With Worlds as Content: An investigation on Possible Worlds Semantics and its Problems

(1)

With Worlds as Content

An investigation on Possible Worlds Semantics and its Problems

C-Essay, 15 HP

Uppsala University VT 2019 Department of Philosophy Author: Tove Fäldt

Supervisor: Jessica Pepp Examiner: Sebastian Lutz

(2)

1. Introduction

That things could have been different is an interesting topic, to say the least; what if the season finale of Game of Thrones would have ended differently? What if the currency used in Sweden was beets instead of the Swedish Crown? Imagining different ways the world could have been, or even so, imagining that there is a possible worlds in which we do in fact bring a number of beets when we go grocery shopping, is an interesting philosophical topic. It is not only shared by those who practice philosophy on a daily basis. It is the topic of common day to day discussion during lunch, the sudden realisation of the arbitrariness of words while reading a magazine, things to converse with your friend in the middle of the night and so forth. So, other than being useful tools for philosophers, possible worlds are interesting to discuss from any point of view. But in this paper, I am interested in the way possible worlds have been used in a theory of semantics, it would not be too far fetched to imagine that it can bring some well-needed clarity in the debate about meaning. The importance of meaning when we use and interpret words and sentences is tremendous. It is therefore equally important to develop a theory of meaning that focus on expressions of language, that is, a theory of semantics.

In this paper, I will present Possible Worlds Semantics, as developed by Robert Stalnaker (1984). The purpose is to investigate if the account is successful. The focus will naturally be to discuss the problems that the theory faces as well as the solutions provided by Stalnaker and assessing whether these solutions are sufficient. I will then propose a diagnosis of what goes wrong with the view. In doing this, I will be able to give a good overview of the theory.

First, I will introduce a general way of thinking about a theory of semantics in section 1.1.

Following this, I will briefly introduce Possible Worlds Semantics as Stalnaker develops it in section 2, thereafter I will discuss some reasons why such a view would be attractive in section 2.1. The next part of the paper will be the discussion of the problems it faces. I will start with two problems often posed for Possible Worlds Semantics, that of belief ascriptions and necessary equivalence in section 3. The next sections, 3.1 and 3.2, will be the two solutions that Stalnaker provides to the problems presented. I will then evaluate if these solutions are satisfactory by using the works of Jason Stanley and Jeff Speaks in sections 3.3 through 3.5. Lastly, I will make some concluding remarks on what I have been doing throughout the paper in section 3.6 and then present the results gathered in a conclusion in section 4.

(4)

1.1 A theory of Semantics

Exactly what a theory of semantics is can be complicated to pinpoint, as there are a lot of ways in which the focal points of semantics differ. It is, I think, therefore important to position myself in questions such as what or why in regards to semantics. I will be using the term “semantic” and the theory that follows with it in alignment with Jeff Speaks’ entry “Theories of Meaning” (2018) from the Stanford Encyclopedia of Philosophy.

A theory of semantics is needed to explain what we mean with words and sentences. When uttering sentences we do not just say random words, or even just make random sounds. We have very specific sounds and squiggly figures on paper that mean things. Just as, if I write “gkj rngd”, you know that this does not have a meaning (other than showing you that it is not a sentence and does not have a meaning). However, you can somewhat understand what I am writing in this sentence by looking at these squiggly figures. So, in short, the interest of a semantic theory is to provide an explanation of how these specific sentences, words or utterances mean things while others do not. More precisely, we can then distinguish two questions that are central in theorising about meaning. The first one is about what a specific set of symbols means to a set of agents or a community of speakers. The second being in virtue of what is that very set of symbols meaningful to a set of agents (Speaks, 2018). A theory of semantics aims to answer the first question. Speaks says that, even though the semantics of English differ from the semantics of French, the main task for a semantic theory is more so in finding a general way that would apply to all natural languages on how meaning is given (Speaks 2018). This means that the meaning of a sentence is not necessarily connected to a certain syntax. The theory that I will focus on in this paper is one in which the meaning is a proposition. There are plenty of semantic theories that claim that sentences express propositions. This is one of the reasons as to why the natural language that expresses the proposition does not really matter. For example, the English sentence “the grass is green”

expresses the same proposition as the French sentence “l’herbe est verte”, and the language it is uttered in does not change the proposition that the sentence expresses. I will discuss the nature of propositions, according to Stalnaker, in my next section.

In the following section, I will introduce Stalnaker’s Possible Worlds Semantics as a semantic theory.

2. Possible Worlds Semantics

In this section, I will describe the theory and how it works. Possible Worlds Semantics (PWS) is a theory of semantics that focuses on what contents are. There are a few different proponents of

(5)

the view and as a consequence some slight differences in regard to definitions. For this paper, I am going to be using Robert Stalnaker’s view exclusively unless stated otherwise.

“Possible worlds” is probably what piques the interest of many with this theory, so this notion requires some explanation before moving on to its purpose in a theory of semantics. The concept of possible worlds can be found very far back in philosophy. The first use of possible worlds is most often attributed to Gottfried Leibniz in 1710, where he made use of the concept to argue for God allowing evil in this world. The ontological existance of possible worlds is mostly what is under dispute. But, as we shall see, possible worlds can be quite powerful to use as tools.

When it comes to possible worlds in semantic theory, they can be seen as abstract objects as in ways things might have been, or real, concrete worlds like the actual one, only different and perhaps not available to us. For this paper, deciding on one mental image might guide you in my discussion. In that way, you have some sort of vague idea of what they could be. For instance, you can view them as possibilities if you are sceptical to imagining them as an entire armada of worlds.

In any case, their ontological status is, however, not of direct interest for what I will be doing in this paper. I will, therefore, leave their metaphysical existence for another author to discuss.

However, the concept of possible worlds is crucial for the theory, as I will show in the following paragraph.

Let me now show how possible worlds would serve in this semantic theory. Expressing things with sentences is something that we do all the time, whether in writing or speaking or any other form. We often make claims about the world, about ourselves and others, about abstract objects and words and so on. The question is what do we mean by sentences such as “the grass is green” or “Bruce Wayne is Batman”? As mentioned, this is a problem that a theory of semantics wants to solve. Clearly, these words, scribbles on a piece of paper or utterances, have a special connection to the world that gives them meaning. According to Stalnaker’s PWS, these sentences have meaning because they express propositions. Naturally, then, is the question: what is a proposition? PWS claim that propositions are unstructured in the sense that they lack components similar to what sentences have. That is, sentences have words and these words might be structured in a very specific way. Propositions do not have these components, instead, Stalnaker defines them as only having a logical structure. Therefore, they do not have an equivalent sort of grammatical structure with components like what sentences have (Stalnaker 1984, 23). The specific definition of a proposition according to Stalnaker is as follows:

a proposition is a function from possible worlds into truth values. (Stalnaker 1984, 2)

(6)

Let us look at this in detail, since there is at least one word that is in need of further explanation - namely, a function. Stalnaker does not have a special use for this notion, he uses it in an ordinary way, however, it can be good to explain its place in his definition. A function can be thought as mapping each element of one set to an element of another set. A proposition, according to Stalnaker, maps each element of the set of possible worlds to an element of the set of truth values.

For example, the function which is the content expressed by “the grass is green” maps each possible world to a truth value - which is either True or False. It maps a possible world to True if and only if the grass is green in that world, and it maps a possible world to False if and only if the grass is not green in that world. The content of the sentence is the proposition, which in turn is a function from possible worlds to truth values. In PWS, truth values are only True or False. The content expressed by “the grass is green”, just is this function which maps any given possible world to True or False, depending on whether the grass is green in that world. It is now clear that according to PWS, the content expressed by sentences, which is a proposition, is determined by a range of truth values in possible worlds. Thus, this is how PWS gives content to propositions and moreover making sense of what we are saying with our sentences.

PWS, as described here, can be seen as rather intuitive and simple. In my next section, I will discuss why one might favour the view over any other semantic theory.

2.1 Why Possible Worlds Semantics?

Before going any further into the analysis of Possible Worlds Semantics, I will explain why Stalnaker, and perhaps others, believes that this view is attractive.

There are at least two features of the view that Stalnaker deems to be reasons for why we should adopt it. Let me discuss these one at a time, beginning with the feature I will call the demystification feature.

The demystification feature tells us that content is not this overly complex array of senses.

From a naturalist point of view, this sounds very strange. Instead, PWS allows us to make a more simple and straightforward view of what content is. This is because the account fits seemingly well with the intuitions we have about content, that we talk about states of the world or possible states of the world, for example. For Stalnaker, propositions are mainly ways of dividing up. Since propositions are defined as a function from possible worlds into truth-values, it thereby avoids problems that come with trying to define propositions and contents as reflecting the structures of linguistic expressions, such as the apparent difficulty in making a notion like the Fregean sense intelligible. The worry for Stalnaker is mostly that a proposition understood by these linguistic

(7)

measures is difficult to include in a naturalist order of the world, something that I will also develop more in the next paragraph. The simplicity for the account can be acknowledged to how PWS makes a proposition to be something that seems ontologically simple and clearer than the other ways of interpreting them. Instead of creating specific notions that describe certain states, it makes use of how we understand the world around us were the world as we take it to be. Because of this, PWS gives us a good and simple answer to what content is. Namely, the content of a sentence is a proposition determined by a function of possible worlds to truth values.

This leads us on to the next feature of the view, which is primarily a solution to the problem of intentionality. The problem of intentionality is essentially a problem of representation. As rational agents, we have the capacity of representing things that are out there in the world with pictures, names or even utterances. Our mental representations can provide us with ways of communicating with each other without being in any direct contact with the thing talked about. This leaves the problem being how this intentionality, or representation, can fit into a naturalistic view of the world (Stalnaker 1984, 6). Seeing as this motivation is of importance to the view in general, I will look at it in greater detail than the former.

Stalnaker develops an account of mental representation that supposedly entails the success of a coarse-grained account of semantics. The idea of a coarse-grained account of semantics is, simply put, that propositions do not need to be individuated very finely, what seems to be a cluster of different is a single proposition. The view that Stalnaker develops entails this coarse-grainedness is the causal-pragmatic view of mental representation, which he claims solves the problem of intentionality; the core problem sought to be solved by an account of mental representation. It is in addition to this that he argues further for PWS. I will discuss how Stalnaker thinks that the causal-pragmatist solves the problem of intentionality, and further how it entails PWS.

I previously mentioned that Stalnaker wants a semantic theory to fit into a naturalistic view of the world. He also believes that the same goes for a theory of mental representation. Stalnaker’s motivation for a naturalistic view is that human beings, as part of the natural order, are to be explained by just the same measures used to explain any other natural object or natural system.

Natural systems, objects and relations in between them should be explained by each other in some law-like or causal way. Naturally then, the solution needs to have this in mind too. Without leading too astray of the subject, I will now demonstrate how the causal-pragmatist view allegedly solves the problem of intentionality.

Stalnaker offers the causal side of the response to the problem. This is based on the idea that mental content is fundamental and prior to language, and that we should use this to explain the intentionality of language. In bridging the gap between these mental representations and the

(8)

external world, Stalnaker lists some examples of what he calls indication relations. An indication is a way of noting how an agent responds to the environment around it. One of these examples brought up being how a thermostat behaves in the different temperatures in its environment. If the temperature is above or below a certain degree, the mercury in the thermostat would react and cause the thermostat to measure a certain degree in accordance with its surrounding, thus indicating how warm or cold it is in the vicinity of the thermostat. Another example might be that when a tree has 78 rings in its trunk, then that would indicate that it has been growing for approximately that many years. And so, the indication relation is that between an agent and its environment. This can be applied to persons as well as objects in nature. For example, if a person believes in the proposition p, it is because the persons belief in p indicates that p is true of the environment. Either it indicates p because p is the case, or something entails that p. Stalnaker thus concludes that indication is a fully acceptable notion in a naturalistic order of things (Stalnaker 1984, 13-14).

Stalnaker further develops the causal side. The indication relation between agent and proposition needs to be spelt out in more precise causal terms than previously described. As shown, the causal part says that belief and mental representation is caused by the environment or speech acts that surround us. Belief is both a forwards and a backwards-looking internal state, making it similar to the only backwards-looking indication relation mentioned earlier. It is forwards-looking by its connection with the action, that is to say, a belief is what causes us to act in certain ways. Belief is backwards-looking as well since it is partly defined in what causes the belief to be had in the first place. These forwards and backwards-looking states mean that we are in a certain relation with our environment and beliefs as a consequence of former beliefs and actions. Just as the environment influences us in the way that it causes us to have certain beliefs, our actions can have further consequences on our surroundings. And, because of this causal connection to the world and with action, it would mean that belief has determinate content since it is closely connected with desire to bring about certain things that align with our beliefs (Stalnaker 1984, 19). Because of the relations that belief has with action and desire, belief has a functional role when it comes to distinguishing between different outcomes. The functional role it has is to bring about actions that would satisfy these desires. For example, the belief that there is water in the glass in front of me would guide my actions to fulfil my desire to drink some water. What is needed is just the content of the belief necessary to differentiate between the outcomes available to me. The differentiation process, so to speak, is what gives the account its pragmatic side.

To summarise, the view gets the causal side from the notion of indication and the pragmatic side from its functional use of deciding between possibilities. This leaves us with the

(9)

causal-pragmatic view, which entails a coarse-grained account of semantics that makes use of these different possibilities. There are two reasons why Stalnaker believes that the causal-pragmatic account would entail a coarse-grained view. First, because of his indication theory of belief, if an agent stands in a certain relation with proposition p and it is, in turn, equivalent to the proposition q, then the agent would be in the same relation to the proposition that q (Stalnaker 1984, 24). In other words, the conditions for beliefs are coarse-grained. The second reason is because of belief’s strong connections with action, the only thing that is important for content is to be able to differentiate between different possibilities (Stalnaker 1984, 23). In this way, content does only have to be just enough fine cut for the agent to be able to take action.

These are adequate reasons for us to adopt such a view, at least according to Stalnaker. It adheres well to our intuitions about how we use our language. And, if we want our semantic theory to ascribe to naturalist reason, the causal-pragmatic account solves the problem of intentionality and thereto leads us towards a coarse-grained theory of content such as PWS. However, PWS is far from perfect and even though these features are what makes the theory attractive, it is also here some of the problems with the theory emerge. In my next section, I will begin looking at the problems that PWS faces.

(10)

3. Problems with Possible World Semantics

Two problems are often raised when it comes to PWS. One is a problem of belief ascriptions and another about problems of necessary truths. Moreover, these problems can together bring further trouble when you introduce belief ascriptions containing necessary truths or falsehoods. However, because of this, these problems are hard to make a proper distinction to where one of them ends and the other one begins. I will begin this section with the problem of necessary truth equivalence, and from there move on to the problem of belief ascriptions.

The problem of necessary truths is a problem concerning how some sentences expressing necessary truths seem to differ in meaning while having the same truth-value in all possible worlds.

One example might be that of sentences like “2+2=4” and that “there is an infinite amount of primes”. These two sentences express propositions that are true in all possible world. This means that the proposition would map the same possible worlds to true. So, if propositions are functions from possible worlds to truth-values, then the propositions would have the same content. In other words, the two sentences express the same proposition. But it seems that this cannot be right, because there seems to be a difference in content between these two sentences, and not only in their linguistic form. The sentence that “there is an infinite amount of primes” seems to say a lot more about many things rather than what the sentence “2+2=4” says. “2+2=4” says something about a specific mathematical case, in which the numbers stand in a particular relation with each other. Of course, this sentence can be used in many ways. For example, if a young child were to utter these words we might react with being proud and supportive of this mathematical claim and this might change what we think of the sentence and its content. But apart from speaker-relativity, this sentence does not seem to have as much, say, impact as “there is an infinite amount of primes”.

The sentence about primes tells us that there are these things called primes and there is an infinite amount of them. It makes a more general claim about mathematics, a claim that can apply to many mathematical situations. So, in one sense, this sentence might be more useful, or carry more information than the sentence “2+2=4”. Most people understand that 2+2=4, they see the connection between the numbers and symbols that link them together. The sentence about primes is not as obvious. In this way, the sentence “there is an infinite amount of primes” might be more informative and therefore tell us more than the simple “2+2=4”. These sentences are different and, looking closer, it seems like they at least intuitively would express different propositions and therefore differ in meaning. It is thus natural to assume that it is something more to content than being a function from possible worlds into truth-values. This becomes even more clear when you combine this objection with belief ascriptions.

(11)

Adding to the problem mentioned above, we have the problem of belief ascriptions. This is partly conjoined with the problem stated above. When someone believes a necessary truth or falsehood, they would also believe any of its necessary consequences. Or even worse, if you believe any proposition at all, you are dedicated to also believe its necessary consequences. This is since, if they have the same truth-value in all possible worlds, they have the same content. So, for example, this would mean that if you believe in 2+2=4 it would mean that you would believe any of its necessary consequences, perhaps that there is an infinite amount of primes or any other mathematical truth. This seems odd. We should be able to think about plenty of scenarios when someone would willingly ascribe the belief to someone who has said “I believe that 2+2=4” but would be hesitant to ascribe the belief of the sentence that “there is an infinite amount of primes”.

PWS would entail that since these sentences express the same necessary true proposition, then it is necessarily so that you also believe the other sentence. However, a lot of people, for example, believe that 2+2=4, and can easily understand why it is true through simple rules of mathematics.

However, the claim that “there is an infinite amount of primes” is not as easy to perceive as something obviously true for everyone. Therefore, it makes it more difficult to ascribe to anyone that knows that 2+2=4, that they also necessarily know that “there is an infinite amount of primes”.

These are some of the consequences of a coarse-grained account such as Stalnaker’s PWS.

It runs into trouble with necessary equivalent truths. Furthermore, it becomes especially troubling in combination with belief ascriptions. In my next section, I will present what Stalnaker has to say about the problems mentioned and discuss the solutions he provides for them.

3.1 Stalnaker’s response - Belief ascriptions

In the following sections, I will present Stalnaker’s responses to the problems I have just discussed.

I will mainly focus on his solution to the problem of necessary equivalence since this is where I believe the core problem is. Before getting to that, I will show the solution Stalnaker provides to the problem of belief ascriptions.

When it comes to the problem of belief ascriptions, Stalnaker offers a solution for PWS.

The example he gives is that of “O’Leary believes that Hesperus is Mars”, which expresses a proposition (that O’Leary believes that Hesperus is Mars), ascribing O’Leary a belief in a proposition that “our semantic theory” tells us is a necessary falsehood (Stalnaker 1999, 124). But this does not seem to make sense according to Stalnaker. He thinks that we could easily imagine a situation where a sentence like “O’Leary believes that Hesperus is Mars” is true and make

(12)

O’Leary’s belief to not be necessarily false. But, how can a sentence like “O’Leary believes that Hesperus is Mars” be a necessary falsehood? Stalnaker tells us to imagine a possible world in which Mars maybe acts in another way and O’Leary’s belief is not a false one. Perhaps it could be a possible world in which Mars has switched places with Venus in some kind of astronomical event so that we call the planet Venus “Mars”. In turn, this is what could be making O’Leary believe that it is Hesperus in the shape of Mars and not Venus that is visible. Because instead of Venus, Mars has been called Hesperus, and so the celestial body that appears in the evening has been called by that very name with that planet as the referent. The name has since travelled via a causal chain from the one who named it Hesperus, to present day and O’Leary hearing this name in relation to this planet. And so, O’Leary believes this simply because in that possible world: Mars is called

“Hesperus”. What we end up with is the actual world, where the sentence “Hesperus is Mars” is false, and another possible world where this sentence is true. O’Leary is then speaking as if he is in the world in which “Hesperus is Mars" is true, rather than the other one. This is the content that O’Leary wants to mediate, and furthermore, this is the belief being ascribed to O’Leary - that the sentence “Hesperus is Mars” is true in the actual world. This seems like it could be a good solution, but it needs some more substance for it to fully make sense.

Stalnaker introduces his notion of propositional concepts in order to explain how to describe assertions and the context these are uttered in. Just as propositions themselves are functions from possible worlds into truth-values, propositional concepts are functions from possible worlds into propositions. Think about them as propositions working two-dimensionally.

Propositional concepts practical use is founded on two facts. First, acts of assertion are performed in a context in which certain information is taken for granted as common background knowledge.

Second, among these pieces of background knowledge or presuppositions, will be the proposition that the act of assertion itself is actually taking place (Stalnaker 1999, 121). The second fact tells us that in every possible world where the background information, presuppositions or something of the sort, is compatible with the world in which the assertion is taking place, it is also taking place in those worlds. In this case, that would mean that “O’Leary believes that Hesperus is Mars” is an assertion that is also part of the background knowledge between these possible worlds. So, let us call the actual world i and the world that O’Leary think is actual j. In the actual world i, the sentence

“Hesperus is Mars” expresses a necessary falsehood, as we have noted. This would, in turn, mean that it is also false in the possible world j. But, let us imagine the world similarly to how O’Leary sees it. In the world that O’Leary takes to be actual, the sentence “Hesperus is Mars” expresses a truth. That is, it expresses a proposition that maps that world to True. In that possible world, it could be the case that “Hesperus” is just another name for Mars and so the assertion is accurate.

(13)

In world j, it could be the case that was previously described, Mars has for some reason switched places with Venus and Venus is called “Mars”. The planet we call “Hesperus” is therefore rightfully called “Mars”. In this case, it would be true yet again. That would give us a table that looks something like this:

i j

i F F

j T T

In this table, the columns are ways in which the world can be. As for “Hesperus is Mars” it is necessarily so that “Hesperus” and “Mars” are distinct, and so the sentence “Hesperus is Mars” is false in the actual world i and the possible world j. The rows, however, are ways in which the semantic rules could have been different. So, for example, the name for “Mars” in world j denotes Venus, and thus the proposition expressed by “Hesperus is Mars” is true (Stalnaker 1999, 124).

Stalnaker says that what we are looking for is not the thing expressed in the horizontal line, but more so the diagonal one. This gives us a way in which “Hesperus is Mars” is contingent, and so the sentence O’Leary says does express a proposition that is not necessarily false if the world were as he believes it to be. Once again, this fits well with our intuitions about what we are saying.

O’Leary does not express a necessarily false proposition by uttering the sentence “Hesperus is Mars”. He is, in fact, expressing a contingent proposition that, were the world the way O’Leary takes it to be, then the sentence “Hesperus is Mars” would be true, thus allowing the content to be what O’Leary means it to be.

This was the response given by Stalnaker for the problem of belief ascriptions. The other problem that Stalnaker responds to is that of necessary equivalence, which I will present in my next section.

3.2 Stalnaker’s response - Necessary Equivalence

Stalnaker's response to the necessary equivalence problem is about the differences between a sentence and a proposition. The proponents of the linguistic picture, that Stalnaker sketches in contrast to his pragmatic picture thinks that propositions and sentences are constituted by the same or similar things and also in similar ways. In other words, sentences and propositions have the same structure and therefore they should behave in the same ways. Stalnaker does not agree

(14)

with this. He argues that there are at least three ways in which they differ. Firstly, recall that PWS claim that propositions lack structure and they do not have constituents either. Therefore, they do not behave in the same way as sentences do. Second, since propositions are determined via relations to possible worlds, the identity relations for a proposition are relative to a set of possible worlds. The third significant difference is that, since propositions are nothing like sentences in the way that they don’t have components, beliefs do not have to be thought of as a collection of items similar to sentences. This means that having beliefs are not limited to language-users: other sentient beings can have beliefs about the world. From this, we can easily conclude that propositions differ from sentences (Stalnaker 1984, 71). Now that we have settled some differences between propositions and sentences we can take the next step in arguing for how the necessary equivalence problem does not disturb PWS.

According to PWS, it follows that if a person believes that p, then if p is necessarily equivalent to q, the person also believes that q. Note that p and q are propositions here and not sentences. Stalnaker says that “p is equivalent to q” is a way of saying that there is a relation between these expressions. “P” and “q” are therefore expressions that denote the same proposition which is p, but the expression “p is equivalent to q” is only referring to the relationship standing in between the two. Illustrating with an example, let us exchange p for our known example “2+2=4”, and q for “there is an infinite amount of primes”. The necessary equivalence of these two propositions and the consequence according to PWS would mean that if this person believes that 2+2=4, they would also believe that there is an infinite amount of primes. But as shown by the problem previously stated in section 3, it is possible to believe one and not the other. Stalnaker holds that this is a matter of not seeing the relation that holds between them. The person believing that “2+2=4” simply fails to see the equivalence relation to “there is an infinite amount of primes”.

This is because taken as sentences they do not seem to express the same proposition. The two sentences are two ways of expressing the same proposition. Meaning that the agent can only recognise one of the sentences as expressing that very proposition. So there is, according to Stalnaker, a gap between a proposition and how this proposition is expressed by a sentence (Stalnaker 1984, 72). This gap of ignorance makes it possible to not believe a sentence expressing the consequence of a necessary truth, something that was a major issue for PWS.

This is a nice way of avoiding the problem, but not everyone is entirely satisfied with this.

In this section, I discussed Stalnaker’s responses to the two problems I have presented. In the coming section, I will further argue how these are not sufficient responses and that they encounter additional problems.

(15)

3.3 Further problems

In this section, I will sharpen the criticisms with the help of other philosophers who do not believe the solutions that Stalnaker provides are satisfactory. I will use the works of Jason Stanley (2010) and Jeff Speaks (2006) in my discussion. I will now present and evaluate the objections they point out.

One of the main problems facing PWS, I argue, is about necessary truth equivalence. As I showed in the example stated in the section above sentences such as “2+2=4” or “there is an infinite amount of primes” have the same content in the actual world, since they express the same true proposition in every possible world. This is what the coarse-grainedness of the view involves, and I will investigate whether it is fruitful for a theory of semantics to be coarse-grained or if problems like this hinder it from being successful. I will attack this from two directions. First, I will discredit how the causal-pragmatic view would entail PWS. Seeing as this is one of Stalnaker’s main motivations for a coarse-grained theory of semantics, it is important to question exactly how this was accomplished. Second, I will assess how Stalnaker’s response to the necessary equivalence problem does not seem to solve it at all.

Stalnaker believes that PWS, or at least a coarse-grained account of semantics, is a sensible entailment originating from the causal-pragmatic view. As mentioned in section 2.1, this causal- pragmatic view has its motivation in the explanation of things in naturalistic terms. Jason Stanley argues in his paper that the sensible entailment of a coarse-grained view from the causal-pragmatic account is not the case. In fact, Stanley argues, the causal-pragmatic view should lead us to a more fine-grained view of contents. At least, that is what the pragmatic side of the view would mean.

Stalnaker’s pragmatic account tells us that what it is to give content to belief is to distinguish between different possibilities in which one’s action is directed to fulfilling the desire connected with the belief. For example, my desire to drink water can be satisfied by my belief that it is water in the glass in front of me, guiding me to take the action of drinking it. The belief would distinguish between different possibilities such as me deciding to take the action of drinking if there is water in the glass in front of me. Another possibility such as the glass being empty, or filled with something else, and me not picking up the glass to drink from it. Recall that PWS claims that content is determined by truth-values in relation to possible worlds. In the case of necessary equivalence, PWS hold that the sentences “there is water in the glass” and “there is H2O in the glass” express the same proposition since water is necessarily equivalent to H2O. Suppose that I do not know that H2O is the chemical formula for water and, remaining oblivious to their equivalence, I decide not to drink after my friend tells me; “drink from the glass, there is H2O in it”. After all, I wanted to drink water and not this to me unknown liquid called H2O. But the

(16)

content of the belief, according to PWS, should be the same. In the example, we can see that the pragmatic side of the causal-pragmatic account would entail an account of content that individuates content more finely. There must be something more to the content of my beliefs since in one situation I decide to drink the water and another refrain from it. If my actions are decided by the beliefs I hold, PWS cannot differentiate beliefs finely enough. Stanley believes that what the pragmatic account is actually telling us is that content needs to be individuated more finely than what PWS is telling us (Stanley 2010, 106).

So, the motivation for Stalnaker’s PWS was that coarse-grainedness was entailed by the causal-pragmatic view. On a closer look, it seems like it does not lead us towards a coarse-grained account, but rather it might motivate an account that is more fine-grained from the perspective of the pragmatic side. In addition to this, the causal side of the account also runs into trouble.

The causal side is founded on the indication relation, as I explained in section 2.1. This simple theory of causality is sensitive to the disjunction problem. For example, the causal theory tells us that if an agent believes that p, it is because the belief of the agent is indicating that p is the case.

Consider that p is not correct, it is in fact q that is the case. This would mean that the agent formed the belief that p because q is the case, and that the agent is in this state as a result of either p or q.

This is what seems to follow if the causal view of belief is correct, but it seems that it is clearly not right. Instead of having a false belief that p, the agent holds the true disjunctive belief that p or q (Speaks 2006, 439). The disjunction problem is thus provoked by the claim that a causal theory of belief, such as this one, cannot explain the chances of agents having false beliefs. In short, it is called the disjunction problem because instead of agents having false beliefs, it is mistakenly seen as agents having true disjunctive beliefs.

Stalnaker has a response to this problem. He introduces optimal conditions, meaning that the agent would have the belief that p if they were in these optimal conditions. Optimal conditions are what they sound like, basically, it includes an agent having a perfectly functioning cognitive system relative to that agent. In other words, no illusions, no heavy drugs that could alter the agents' grasp of reality, not being deceived or something of the sort. This then allows an agent to have beliefs such as the ones earlier mentioned, since were the agent in optimal conditions, then she would have believed that q. Speaks argues that the introduction of optimal conditions generates a different problem. Optimal conditions, as taken together with the causal-pragmatic account, presuppose the agent to be in a state where there are no cognitive errors. Furthermore, for the pragmatic side of the account, optimal conditions presuppose that the agent would act in such a way that she would act, were she is in a world in which all of her beliefs are true (Speaks 2006, 17fn). Now, Speaks imagines a case where an agent a is in a belief state b because of p being the

(17)

case. The indication of it being the case that p is since a is in optimal condition. This means that a only believes p, if she also believes p in conjunction with the fact that she is in optimal condition, since in order for her to believe that it indeed is p that is the case, she must know that she is in optimal condition. So, the agent is in belief state b because of the fact that p together with the conjunction of p and the agent being in optimal condition (Speaks 2006, 443). The agents' belief state would indicate that p is the case if and only if it indicates that p is the case and that she is in optimal conditions. But then, if a belief state is just the belief in whatever it might be that it indicates, then believing that p is the case means believing that p is the case and one is in optimal conditions. This cannot be the case. Surely, you can have beliefs whilst having false beliefs, that is to say, you can have beliefs without being in optimal condition.

Of course, the motivation for PWS might not be what is making it interesting for Stalnaker in pursuing it. Coarse-grainedness can be motivated in other ways than by the causal-pragmatic account, I am sure, but weakening one of the stronger motivations is arguably one way in weakening the account’s credibility overall. To further strengthen my claim that if PWS wants to treat propositions as being coarse-grained, it is not sufficient as a semantic theory on its own. I will investigate one of Stalnaker’s further responses to the necessary equivalence problem.

3.4 Necessary Equivalence problem: Solved or Unsolved?

After showing how one of Stalnaker’s motivations for a coarse-grained account of semantics fails, I will now press an issue at hand for such an account. As my previous section concluded, there is are reasons to believe that the causal-pragmatic account should entail a more finely individuated account of contents. In this section, I will discuss whether the necessary equivalence problem is solved or if it remains an issue for PWS.

Let me shortly summarise the discussions I have had so far. In solving the necessary equivalence problem, Stalnaker employs the diagonal propositions to generate a contingent proposition suitable to what the agent might be saying when expressing necessary falsehoods. I showed that what O’Leary was saying with his sentence “Hesperus is Mars” was a contingent proposition. Stalnaker believes that beliefs are closed under necessary consequence, which is because of his indication theory of belief. So, as mentioned, the solution Stalnaker provides is that sometimes the agent believes in a meta-linguistic proposition she expresses using the sentence, rather than the necessary true proposition the sentence semantically expresses.

Speaks further argues that the appeal to the meta-linguistic proposition that Stalnaker provides does not manage to fully solve the problem. Let me illustrate with the examples I gave in section 3, the necessary true claims that 2+2=4 and that there is an infinite amount of primes.

(18)

According to Stalnaker, when someone believes that the sentence “2+2=4” is true, they need not also believe that proposition expressed by the sentence “there is an infinite amount of primes” is true. This is since, taken as sentences, the agent does not realise that the sentence “there is an infinite amount of primes” is identical to the proposition that is expressed by the sentence

“2+2=4”. Speaks then points to that it follows that when an agent understands “p”, they believe the proposition expressed by “‘p’ means that p” (Speaks 2006, 449). Using our example, it would mean that when the agent understands the sentence “2+2=4”, they believe that “2+2=4” means that two plus two equals four. However, seeing as “there is an infinite amount of primes” expresses the necessary true proposition just as “2+2=4”, and since everyone who has any beliefs believes in the necessary true proposition, then the agent does, in fact, believe the proposition expressed by the sentence “there is an infinite amount of primes”. This means that if an agent believes a) the necessary true proposition, and believes that b) the sentence “there is an infinite amount of primes”

expresses the proposition that there is an infinite amount of primes, then it entails that the agent believes that the sentence “there is an infinite amount of primes” expresses the necessary true proposition. The agent then believes that the meta-linguistic proposition is true and she believes the necessary true proposition. Given that she believes that the sentence “there is an infinite amount of primes” means the necessary true proposition, and she believes the necessary true proposition, this entails that she believes that the sentence expresses a truth. This would mean that the agent does believe that the sentence, “there is an infinite amount of primes”, is true, which was something Stalnaker set out to avoid. Thus, the problem is not solved at all, so it seems.

Stanley defends on Stalnaker, preventing the objection presented by Speaks. The problem Speaks poses is that Stalnaker’s view would entail that the agent actually believes the sentence which expresses the necessary true proposition to be true, even though there might be cases in which the agent believes that a sentence expressing the necessary true proposition is false. In fact, Stanley argues, this is exactly what Stalnaker denies (Stanley 2010, 102 14fn). Again, the agent does not realise that the sentence in question expresses the necessary true proposition. Even if the agent believes in the necessary true proposition, this does not mean that the agent believes in the sentence that expresses it. Stanley’s point is that all it takes for an agent to understand the sentence

“p” is to believe that the sentence “‘p’ means that p” is true (Stanley 2010, 101-102). Or, as Stalnaker would put it, the agent only needs to believe that the diagonal proposition expressed by the sentence “‘p’ means that p” is true in the actual world. The agent therefore only takes the sentence

“‘there is an infinite amount of primes’ means that there is an infinite amount of primes” to be true in that context, relative to that agent. What the agent understands is, at most, the diagonal

(19)

proposition expressed by the meta-linguistic proposition and not the meta-linguistic proposition itself (Stanley 2010, 102 14fn).

This would mean that Speaks’ objection does not hold, after all, since Speaks’ argument builds on the fact that it is the meta-linguistic proposition that the agent does in fact grasp, and not the diagonal proposition expressed by the meta-linguistic proposition relative to the agent. In my next section, I will investigate how the defence of Stalnaker instead gives rise to a slightly different problem.

3.5 Believing propositions and understanding sentences

Nevertheless, I think, there is still some issue with the response given, but it is now apparent in a different form. The worry is, would it really be sufficient to believe in the contingent diagonal proposition expressed by “‘p’ means that p”, in order to understand ‘p’? Stanley would argue that Stalnaker thinks it is enough, all you need to believe is in this diagonal proposition in order to understand what the sentence p means. In fact, Stalnaker believes that you should not need much at all. For Stalnaker, what is sufficient for an agent to understand something is to be able to know which possibilities that can be excluded from the context set of the agent. This also applies to agents with varying degrees of understanding a sentence. This is what is needed for you to be able to grasp what proposition is expressed, given that the standard semantic rules are accepted (Stalnaker 2010, 148). That is, all you need to be able to understand to grasp the proposition is the semantic value of the words in relation to our world. For example, I could tell you “there is a blue dog outside of matikum”, and you would understand what I am saying in the sense that you could grasp what proposition I might be expressing. However, if you do not know what matikum is your context set would be different from when you know what it is, but it would still be possible for you to exclude possibilities. In one possible world, perhaps “matikum” would be the local museum, and in another, it would be the train station. You would then proceed to exclude all of the possibilities where it is not a blue dog outside of that place. Eventually, you grasp the proposition that the sentence expresses, that is by excluding possibilities from the context set available.

Just believing in a contingent diagonal proposition, “‘there is an infinite amount of primes’

means that there is an infinite amount of primes”, might necessitate you also believe in the necessary true proposition, since Stalnaker argues that everyone who has any beliefs at all does this. However, would it mean that you also understand p, a sentence expressing the necessary true proposition, as you would understand a sentence like “there is a blue dog outside of matikum”?

When it comes to a sentence expressing the necessary true proposition, such as “‘there is an infinite amount of primes” you understand what it means in ways which are described above.

(20)

You grasp the semantic values of the words, allowing you to divide between possibilities. If you, as described in Stalnaker’s case, are ignorant of the fact that this particular sentence expresses the necessary true proposition, you would believe in a diagonal proposition conveyed by the meta- linguistic sentence and that it is true in the actual world. So for example, an agent who is ignorant would believe in the diagonal proposition expressed by “‘there is an infinite amount of primes’

means that there is an infinite amount of primes”. I think both Speaks and Stanley are wrong about understanding, as it seems to me that even believing that a sentence expresses the necessary true proposition is not sufficient for understanding it. When it comes to “‘p’ means that p”, and p expresses the necessary proposition, believing that the sentence ‘p’ is one sentence that expresses the necessary proposition is, I argue, not enough to understand the sentence ‘p’. There is something missing between the step of believing a meta-linguistic proposition to be true, or the diagonal proposition expressed by it to be true, and understanding a sentence.

Stalnaker’s claim is that to understand is to be able to differentiate between possibilities in the given context set, given that the standard semantic rules are accepted. However, as Stanley argues, it is not correct to say that the agent understands ‘p’ as the necessary true proposition, but rather the agent believes the diagonal proposition expressed by “‘p’ means that p”. In other words, the agent believes that that sentence, as it is actually used, express a proposition that is mapping the actual world to true. But it is odd to say that just because you believe a contingent diagonalisation of a sentence “‘p’ means that p”, in which the sentence “p” is actually an expression of a necessary truth, it does not mean that you understand the expression of the necessary true proposition as is. For example, I believe that the sentence “there is an infinite amount of primes”

is true, and I also believe that it is a necessary truth. I believe this for no other reason than the fact that I have been told by people I trust that this sentence expresses a necessary truth. But I do not, because of my limited knowledge in mathematics, understand how this sentence would relate to the necessary true proposition. You could say, I only possess the knowledge of the diagonal proposition being true, and do not, therefore, understand the sentence in its whole. Believing in the diagonal proposition expressed by a sentence means that I believe the proposition that the sentence “there is an infinite amount of primes”, as the sentence is used in the actual world, expresses a proposition that maps the actual world to true. In addition, I believe that the sentence, as it is used in the actual world, expresses a proposition that maps all worlds to true. In other words, seeing as it maps all the worlds to true, the sentence expresses the necessary true proposition. I believe the sentence and the proposition it expresses, but I do not know exactly why it expresses a necessary truth, or barely even why it would not be a contingent truth, so it is not clear to say that I understand the sentence in virtue of me believing in the necessary true

(21)

proposition. Furthermore, if it is correct that believing that the sentence expresses the necessary true proposition is not sufficient for understanding it, then it would be clear that “‘there is an infinite amount of primes’ means that there is an infinite amount of primes” is not sufficient either in order to understand it. In other words, it is not sufficient to believe in the diagonal proposition expressed by the sentence for me to be able to understand the sentence. This is not sufficient since it would mean that just believing in a diagonal proposition expressed by a sentence would make me understand the sentence, no matter how the sentence in question would be formulated. It seems to me then, that I do not fully understand the sentence. Something is missing from Stanley’s version of Stalnaker’s notion of understanding, and also from Speaks’ notion of understanding. I do, after all, believe that the sentence is a necessary truth, since it maps all the possible worlds to true, but I also do not know that it is a necessary truth. I would say that I do not know it since, for example, I do not know of any mathematical proof that concludes it to be a necessary truth.

However, I recognise that this is a controversial claim, and arguing for it would take me away from the main line here. It is in between these things that there is something missing. The only understanding I have of the sentence p is the contingent diagonalisation one, which would be far from sufficient from understanding p. For example, take a meta-linguistic sentence like “‘det finns oändligt många primtal’ means that there is an infinite amount of primes”. According to Stanley’s version of Stalnaker's notion of understanding, this would mean that an English speaker without any knowledge about Swedish could say that they believe the meta-linguistic sentence “‘det finns oändligt många primtal’ means there is an infinite amount of primes” is true. But would it be fair to say that he understands “det finns oändligt många primtal”? For all he knows, he could be tricked by a friend into believing that the meta-linguistic proposition is true. What if the sentence

“det finns oändligt många primtal” meant “there is no such thing as a prime”, and the meta- linguistic proposition that the agent believes in is actually false? Would this sort of trick be possible if he understood the sentence? If he understood the sentence, using a notion of understanding that is aligned with our intuitive connotations with the word, he would not believe a necessary falsehood to be true. Or even still, could the Englishman explain to someone else that the sentence

“det finns oändligt många primtal” is Swedish for the sentence “there is an infinite amount of primes”? Probably not, because all he believes is the meta-linguistic proposition, and not the sentence expressing it. So, it would not make any sense, intuitively, to say that he understood the sentence, seeing as what he believed to be true was a meta-linguistic proposition about a sentence.

To make it more convincing, there could be two languages that are unknown to the speaker. That would mean that a person who only knows and understands English, would understand a diagonal proposition expressed by “‘det finns oändligt många primtal’ veut dire qu’il

(22)

y a une infinité de nombres premiers”. Perhaps because he was told by a good friend that this sentence, as it is used with its actual meanings, is true. This seems strange. How could he believe that this is true? Seeing as he does not understand the Swedish sentence “det finns oändligt många primtal”, just as he does not understand what the French sentence that is translating the Swedish one would mean. Even if he trusted his friend very much, it would at least mean that he only believes in the friend and does not understand what it actually means. But according to Stalnaker, it would be perfectly reasonable for someone to understand the Swedish sentence, even though it is in a to the agent unknown language, only by believing the diagonal proposition it expresses, also in a to the agent unknown language. This is something that I think is highly counter-intuitive. So, the suggestions of understanding that Stanley makes on Stalnaker’s behalf are too weak. It seems to be something more to be required for understanding.

What then, would it take for you to understand the sentence ‘p’? Perhaps it would require you to know other sentences of the same sort and to integrate the beliefs you have about these sentences. For example, if an agent wants to understand the sentence “there is an infinite amount of primes”, she must integrate beliefs that she has about sentences containing primes, such as “a prime is a natural number greater than 1” or “a prime can only be divided by a positive number that is 1 and the number itself” and so forth. If you understand these sentences about primes, you must see them mentally as being linked together since they are about similar things. In addition to this, since the sentence “there is an infinite amount of primes” actually expresses a necessary truth, integrating beliefs about sentences expressing the necessary truth might aid the agent in seeing the semantic pattern they have in common. What they have in common might be something that links them together in this mental way. However, if their content is just the necessary truth or falsehood, there is nothing to link them in particular to one another. For example, what would make “a prime is a natural number greater than 1” different from the sentence that “there is an infinite amount of primes”, if both of them are linked to any other belief in mathematical truths or falsehoods? It seems like, if you should be able to link beliefs about the contents of sentences together, it should be individuated more finely than what Stalnaker argues that contents are. So, perhaps, to understand a sentence is to know which proposition it semantically expresses and this is done via inquiry to other beliefs available to the agent.

But this would return us to a similar issue that Stalnaker was trying to solve, to begin with.

If a proposition is the content of a sentence, and the proposition is what the agent should be able to grasp, then the transparency between a sentence and the proposition it expresses is important.

The transparency can be understood as an agent being able to see through the sentence directly to the proposition it expresses. Furthermore, this sort of transparency is what I argue Speaks is

(23)

pointing towards when discussing the problem of necessary equivalent propositions. Seeing as Stalnaker believes it to be just one necessary true proposition, any time when you can understand a sentence that expresses a necessary truth, you will see that it is the necessary truth that is being expressed. For example, that would make you understand and believe every sentence expressing the necessary true proposition, whether it would be “2+2=4” or “there is an infinite amount of primes” since there is just one necessary true proposition. This cannot be right.

How come that even the defence with the notion of understanding end up with a similar problem that it was set out to solve? In my next and final section, I will diagnose the possible source of the problem for PWS.

3.6 Concluding remarks - Problems for a coarse-grained theory

As my previous section concluded, it seems to be a similarity between what causes the problems for the notion of understanding as well as the necessary equivalence problem. The common factor for these two cases would appear to be that they are coarse-grained, something that I have discussed in previous sections. Even though a coarse-grained account is what Stalnaker wants, and it might be the source of the strength of PWS, it is also the greatest weakness of PWS.

First, according to PWS, the way in which you understand sentences is essentially coarse- grained, since you do not need to know much in order to do so. For Stalnaker, an understanding was only a matter of knowing which possibilities an agent could exclude from a context set. As shown in my previous section, this cannot be the case. This notion of understanding originated from trying to solve the problem of necessary equivalence. Second, for PWS, propositions are coarse-grained since they are functions from possible worlds to truth-values. To be more precise, it is because it is possible for two sentences to express the same proposition, even though they might seem to be expressing two different propositions. That is to say, the proposition expressed by the sentences relates to the same set of possible worlds, and that is why it is coarse-grained.

However, this is what ended up being an issue for PWS. Namely, that an agent can believe in p but disbelieve in q, even though these propositions are equivalent. It is very clear, that a significant part of Stalnaker’s semantic theory is that PWS should be coarse-grained. One of his primary motivations, as I argued, was that the causal-pragmatic view entailed a view that is coarse-grained.

This was also something that turned out to be a misconception.

Is it possible for Stalnaker to justify PWS to be coarse-grained? Consider my discussion of the transparency of a sentence and the proposition expressed by it. It would seem like it would be complicated for Stalnaker to propose a way in which PWS can be both coarse-grained and

(24)

intelligible, while not eventually end up being tricky problems for the view similar to the ones I have discussed. Problems such as believing in one sentence that express the necessary truth, but not the other sentence also expressing the necessary truth, or understanding a sentence simply by the means of believing in the truth of the meta-linguistic proposition about the sentence. Even if it is coarse-grained in the way our beliefs guide our actions according to which possibilities we can divide, it would still be something lacking in the steps between the proposition and the information available to the agent. This was also something I discussed. For example, given that my desire is to drink water, the actions when I would express what I believe by “there H2O in the glass” versus when I would express what I believe by “there is water in the glass” could be different. Perhaps because I am not aware that H2O is the chemical formula for water then I would refrain from drinking the liquid that I believe, mistakenly so, is not water.

I mentioned briefly in section 3.2 that it in many cases seem to be a missing step between sentences and propositions. Finding out what the missing step between the sentence and the proposition it expresses is might be what could save PWS. However, it could mean that the account would have to transform into a more fine-grained theory of semantics. Exactly what this step might be is not very clear, and also not in the scope of this paper. Perhaps it could be an additional step that would serve as Frege’s sense does. A more fine-grained notion of content would be able to individuate possibilities more finely, which the pragmatic side of the account would entail.

Furthermore, it would serve a role that might block the problem of necessary equivalence. If my discussion on what it takes to understand a sentence is correct, then it seems like that too would entail a more fine-grained theory of content. It would make sense if the proposition that you grasp when understanding a sentence is not coarse-grained, as Stalnaker wants them to be, it would lead us towards a more fine-grained notion of content.

(25)

4. Conclusion

In this essay, I have presented the semantic theory called Possible Worlds Semantics and the problems facing a coarse-grained account of semantics. The purpose was to investigate if the account is successful. I have done this by introducing the view as developed by Stalnaker, also showing the main attractions one might have for the view. I then investigated the problems that PWS are facing, specifying in the problems that seem to originate from the view being coarse- grained. I evaluated the defences given by Stalnaker and concluded that they are not sufficient, since they give rise to a different set of problem. While trying to solve the problems left for a coarse-grained view, however, I gave reasons to believe that perhaps a more fine-grained theory of content is what should be had. I suggested that a way to possibly avoid these problems is by developing such a fine-grained account of semantics.

(26)

5. Bibliography

Works used

Speaks, Jeff. 2006. “Is Mental Content Prior to Linguistic Meaning?”. Noûs, Vol. 40, No 3 (September 2006): 428-467. https://www.jstor.org/stable/4093992 (acquired

2019-05-20)

Speaks, Jeff. 2018. “Theories of Meaning”. The Stanford Encyclopedia of Philosophy. (Winter 2018 Edition), Edited by: Edward N. Zalta (acquired 2019-05-24)

Stalnaker, Robert. 1984. Inquiry. Cambridge, Massachusetts: The MIT Press.

Stalnaker, Robert. 1999. Context and Content: Essays on intentionality in speech and thought. Oxford: Oxford University Press.

Stalnaker, Robert. 2010. “Responses to Stanley and Schlenker”. Philosophical Studies:

An International Journal for Philosophy in the Analytic Tradition. Vol. 151, No. 1 (October 2010): 143-157. https://www.jstor.org/stable/40856595 (acquired 2019-05-20)

Stanley, Jason. 2010. “‘Assertion’ and intentionality”. Philosophical Studies Vol. 151, No. 1:

87-113. https://doi.org/10.1007/s11098-010-9588-y (acquired 2019-05-20)

Works mentioned

Leibniz, Gottfried. 1710. Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme et l'origine du mal

With Worlds as Content: An investigation on Possible Worlds Semantics and its Problems