2.2 Contingent metaphysics



If your are not particularly interested in a short introduction to philosophy (or already know this subject) you are welcome to skip the rest of this chapter (based predominantly on a first or a second year philosophy text-books). Note that we are going to touch on possible worlds theory in this chapter and also highlight epistemological reasons for the uncertainty of our knowledge - if you are not sure what all this is about, keep reading.

A short introduction to metaphysics, given in this section, is largely based on the text-book by Loux (2006) with the occasional references to other sources. The goal is to illustrate how many “respectable” theories of real entities has been developed in science and philosophy. A feature characteristic to most of them is that we still don’t know their truth value.

Metaphysical realism

There are cats, there are dogs and there are elephants and it is not up to us to call a dog by another name – be it an elephant, or a cat, or an ant. The dog is a dog and the fact that there is such kind of species as “a dog” seems to be something out there in the nature, independent of our thoughts and desires and, hence, real. This idea underpins the venerated theory of Plato which tells us that “a dog” considered as a kind is not least real than a particular physical dog we can point a finger at. In fact, according to Plato, “a dog” is an eternal never changing entity which belongs to some metaphysical realm of forms and these forms are more real than their physical counterparts. All physical objects are just imperfect copies or instances of the ideal and eternal forms. To illustrate this point, he tells us a story about men in a dark cave chained to the ground. The only source of the light in this cave is a fire behind these men, and the only thing they can see is shadows cast on the wall by various objects in that cave. People take these shadows to be the only real stuff in that cave.

For a metaphysical realist all items in the world belong to either the class of particulars (shadows on the wall) or the class of universals (metaphysical objects that cast that shadow) and the universals are not least real than particulars. A characteristic feature of particulars is that they exemplify universals. The ball is red because this particular ball exemplifies a universal entity red. Loux defines particulars as follows “First, … they (particulars) are all things that cannot be exemplified, but they all have or exemplify many attributes. Furthermore, they are things with temporally bounded careers: they come into existence at a time, they exist for a certain stretch of time, and then they pass out of existence at a time. Accordingly, they are all contingent beings, things that exist, but whose nonexistence is possible. They are also things whose temporal careers involve alteration or change: at different times in their careers they have different and incompatible attributes. They are also things that have, at each moment in their careers, a determinate position in space; and unless they are physical simples, they have physical parts that likewise occupy a determinate region of space.”

The universals, on the other hand, do not occupy space and typically are subdivided into three categories: properties, kinds, and relations. Properties are characteristics of particular things, something that these objects possess. Kinds are described in terms of something that an object belongs to (rather than possesses). And relations are just relations between particular objects. According to another definition (Swoyer, 2008), universals (real things) are called abstract entities, or abstract objects, and comprise numbers, sets, properties, kinds, relations, propositions, and even abstract worlds. They are “atemporal, non-spatial, and acasual – i.e., they do not exist in space and time, they cannot make anything happen, nothing can affect them, and they are incapable of change. … we do not see them, feel them, taste them, or see their traces in the world around us. Still, according to a familiar metaphor of some philosophers, they exist “out there”, independent of human language and thought.” (Chris Swoyer in “Contemporary debates in Metaphysics, eds by T. Sider, J., Howthorne, D.Zimmerman Blackwell Publishing, Oxford, 404 p., 2008.)

The reader (particularly the reader with a background in natural sciences) might be surprised to learn that the idea of abstract entities while a bit old fashioned today, is far from being dismissed in philosophy. The problem is that there are arguments for and arguments against it and many philosophers take these arguments dead seriously. While not all realists share the details of the Platonic theory, most of them commit to the same basic idea. The reason for such commitment is that realists believe that their theory provides them with the resources needed to understand and explain some philosophical issues which other theoretical frameworks, they believe, struggle to handle (e.g. attribute agreement, attribution of truth to subject-predicate sentences, and abstract reference – we will talk more about these issues later in this section). As C. Swoyer puts it “when we turn to the ways philosophers actually evaluate views about abstract objects, we typically find things turning on the pluses and minuses of one view compared to those of its competitors. And a very common feature of the (putative) pluses is that they involve explanations.” (Swoyer, 2008). To be specific, let me consider briefly a few arguments for and against abstract entities.

Arguments for abstract entities
Abstract entities provide a framework where we can explain the truth of subject-predicate sentences. The reader may wonder, why would we bother, in the first place, with explaining such sentences? The answer is that this kind of sentences generalise practices of special sciences. Every special science has a specific subject of the study and is concerned with explaining the properties of that subject. Physics, for example, is about material objects, plant science is about the properties of plants, social sciences are about people and societies. The knowledge that special sciences accumulate about their respective domains often takes form of subject-predicate sentences. The task of philosophy is to generalise all these specific subjects and properties through the study of the subject-predicate sentences in general, as entities abstracted from a particular application. So, if we have a framework which explains the truth value of such sentences, such framework must have a significant advantage as compared to an alternative framework where such explanation is not quite clear.

Metaphysical realists explain the truth of the subject-predicate sentences through the referential relations established between the words in the sentence and their physical or abstract counterparts. For example, take a simple subject-predicate statement:

“This apple is red” (1)

According to metaphysical realism, for this statement to be true, (a) the subject “apple” must refer to the particular real thing - an instance of an apple, (b) the predicate red must refer to an abstract real thing called “red”, and (c) the referent of the word apple (particular object) must stay in a special relation to the referent of the word red (abstract object), and we say about that relation that this particular apple exemplifies an abstract entity “red”. In short, the above statement (1) is true in virtue of referring to the real thing (the particular apple) which exemplifies another real thing (an abstract red). Note that an abstract object “red” is not accessible directly, but only via a particular object “apple” which exemplifies the property of being “red”.

Statements which include predicates with no reference (abstract reference) are explained in a similar fashion. For example, a statement

“This man is wise” (2)

(where “wise” does not seem to refer to anything that exists in the physical world) is translated into the statement

“This man exemplifies wisdom” (3)

The term “wisdom” here points to the abstract entity “wisdom”, which exists in the realm of forms.

Abstract entities also explain the fact that different objects may have the same properties. It says that objects have the same properties, just because they exemplify the same abstract entity. If you think that the fact that different objects may have same properties is straightforward and does not require further explanation – you just do not know philosophers.

One more argument in favour of abstract entities comes from the fact that rival metaphysical theories, which do not endorse the idea of abstract entities, have their own problems in trying to build a coherent picture of metaphysics. When you weigh the theory of abstract entities against these theories, it may not be trivial to decide which theory is better.

Finally, besides these (and other not mentioned here) purely philosophical reasons, I think, many people would be inclined to believe abstract entities, just because such belief is consistent with the idea that the world is bigger than what it seems to be. To appreciate the power of this argument, consider why someone like Plato would be so much overwhelmed with this idea as to dedicate the whole life to it. What is so special in it?
I think, the key point here is that with abstract entities the world makes sense. They introduce rules, laws, and make space for sacred values. Take them out and the whole world reduces to meaningless collection of particulars.

Arguments against abstract entities
With the rise of science and empirical methods, people in general and particularly scientists became more and more suspicious about entities that no one can see, smell, or touch. You may say that same comment must apply to electron particles, we never see, smell or touch them. Yes, but … particles invisible by naked eye have very strong theoretical and experimental support - every time we turn the lamp on, we have one more proof of their existence, while in the case of abstract entities, they are often poorly defined and detached from our day-to-day practices.

Another problem with the realist’s account of the universals is that of an infinite regress that we enter when describing a universal things in terms of examplification by particulars. Take for instance, statements (2) and (3). We replaced the sentence “This man is wise” with “This man examplifies wisdom” to explain the abstract predicate “wise”. However, the words “exemplifies wisdom” can be considered another predicate that describes its subject “This man”. To explain this new predicate, according to this schema, we have to exemplify “examplifies wisdom” to produce a sentence like: “Something exemplifies ‘exemplifies wisdom’ ”. Further, to explain “exemplify ‘examplifies wisdom’ ” we will have to have another, the next examplification cycle. Loux believes that the regress in this case is not vicious, and the fact that we explain truth value of subject-predicate statements in terms of the reference to universal things, which in turn calls for an explanation of an infinite number of other universals, is not a problem as long as we make certain reservations to our definitions. To my mind, we can put a plug into this hole, by postulating a special status of the word “examplifies” (e.g. considering it, for example, basic, self-evident entity, which does not need to be further examplified). This argument does not pose a real threat to abstract entities.

More serious problem with the metaphysical realism is that it is not obvious which predicates must be referring to real things and which of these must be considered complex structures built out of more primitive entities. For example, the notion of “a bachelor”, one could define in terms of someone being a human being, and being unmarried. Hence, according to this definition “bachelor” is composed of two other entities and by itself may not represent a primitive abstract entity which exists in the realm of abstract. In other words, there is an abstract entity called a human being and another abstract entity called unmarried. The notion of "bachellor" is just a combination of these two abstract entities.

This example can be elaborated further. Consider predicates exemplified by particulars which could have existed but do not. Do they (such predicates) represent real things? And what about predicates exemplified by particulars that can never have existed (e.g. something of a triangular square shape)? Do such predicates (e.g. triangular square shape) refer to an abstract item which belongs to the realm of universals? Which particulars exemplify them?
According to Loux, there is no one single answer to these questions shared by all realists.

Some philosophers believe there is no point to argue whether abstract entities are real or not. Nothing substantial hinges on answering this question either one or another way. We talk here about purely linguistic conventions. You may consider a set comprising (or exemplified by) this manuscript and the Sahara desert an abstract entity and attach to it the label “real” or you may consider it as not real and attach the label “not real”. There is no objective criterion to decide which label is right. Furthermore, according to this line of reasoning, it does not matter.
To my mind, this conclusion is indeed right in this particular example, but in other cases when it comes to questions pertaining, for example, to our ethical norms and practices, or our beliefs about Gods and free will or the reality of afterlife the question of “what is real?” spills well beyond the boundaries of a purely academic discussion. It makes difference to the way we perceive ourselves and the way we plan and enact our lives.

To summarise ups and downs of the metaphysical realism, I refer again to Chris Swoyer - “we should acknowledge at the outset that there will rarely (probably never) be knock-down arguments for (or against) the existence of any type of abstract entity. On this approach metaphysics (including ontology) is a fallibilistic, ever-revisable enterprise…. In concrete historical settings, constraints (NM guiding philosophical discussions) can seem very real, sometime inevitable, even if at a later time they seem arbitrary, even quaint. This needn’t make metaphysics “subjective” in any debilitating sense (so that whatever a particular culture happens to think about it “is true for them”). But it is a useful reminder that metaphysics, like any other intellectual enterprise, is a human endeavour that takes place in, and is highly coloured by, a time, culture, and tradition.“

Nominalism

According to nominalism, only particulars really exist and all our talks about universals are just a round-about talk about particulars. The key motivation for nominalism stems from the requirement of simplicity and economy of metaphysical foundations of philosophy. Out of two theories each having the same explanatory powers the preferences must be given to the theory which makes the list prior assumptions.

Metalinguistic nominalism and the problem of abstract references
For an austere nominalist nothing exists apart from particulars and for any subject-predicate sentence both the subject and the predicate must refer to particulars. If we exclude all abstract entities from consideration and take only items conventionally called particulars to form our vocabularies, then we have the problem of a poor foundation of knowledge. With such language we cannot express many thoughts and sentiments going beyond the realm of particulars. An alternative scenario is to include abstract entities into consideration but treat them in a special way, for example, by providing them with references to the corresponding particulars. This raises the problem of abstract references. What are the particulars for such abstract notions as courage, wisdom, beauty, red colour? Or what reference we can allocate to the prediction of the future which may never eventuate, or how to reference some imaginary objects - a flying pig, Peter Pen, etc.?

To resolve the problem of abstract referencing, metalinguistic nominalists argue that abstract words refer to linguistic constructs rather than real objects as realists and austere nominalists claim. In other worlds, the notion of “flying pig” refers to the linguistic construct “flying pig” rather than to some external real object. However, if we take language as a new entity not reducible to particulars then we raise a suspicion of introducing new abstract entities. To be faithful to nominalism, the metalinguistic nominalist must treat linguistic terms as a succession of dots and lines on a paper – particulars. In this case, he has also to explain how it is possible for different inscriptions of the same word in different languages to mean the same entity. If he explains this similarity by the reference to the meaning of the word (something hiding behind individual inscriptions) then again he raises suspicion of smuggling into his nominalist picture another abstract entity - the meaning.

An alternative strategy (advocated by Sellars who calls it a dot bracketing) is to explain the meaning by comparing same words in different languages on a functional level, e.g. as that participating in various inference procedures, and guiding our behaviour. If two different inscriptions from two different languages function same or similar way in our practices, they have close or the same meaning. This way we explain the meaning of the inscription with the reference to practice (rather than some abstract entity). To be consistent with the nominalist picture, we have also to get rid of all references to abstract entities appearing in our nominalist language. Can we always achieve this goal? Take, for example, the notion of practice. Practice implies certain actions and hence changes with time and thus includes reference to the future. To dress up the future event (which, by the way, may never eventuate) into particularist language we will have to make a reference to the inscription that encodes that future event and then explain the meaning of this inscription. We agreed to explain the meaning of inscriptions referring to abstract entities through the reference to practice. Hence, we have gone the full cycle - to explain the meaning of the inscription, we need to explain the meaning of practice, and to explain the meaning of practice we invoke the reference to the meaning of the inscription. Another point worth mentioning here is that it is not obvious whether the notion of practice itself refers to abstract or particular entity, or, perhaps, it is a composite term integrating different notions, or may be it represents the third class of entities reducible to neither the class of abstract nor the class of particulars.

Apart from the reference to the utility of language in our practices, another way to attach the meaning to words is by pointing a finger to a particular object and attaching a tag with a name of the object written on it. In this case we ignore all entities which we cannot observe, including all abstract entities and thus reducing this case to that of austere nominalism. The problem with this account of nominalism, as mentioned earlier, is a poor foundation for knowledge produced out of such limited set of particulars. Math inclined reader may argue that instead of pointing a finger, we can use sets of particulars to define meaning of words referring to abstract entities. For example, a set comprising all red objects, defines the colour red as a feature shared by all objects within this set. The problem however is that this way we cannot define imaginary objects because they do not belong to the class of particulars (at least in a monoverse interpretation of the world. We will talk later in this chapter about Lewis’s interpretation of possible worlds as an attempt to address this issue via introducing sets over the multiverse). If we take words as pointing to imaginary objects to explain their meaning, then we again face the aforementioned problems of metalinguistic interpretation of nominalism.

The least we can conclude from the above example is that it is not obvious how to express all our knowledge in terms of particulars without recourse to abstract entities. In fact, a more strong statement saying that it is not possible to abandon all abstract entities and express all our knowledge in terms of only particulars, might be true, but we have not proved it yet (and it might be impossible to prove it at all). Since we did not prove it, let’s assume we can express all our knowledge in terms of particulars. Does it solve the problem? It does not. There is another problem, not least fundamental. The nominalist teaching flavoured with a metalinguistic treatment of abstract entities is conducive to the picture of the world as a computer machine simulating a set of instructions – the world of deterministic machinery with no free will. We may feel uneasy with this interpretation of the world and may not be willing to endorse it.

The conclusion we are reaching here is that we can neither prove nor disapprove abstract entities. Eventually, it is up to us to either believe them or not. Analogously, it is up to us either to believe or do not in a nominalist picture of the world. If for some reasons (which may go well beyond epistemology and metaphysics) we feel uneasy with the nominalist teaching, there is nothing to stop us rejecting this teaching and choosing something else that would better suit our project.

Trope nominalism and the problem of poor foundation
An alternative to the linguistic nominalism is a trope nominalism. The proponent of the trope nominalism claims that, in addition to concrete particulars, there are such things as attributes, but attributes have nothing to do with abstract entities – they are also particulars. So against the metalinguistic nominalist, they hold that there are things like colours, shapes, sizes, and character traits; but against the realist, they hold that these things are particulars. As they see it, concrete particulars have colours, shapes, and the like; but the attributes those particulars have are every bit as particular or individual as their possessors. One of the problems with this account of nominalism, as we seen earlier, is that it is not obvious how to define these properties. The particulars which refer to the future events must be different from the particulars which describe an apple on the table which we can see now. We will have to define at least two classes of particulars, one of them representing abstract entities. Another problem is that it leads to the commitment to too many basic, unanalysable entities, we may want to analyse, and perhaps synthesise under certain semantic rules. With regard to this problem, it makes sense to distinguish eliminative nominalists and conventional nominalists. The former claims that only some elementary particles of physics can be considered as real, while all the rest are ontologically secondary, derived entities. The latter takes ordinary objects of our everyday experience as candidates for particulates.

Particulars (substrate, bundle and substance theories)
Let’s have a look on particulars themselves. What kind of entities they are? I will give a very short outline of 3 major theories in this area – the substratum theory, the bundle theory and the substance theory.

Let’s assume there are smallest basic particles out of which all other objects are made. These particles have some properties, for example, some of them are red. The sentence “particle is red” has two components the subject “particle” and the predicate “red”. According to substrate theory, the subject and the predicate in our example represent two distinct entities. Get rid of all properties of the particle and you are left with a particle itself with no property. That ghostly something which is a particle with no properties is a particle in its pure form called the bare substrate.

Empiricists have found the idea of an underlying substratum objectionable and have been predominantly bundle theorists. According to this theory, a particular is just a bundle of all its properties. The notion of “bare substrate” does not make sense. To fit a bundle theory into the nominalist picture, however, they will have to define properties in terms of particulars (i.e. sets of properties) which introduces cyclic reasoning. The third theory of particulars, Aristotelian substance theory, states that some of the familiar particulars are literal exemplifiers of universals associated with these particulars. “Particular objects are considered as instances of the kinds to which these objects belong. And the fact that they belong to a particular kind makes them distant from species of other kinds as well as individuates them and makes different from other members of the same kind. Not all particulars we can see in the world have been granted with the status of basic, fundamental particulars. On Aristotle’s account only alive creatures, plants and elementary physical entities were considered to be basic, and all other particulates being just aggregate entities lacking their own ontological identity.” Since alive creatures consist of physical elements, the question arises about reducibility of these systems to physics. On Aristotle’s account physical particles when bound within alive systems somehow change the status from being basic elements to somewhat less basic entities. With regard to nominalist theory, this vision of particulars which includes explicit reference to abstract entities, does not quite fit into the nominalist picture of the world.

To summarise this section, the nominalist picture of the world provides some ontological economy, but it may not necessarily provide a better explanatory power as compared to metaphysical realism. Out of the three species of nominalism considered above (austere nominalism, metalinguistic nominalism, and trope nominalism), I think, metalinguistic nomnalism provides the most convincing account of abstract entities and attribution of truth to subject-predicate sentences. However, I believe, nominalism in general (and metaliguistic nominalism in particular) does not provide sufficient resources to meet requirements of our project. The reader interested in more details on this theory is directed to Loux (2006).

Propositions and facts, states of affairs, events

Definition
Till now, we talked about universals in terms of words and references to objects these words refer to. We say that sentence “this apple is read” means that there is an apple (the particulate) and the word “apple” refers to that particulate, and there is also an abstract entity “red” and the word “red” refers to the universal “red”. Now, when we say “this apple is red” we express by this sentence some commitment to the specific truth about the relationship between “apple” and “red” (i.e. a particular object “apple” exemplifies an abstract object “red”). Another way of expressing the same commitment would be to say that “it is true that this apple is red”. In either way we are making certain assertion about the way that the world is. We can form similar assertions by using “that” clause together with the words expressing our attitude to form sentences beginning with “I can see that”, or “ I can hear that” or “ I smell that” and similar. In either case “that” clause is referring to something which exists out there in the nature. Using this analogy we can also consider statements like “I know that”, I believe that” and “I fear that”, etcetera and consider subjects of “that” clause in these statements as pointing to something which exists out there in the nature. The complexity of the “that” clause could be as large as we wish. We may say, for example, “I believe that this storied world is such that ….” and provide a lengthy description of one or another storied world.

The subject of the “that” clause in such assertive statements are what metaphysical realists call “propositions” - abstract entities referred to by “that” clause of assertive statements. Another key feature of propositions is that they are truth bearers. The assertive sentence is true by the fact that the corresponding proposition is true (and not vice versa).

Propositions are distinguished from sentences because, for example, you may have two different sentences in different languages referring to the same subject (i.e. same proposition). There might be the same sentence but with different meanings, depending on the context (i.e. same sentence referring to different propositions), and there are synonyms, i.e. again different sentences refereeing to the same subject. Further, one may argue that inventions and discoveries to be made in the future (not known yet) represent truth which has not been yet articulated in the form of sentences. These future discoveries are not sentences because they are independent from the way we may express them in the future. Hence, they are propositions.

Propositions must be also distinguished from the collection of objects comprising that proposition, because such collection is not equal to what we assert in a sentence. Propositions are atemporal, non-spatial, they belong to the realm of abstract entities.

Arguments for propositions
According to (…) there are two key motivations for introducing propositions. The first one is associated with the intentional nature of our thought. Whatever we think, we think about something, and because any though is referring to “something”, that later could have its own existence independent of the though itself. On this account there is an infinite number of various propositions some of which might describe flying pigs and talking donkeys (for some reasons favourite examples of impossible states by philosophers). Only some of these propositions are exemplified by particular objects in our world.

Another motivation for propositions is that of meaning. Propositions are said to express the meaning of sentences. There might be different sentences with the same meaning (synonyms pointing to the same proposition) and same sentence with different meanings (i.e. different propositions). Hence, propositions must be distinguished from sentences – they express the meaning of sentences.

Arguments against propositions
The opponents of propositions argue that analogies between statements like “I can see that this apple is red” and “I think that I see the flying pig” are farfetched. They might be valid in terms of the grammatical expressions but may not necessarily extend towards the content of these sentences.

Quine criticised the appeal to meaning as an attempt to explain obscure notion of propositions with not least obscure notion of meaning (ref …). To explain the meaning, he argued, we must explain synonymous statements (because synonymous statements have the same meaning and once we know they are synonymous we know they share something in common which is the meaning). However, he argues it is impossible to prove two statements synonymous because of the “indeterminacy of translation”. Say, if one can observe only the behaviour of an alien culture, and the task is to translate sounds people from that culture make into the words and sentences of the familiar language, there will be always some degree of the uncertainty associated with this translation. As an example Quine takes a man shouting “gavagava” whenever he observes a rabbit. This man could be referring to some parts of the rabbit, to some abstract entity associated with rabbits, to some rituals, etc. We will have no idea what exactly his “gavagava” means. The only knowledge we have is that this sounds are triggered by the presence of rabbit. We do not know whether “rabbit” and “gavagava” are synonymous. No synonyms implies no meaning. If the meaning is indeterminate then so is a proposition defined in terms of this meaning.

Quine’s argument does not look very convincing to me (ye-eh, I know, my opinion is not particularly authoritative in this area and may not represent the final truth, but still ... that is what I think about it). While we may not know exactly the meaning of words in other cultures, we still manage somehow communicate with each other by establish shared common grounds. It seems to me that one can refer to that common ground as a place-holder for either the meaning or a proposition.

Another objection to equating propositions with meanings comes from Witgensteinian “game-like” treatment of language, where to understand the meaning of the sentence is to know how to use this sentence during the communication which necessarily involves other statements. The point is that meaning of the sentence is not atomistic, something attached to a particular sentence and isolated from the rest of the language. Attribution of the meaning to sentences is a holistic process requiring the knowledge of the whole language. From this perspective any talk about propositions as representing meanings of isolated sentences does not make sense at all.

The claim that propositions are required because same sentence may have different meanings, and hence in some circumstances be true and in other circumstances false, and hence refer to different propositions, can be questioned on grounds that we can explain different meanings by contextualising these sentences to contexts in which they arise. We do not have to invoke the reference to propositions to define the truth value of the sentence and can describe an attribution of truth in this case by bringing up and making explicit the context of that particular statement.

The point referring to propositions as means to explain synonyms is met by considering Searle’s dot bracketing of the same statement in different languages. In other words, instead of focusing on the syntactical features of the sentence, we compare them on the functional level and then claim that two sentences are the same, with no reference to propositions (but, again, analogous to earlier discussion of abstract entities, the definition of the functional level must be examined carefully so that we do not smuggle in propositions through these functions).

Further arguments against propositions
Loux (2006) indicates further arguments against propositions and, in general, against all abstract entities: “Two-world ontologies and the epistemological problems they generate. The claim, … is that theories which divide things into the concrete and spatiotemporal, on the one hand, and the abstract, timeless, and nonspatial, on the other, cannot accommodate causal relations between entities of the two types; consequently, such ontologies leave it a mystery how concrete beings like ourselves could have epistemic access to the abstract entities they postulate. And the critic adds that, in the present context, this difficulty has a special urgency since it suggests that the ontology of propositions lacks the resources for making sense of the very facts it is introduced to explain, the possibility of human thought and communication.

And other objections to propositions are equally familiar. We are told, for example, that since propositions cannot be identified except by way of the phenomena they are supposed to explain, the appeal to propositions is mere pseudo-explanation. Realists bring forward certain facts – that statement making and thinking take objects, that there are intersubjective bearers of the truth values, that that-clauses require referents and then conclude that propositions exist; but since we can say what propositions are only by reference to these facts, their introduction is the appeal to a virtus dormitiva (NM: tautology).

And, finally, we are told that the appeal to propositions violates Ockham’s Razor. The charge is that since metaphysicians can accommodate all the phenomena of interest to realists by way of a theory in which propositions play no part, a theory including propositions multiplies entities beyond necessity. By far the most popular strategy is to argue that the claims realists take to be about propositions are really just disguised ways of making metalinguistic claims, claims about sentences. “

Concluding remarks on propositions
Propositions play critical role with regard to truth attribution to subject-predicate sentences. We are told that propositions are truth bearers of the sentence - the sentence is true because the corresponding proposition is true, and not vice versa. It is not obvious, however, how we know the truth value of the proposition itself, since the later belong to the realm of abstract where we have no empirical evidence whatsoever and may have little aid from intuitions as well.

Apart from propositions there are other abstract entities (e.g. states of affairs, facts, events) at different time by different philosophers considered solid enough to furnish ontological background of reality. I am not going to go through all these theories. The reader interested in this topic is referred to Loux (2006). As for propositions themselves (and abstract entities in general), the bottom line, according to …., is that the jury is still out (ref). There are arguments for and arguments against propositions, and no one really knows whether they are real or not, and how useful the theory of propositions is at present or might become in the future.  

Possible worlds

The totality of the Modal
Apart from many things out there in the big world studied by science and philosophy (so called categorical entities), there are many other items which could have been out there but they are not (hypothetical or modal entities). There is a chair in this room, a moon on the sky and there is a lamp on the table and the lamp is on. On the other hand, this chair could have been in another room, the earth could have had two moons and the lamp could have been switched off. There is enormous number of ways this world could have been otherwise in the past, and in the present. And there is not least number of ways it might be in the future. According to advocates of the modal theory, if we had a theory that explains and predicts the location and movement of all particles in this world (the way these particles actually are), this theory would be still incomplete unless it also describes all the ways that these particles could have been in the past or might be in the future. The world of possible states is much bigger that what we can see with a naked eye or what we can measure with our devices.

Necessary and possible truth
Attribution of truth to statements concerning possible states is coloured with different shades of certainty (or necessity). We can be very certain that had we dropped this glass on the hard flour, it would break. This sentence expresses a necessary truth. On the other hand, the glass may or may not break if we drop it on the soft flour. In this case, it is possible that this glass will break but it is not necessary. This sentence expresses possible truth. We may also say something about things, which never happen, but we can imagine them as happening. The glass, instead of falling down, will fall upwards. In theory this is possible, but it never happens in practice because of the law of gravity. This sentence expresses necessary truth about the glass – it never falls upward. On the other hand, we can say things which contradict to logic and, hence, again are necessarily impossible, but they are impossible even in theory. For instance, the statement that this glass will fall down, same time as it will fall upwards, is necessarily false. This is just impossible to happen and may not be possible to imagine (at least unless some further assumptions are made about the nature of the glass and the meaning of the worlds etc). This sentence again expresses truth which is necessary but the degree of that necessity is much stronger than that in the previous example of the glass falling upward. So, when we use such words as necessary and possible, in our modal talks, we may use these words to express different degrees of certainty. We may also distinguish between say a scientific hypothesis which we believe could be true and amenable to experimental testing, and fairy tales which we know upfront to be fake and we never bother to check their truth value.

De-re, de-dicto necessity
We can ascribe the truth value to the whole sentence and such ascription is called de-dicto modality. For example, the sentence < necessarily “joe is bold”> expresses de-dicto modality, meaning that it is not true because “joe” could be referring to almost anything we may wish to call “joe” – a human being, a star, a tree, and many of these are not bold. Unless we say which “joe” we have in mind the sentence is false.

We can assign properties to a particular object and ascribe the truth vale to the corresponding statement. We can say, for example, and then it could be either true or false depending on which “joe” we refer to in this sentence. We may need to take care in this case to discriminate between this “joe” and many other “joes”, which may not be a trivial task. Say, if we say while the “joe” is experiencing a clinical death, it may not be a trivial task to figure out whether this sentence is true or false because we do not know whether we refer to the right, alive “joe”. In philosophy textbooks, instead of one often finds an equivalent sentence < “joe” is necessarily alive> which sounds more natural. Regardless the form, the point is that in this case we ascribe the truth value to the description of some specific object which needs to be properly identified and distinguished from many other possible objects having the same name. This type of sentences are said to express de-re modality. To discriminate between these two modalities, I suggest the following mnemonic rule:

De-re: < “joe” is necessarily bold> is equivalent to < THIS “joe” is necessarily bold>

De-dicto: < necessarily “joe is bold”> is equivalent to < necessarily “ANY joe is bold”>

This distinction between de-re and de-dicto modalities will be important when we discuss identity issues in possible world theories.

Ubiquitous modality
The talk about modal things (things which do not exist but could have existed) adds an extra level of complexity to our theories of the world. Instead of worrying about real things, one now has to take care about some, let’s call it, less real stuff, something that we may talk about but may not necessarily exist. Mind it that there are enough puzzles and problems with the world as it is. Adding more things to the pool of the real stuff can make its description even more complicated. But do we have to worry about this extra stuff? Is it really important? Can we just ignore it and get away by talking only about things that we are confident to exist out there in the big real world? Things that we describe using declarative sentences involving “is” or” are” or “were” or “will”, rather than sentences with “may be”, “could have been” etc.

Many philosophers believe we cannot. I will follow below Josef Melia’s “Modality” to provide some arguments showing that non-existent modal stuff is integral and irreducible part of science, philosophy and our everyday life.

Any plausible scientific hypothesis refers to things which are possible. If we exclude anything going beyond observations of what is out there (whatever it could be and regardless whether it is possible at all) we are pretty much closing science and almost any kind of enquiry people may have. Any “what if scenario”, for example, that may underpin decision making, without reference to modal terms becomes meaningless. “If the positivist rules that a proposition is meaningless simply because it is not known, then any debate over a currently unresolved issue turns out to be a meaningless one.” (Melia, “Modality”)

Any scientific law which says that “b” necessarily follows from “a”, involves modal language. To understand this sentence, one must have to admit alternative possibilities and understand what these possibilities could mean. Furthermore, “with the advent of irreducible probabilistic physics, such as quantum theory, it is possible that at the fundamental level, there is nothing more to say about the basic kinds of entities than that they have irreducible tendencies and dispositions to behave in certain ways under certain conditions.” (Melia, “Modality”)

“As well as in science, modal notions also appear to be fundamental in the study of logic. One of the main concepts … in logic is the notion of a valid argument. … an argument is valid if it is not possible for the premises to be true and the conclusion false.”

There are anti-realists which say that modal stuff is not real and hence there is no really new knowledge attached to such statements. And yet, if we talk about predictions of the future, we seem to believe that at least some of these predictions could be true. It is not difficult to see that some knowledge can be attached to modal sentences referring to the past as well – e.g. when we say how things could have been. For example, when we say “had I dropped this glass it would be broken”, we seem to express some knowledge about properties of that glass, and that knowledge comes from experience we may had earlier.

Quine, fierce opponent of modal talks, suggested that all modal sentences could be rephrased in non-modal terms. “Salt is soluble” can be interpreted as “for any x such that x has structure of salt, salt has been placed in water, salt has been dissolved”. The paraphrase uses no modal notions: it talks only of what there is, what has happened, and properties actual things possess. On Melia’s account, this argument is not valid because “salt would still be soluble whether or not it … had ever been placed in water. Yet, for Quine’s paraphrase to work, there must be at least one substance that actually has been placed in water and actually dissolved”

All these examples suggest that we cannot just simply get rid of the modal talk. Modal statements are integral to our knowledge of the universe and ourselves. An interesting question that follows is how we interpret these modal statements? Do they refer to anything real or they are just linguistic constructs suspended in thin air with no any other ontological foundation than that one can attribute to abstract theoretical constructs?

Monoverse interpretation (modalism)
A paradigm interpretation of modal statements is that arising from the monoverse picture of the world. There is one world and one single description of that worlds captured by the language of categorical statements. All other descriptions representing how the world could have been or could be in the future are false. They are just linguistic constructs, kind of fairy tales, with no ontological underpinnings.

The question that immediately follows is about the meaning of these linguistic constructs. If we dismiss abstract entities as incommensurable with science, then we are stuck with one of the forms of nominalism and thus inherit all strong and weak points associated with this view.

Multiverse interpretation of modal sentences
Another interpretation of modal statements involves possible-worlds theory and holds that modal sentences do have ontological foundations. The logic of introducing possible-worlds could be as follows. So far, we talked about universals (properties, kinds, relations) and propositions (“that clauses” of the assertive sentences). We have seen that there are arguments for and against introducing these items into the vocabulary of philosophical explanations and there are those who believe in abstract entities (Platonists and alike-minded philosophers) and those who do not (nominalists). Talks about abstract entities may sound strange to a physicist but many philosophers take these talks seriously. If we admit that universals (properties, kinds, and relations) and propositions (“that clauses”) could be real, then the question that follows is - why we stop here and do not include possible worlds in the collection of abstract entities. We can take the totality of how things could have been otherwise and dub it as a possible world. As Loux, ironically, puts it, “as if universals and proposals were not enough to amuse the public, further not least controversial items, called possible worlds, have been added to the collection of the abstract entities”.

There are two major strands of possible-world theories called extreme realism (or possibilism) and ersatz modalism (or actualism). According to actualism, there is only one actual world that we inhabit and which is an instantiation of some abstract entity, the corresponding possible world. But there is an infinite number of other possible worlds which have not been instantiated and which exist in their own realm of possible worlds. The ontological status of the actual world is different from the ontology of many other possible worlds (e.g. Plantinga, Adams).

An alternative to this interpretation of possible worlds is called “possibilism” (extreme realism), exemplified by the Lewes’s nominalism, where each possible world is treated as a one more kind of the actual world. According to this conception of possible worlds, there is no fundamental ontological difference between our world and any other possible world. Let’s have a closer look on this theory.

Extreme realism (possibilism)
According to Lewes, possible worlds are not least real as our actual one. The only reason we cannot perceive them is because they are spatially and temporally isolated from our world. The Lewis’s commitment to possibilism follows from his dedication to the project of the possible world nominalism. The goal is to consider possible worlds as basic fundamental entities (kind of particulars which are given by default) and build upon this foundation the rest of philosophy including an account of modality and abstract entities (e.g. properties and propositions). For example, the necessary and possible propositions are defined as follows:

A proposition is necessary or necessarily true when it is true in every possible world.
A proposition is possible or possibly true when it is true in some possible world or other.

According to possibilism, there are actual worlds with “flying pigs” and we can test statements pertaining to at least some abstract objects by referring to the corresponding worlds where these abstract entities are represented by particulars. The truth value of a statement in such particular world is established as a trivial empirical fact not requiring further proof. While the worlds of possibilia are spatially and temporally isolated, we still have an intellectual capacity to travel across these worlds and thus establish the truth values of propositions. On top of that we can even build different grades of certainty to our truth attribution. We can contrast this account of propositions with our earlier discussion of propositions as abstract entities with a very little understanding of the truth attribution in the realm of abstract. The framework of possible worlds provides a vivid and easily comprehensible description of the process of truth attribution to propositions.

The definition of the necessarily true proposition requires further clarification. As mentioned earlier, we can ascribe the truth value to a proposition as a whole (de dicto modality), and we can ascribe a truth value to some part of that proposition (de re modality). To make it simple, assume that the proposition is given by the subject-predicate sentence. The predicate describes some property of the subject (Jim is bold). We can read this statement as (Necessarily Jim is bold, de dicto necessary) and (Jim is necessarily bold, de re necessary). The first reading implies that there is Jim in every possible world and Jim is bold. This seems to be never true. Another statement means that in every possible world where we find Jim, he is bold. In other words, the definition of necessary true, in this case is conditioned on the worlds which have Jim present in it. The problem we have immediately is about deciding how do we know that Jim (and not some other person which may resemble Jim) is present in that world. In order to track Jim’s identity in various worlds, we have to take on board the notion of some essence that would distinguish real Jim from all Jim-like persons. Instead of considering him a bundle of properties which may change from one world to another, we have to commit to the vision of Jim as having some core essence which defines this particular human being. Many philosophers feel uneasy with these talks about the human essence, and some consider this as an argument against possible worlds.

Lewis’s solution to the problem of identity was the theory of counterparts. He takes that individuals are “world–bound”, in other words, there is only one particular individual over one possible world. However, there are people who may resemble this particular individual in other worlds. Lewis calls this relation the counterpart relation; it is a relation of similarity or resemblance:

“you are in the actual world and no other, but you have counterparts in several other worlds. Your counterparts resemble you closely in content and context in important respects. They resemble you more closely than do the other things in their worlds. But they are not really you. For each of them is in his own world, and only you are here in the actual world. (On plurality of worlds)”

With Lewis’s framework in hand one can reduce properties and propositions to sets. The properties and propositions are explained in terms of sets of particular items found in possible worlds or sets of possible worlds themselves. For example, the property of triangularity is defined as a set of all objects across all possible worlds, such that they (objects) all are, as Loux calls it, triangular-ish. What does that triangular-ish means is a bit vague. We can’t say triangular-ish means triangular, because this way we introduce circular reasoning, where something to be defined is defined in terms of the original word. Perhaps, we shall ascribe to a human being the inherent capacity to distinguish, in a particular world, triangular objects from all other objects.

Similarly, a proposition is defined as a set of all possible worlds, where that proposition is true. How do we know that proposition in that world is true? Again, we introduce the notion of true-ish worlds (where propositions might be represented by particulars), that we know somehow.

Issues with Lewis’s nominalism

There are a number of issues with Lewis’s nominalism. A major problem is unparsimonous ontology. Some other, more technical problems include definition of the necessary proposition as a set of possible worlds were that proposition is true (and, hence, comprising all possible worlds), which implies that there is only one necessary proposition. Another argument against Lewes nominalism states that propositions represent an attitude and assertion we may or may not believe, while sets do not represent anything and cannot capture the assertive elements of the proposition.

On the other hand, Lewis’s possible worlds provide a convenient framework for articulating and explaining the notions of universals and propositions, de-re de-dicto modalities. This framework explains some technical issues associated with modal logic and eliminates primitive modalities.

I shall conclude this section on Lewes’s modal realism, with the reference to Phillip Bricker: “ When Lewes first begin advocating the thesis that there exists a plurality of concrete worlds, he received in response mostly “incredulous stares”. That soon changed. Over the ensuing years, arguments for and against Lewisian realism have filled philosophical books and journals. Lewisians have had to develop and revise their position in the light of powerful criticism; non-Lewisian alternatives have sprouted like weeds in the philosophical landscape. The debate goes on; as with other metaphysical debates, a decisive outcome is not to be expected. And through it all, the incredulous stares remain: Lewisian realism does disagree sharply, as Lewes himself concedes, with common-sense opinion as to what there is. There seems to be a fundamental rift – unbridgeable by argument – between ontologically conservative philosophers who have, what Bertrand Russel called, “ a robust sense of reality”, and ontologically liberal philosophers who respond echoing Hamlet: “ there is more on heaven and earth than is dreamt of in your philosophy”. No doubt, the Lewisian approach to modality will always be a minority view. But the power and elegance of the Lewisian approach has been widely appreciated by philosophers of all stripes. The bar is set high for the assessment of alternative views.” Bricker Phillip (2008). Metaphysics, Contemporary debates in Philosophy. Eds. T. Sider, J. Howthorne, D. Zimmerman, Blackwell Publishing, Oxford UK, 404 p.

Ersatz modalism (Adams, Stentort, Plantinga)

An alternative to possibilism provides ersatz modalism (actualism). Melia further subdivides this kind or modalism into “quiet” and “linguistic” theories. The key point of these theories is that there is only one actual world and all other possible worlds are not quite real, at least not in the same sense as the actual one.

An example of “quiet” modalism provides theory of possible worlds made out of the maximally consistent set of propositions, i.e. abstract entities. The definition clearly involves reference to modal terms (e.g. maximally consistent means that not other proposal can be added such that the consistency is still preserved) implying that modalities are treated as primitive entities rather than being explained in terms of possible worlds as done in Lewes’s theory. The notion of the proposition itself is vague and not well defined. To build the whole theory on such a loose foundation, according to Melia (and, I guess, many others), is a big challenge. The reason this sort of theories are called “quiet” modalism is that they take the notion of truth as a primitive, basic notion. Remember that a proposition was defined as an abstract entity which makes a statement true or false. Not the other way around. And what then underpins the truth value of the proposition itself? We do not know. We have neither intuitions nor empirical evidence to guide our decisions in the realms of abstract propositions. Perhaps, the best strategy is just take that notion of truth as a primitive one, and keep silent about any reasons that may explain our ascriptions. That is exactly what the proponents of the “quiet” modalism do.

“Extreme realism is often met with an incredulous stare, and quite rightly so. Quiet moderate realism is not. It should be. … it’s not hard to discern a blueprint for generating realism here (NM with quiet realism). … Say that there exists a collection of circumstances, or situations, or natures, or incidents … you should use your own creativity and find some other word to introduce a new brand of entities (NM e.g. storied worlds). Feel free to use these familiar words to give you the illusion that you are doing nothing more than you are introducing a category of entity that is entirely natural and with which you are entirely familiar. Feel free to ignore all aspects of our ordinary thought and talk of circumstances or situations or natures or incidents that are incompatible with your particular understanding of these entities. Distinguish between those circumstances that hold and those that do not, or those situations that happen and those that do not, or those natures that are instantiated and those that are not, or those incidents that occur and those that do not. Feel free to say nothing about the nature of these entities, other than that they are all existent, are all abstract and are all actual; feel free to say nothing about the nature of trans-world identity; feel free to say nothing about how these entities manage to represent all the possibilities that there could be; feel free not to postulate anything that can do the work of the domain D; feel free to say nothing about how these things help with the analysis of our ordinary modal thought and talk, such as sentences comparing the domains of different worlds, modalised comparatives or supervinence claims; feel free to omit the necessary details that would explain how your theory can help to us analyse counterfactuals; finally, feel free to claim that the theory has all or most of the benefits associated with a theory of possible worlds and stop right there. And now feel free to feel ashamed of yourself for thinking that the little language game you’ve set up deserves to be called a theory of modality. Anyone offering up such meagre picking warrants as much of an incredulous stare as the extreme modal realist. This is a theory of modality?” (Melia, “Modality”) (NM. Well… that was tough – I’m not sure our storied multiverse will meet all these requirements, but hope eventually there will be more arguments for than against it)

Another version of multiverse (different from that based on propositions), called linguistic modalism, takes possible worlds to be represented by a set of maximally consistent sentences. One possible interpretation of such a linguistic multivers is that of a collection of books (written and not yet written). The reference to stories makes it easier to define the notion of truth. The truth is defined with the reference to a particular context given be the collection of sentences, which is a story or a narrative which has its own structure and logic. The modal notions though are still considered primitive entities. The key problem with this account of the multiverse is the lack of capacity to describe alien entities, the entities which go beyond the recombination of things from the actual world. In other words, linguistic worlds are enclosed within the realms of reason and have no resources to break out beyond this cage – they are missing new empirical evidence associated with the new worlds. We may think and hypothesise as much as we like about new stuff, but there is no place for really new empirical evidence to show up, something that we never knew and couldn’t have thought about unless we live in and do something in that new world. All these stories seem to represent artificial constructs that we project from the actual world.

Cons and Pros of multiverse interpretation

I shall start with arguments against multiverse theories. In case there is an impenetrable impediment to the mulitverse theory it makes no sense to talk about arguments for it.

Arguments against multiverse

  1. Correspondence truth. One of the key arguments against multiverse interpretation of modal sentences is the lack of empirical evidence - an argument common to all other abstract entities. However significant and authoritative this argument is, according to Melia and others (e.g. Rorty) it is not decisive: “Empiricism by itself is contentious, and there is little agreement about how it should be understood. On the one hand, if we take empiricism strictly and say that we should count as knowledge these propositions that we can immediately observe to be true, than we run the risk of discounting many beliefs that we do want to count as knowledge. We cannot directly see the future, we cannot directly observe quarks and electrons, we cannot directly see that something is a law of nature, yet to conclude that we cannot have the knowledge of the future, of quarks and electrons and of laws of nature is an overreaction…. On the other hand, if we take empiricism loosely, and admit truth that can be indirectly confirmed or justified, than we run the risk of bringing the modal back in, for we do have plenty of good evidence that glasses are fragile, that uranium tends to decay, and that if I drop the computer it will fall down the stairs rather than levitate in the air. These truths may not be directly observable, but nor do we come to know them simply by closing our eyes and thinking. Empirical evidence exists that supports all these propositions. The empiricist, then, has some way to go before he is in a position to justify his scepticism about the modal, let alone in a position to justify his empiricism.” (NM we will come back to this last observation later in the section on epistemology where we will consider “the Challenge and Defend” argument against scepticism in epistemology advocated by Williams)
  2. Coherence truth. Another critical objection against modal talks has been raised by Quine. From the monoverse perspective, modal talks do not make sense because there is no proper logic underpinning such talks. Modal language is not extensional, meaning, for example, that when parts of a statement are replaced with co-referential terms, the truth value of the whole sentence changes. Subsequently, the modal statements are not truth functional, meaning that the truth value of the statement is not uniquely defined by the truth value of its constituents. Furthermore, modal language is not sufficiently expressive to capture many ordinary talks we may want to be represented in a formal scheme. Finally, it is not unique. Different logicians have come up with many different logics that give different answers to the same question. I believe, all of these issues eventually have been addressed through the reference to possible-worlds semantics. Because of a much more technical nature of the discussion involved in this argument, the reader is directed for details to the relevant text-books (ref the appendix B “Modal logic and possible worlds”).
  3. Pragmatic truth. Several philosophers seem to be interested in possible worlds but apart from them, no one is really interested in these theories. They have little relevance to our everyday life. What is the point of worrying about spatially-and temporally isolated worlds, if we never can reach these worlds? Or take ersatz worlds, which cut out one actual world where we live, and postulate a bunch of other abstract worlds. There is only one world which matters - our actual world. All other abstract worlds resemble fairy tales. Why would we care about them?

    4. Other arguments against modal theories

  4. Possible world theories have also been blamed for their commitment to essentialism. The line of reasoning goes as follows. Consider a modal statement: there is x such as possibly x has a feature F. In PW language this statement translates as follows: in the actual world W0 there is x such that there is world W1 where this x has a feature F. The problem is that we refer to the same x been present in two different worlds W0 and W1, which requires us to identify properties essential to x.
    It is suffice to say here that the problem is analogous to that arising in a discussion of the identity of human beings through time. We may not need to insist that the time is not real on the ground of the problem of the identity inherent to it is still not solved.
  5. Ontological un-parsimony. Many people cannot digest Lewes’s panopticon of talking heads and flying pigs. And yet others argue that this unparsiminy is only quantitative and hence less detrimental as that of the qualitative unparsimoiny. Once we have one possible world, all others do not make the qualitative difference to the level of the complexity involved in the discussion. Further they may argue about the benefits of the explanatory simplicity as outweighing the ontological burden.
  6. Claustrophobic enclosure into the linguistic cage (i.e. lack of practice and empirical evidence). Another name for this problem is that of the alien properties. An issue here is that anything we know about possible worlds is based on our speculations (plus experience in this world). There is no empirical evidence for other possible worlds. How can we know about something that in principle does not exist in our world? Something that is fundamentally new to us. This raises the suspicion that these possible worlds may not be real, because when it comes to something real we must expect news that do not fit into our established knowledge.
  7. Static nature of the PW. Typically, nothing is said about the way these PWs may behave with time. One of the reasons for that, I guess, is our limited understanding of what these worlds actually are since we cannot have direct empirical access to them.
  8. Vagueness of the description. Why some worlds are instantiated and others are not? How they are instantiated? Do they instantiate once and forever or they are dynamic entities? All these and many other similar questions remain unanswered.
  9. Large variety of the existing PWs. Too many theories might be indicative of the lack of a single truth.
  10. Incredulous stares. Counterintuitive nature of the PW theories.


Arguments in support of multiverse

  1. None of the aforementioned objections to PW theory are decisive and can knock down PW theory
  2. Utility of PW theory in terms of underpinning formal logic (see appendix for details). I believe, this is a strong point, even if not decisive. If PW language is required to make sense out of the modal language (which is indispensable to our practice), then perhaps we should take these possible worlds seriously. If the language says there are PWs, then perhaps we should take it as there are PWs.


Conclusion on PWs

To summarise arguments for and against PW, there is, I believe, one key objection to PW theory which is the lack of the empirical evidence, and subsequent lack of the utility of these theories to our practices. As a theoretical construct they do possess a certain degree of self-consistency and cohesive unity. They seem to be integral to our ability to provide a logically sound interpretation of modal sentences. But there is nothing that goes beyond theoretical speculations, something that would let us to discriminate between different interpretations and build on top and beyond of what we already know in the actual world.  

Multiverse theories in physics

In this section I will give a brief overview of a number of mutilverse theories as advocated by physicists, with a particular attention given to arguments they offer for or against these theories. Mulitverse theories produced by physicists predominantly are confined to the realms of material worlds. Some of these theories allow different worlds to have different physics thus making them to some extent analogous to the Lewis’s interpretation of possible worlds. In general, different physical theories advocate different forms of multriverse. The term “mulitverse of physics” refers to the suite of different multiverses rather than a single description. A feature common to all these theories is that they arise from physical theories and they all tend to exclude abstract, metaphysical dimension.

One of the proponents of the multiverse framework, Max Tegmark, begins his famous article about parallel worlds (Tegmark, 2003), with the following vivid description: “Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on. The idea of such an alter ego seems strange and implausible, but it looks as if we will just have to live with it, because it is supported by astronomical observations.” He goes on further to introduce 4 classes of multiverse.

Level 1

The level 1 multiverse is based on an assumption of the infinite and uniform space. Cut out any finite volume from such space, and you will find an exact copy of that volume somewhere else in the infinite space. The key idea is that there is a finite number of ways you can pack particles into the finite volume, and because of the infinite size of the universe you are bound to find exactly the same configuration of particles elsewhere. The size of particles comprising the level 1 multiverse is small but fixed. The nature of particles is the same across the whole universe, and the same physics governs their behaviour.

Level 2

The Level II multiverses are predicted by the theory of chaotic eternal inflation. According to this theory “space as a whole is stretching and will continue doing so forever, but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread. Infinitely many such bubbles emerge. Each is an embryonic Level I multiverse: infinite in size and filled with matter deposited by the energy field that drove inflation. Those bubbles are more than infinitely far away from Earth, in the sense that you would never get there even if you travelled at the speed of light forever. The reason is that the space between our bubble and its neighbours is expanding faster than you could travel through it. Your descendants will never see their doppelgängers elsewhere in Level II. For the same reason, if cosmic expansion is accelerating, as observations now suggest, they might not see their alter egos even in Level I.”

“The concept of inflation goes back to the 1980s, and physicists have elaborated on it based on their most comprehensive theory of nature: string theory. String theory allows bubbles to look very different from one another. In effect, each begins life not only with a random distribution of matter but also with random types of matter. Our universe contains particles such as electrons and quarks interacting through forc¬es such as electromagnetism; other universes may have very dif¬ferent types of particles and forces—which is to say, different lo-cal laws of physics. The full set of allowed local laws is known as the landscape. In some interpretations of string theory, the land¬scape is immense, ensuring a tremendous diversity of universes” (Ellis, 2011).

Level 3 multiverse

The next level of multiverse arises from many-worlds interpretation of quantum mechanics developed in 1957 by Princeton graduate student Hugh Everett III. The idea is that random quantum processes cause the universe to branch into multiple copies, one for each possible outcome. Quantum mechanics describes micro-particles with a special function (called wave-function). The square of the wave-function indicates the probability of the particle to be observed at a particular location. Until this particle is being observed it does not exist at a specific spot. Instead it can be represented as a superposition of different particles at different locations. In many worlds interpretation each of these particles reside in different parallel worlds. When we make an observation and pin-point a micro-particle to a particular spot, we select one out of many other possible parallel worlds. Our doppelgangers in parallels universes select other locations for that particle. The world is teemed with parallel universes.

Level 4 multiverse

The level 4 multiverse encompasses all the previous multiverses and many more. Max Tegmark introduces it as follows. “According to the Aristotelian paradigm, physical reality is fundamental and mathematical language is merely a useful approximation. According to the Platonic paradigm, the mathematical structure is the true reality and observers perceive it imperfectly. The Platonic paradigm raises the question of why the universe is the way it is. To an Aristotelian, this is a meaningless question: the universe just is. But a Platonist cannot help but wonder why it could not have been different. If the universe is inherently mathematical, then why was only one of the many mathematical structures singled out to describe a universe? A fundamental asymmetry appears to be built into the very heart of reality. As a way out of this conundrum, I have suggested that complete mathematical symmetry holds: that all mathematical structures exist physically as well. Every mathematical structure corresponds to a parallel universe. The elements of this multiverse do not reside in the same space but exist outside of space and time. Most of them are probably devoid of observers. This hypothesis can be viewed as a form of radical Platonism, asserting that the mathematical structures in Plato’s realm of ideas or the “mindscape” of mathematician Rudy Rucker of San Jose State University exist in a physical sense. It is akin to what cosmologist John D. Barrow of the University of Cambridge refers to as “" in the sky,” what the late Harvard University philosopher Robert Nozick called the principle of fecundity and what the late Princeton philosopher David K. Lewis called modal realism. Level IV brings closure to the hierarchy of multiverses, because any self-consistent fundamental physical theory can be phrased as some kind of mathematical structure.”

Another classification of multiverses suggested by Brian Greene (2011) comprises 9 key classes of multiverse (see schema below). In Greene’s classification the “Quilted Multiverse” corresponds to Max Tegmark’s Level 1 multiverse, the “Inflatory Multiverse” represents Level 2 multiverse. The Quantum Multiverse is equivalent to Level 3 many-world interpretation, and the “Ultimate Universe” represents level 4 multiverse. Apart from that, the extended list of multiverses includes an exotic member called a “Simulated Multiverse” and a few other multiverses based on different physical theories. Some of these (e.g. brain and cyclic multiverses), according to Tegmark belong to Level 2 multiverse.

  1. Quilted Multiverse: Conditions in an infinite universe necessarily repeat across space, yielding parallel worlds
  2. Inflationary Multiverse: Eternal cosmological inflation yields an enormous network of bubble universes, of which our universe would be one.
  3. Brain Multiverse: In string/M-theory’s braneworld scenario, our universe exists on one three dimensional brane, which floats in a higher-dimensional expanse potentially populated by other branes – other parallel universes.
  4. Cyclic Multiverse: Collisions between braneworlds can manifest as big big-bang like beginnings, yielding universes that are parallel in time.
  5. Landscape Multiverse: By combing inflationary cosmology and string theory, the many different shapes for string theory’s extra dimensions give rise to many different bubble universes.
  6. Quantum Multiverse: Quantum mechanics suggests that every possibility embodied in its probability waves is realised in one of a vast ensemble of parallel universes
  7. Holographic Multiverse: The holographic principle asserts that our universe is exactly mirrored by phenomena taking place on a distant bounding surface, a physically equivalent parallel universe
  8. Simulated Multiverse: Technological leaps suggest that simulated universes may oneday be possible
  9. Ultimate Multiverse: The principle of fecundity asserts that every possible universe is a real universe, thereby obviating the question of why one possibility – ours – is special. These universes instantiate all possible mathematical equations.


The reader interested in further details about multiverse models is directed to papers by Alan H. Guth and Andrei Linde, Paul J. Steinhardt and Neil Turok, David Deutsch and Michael Lockwood and others.

Arguments for multiverse theories

  1. Ockham’s razor: Ontological vs explanatory simplicity. The first argument is that multiverse theories are vulnerable to Occam’s razor because they postulate the existence of other worlds that we can never observe. Yet, as pointed by Max Tegmark, this argument can be turned around to argue for a multiverse. What precisely would nature be wasting – ontology or explanation? The higher-level multiverses are simpler. Going from our universe to the Level I multiverse eliminates the need to specify initial conditions, upgrading to Level II eliminates the need to specify physical constants, and the Level IV multiverse eliminates the need to specify anything at all. The opulence of complexity is all in the subjective perceptions of observers— the frog perspective. From the bird perspective, the multiverse could hardly be any simpler.
  2. Capacity to explain probabilistic nature of observation in quantum mechanics (i.e. many-worlds interpretation of quantum mechanics)
  3. Anthropic reasoning to explain life-tuned physical constants. As it happens fundamental physical constants governing, for example, interaction between elementary particles are fine-tuned to make life in this universe possible. Were these constants slightly different, and the universe may have collapsed into singularity or have exploded or become something else completely incapable of sustaining life forms. The question is why our universe is fine-tined to make life possible? An answer offered by the proponent of the multiverse framework is that there is nothing mysterious in this fine-tuning because there is not one but many universes and we just happened to live in one of these. This kind of reasoning was dubbed anthropic reasoning. Max Tegmark (2003) illustrates it as follows. “The mass of a star determines its luminosity, and using basic physics, one can compute that life as we know it on Earth is possible only if the sun’s mass falls into the narrow range between 1.6 E30 and 2.4 E30 kilograms. Otherwise Earth’s climate would be colder than that of present-day Mars or hotter than that of present-day Venus. The measured solar mass is 2.0 E30 kilograms. At first glance, this apparent coincidence of the habitable and observed mass values appears to be a wild stroke of luck. Stellar masses run from E29 to E32 kilograms, so if the sun acquired its mass at random, it had only a small chance of falling into the habitable range. But … one can explain this apparent coincidence by postulating an ensemble (in this case, a number of planetary systems) and a selection effect (the fact that we must find ourselves living on a habitable planet). Such observer-related selection effects are referred to as “anthropic,” and although the “A-word” is notorious for triggering controversy, physicists broadly agree that these selection effects cannot be neglected when testing fundamental theories.”
  4. The fact that multiverse appears naturally from the math theories (eg string theory). “The first seven of these multiverses (NM: see table 1) emerged from mathematical laws developed by physicists in their pursuit of nature’s deepest workings. The credence accorded one set of rules or another varies widely - quantum mechanics is viewed as established fact; inflationary cosmology has observational support; string theory is thoroughly speculative – as does the type and logical necessity of the parallel worlds associated with each. But the pattern is clear. When we hand over the steering wheel to the mathematical underpinnings of the major proposed physical laws, we are driven time and again to some version of parallel worlds” (Greene, 2011).
  5. Past observations. Can we prove assumptions underpinning the level 1 multiverse - that the universe is infinite and homogeneous? According to Tegmark, there are observations that encourage us to think that the space is indeed infinite and uniformly filled with matter. Namely, there are measurements of the cosmic microwave background radiation that suggest that we live in a flat universe. As for the assumption that it is infinite, there is nothing we have observed so far to suggest that it is not. So, there is at least some empirical evidence that supports the idea of this kind multiverse.
  6. Appeal to the future measurements which may either prove or refute multiverse theories. This argument raises a more general issue concerning the status of multiverse theories in science. “Do we define science – “respectable science” – as including only those ideas, realms, and possibilities that fall within the capacity of contemporary human beings on Planet Earth to test or observe? Or do we take a more expansive view and consider as “scientific” ideas that might be testable with technological advances we can imagine achieving in the next hundred years? The next two hundred years? Longer? Or do we take a still more expansive view? Do we allow science to follow any and all paths it reveals, to travel in directions that radiate from experimentally confirmed concepts but that may lead our theorizing into hidden realms that lie, perhaps permanently, beyond human reach? There is no clear-cut answer. It is here that personal scientific taste comes to the fore” (Greene, 2011).
  7. “Our descendants are bound to create an immense number of simulated universes, filled with a great many self-aware, conscious inhabitants. If someone can come home at night, kick back, and fire up the create-a-universe software, it’s easy to envision that they’ll not only do so, but do so often. … One future day, a cosmic census that takes account of all sentient beings might find that the number of flesh-and-blood humans pales in comparison with those made of chips and bites, or their future equivalents. And, Bostrom reasons (Oxford philosopher Nick Bostrom), if the ratio of simulated humans to real humans were colossal, then brute statistics suggests that we are not in a real universe. The odds would overwhelmingly favour the conclusion that you and I and everyone else are living within a simulation , perhaps one created by future historians with a fascination for what life was like back on twenty-first-century earth.” (Greene, 2011)
  8. At the time of the Copernican revolution, the supposed whole universe was just the solar system. But the sun eventually was revealed to be just one star in a vast galaxy, and in the 20th century, that galaxy became just one speck in space among billions and billions of others. Advocates of the multiverse theories suggest that the story repeats again.
  9. Appeal to intuitions vs appeal to math. The complaint about weirdness of multiverse theories is dismissed by Tegmark (2007) as being aesthetic rather than scientific. Evolution provided us with intuition for the everyday physics that had survival value for our distant ancestors, so whenever we venture beyond the everyday world, we should expect it to seem bizarre.
Let us see now what sceptics have to say about the multiverse theories. Most of arguments presented in this section are taken from an excellent paper by George Ellis “Does the Multiverse Really Exist?” Scientific American 2011, 38-43. Unless otherwise stated, italicised text in the rest of this section refers to this paper.

Arguments against multiverse theories

  1. Probabilistic arguments only make sense if these parallel universes actually exist. And logic cannot prove their existence. For instance, a multiverse model may predict a likely value of the cosmological constant, but the reverse is not true. A particular measurement of the cosmological constant does not require a multiverse. (George Ellis, The untestable multiverse, Nature, vol 469, 20 January 2011, p. 294-295.)
  2. If the Universe is a simulation, then anything is possible. However, the existence of a computer allowing such a simulation is not remotely feasible. Scientists are beginning to confuse science with science fiction. (George Ellis, The untestable multiverse, Nature, vol 469, 20 January 2011, p. 294-295.)
  3. Gross fears that anthropic infections might incapacitate attempts to find unique answers to tough questions by inducing people to give up the quest…. seemingly incalculable features of nature—say, the spacing of energy levels in atomic nuclei—eventually yielded to reductionist explanation. In fact, nearly all the normal, observable world can in principle be explained by the standard model of physics without resorting to any anthropic considerations. (Siegfried, 2006)
  4. For a cosmologist, the basic problem with all multiverse pro¬posals is the presence of a cosmic visual horizon. The horizon is the limit to how far away we can see, because signals travelling toward us at the speed of light (which is finite) have not had time since the beginning of the universe to reach us from farther out. All the parallel universes lie outside our horizon and remain be¬yond our capacity to see, now or ever, no matter how technology evolves. In fact, they are too far away to have had any influence on our universe whatsoever. That is why none of the claims made by multiverse enthusiasts can be directly substantiated. The proponents are telling us we can state in broad terms what happens 1,000 times as far as our cosmic horizon, 10100 times, 101,000,000 times, an infinity—all from data we obtain with¬in the horizon. It is an extrapolation of an extraordinary kind. Maybe the universe closes up on a very large scale, and there is no infinity out there. Maybe all the matter in the universe ends somewhere, and there is empty space forever after. Maybe space and time come to an end at a singularity that bounds the universe. We just do not know what actually happens, for we have no information about these regions and never will.
  5. The inflation theory that predicts an infinity of universes does not pass a key observational test. The cosmic microwave background ra¬diation reveals what the universe looked like at the end of its hot early expansion era. Patterns in it suggest that our universe really did undergo a period of inflation. But not all types of inflation go on forever and create an infinite number of bubble universes. Ob¬servations do not single out the required type of inflation from other types. 6. Fundamental constants are finely tuned for life. But we have no hope for proving this statement obser¬vationally. Additionally, most analyses of the issue assume the ba¬sic equations of physics are the same everywhere, with only the constants differing—but if one takes the multiverse seriously, this need not be so (Jenkins and Perez, 2010).
  6. An argument that fundamental constants match multiverse predictions is not valid. This argument refines the previous one by suggesting that the universe is no more finely tuned for life than it strictly needs to be. Proponents have assessed the probabilities of various values of the dark energy density. The higher the value is, the more probable it is, but the more hostile the universe would be to life. The value we observe should be just on the borderline of unin¬habitability, and it does appear to be so. Where the argument stumbles is that we cannot apply a proba¬bility argument if there is no multiverse to apply the concept of probability to. This argument thus assumes the desired outcome before it starts; it simply is not applicable if there is only one physically existing universe. Probability is a probe of the consis¬tency of the multiverse proposal, not a proof of its existence.
  7. An argument that string theory predicts a diversity of universes is not convincing. String theory has moved from being a theory that explains everything to a theory where almost anything is possible. In its current form, it predicts that many essential properties of our universe are pure happenstance. If the universe is one of a kind, those properties seem inexplicable. How can we understand, for example, the fact that physics has precisely those highly constrained properties that allow life to exist? If the universe is one of many, those prop¬erties make perfect sense. Nothing singled them out; they are simply the ones that arose in our region of space. Had we lived elsewhere, we would have observed different properties, if we could indeed exist there (life would be impossible in most plac-es). But string theory is not a tried-and-tested theory; it is not even a complete theory. If we had proof that string theory is cor¬rect, its theoretical predictions could be a legitimate, experimen¬tally based argument for a multiverse. We do not have such proof.
  8. In seeking to explain why nature obeys certain laws and not others, some physicists and philosophers have speculated that nature never made any such choice: all conceivable laws apply somewhere. The idea is in¬spired in part by quantum mechanics, which, as Murray Gell- Mann memorably put it, holds that everything not forbidden is compulsory. A particle takes all the paths it can, and what we see is the weighted average of all those possibilities. Perhaps the same is true of the entire universe, implying a multiverse. But as¬tronomers have not the slightest chance of observing this multi¬plicity of possibilities. Indeed, we cannot even know what the possibilities are.
  9. All in all, the case for the multiverse is inconclusive. The basic reason is the extreme flexibility of the proposal: it is more a con¬cept than a well-defined theory. Most proposals involve a patch¬work of different ideas rather than a coherent whole. The basic mechanism for eternal inflation does not itself cause physics to be different in each domain in a multiverse; for that, it needs to be coupled to another speculative theory. Although they can be fitted together, there is nothing inevitable about it.
  10. The key step in justifying a multiverse is extrapolation from the known to the unknown, from the testable to the untestable. You get different answers depending on what you choose to ex¬trapolate. Because theories involving a multiverse can explain al¬most anything whatsoever, any observation can be accommodat¬ed by some multiverse variant.
  11. The various “proofs,” in effect, propose that we should accept a theoretical explanation instead of insisting on observational testing. But such testing has, up un¬til now, been the central requirement of the scientific endeavour, and we abandon it at our peril. If we weaken the requirement of solid data, we weaken the core reason for the success of science over the past centuries.
  12. Ockham razor. Now, it is true that a satisfactory unifying explanation of some range of phenomena carries greater weight than a hodge¬podge of separate arguments for the same phenomena. If the unifying explanation assumes the existence of unobservable en-tities such as parallel universes, we might well feel compelled to accept those entities. But a key issue here is how many unverifi¬able entities are needed. Specifically, are we hypothesizing more or fewer entities than the number of phenomena to be ex¬plained? In the case of the multiverse, we are supposing the exis¬tence of a huge number—perhaps even an infinity—of unobserv¬able entities to explain just one existing universe. It hardly fits 14th-century English philosopher William of Ockham’s stricture that “entities must not be multiplied beyond necessity.”
  13. Scientists proposed the multiverse as a way of resolving deep issues about the nature of existence, but the proposal leaves the ultimate issues unresolved. All the same issues that arise in rela¬tion to the universe arise again in relation to the multiverse. If the multiverse exists, did it come into existence through necessity, chance or purpose? That is a metaphysical question that no phys¬ical theory can answer for either the universe or the multiverse.
  14. To make progress, we need to keep to the idea that empirical testing is the core of science. We need some kind of causal contact with whatever entities we propose; otherwise, there are no limits. The link can be a bit indirect. If an entity is unobservable but ab¬solutely essential for properties of other entities that are indeed verified, it can be taken as verified. But then the onus of proving it is absolutely essential to the web of explanation. The challenge I (NM: i.e. George Ellis) pose to multiverse proponents is: Can you prove that unseeable parallel universes are vital to explain the world we do see? And is the link essential and inescapable?
  15. Parallel universes may or may not exist; the case is unproved. We are go¬ing to have to live with that uncertainty. Nothing is wrong with scientifically based philosophical speculation, which is what multiverse proposals are. But we should name it for what it is.