and properties, or facts, in space and time. But how do independent abstract contents exist and how do they relate to acts of persons and objects and properties, or facts, in space and time?

2. Access. Supposedly, we think Fregean thoughts, relate to them through propositional attitudes, and express them through sentences, which acts in turn truly or falsely represent objects and properties, or facts. But how do persons have access to independent abstract contents so that they can think, believe, or express them?

3. Representation. Supposedly, Fregean thoughts truly or falsely represent objects and properties, or facts, and by thinking, believing, or expressing such thoughts, cognitive acts in turn truly or falsely represent these objects and properties, or facts. But how do independent abstract contents truly or falsely represent objects and properties, or facts?^[63]

A crucial task in elaborating a convincing view on thoughts consists in retaining the explanatory advance over Russellianism that was gained in Fregeanism by introducing contents, while at the same time providing explanatory resources to close the gaps that come with admitting Fregean thoughts.

A first step in this direction is to identify the source of these difficulties for Fregeanism. I suggest that it consists in supposing that thoughts are mind-independent, and, using Sellars’ distinction, that cognitive acts are individuated through contents extrinsic to them rather than through intrinsic features. It only proves difficult to understand how contents can exist (a), how persons can access them (b), and how they can truly or falsely represent objects and properties, or facts (c), if they are supposed to be independent of and extrinsic to minded subjects and their cognitive acts. To say it with Burge: “The problem lies […] in the postulated independence of sense, or representational thought content, from thinkers.”^[64]

Above, gap (c) was already shown to apply to Russellianism. These difficulties for Fregeanism and Russellianism have the same source. Granted a need to explain propositions’ truly or falsely representing objects and properties, or facts – instead of treating it as a primitive –,^[65] supposing that thoughts and their constituents are mind-independent dooms both Russellianism and Fregeanism.^[66] Neither the mind-independent objects and properties constituting Russellian propositions nor the mind-independent contents constituting Fregean thoughts are the kind of thing that could possess the required unity and truly or falsely represent objects and properties, or facts:

First, distinguishing between kinds of constituents as attempted by Frege and Russell, implying that one of them is responsible for this unity – the assertive role of predicates in Russell^[67] or their unsaturated sense in Frege^[68] –, merely shifts the issue to how this constituent can accomplish a true or false unity among constituents. How the unity of thoughts is different from lists of exactly the same constituents cannot be sufficiently explained by simply attributing a predicative nature to one of them and a uniting power to this nature.

Second, and more fundamentally, Russell’s and Frege’s attempted explanations must remain mysterious supposing the mind-independence of thoughts. Both try to understand the unity of thoughts independently of cognitive acts as exercisable by persons, mainly to secure their shareability (iv) and objectivity (v). But if anything, only exercises of abilities by persons are suited to explain representational features like truth and falsity, whatever possesses them.^[69] After all, we are trying to understand the successful or failed representation by minded subjects. Being instances of such representation,^[70] truth and falsity must explanatorily be referred to cognitive abilities and acts of persons. As Russell himself later put it: “there could be no falsehood if there were no minds to make mistakes”^[71]; and, generally: “there can be no truth or falsehood if there are no minds to judge”.^[72]

I suggest that key to retaining the explanatory advance from Russellianism to Fregeanism is a reversal in order of explanation where cognitive acts’ truly or falsely representing objects and properties, or facts, is no longer explained by reference to mind-independent propositions, but, conversely, thoughts’ truly or falsely representing objects and properties, or facts, is explained by reference to intrinsic features of cognitive acts. Thereby, thoughts are construed as mind-dependent cognitive act-types, depending on possible token-acts of cognition, which promises to render intelligible not only their representation of objects and properties, or facts, but also their existence and our access to them. Thusly individuating cognitive acts intrinsically requires giving an analysis of them as representing objects and properties, or facts.

The two explanatory orders can be presented as follows (arrow=direction of explanation):

Although such a reversal in order of explanation has recently been suggested anew,^[73] and Soames, among others, has suggested identifying propositions with cognitive act-types,^[74] it yields a traditional view. Its most prominent and elaborated form can be found in Kant.

4 Kantianism: Thoughts as act-types of judgment in relation to sensible intuition

For Kant, “[t]hought [Denken] is cognition through concepts”,^[75] where concepts are referred to objects through judgments. In the “Analytic of Concepts”, he analyzes our capacity for thought by investigating what representational abilities and acts are required to realize this purpose of the understanding.^[76] Judgments are “functions of unity among our representations”,^[77] i. e., cognitive acts of combining representations that thereby constitute a true or false unity.^[78] They are exercises of cognitive abilities shared by persons (iv), and, unlike lists or complex concepts,^[79] form an objective unity of representations truly or falsely representing objects and properties, or facts, independent of subjects and acts of cognition (v).^[80]

A judgment’s unity can be constituted in various ways, depending on what representations, particularly what concepts, are combined in what way. Different token-judgments can combine the same representations in the same way, instantiating a common act-type of judgment. E. g., different token-acts of thinking, believing, or saying <bodies are divisible> can combine the same concepts (<body>, <divisibility>) in the same way (predicating <divisibility> of <body>), making them different token-acts of the same act-type of judgment.

For Kant, constituents of propositions are cognitive act-types of representing objects or properties in judgment, say, through predicates. Kantian propositions are act-types of judgment constituted of such act-types of representing objects or properties, namely, cognitive act-types truly or falsely representing objects and properties, or facts, say, through sentences.

Thus:

Kantianism: Thoughts are acts. Thoughts consist of cognitive act-types (singular or general) through which we can represent objects or properties by exercising token-acts in judgments so that thoughts, as constituted of such act-types, are cognitive (propositional) act-types of judgment through which we can truly or falsely think, believe, or express objects and properties, or facts, by exercising token-acts of judgment.

Regarding true and false thoughts, what can be thought, believed, or expressed through cognitive token-acts are act-types of judgment. Such act-types are true or false because their tokens are. Thus, same as in Fregeanism, what can be thought, believed, or expressed through cognitive acts are representational contents. But unlike in Fregeanism, act-types individuate contents, not vice versa. No relation to an independent content individuates an act. Rather, being an act with certain features and thus of a certain type makes it an act possessing a certain content that represents certain objects and properties, or facts.

Kantianism implies that cognitive acts are the acts they are by possessing intrinsic features. Features individuate acts. To again use the distinction given by Sellars: Cognitive acts are individuated intrinsically through their own features (and not, as in Russellianism and Fregeanism, extrinsically through their relation to something other and independent). The specific form this takes depends on what are construed as these features. In Kantianism, they consist of shareable cognitive abilities exercised in token-acts. More precisely, individuated are act-types: A cognitive token-act is of a certain type by consisting in the exercise of certain general (shareable, repeatedly exercisable) cognitive abilities.^[81] E. g., a token-act of thinking, believing, or saying <bodies are divisible> is of that type by exercising the abilities to represent bodies as divisible, namely, using the concepts <body>, <divisibility>, and predicating <divisibility> of <body>. Here, too, such a token-act of cognition is individuated through, additionally, its exercise, actual or possible, by a person, at a location in space and time, and in contextually relevant relations to objects and properties, or facts.

This illustrates truth and falsity (line=type-token relation; arrow=true/false relation):

By contrast to Fregean senses, Kantian contents are conceived in terms of representational features of cognitive token-acts through which they truly or falsely represent objects and properties, or facts. No mind-independent contents are introduced for explanatory reasons. Rather, representational features these token-acts themselves share, making them acts of a type, are analyzed.

This allows, in principle, to close the gaps of Fregeanism by transitioning from token-acts to their types:^[82]

1. Existence. There are act-types of judgment in virtue of there being actual or possible token-acts of judgment possessing shareable features. Act-types exist if actual or possible token-acts of these types exist. If there is a token-act of thinking, believing, or saying <bodies are divisible>, then there is the corresponding act-type representing bodies as divisible.

2. Access. We think, believe, or express act-types of judgment by exercising token-acts of judgment possessing shareable features. We have access to act-types by being able to exercise token-acts of these types. If we are able to exercise token-acts of thinking, believing, or saying <bodies are divisible>, then we have access to the corresponding act-type representing bodies as divisible.

3. Representation. Act-types of judgment truly or falsely represent objects and properties, or facts, in virtue of their token-acts doing so. Act-types possess representational features in virtue of token-acts of these types possessing them. If token-acts of thinking, believing, or saying truly represent bodies as divisible, then the corresponding act-type truly represents bodies as divisible.

But clearly, considering (c) reveals that there is still a gap left open. Namely, the crucial question for Kantianism becomes this:

How exactly do token-acts of judgment (thinking, believing, or saying) truly or falsely represent objects and properties, or facts?

In Soames, there is no answer to this question. Instead, he treats the notion of predication as a primitive, even though, supposedly, it single-handedly explains representation.^[83] But to assume cognitive token-acts to be representations such that they can transfer their representational features to types is almost as unsatisfying as to assume abstract contents to be representations such that they can transfer their representational features to cognitive acts,^[84] as done in Fregeanism and justly criticized by Soames.^[85] Even if Soames adequately locates representation in acts of mind, it continues to lack explanation. Representation, again, is treated as a primitive, inherent feature, even though, this time, of cognitive acts.

By contrast, Kant actually analyzes cognitive abilities and acts into their fundamental aspects, which, moreover, being construed as abilities and acts of combination, seem suited particularly well to explain the unity of thoughts. Unlike in Russellianism and Fregeanism, the unity of Kantian thoughts appears to be explainable, at least in principle, by being tied to cognitive acts that Kant, unlike Soames, gives a proper analysis of. I now turn to this analysis.

Referring concepts to objects that are independent of us and of our cognitive acts ultimately requires sense perceptions of objects, or empirical sensible intuitions, as Kant calls them.^[86] In judgments, we essentially refer concepts to objects of intuitions. This involves the elementary capacities to use concepts and to have perceptions. A cognition through concepts requires,

first, fundamental abilities and acts of judgment, presented in the table of logical functions;^[87]

second, fundamental abilities and acts of a synthesis of intuition, presented in the table of categories.^[88]

Now, what acts need to be exercised in token-judgments in order to refer concepts to objects?^[89] In a key passage from the Metaphysical Deduction Kant argues the following:

The understanding can make no other use of these concepts than to judge through them. Since no representation but intuition refers to the object immediately, a concept is never immediately referred to an object, but always to some other representation of it (be it intuition or itself already a concept). Judgment therefore is the mediate representation of an object, i. e., the representation of a representation of it [the object].^[90]

Due to their generality, concepts can apply to various objects, and their reference is always mediate. Concepts are general in that they stand for kinds or properties of objects.^[91] They always refer to objects mediated by the representation of a kind or property. Because they are in need of mediation by other representations, concepts are essentially predicates: “predicates of possible judgments”.^[92] As cognitions through concepts, judgments require, first, a mediated representation of the object: a predicate-concept.

For this, another representation specifying or individuating the reference of the predicate is needed: a representation the concept is predicated of. Thus, judgments require, second, a mediating representation of the object: a subject-representation.

These two roles demand a third in any judgment true or false of objects and properties, or facts: an act of combination. Otherwise, predicate-concept and subject-representation merely relate to each other like the component concepts of a complex concept, or the entries in a list, and do not form a unity where concepts are truly or falsely referred to objects and properties, or facts. Thus, judgments require, third, a mediation, in its simplest form of the predicate-concept by the subject-representation in predication, or, generally, through combination.

If the mediating subject-representation is itself another concept, then it only specifies that reference, and its own will require mediation in turn. As a concept, it can, again, only refer to objects mediated by the representation of a kind or property. Purely conceptual representation leads into an infinite regress of mediated reference. The only way to stop it is to eventually refer concepts to representations immediately (say, demonstratively) referring to and individuating objects.^[93] The only such representations, for Kant, are sensible intuitions as had by persons in space and time.^[94] Thus, judgments require, fourth, some reference to an immediate representation of the object, i. e., to (at least possible) sensible intuitions as their ultimate subject-representations.^[95]

This hints at how, ultimately, judgments have to refer to individual objects to even be cognitive token-acts that are true or false of objects. Eventually, individual subjects need to truly or falsely refer token-acts of judgment to some individual object(s) of perception, where both the cognizing subjects and their object(s) are to be located in space and time.

Kant thus analyzes a cognition through concepts in terms of fundamental act-types we need to exercise in any token-judgment. Above four features are individually necessary and jointly sufficient for referring concepts to objects (read from bottom left to bottom right):

E.g., the thought=act-type of judgment and any token-act of thinking, believing, or saying <bodies are divisible> truly represents bodies as divisible by involving predicate-concept <divisibility>, subject-representation <body>, by predicating <divisibility> of <body>, and by referring these concepts, ultimately, to possible intuitions of bodies.

Correspondingly, above four features of judgment form the headings of the table of logical functions of judgment:^[96]

To elaborate:

1. The quantity of judgment consists in quantifying a subject-representation through a predicate-concept where the predicate-concept represents objects referred to through the subject-representation as of the same kind or as sharing some property. The elementary variants – quantifying in a universal, particular, or singular way – are expressible as ‘All S are P’, ‘Some S are P’, and ‘One/This S is P’.

2. The quality of judgment consists in specifying a predicate-concept through a subject-representation where the subject-representation represents specific kinds or properties of objects. The elementary variants – specifying in a positive, negative, or infinite way – are expressible as ‘S is P’, ‘S is not P’, and ‘S is non-P’.

3. The relation of judgment consists in combining the representations in the judgment so that they form a unity truly or falsely representing objects and properties, or facts, through concepts. The elementary variants – predication, combination of two or several predications – are expressible as ‘S is P’, ‘If S is P then T is Q’, and ‘Either S is P or S is Q…’.

4. The modality of judgment expresses the relation of judgment to object, ultimately depending on sensible intuitions as ultimate subject-representations of judgment, giving it modal status. The elementary variants – the possibility (in conceptual thought), actuality (in sensible intuition), or necessity of a judgment’s truth – are expressible as ‘S is possibly P’, ‘S is actually P’, and ‘S is necessarily P’.

Since mediate reference of concepts to objects requires sensible intuitions, Kant also needs to explain how they in turn represent individual objects and their qualitative and formal properties. According to Kant, an act of synthesis brings about the “unity of intuition through which an object is given”,^[97] namely, “that unity […] which must be encountered in a manifold of cognition insofar as it stands in relation to an object.”^[98]

Kant’s elaboration of synthesis takes, again, the shape of an enumeration of (mostly sub-personal, sub-conscious) representational abilities and acts individually necessary and jointly sufficient for constituting this unity of intuition. The fundamental act-types of synthesis are apprehension, reproduction, and recognition.^[99] The token-acts of these act-types combine a manifold of sense-impressions given in receptivity.^[100] Representing objects in sensible intuition requires

1. apprehending a manifold of sense-impressions “as such”^[101] by “running through the manifold and then taking it together”,^[102] i. e., to apprehend it as the representation of a manifold of sensible qualities, thereby representing the perceivable qualitative properties of an object of sensible intuition, e. g., the color, weight, etc. of a body;

2. reproducing the homogeneous (spatial or temporal) parts of an intuition, i. e., “to grasp one of these representations [of parts] after the other”,^[103] and “reproduce them while going on to the following”^[104] so that “a whole representation”^[105] originates, thereby representing the formally homogeneous whole of an object of sensible intuition, e. g., the extension and shape of a body;

3. recognizing the unity of above acts of apprehension and reproduction as partial acts of the same act of synthesis, i. e., to have “consciousness of that unity of synthesis”^[106] and thus recognize “that what we think is the very same […] in the series of representations”,^[107] thereby representing the unity of objects and properties as they are represented through these acts, say, the unity of a substance and its properties, e. g., the unity of a body and its qualitative and formal properties;

4. relating to the object on the basis of a manifold of sense-impressions, i. e., presentations of simple sensible qualities such as color, weight, etc. produced by objects of sensibility^[108] given in receptivity as the passive ability to receive sense-impressions within certain forms^[109] (space and time), due to which sensible “intuition contains manifoldness [of sense-impressions]”.^[110]

The synthesis of intuition is the foundation for Kant’s account of the categories: concepts of objects in general representing the most general characteristics of objects of intuition.^[111] They are “concepts of synthesis”^[112] in that they are formed regarding above act-types of synthesis, which determine their contents. The contents of the categories derive from fundamental acts of synthesis.^[113] Correspondingly, above four features of synthesis form the headings of the table of categories:^[114]

To elaborate:

1. The categories of quantity – <unity>, <plurality>, and <totality> –, concerning “objects of intuition”,^[115] originally consist in reproducing a homogeneous (spatial or temporal) part of an intuition, a plurality, or a totality of such parts, representing homogeneous parts or wholes of objects of intuition.

2. The categories of quality – <reality>, <negation>, and <limitation> –, also concerning “objects of intuition”,^[116] originally consist in apprehending the form of intuition (space or time) as filled by sense-impressions, empty, or partly filled, representing the reality or lack of reality of perceivable properties of objects of intuition.

3. The categories of relation – <substance-accident>, <cause-effect>, and <community> –, concerning “the existence of these objects [of intuition] […] in relation to one another”,^[117] originally consist in recognizing the unity of acts of synthesizing one, two, or several intuitions, representing the objective unity of one, two, or several objects of intuition and their properties.

4. The categories of modality – <possibility>, <actuality>, and <necessity> –, concerning “the existence of these objects [of intuition] […] in relation […] to the understanding”,^[118] express the relation of synthesis to object: the conformity of the object with the synthetic (categorial) and sensible (spatial and temporal) form of cognition, its connection also to the matter of cognition (sense-impressions), or its necessity.

With logical functions of judgment, acts of synthesis, and categories at my disposal, I can finally sketch Kant’s considered view on the unity of thoughts. Judgments not only depend on the possibility of sensible intuitions for their reference of concepts to objects. Furthermore, the unity of judgment needs to conform to the unity of intuition: the combination of representations in a judgment by which it is true or false of objects and properties, or facts, has to conform to the combination of sense-impressions and homogeneous parts in an intuition by which it represents an object with its qualitative and formal features. The representations in a judgment

belong to one another in virtue of the necessary unity of apperception in the synthesis of intuitions, i. e., according to principles of the objective determination of all representations insofar as cognition can come from it […].^[119]

These principles of unity in intuition that representations in judgment must conform to are the fundamental acts of synthesis, i. e., the original contents of the categories. Only intuitions relate to something distinct from us and from our cognitive acts since only they incorporate sense-impressions as what is given independently of thought. By constituting unity of intuition, the acts of synthesis originally constitute our representational relation to objects as distinct from ourselves and from our cognitive acts. Thus, if judgments are to refer concepts to objects, their unity must partake in the unity of intuition. Judgments only truly or falsely represent objects and properties, or facts, if their unity conforms to the synthetic unity of intuition. The unity of perception ultimately explains any possible representational relation to objects whatsoever.

The categories are “concepts of an object in general by which its intuition is regarded as determined in regard to one of the logical functions for judgments”.^[120] In virtue of being synthesized by acts of synthesis, sensible intuitions contain the original contents of the categories. By reflecting on these acts, we form the categories as general concepts representing the most general characteristics of objects of sensible intuition. Now, the applicability of specific categories to sensible intuitions determines the specific exercises of judgment through which to think the objects of these intuitions.^[121] If something is only thinkable through a specific categorial characteristic, i. e., if it requires to bring intuitions of it under a particular category, this commits to judge of it using the corresponding logical functions if the judgment is to be objective. Whatever is categorizable only as a reality must be judged through an affirmative judgment; as a substance: the subject-concept of a categorical judgment; as a cause: the antecedent of a hypothetical judgment; etc.

Judgments exhibit propositional unity only insofar as the way they combine representations conforms to the synthetic unity of intuitions. Subject-representation and predicate-concept in a categorical judgment, say, need to be combined in the way the acts of intuitively representing a bearer and its properties cohere in the synthesis of intuition, i. e., how they cohere in the representation of an individual object. If, e. g., the intuitive representings of divisibility and a body only combine in synthesis such that the body is represented as the bearer of divisibility, and not the other way around, then the concept of body must be the subject-representation in the corresponding judgment, the concept of divisibility its predicate-concept.^[122] Only then does the unity of judgment conform to the unity of objects, which is nothing other than the unity represented by the synthetic unity of intuition.^[123]

This, ultimately, is how Kant explains the unity of propositions. Act-types of judgment truly or falsely represent objects and properties, or facts, in that they conform to the unity of perceptions of objects and properties. The unity of perception, as what puts us in touch with objects and lets us know about them, determines what can be predicated of what and thus how thoughts can truly or falsely represent objects and properties, or facts, in the first place.