1 Introduction

3Given the diversity of the literature on iconic representation, I also want to be clear about the scope of this paper. There are at least three conspicuous literatures on iconic representation: (example)

(1) The literature on depiction in aesthetics.

• 5 Sometimes maps can go under (1) or (2). Some of the work of John Kulvicki could fall under (1) and (...)

(2) The literature on scientific modeling, diagrams, and scientific representation generally in the philosophy of science.5

(3) The literature on iconic content vehicles in cognitive science.

4We’ll call my project—of characterizing iconic propositions in an M1 context—IP. IP differs from, and is similar to, (1)–(3). (1) and (2) concern the question of how we use entities external to the mind (pictures, models, e.g.) to represent the world while IP doesn’t concern such entities external to the mind. According to the mental processes that I base IP on, “we” don’t interpret our own representations (I say more about this below). For (1) and (2), there is a plausible desideratum that a theory should make sense of the multiplicity of representational formats—i.e., the vastness of different kinds of pictures and models. IP doesn’t share this desideratum since biology will severely limit the mental formats that undergird IP. (2) and IP share something in common that isn’t present in the picture-focused sub-literature of (1): A key desideratum for IP is that iconic propositions must guide us in our action in virtue of our ability to reason about the icon’s target via reasoning about the icon. This constraint—what Frigg & Nguyen call the surrogative reasoning requirement [Frigg & Nguyen 2016, §1]—is familiar in the modeling sub-literature of (2). Finally, IP and (3) are closely linked and best understood by analogy with King’s theory. His propositions are abstract objects gleaned from the mental processes responsible for calculating linguistic meaning. Iconic propositions are abstract objects gleaned from the mental processes responsible for creating mental maps and models. In §2, I make the case for the need for iconic propositions on the basis of the aforesaid assumptions and argue that they are different kinds of propositions rather than merely different mental formats that express garden variety propositions. Because of the limited scope of this paper, I don’t discuss some of the greatest hits of iconic representation, such as the works of C.S. Peirce or Tractatus-era Wittgenstein.

5In §3, I present my theory sketch of iconic propositions according to which such propositions are properties, and representation is analyzed in terms of the co-instantiation of properties. Numerous questions will then have to be answered: What makes an iconic proposition representational in any sense? What makes an iconic proposition about whatever it’s about? When does an iconic proposition accurately characterize its target? Are iconic propositions holistic or atomic? I will answer these questions to form the sketch. To fill out the theory, for the reset of the paper, I consider various propositional issues vis-à-vis the theory.

2 From M1 to iconic propositions

6I first characterize M1 and P1 and then argue that M1 creates a need for iconic propositions. I then argue that these are a different kind of proposition.

2.1 General character of each thesis

7Schiffer captures how philosophers have traditionally understood propositions [Schiffer 2003]. According to this view, propositions are abstract objects that have truth conditions essentially and absolutely—i.e., respectively, it’s necessarily true that a proposition has its particular truth conditions, and a proposition has those truth conditions without relativization. Contrast that essentiality and absoluteness with sentences: It’s contingently true that sentences have their particular truth conditions, and they have their truth conditions only relative to a given language with its various conventions. Though Schiffer doesn’t use this language, traditionally, propositions represent, or have their truth conditions, intrinsically—i.e., they represent the world purely in virtue of the way the proposition is. Any duplicate of a proposition will represent like the original copy. Last, propositions are mind- and language-independent in two senses. First, their existence doesn’t depend on humans or agents of any kind. Second, multiple languages can express the same proposition, but any one proposition doesn’t belong to a given language. Quintessential P1 theories include the possible worlds theory of propositions, according to which the proposition that p is the set of worlds where p is the case (or the characteristic function of that set); and the tuple theory of proposition, according to which the proposition that, e.g., Rachel reads, comprises an entity having to do with Rachel and something to do with the property of reading, and the proposition is structured in some way related to the syntax of the sentence “Rachel reads”, something like the following:

〈R, r〉

8The kinds of entities involved in the tuple will depend on the theorist’s semantic and metaphysical commitments, whether Russellian or Fregean.

9The important aspect of this traditional picture is the mind-independent bit. As noted, with the work of King and Soames, the recent propositions literature has taken an empirical turn in which the nature and existence of propositions is in some way mind dependent. To start, we can understand this turn to mind dependence in terms of whether propositional representation is derivative or fundamental. Some things represent because we confer that power upon those things. The sentences on this page represent in virtue of various conventions set up regarding written language. Thus we humans partially conferred representational properties on written language. But what about our human representational capacities? Are we the ultimate wellspring of representation, or do our mental states represent derivatively because they express propositions which themselves are the ultimate wellsprings of representation? Note that this question is distinct from the question of whether propositional representation is intrinsic or extrinsic. The source of a property and whether an object has that property intrinsically are different issues.

10M1 rejects the fundamentality of propositional representation. For reasons of space, I will assume some familiarity with the works of King and Soames, whom I count as the two key mind-first theorists. Both reject the fundamentality of propositional representation and perhaps see the rejection as the key innovation of their views. King’s propositions are syntactic-semantic facts that inherit their representational capacity from the mind, in particular that these facts encode the instantiation function, which they inherit from our minds. Soames’ propositions are act types the tokens of which involve mental actions, such as predication, and the representational capacity of these acts derive from these mental actions.

(4) ∃r(S Att r & r expresses p).

12For S to have an attitude whose object is p is to bear a relation, functionally defined as a given attitude, to an inner content vehicle whose content is p. For the language of thought theory, the content vehicle will be a sentence of mentalease. For a model/map theory, the content vehicle will be some inner model/map. King and I will pay greater attention to r and especially the process that gives rise to r when crafting the theory of p in the second conjunct. Conversely, a P1 theorist can craft a theory of p while ignoring some facts about the mechanism by which the brain carries out its representational function. If the M1 theorist doesn’t have good reasons to show that the mind in fact represents the way she claims, then we have no reason to accept the existence of the abstract objects, i.e., her propositions. The propositions-first theorist doesn’t face such a dependency.

Proposition-First (P1) The thesis that propositions exist, and have their nature, independently of minds, and propositions are the ultimate source of representation while mental representation is derivative.

Mind-First (M1) The thesis that propositions depend for their existence and nature on the mind, and minds are the ultimate source of representation while propositional representation is derivative.

2.2 From M1 to iconic propositions

14The purpose of this subsection is to argue for the conclusion that if one accepts the M1 framework, and if one accepts a rich system of iconic mental representation (specified in §3.1 below), then that motivates the project of the next section—to sketch a theory of iconic propositions. The project, however, will be limited in scope: it will be a sketch of a theory of propositions for a particular mental representational format. A natural worry for this approach is that different mental representational formats shouldn’t require different kinds of propositions in much the same way that different languages don’t require different kinds of propositions. The benefit of the limited approach is that it has the potential to avoid the Benacerraf problem.

15If we accept M1, as we provisionally do for this paper, then we commit to propositions that depend on some etiology that is responsible in the end for some kind of human representation. If the M1 theorist is wrong about the etiology that is responsible for her content, then we can call into question her theory of propositions. If mainstream formal semantics is seriously mistaken in the way that we calculate semantic content, then King’s theory may be in trouble. But even if the M1 theorist is right about the ground-level processes that are responsible for the content on which she bases her theory, it’s important to see the scope of such a theory. An M1 theory will be a theory of that kind of content—the kind that a given mental process is responsible for.

16King recognizes this point. King wrestled with the worry of the origins of his propositions: to explain how our ancestors first brought Kingean content into the world [King 2007, chap. 3]. To explain, e.g., how lexical items came to have semantic values, it seems we would have to appeal to our ancestors’ beliefs and desires, so propositions would need to exist in the first place. In his book, King sketches a quick story about how our pre-linguistic ancestors had “proto” intentional states before the dawn of propositions. Later, King says a bit more about these proto-intentional states, that they may have been perceptual states that had their own kind of content, which is different from linguistic content [King 2014, 60]. He thus recognizes that the etiology that produces his content should limit the scope of his theory: His book, as he says, should have been titled The Nature and Structure of Linguistic Content instead of just content [King 2014, fn. 19]. He then goes on to say the following:

I believe that many things have content other than sentences of natural languages. Maps, diagrams, perhaps pictures and, most importantly for present purposes, perceptual experiences have contents. In the case of each sort of thing that has content, there will be an account of those contents in the spirit of the present account of the contents of natural language sentences. Due to limitations of space, time and knowledge, the details of the theory of the contents of perceptual experiences that is in the spirit of the present account of contents of natural language sentences cannot be sketched here. [King 2014, fn. 19]

19If this is where the M1 movement has gotten us—basing propositions on mechanisms that give rise to content and possibly forcing us to countenance different kinds of propositions for different mechanisms—then maybe the movement is mistaken. Aren’t propositions supposed to capture the information that different sentences, languages, and representational formats, including different mental representational formats, express? If this is the case, then we shouldn’t end up with different kinds of propositions but different mental formats that express the same kind of proposition.

21As we’ve seen, the key feature of M1 is the introduction of an empirical element into propositional theorizing. There are two main, related motivations for this. First, both King and Soames have argued, or perhaps recognized, that it’s hard to see how traditional P1 propositions, e.g., set theoretic propositions, intrinsically represent. Why does the function that maps white-snow worlds to T and non-white-snow worlds to F intrinsically represent snow as white? That function seems to represent only in virtue of our interpretation. To see this, we could easily swap out T and F with 1 and 0 or a fish and a bird—it doesn’t really matter what so long as we have two distinct entities. Or why does the set of white-snow worlds intrinsically represent snow as being white while the set containing some random assortment of things not? The answer, again, seems the same: we interpret the former set as representing the proposition that snow is white.

22That we need to interpret these propositions in order for them to represent results in formally equivalent propositional candidates that no possible evidence could discern among—i.e., the Benacerraf problem. This scenario is very similar to the classic Benacerraf identification problem concerning set-theoretic reductions of numbers. In such purely metaphysical situations, as Clarke-Doane notes, our concepts resolve indeterminacies, and in many such situations, our concepts don’t discriminate among various competitors [Clarke-Doane 2013, 472]. In the empirical realm, however, Clarke-Doane notes that causal chains help to resolve indeterminacy in that they help fix the extensions of empirical concepts—water, electron, etc. When such casual chains give out, we end up in a situation that is common in science, especially scientific modeling: brain and behavioral facts, e.g., might metaphysically (not merely epistemically) underdetermine whether, say, all syntax is binary branching or is sometimes n-ary branching. Thus if King ends up with multiple propositional candidates vying to be identified with the proposition p, and the empirical facts don’t discriminate among the candidates, then he ends up in a common, benign situation that empirical investigators can end up in.

23Now what if we decide to say that, supposing the brain represents multi-modally, those modes are merely different formats that encode the same information, and we understand this common informational content with some abstract objects qua propositions. The worry here is that our freedom to stipulate that information removes us from a situation in which causal chains resolve indeterminacies and where their irresolution is benign. For example, in the depiction case, some have expressed sympathy for the claim [e.g., Grzankowski 2015, 152], that pictures express possible-worlds propositions. This is a plausible suggestion since iconic and linguistic mental representations have radically different syntax. Why not say that both linguistic mental representations and iconic mental representations both express possible worlds propositions? The problem, though, is, which version? The set version or the function version? Here we face the Benacerraf problem that moving to M1 was supposed to eliminate. I won’t pretend that this worry is unanswerable, but I present it as a reason to think that M1 leads us to the view that multi-modal representation leads to different kinds of propositions, to a kind of pluralism, and not merely multiple formats that express the same kind of proposition.

3 Iconic propositions: The theory sketch

24To sketch an M1 theory based on an iconic basis of content, we first need to get clear on just what that basis is, which I consider in the next subsection. In the following subsection, I state the theory template and theory sketch and then consider the theory sketch in relation to various propositional issues.

3.1 The iconic base

29Let’s see what notion of structure may be relevant to iconic content. Braddon-Mitchell & Jackson claim that a content is structured if the similarities and differences of content are systematically related to the similarities and differences of the objects of the content [Braddon-Mitchell & Jackson 2007, 178]. If we have representations R₁, R₂, … R_n that correspond to states of the world W₁, W₂, … W_n, differences in the Ws will correspond to differences in Rs. The level at which we find this correspondence may be highly abstract. To use an example from Braddon-Michell and Jackson, Arabic numerals are structured representations, the objects of which are numbers since there is a systematic correspondence between the similarities and differences of the Arabic numerals and their number objects. The idea when applied to iconic contents is that there will be systematic differences and similarities in iconic representations that correspond to similarities and differences among their objects.

3.2 Recipe template and sketch

32To give an M1 iconic theory of propositions, I answer these questions. Below each question I state what my answer, for this paper, will be.

33Iconic Proposition Recipe Template

34(Q1) In virtue of what does an iconic proposition characterize the world and how, metaphysically, ought we understand that characterization?

• Icons characterize the world in virtue of isomorphism. I understand iconic propositions’ characterization of the world, metaphysically, in terms of property co-instantiation.

35(Q2) Iconic propositions, to be propositions, need to have determinate content, but how?

• This question is somewhat complicated, but natural teleology will play a major role.

36(Q3) Does a theory prioritize holistic or atomistic propositions? That is, to characterize an agent’s mental state, do we first characterize large propositions from which we derive atomistic propositions—e.g., do we, as a possible worlds theorist might do, first characterize an agent’s entire mental state in terms of a set of worlds and then derive the propositions that the agent’s individual thoughts express; or do we start straight away with the propositions that individual beliefs express and take the holistic belief state as the sum of those atoms?

• I prioritize holistic content and employ possible worlds as a model, in the sense of scientific model, of iconic propositions.

37(Q4) How do we understand basic propositional issues, such as logical relations, accurately and inaccurately characterizing the world, etc.?

• At the level of ontology, basic propositional issues are understood in terms of property co-instantiation and restrictions thereof, and the analysis of these issues is cashed out in terms of possible worlds models in the sense of scientific models.

I’ll answer questions 1-3, then state the theory, and then move to Q4.

[T]he pattern of relations among the constituents of the represented phenomenon is mirrored by the pattern of relations among the constituents of the representation itself. And because the arrangement of things in the representation are like shadows cast by the things they portray, we can encode information about the original situation as information about the representation. Much of this information is preserved in inferences about the constituents of the representation, so it can be transformed back into information about the original situation. [Swoyer 1991, 452]

40The pattern of relations contained within an iconic representation will be highly complex, but in order to state the theory, let’s zero in on the complex property of having that pattern of relations. Entertaining a mental model, then, will consist in the mind/brain instantiating this complex property, and successful representation will consist in the co-instantiation of properties—the mind’s of a pattern of relations and the world’s instantiation of the complex property of the mirrored pattern of relations. And it is this mirroring of relational patterns that partially underwrites the usefulness of these representations.

41If we set aside for a moment the niceties of the context of propositions and the order of isomorphisms and such, the general idea is that a model comprises a certain pattern of relations—it will be, at the software level and at some level of abstraction, some way or other. And when the model is useful given some purpose, the world will be the same way, under isomorphism. And the idea stays the same when the iconic representation becomes more abstract—e.g., with a diagram. But isomorphism is only one part of the sketch because isomorphism is all too easy to come by. Anything is isomorphic to anything else under some interpretation. A model doesn’t represent merely because it’s isomorphic to some aspect of reality. It represents because it has the right kind of isomorphism to make it useful to us. It is our use to which we put the model plus its pattern of relations’ being isomorphic to some aspect of reality that explains how the model comes to represent reality. Surely it cannot be “we” who interpret our own inner iconic representation on pain of an infinite regress of inner homunculi.

43To show that iconic propositions represent intrinsically and determinately, we show that iconic content can be “run” in a cognitive system that lacks any kind of interpretative intelligence, yet the use to which the icons are put, in addition to isomorphism, underwrites the icons’ representative powers. Ramsey calls this the “mindless strategy” and illustrates it with a two-step analogy [Ramsey 2007, §6.1]. The first step involves an intelligent agent’s interpretation conferring representative powers upon an icon; the second step involves removing the agent while keeping the guiding function of the icon, the result being that its representational capacity still remains. The analogy compares the iconic view with another prominent view of representation—the “receptor view”—in which neural states represent because they reliably detect certain external conditions. To illustrate:

44Step one. Two windowless cars, car A and B, respectively, traverse an “S”-shaped path. They do so as follows:

• Icon. A driver guides the car with a model of the “S” combined with dead reckoning (estimating direction and distance to then calculate estimated location while traveling).
• Receptor. When the car approaches a wall, sensors on the front bumper push inward, closing a circuit, which illuminates a light, which the driver uses to guide the car through path.

45Step two. Now we remove the drivers, and the cars traverse the path as follows:

• Icon. The model is replaced with an “S”-shaped groove, isomorphic to the track, in which a rudder runs. The rudder moves along the groove and controls the steering wheel via arms connected to the rudder, guiding the car through the path.
• Receptor. When the car approaches a wall, sensors on the front bumper push inward, closing a circuit, which controls a rod that pushes the steering wheel in the opposite direction, which guides the driverless car through path.

46Once we remove the driver, the most natural way to interpret the process in the receptor car is that a mere causal process guides the car. There is no component of the process—the sensors, the circuit, the rod—that seems representational. On the other hand, the best way to explain the success of car A in step two is that the groove is a model, a representation, of the track. At some much, much more complicated level, the iconic representations that guide our behavior are analogous to the groove, and the conclusion that Ramsey draws, that I want to employ, is that our cognitive systems can mindlessly use iconic representations to target aspects of reality, and in so doing, the icons acquire their representational powers.

48This determination of content also resolves another immediate worry for the theory: The representation relation should be typically asymmetric, for the objects of representations don’t represent their representers. Language-like representation obviously satisfy this desiderata. I’ve grounded the representational capacity of my propositions partially in terms of a kind of similarity, in particular a kind of isomorphism. Yet similarity is a symmetric relation. If this is the case, then I face an objection: If iconic proposition p represents r, then r will also represent p, which seems strange at the very least. The solution is this: Iconic propositions and their targets may be symmetrically isomorphic, but the targets of such propositions aren’t put to any use and so don’t represent anything.

49Q3. The last decision point is a priority issue. Iconic propositions may not encode the entirety of an agent’s mental state at some time. Still, such propositions can encode lots of information. Yet at the very least, to give a sketch of a theory of propositions, we need individualized propositions. Let’s first consider, at an intuitive level, how we may extract such propositions. If the content of an agent’s mental state with respect to some issue at some particular time is a complex, holistic model, then an individualized proposition will be some part of that model. Just as a map may represent some expanse of land, some portion of that map represents a part of that land. More abstractly, a Venn diagram may represent various properties and relations between sets as a whole and particular relations and properties when we consider an aspect of the diagram—that, e.g., the intersection of two sets is non-empty. In both of these cases, the holistic representation has priority over the less holistic representation—the intersection, e.g., only represents what it does in virtue of its function in the overall diagram. If we can understand a mental model as a complex property of having a certain pattern of relations—one that a cognitive system uses to target, via isomorphism, some aspect of reality—then an individualized content will be some portion of that mental model. In other words, it will still be a property of having a certain pattern of relations, but the pattern of relations will be some portion of the agent’s more holistic content. This just-mentioned property will officially figure into the statement of the theory below, but I want to flag that I am about to discuss possible worlds precisifications of this property. There is an unfortunate double use of the world “model”: mental models and scientific models. These precisifications are scientific models.

51Statement of theory. To recap: According to the mind-first trend, the fundamental source of representation is the mind upon which all others forms of representation, including propositions, are derivative. The mind-first movement requires us to pay attention to the details of mental representation. Toward this end, we’ve considered a diverse view according to which the mind represents partially iconically. Iconic representations represent not only in virtue of isomorphism, but also, according to the option we took, in virtue of a cognitive system’s natural teleology—a kind of use that doesn’t require inner homunculi—that delivers a determinate content for the system. I’ve understood an isomorphism between mind and the world as the sharing of a pattern of relations, and I’ve considered the property of having some particular pattern of relations as a way of specifying that content. We’ve then considered aspects of that highly complex property that are an individualized content, and we’ve sketched different ways to precisify that individualized content. With this in hand, we can now give a statement of the sketch that we’ll refine and expand upon:

Iconic Propositions (IP) An iconic representation c (a mental map, model, diagram, etc.) is a complex pattern of relations that form an isomorph that a cognitive system uses to navigate the world. The content of c is the property i of having the pattern of relations involved in the isomorph. An iconic proposition p is a property r that isolates an aspect of i for which there is a content pairing with i, and the mind represents the world veridically in terms of p when both the mind and world instantiate r.

52Q4. I first consider how the sketch deals with basic issues, which will set us up to discuss the more complex, contemporary issues.

53General content. Can iconic propositions represent anything general? If they couldn’t, I wouldn’t take that as a damning objection. We would still have a software-level process that leads to non-general content for which we should still account. But I think iconic propositions can represent general facts, and the focus on concrete-style maps may lead one to think otherwise. For example, diagrammatic content, in my view, represents general facts—e.g., a diagram may represent that all dogs are mammals, which isn’t about any particular dog or mammal.

54The claim that icons are always specific has the most force in the context of depiction in the aesthetics literature. The claim is much less plausible in the cognitive psychological literature on mental models and maps. As noted, mental models are not egocentric visual images. A cognitive system may use a model to navigate some particular task, say getting a particular book from the library, or an agent might model the general structure of a building type. For example, there is a particular layout for apartment buildings in the city that I used to live—all the building generally had the same spatial layout. If I use the same abstract structure to navigate all such buildings, then that structure is in some sense general.

55Note, however, that here I need not take a stand. Even if iconic mental representations are always specific in their representation, this is not fatal to my project in this paper. My goal is to provide an account of propositions for the modality of iconic mental representation should such representation exist. I shouldn’t take a stand, at this point, on the nature of these cognitive representations, whether they be always specific or sometimes general. If we take the M1 movement to heart, and we need different propositions for different modes of representation, and one of those modes ends up having only specific content, then so be it. If this ends up being the case, and the reader finds this project overly narrow, then that is really a worry for the M1 movement, and it is not my intention to mount a defense of M1.

57Non-existant relata. A necessary condition on the satisfaction of many relations is that the relata of that relation exist. If the loving relation obtains between Abélard and Heloïse, then both need to exist. Not so for representation. Agents can represent the nonexistent: E.g., I can represent Pegasus, though such a being is nonexistent. It’s important to note that accounting for non-existent entities, properties, etc., implicated in a relatum of the representation is a general problem. Here is how IP makes sense of this: The mind instantiates a property that the relevant chunk of reality does not instantiate. The reason that a given simulation represents some non-reality is because that’s the use the cognitive system puts the model to.

58Shareability of content. The way that IP accounts for the shareability of content is perhaps one of the most interesting aspects of the theory in my view. Above, in the midst of stating the theory, we considered how the propositions of IP come to have determinate content rather than representing anything given the right purpose. Considering the key desiderata of shared content will give me a chance to elaborate on the determinacy issue.

59It appears to me that some philosophers take the notion of shared content quite literally. When two people believe the same thing, the content of the states is literally one and the same abstract object—the proposition. Similarly for natural language sentences. This is the case for tuple theories as well as possible worlds theories: You and I both believe that snow is white in virtue of our mental states having literally one and the same proposition expressed, whether it be  or the set of snow-is-white worlds, etc. Some modern writers hold to this literal picture, for example [Schiffer 2003]. Traditionally, then, to share content is to glom onto one and the same object.

61IP diverges from the traditional picture of shared content. My notion of shared content consists in a notion of sharing that we’re familiar with—that of properties. Various minds will process information in different ways, but, when they represent the world as being one way or another, they do so in virtue of an agents’ iconic contents representing it as such. What these minds share is that, at some level of abstraction, they’re all similar—both with each other and with the object of representation. And they’re all similar because they all instantiate the same property—a sample (or attempted sample) of the world. So when agents share content, it’s not in virtue of accessing the same object but in virtue of being relevantly similar to one another.

62One may worry that iconic representation is a poor basis for mind-first propositions because it just seems that mental maps, models, and others kinds of iconic representation are just too variegated from person to person to ground any notion of shared content. I think there is something to this worry, but I think it is a general worry for the mind-first program, which I want to quickly address.

(5) Fighting in Aleppo intensified, and Turkey entered the Syrian conflict today.

65For King, we don’t have this worry since there is no temporal aspect to the order in which semantic values, given some syntactic structure, are composed. Yet for King, much depends on exactly what the syntactician and semanticist are up to at a metaphysical level. While there is a strain of semanticists that see themselves as describing a Platonic grammar, many semanticists and syntacticians see themselves, if only implicitly, as modeling psychological processes at some level of abstraction. If King’s basis of content consists in psychological models of mental processes, then there are possibly minor differences in the way that minds calculate linguistic content.

66These are complicated issues, but my point in bringing them up is that accounting for the sharing of content is a general kind of difficulty for the M1 theorist, and IP doesn’t face a distinctly threatening version of it. At some level of detail, individual iconic representations will surely differ from brain to brain. But if a crowd of people have mental models that all represent the logic books as on the twentieth floor of the library, then there will be some property based on that representation that all of their minds instantiate, and they will share content in virtue of that. If anything, IP fares especially well with the dilemma currently under discussion because the notion of sharing is the familiar notion from the sharing of properties. Many red objects can differ in innumerable ways, and may even differ in their exact shade of redness, yet they may all share the property of being red. Similarly for iconic representation: many minds may vary in exactly how they represent some given fact, but they can still all share a property in common.

67Logical relations. The idea of truth or satisfaction conditions starts from the idea of simulating a fact that obtains. Now this might not fit the mold of traditional truth conditions, but this isn’t a worry: We need some understanding of what it means for the content of someone’s mental state to be accurate, and IP gives us that in terms of property co-instantiation. And we can begin to understand the logical relations that exist among mental contents in terms of properties; one can’t model something’s being maroon without modeling its being red, one can’t model a square’s having three sides, etc., which means that certain kinds of properties instantiate together, some can’t co-instantiate, etc. And given that much of the iconic representation literature, mental models in particular, was introduced to account for reasoning, much of that literature can be worked into an account of the logical relations that hold among mental contents.

68The Benacerraf problem. The Benacerraf problem arises, to recall, when we have multiple propositional candidates to choose among, the choice of which is arbitrary. This problem is most salient when we have multiple formal objects with the right propositional properties, such as grain and structure. This is the classic propositional version of the problem that plagues set theoretic theories of propositions. IP identifies propositions with properties, not formal devices. The decision to employ such formal devices is what leads to the surfeit of choices. If IP had a Benacerraf problem, it would arise from the indeterminacy of the mental representations—if we had no way of choosing which of any iconic content may represent some way the world is because any icon can represent anything with the right interpretation. If this were the case, then to choose one icon over another would be arbitrary. But we provided one way of pinning down unique content, which would prevent a Benacerraf problem of this kind.

4 Conclusion

69This paper has been but a first step to fill out the consequences of the change in propositional theorizing that King and Soames have initiated. I have not argued for this change directly, only having assumed it. If we are to take this change seriously, then it calls for propositional theorizing that pays close attention to the empirical details of mental representation. This paper has attempted to begin this in the context of non-linguistic representation. The idea that iconic formats express propositions is not new, but theorists in this area have worked to show that propositions express propositions at all [e.g., as mentioned Grzankowski 2015]. I’ve begun to fill out what the nature of these propositions might be in the context of mental representation.