A Lewisian Argument for Conceptualism


Below is a revision of a paper I wrote for a class on David Lewis’ On the Plurality of Worlds in which I argue for conceptualism about abstract objects. I tried to make it understandable for general readers, but I apologize for readers who are interested but not very well-versed in philosophical style writings. Hopefully this piece will be self-explanatory enough. Originally the instructions for the paper were to try to mimic Lewis’ style, summarizing some argument or idea he has, criticizing it, and then offering a possible defense. The defense of Lewis that I wrote at the end doesn’t seem very substantial to me, so I will attempt to refute it and thus vindicate my argument for conceptualism. Before actually making the argument, I will give a brief introduction to modal logic for those who are new to the subject.

Modal logic is that area of logic that deals with the necessary and possible. The metaphysics of modality is the part of metaphysics devoted to explaining possibility and necessity and their relationship to various existing things (and to what doesn’t exist). A possible world is an entity that is invoked to explain the relationship between the necessary and the possible. A neutral definition of a possible world is “a way reality could have been”. There are two main camps in the metaphysics of modality about what a possible world is. The first says that a possible world is an abstract entity (or entities) like a number or a set; this is called modal abstractivism. On this view, a possible world is a “maximal consistent collection of propositions” [1]. The second is that possible worlds are concrete entities. This is sometimes called modal realism. On this second view, there are literally gazillions of completely-independent physical universes. Saying that something is possible means that it happens in one of those physical universes. So if I say, for instance, “it is possible that I would have been born in Australia” then this means that there is a physical universe (that stands in no causal relations to our own) in which I am born in Australia.

A Lewisian Argument for Conceptualism


In the early pages of On the Plurality of Worlds David Lewis explains his metaphysics and defends the method behind his conclusions. This paper will attempt to argue that given Lewis’ own criteria, we should prefer a conceptualist construal of propositions to Lewis’ understanding. If reducing the variety of basic entities in one’s ontology is a goal for metaphysicians, then they should pay the price of accepting conceptualism to gain the benefits of explaining a puzzling feature about propositions

Exposition: Lewis’ Framework and Lewisian Propositions

Lewis’ project is to expound on the thesis of the plurality of worlds—the idea that our world is but one among many. He explains the methodological concern that drives his project as follows:

Why believe in a plurality of worlds? – Because the hypothesis is serviceable, and that is a reason to think that it is true… I think it is clear that talk of possibilia has clarified questions in many parts of the philosophy of logic, of mind, of language, and of science – not to mention metaphysics itself. [2]

Lewis suggests that it is good for a theory to reduce unclear concepts to what can be easily understood, and to invoke entities that are uncontroversial in explaining these concepts. If a theory is able to do this, then that gives us some reason to accept it.

Lewis’ modal realism offers a simple analysis of propositions. Instead of classifying them as abstract entities, Lewis’ belief that possible worlds are concrete beings can be used to give a helpful analysis of propositions in terms of physical universes and their properties. He defines them as follows:

I identify propositions with certain properties—namely, with those that are instantiated only by entire possible worlds. Then if properties generally are the sets of their instances, a proposition is a set of possible worlds. A proposition is said to hold at a world, or to be true at a world. The proposition is the same thing as the property of being a world where that proposition holds….[3]

Lewis’ analysis can be fleshed out by example as follows. The proposition “Poodles are green” is reducible to the property of being a world where poodles are green. If the proposition “poodles are green” were true at our world, then our world would have the property of being a world where poodles are green. Instead, the proposition “Poodles are green” is true in a different possible world; so there is some other physical universe that has the property of “being a world where there are green poodles”. Our universe has the property “being a world where there are white poodles”; consequently, the proposition “poodles are white” is true in this world. Thus, for Lewis, a proposition is just a property instantiated by an entire possible world, or a set of possible worlds.

Critique: A Conceptualist Analysis of Propositions

Lewis’ analysis of what it means for a proposition to be true at some world is coherent and interesting. But is there a more conceptually lucid account available? Arguably, yes. A conceptualist articulation of at least one feature of propositions yields an account which may prove preferable – one which makes use of something that is already part of our ontology and is uncontroversial.

The correspondence theory of truth is the view that the truth is what “fits with reality”. Truth is contained in propositions, which are the entities expressed by or contained in sentences. True propositions stand in a correspondence relation to reality; they correspond to states of affairs.

One criticism of the correspondence theory is that it leaves utterly mysterious what the “correspondence relation” is. It remains undefined; the most that can be said about it is that it is supposed to connect up truths with reality and that when it obtains between a proposition and a state of affairs, the proposition is true. But these points identify the function of the correspondence relation—the role that it plays. Yet they name no intrinsic features of the thing. So the correspondence relation eludes analysis.

It would be good to have available to oneself a means of elucidating what the correspondence relation is. What might a believer in correspondence theory who is a defender of the existence of propositions do? One option is to take Lewis’ route and assert that propositions are just properties of the various possible worlds. However, one might wonder how the correspondence relation fits into Lewis’ articulation of propositions. Do Lewisian propositions correspond to reality? If so, can the correspondence relation be analyzed on the Lewisian account?

An alternative to Lewisian analysis of propositions is conceptualism. Conceptualism takes the entities commonly called “abstract” (including such things as numbers, sets, and values) to be reducible to something familiar: concepts. They are mental entities that are the objects of thought. We are all familiar with concepts (whether we think about them or not) and we are all familiar with the feature of concepts and other mental entities commonly referred to as “intentionality” (whether we think about it or not). Intentionality is the “ofness” or “aboutness” of a thing. Some philosophers have called intentionality “the mark of the mental.” It is a characteristic of thoughts, desires, and beliefs. Thoughts, desires, and beliefs are of or about something.

Why believe in conceptualism? Because it provides a useful way of explaining the correspondence relation. The correspondence relation can be identified with the property of intentionality. For a proposition to correspond to a state of affairs means for it to be about that state of affairs. This helps capture what is meant when we say that truth “fits with” reality. Propositions are about reality. Because this account can appeal to a readily-identifiable feature of our experience to analyze an otherwise difficult notion, it is preferable to Lewis’ view about propositions. [4]

Possible Defense of Lewis’ Analysis of Propositions

A Lewisian has available at least four lines of reply. Firstly, he could question whether conceptualism’s helpful analysis of correspondence outweighs the numerous advantages of Lewis’ theory. Does the fact that conceptualism helps explain one feature of propositions mean it is preferable given the manifold advantages of Lewis’ theory? Secondly he could argue that we are more familiar with properties instantiated by entire worlds than with intentionality. This is because properties had by a whole world are more ontologically basic than “ofness”; a property of a whole world can exist independently from “ofness”. After all, there are possible worlds where there are no minds, and so no beings with intentionality. There are more possible worlds than there are worlds with intentionality, so there are more properties had by entire worlds (Lewisian propositions) than there are instances of intentionality. A third criticism is that the conceptualist account thus far only analyzes one aspect of propositions, but leaves their classification and further definition unattended to. Finally, Lewis’ account does indeed seem to have a way of analyzing the correspondence relation: for a proposition to correspond to reality means for it to be exemplified by a world. Thus, for these four reasons, conceptualism seems to be an unnecessary burden when compared with the simplicity of Lewis’ analysis.

Reply on Behalf of the Conceptualist

The first argument offered against the conceptualist analysis of propositions does not challenge the coherence of the conceptualist view, but rather its plausibility in light of larger issues. In reply, it might be suggested that the conceptualist is only embarking on a modest project and defending his account of one small area of the metaphysics of modality—not trying to show that every issue about which Lewis offers a modal realist analysis can be given a comparable conceptualist explanation. Fleshing out a larger conceptualist theory might perhaps tilt the balance in favor of the conceptualist, thus nullifying the objection. A second reply is that this assumes that Lewis’ theory is unproblematic. If there is some kind of conceptual problem or inconsistency in Lewis’ own account, then the “fruitfulness” of Lewisian modal realism becomes irrelevant; any coherent account is better than an incoherent but fruitful account.

The second objection has two problems. Firstly, it is false that on Lewis’ view the property had by an entire world of “being a world where there is intentionality” is more basic than the property of intentionality. The world as a whole would have this property only in virtue of whether or not any of its parts had this property. The order of dependency is wrong, at least with respect to this kind of property. Secondly, the objection confuses familiarity with being ontologically basic. Even if the property had by an entire world of “being a world where there is intentionality” grounds the existence of the property of intentionality, our experience of intentionality and awareness of it—and consequently our familiarity with it—seems to precede our experience of “properties had by entire worlds”. Early in life when I have my first thoughts and beliefs, I become familiar with intentionality (even if I don’t think about it specifically). It is only later that possible worlds enter into one’s mental picture.

The third objection can be met by a reply similar to the reply to the first objection: yes, this only clarifies one aspect of the metaphysics of modality; but that only counts against believing in this view of propositions if no further analysis of other aspects of propositions and modality at large is forthcoming and there are no problems with Lewis’ theory. Indeed, it is not difficult to see how one might expand on the initial analysis of propositions that has been given: a proposition is a concept that is had by minds or a Mind. It has content, expressible in sentences. It is a bearer of truth or falsity, and is the object of belief or disbelief. To believe a proposition means to think that it is of or about something that actually exists. To disbelieve a proposition means to think that the content of said concept is not of or about anything that actually exists.

The fourth objection turns on the assumption that Lewis’ account is unproblematic in explaining modality; if this is not correct, then the objection fizzles. Also, it seems that because we are more familiar with intentionality than properties had by entire worlds, this might offer a reason to think that the conceptualist analysis of the correspondence relation is superior to that of the modal realist. Given Lewis’ disdain for unclear analysis of modal notions, we might, therefore, have reason to prefer the use of the familiar concept of intentionality.


For a metaphysician who accepts Lewis’ method, there may be good reason for thinking that propositions are concepts based on the ease with which a conceptualist can analyze the correspondence relation. Larger issues related to conceptualism (how do we analyze numbers, sets, values, etc.? Where are the concepts located? How do they relate to non-existent things?) cannot be delved into here, but we at least now have some reason being offered for preferring conceptualism to other views of abstract objects; and consequently we have some reason why a metaphysician might prefer an abstractionist account of possible worlds.


[1] Alexander Pruss, “Possible Worlds: What They Are Good For And What They Are”. Propositions are the entities expressed by or contained in sentences. To see what this means and why we might believe it, consider two sentences each written in different languages, that say exactly the same thing. What is that thing that they both say? How can there be common content between those two sentences? If there is a single entity that can be expressed by two distinct languages, then this can explain why the sentences say the same thing. If propositions are indeed real, then they are the objects of belief. When I say “I believe that my shirt is blue” the thing I’m believing is the proposition expressed by the words “my shirt is blue”. Also, they are where truth or falsity is located. So propositions are true or false; sentences are only derivatively so, in virtue of the proposition(s) they express. Propositions stand in logical relations to each other (contradiction, entailment, coherence, etc.). They can be grouped together; some groups will be coherent, and so able to represent how reality can be. So a collection of propositions that describes an entire other way that reality could be is a possible world. If a maximally consistent set or propositions describes how reality actually is, then we can say that it is the actual world.

[2] David Lewis, On the Plurality of Worlds Page 3

[3] Ibid., Page 53

[4] Though I don’t develop them here, there might be more arguments for conceptualism based on its ability to address Lewis’ argument against belief in what he calls “magical ersatzism” about possible worlds (according to which there are possible worlds but they are accepted as basic and unanalyzable); but those issues will have to wait for another time.


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