The Atlas of Reality
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, where w is an actual world and S is the cluster of all actual worlds. All of the theorems of classical logic will be true relative to all worlds and clusters, and so these logical truths will always necessarily be super-true. So we preserve all of classical logic.
This notion of a cluster of worlds could also be spelled out in terms of totality facts (Def D2.5, Section 2.4.2). A totality fact is a fact connecting a property with a set of objects, a set representing the totality of things that instantiate or are characterized by that property. In the case of ontological vagueness, it could be that some properties participate in multiple totality facts, in such a way that those properties have extensions with multiple, inconsistent boundaries. Let's assume that each possible world assigns just a single totality fact to each property. If a property is capable of participating in a plurality of totality facts, then this plurality of facts corresponds to a cluster of possible worlds, all of which could be actual together. If several properties are capable of participating independently in multiple totality facts, then the size of the cluster multiplies accordingly, corresponding to what mathematicians call the “cross product” of the permissible property-totality pairings.
When is ‘Definitely p’ true? It would be best not to identify the proposition that definitely p with the proposition that p is super-true. Instead, we could say something like this: ‘Definitely p’ is true relative to
For example, suppose there were only one actual world w, but suppose that it would have been possible for w to have been joined in actuality by other worlds, including w2. If p is true in w but not in w2, then p would be super-true but not definitely true relative to
Why is Many Actual Worlds preferable to the three-valued proposal? The superiority does not lie in the fact that on the three-valued proposal we have propositions that are neither true nor false, while on Many Actual Worlds some propositions are both true and false. In the Many Actual Worlds case, we do still have truth-value gaps of a kind: propositions can be super-true, super-false or neither. The crucial difference is that Many Actual Worlds can make use of the method of supervaluations, preserving both classical logic and all of the instances of Tarski's Schema.
Many Actual Worlds also enables us to mimic Epistemicism's account of higher-order vagueness. We have to assume that each world has an inherent tolerance for a certain degree of deviation. Each world has only a limited number of possible companions. This limited tolerance for deviant companions bears a close analogy to our finite capacity for knowledge and discrimination.
That is, we can have propositions that are definitely true but not definitely definitely true or propositions that are vague but not definitely vague.
Is Many Actual Worlds compatible with Truthmaker Theory, in particular with Atomic Truthmaker Theory? Prima facie, there are two problems. We want Not-p to be true in a world even if p is also true in another actual world, and we don't want (p&Not-p) to be true just because p is true in one actual world and Not-p in another. So, how do logically complex propositions find appropriate grounds in truthmakers?
We can use facts about worlds (if there are such) to group truthmakers into worldly cohorts. A set S of truthmakers is a worldly cohort just in case there is an actual world w such that, if w were the only actual world, S would contain all and only the truthmakers that exist. With this notion of worldly cohorts in place, we can construct a slightly modified version of Atomic Truthmaker Theory. For example, a negated atomic proposition Not-p is true if and only if there is some worldly cohort that does not include a truthmaker for p. Similarly, a conjunction (p&q) is true if and only if there is some worldly cohort that does include both a truthmaker for p and one for q.
Here is a specific example. RCK is indefinitely 6′ 1′′. There are actual worlds w1 and w2 such that RCK is 6′ 1′′ in w1 and exactly 6′ 1′′ + 1 nanometer in w2. The truthmakers for RCK's being exactly 6′ 1′′ and for RCK's being 6′ 1′′ + 1 nanometer must belong to two different worldly cohorts.
An alternative approach for the defender of Real Ontological Vagueness would be to embrace Truthmaker Maximalism with its totality facts (see Section 2.4.2). In a perfectly precise world, each property would have exactly one totality fact, specifying which things are (and by omission which things are not) in the property's extension. In the case of Real Ontological Vagueness, one or more properties would tremble a bit in their grip on totality facts, resulting in a plurality of totality facts associated with each vague property. When something belongs to the extension of a property according to one totality fact associated with that property but does not belong to its extension according to another totality fact, then that particular will be a vague or borderline instance of the property. If there are spatial location properties, then some entities will have vague spatial boundaries and, consequently, vague material composition.
12.2.3 Can identity or existence be vague?
Gareth Evans (1978) argued that there is at least one set of facts that cannot be vague, namely, facts about identity and distinctness. Evans argues that, for every entity x, it is always definitely the case that x = x. Now suppose, for contradiction, that there is an object y that is vaguely identical to x. That is, it is neither definitely identical to x nor definitely distinct from x.
Now suppose that y is identical to x. Since x has the property of being definitely identical to x, then y must have that property. Thus, if y is identical to x, then it is definitely identical to x.
Suppose instead that y is not identical to x. If y is not identical to x, then it surely cannot be definitely identical to x. In fact, if y is not identical to x, it is definitely not definitely identical to x. However, x is definitely definitely identical to x. So, x and y definitely differ in at least one property, namely, the property of being definitely identical to x. Therefore, y is definitely not identical to x. Thus, if y is not identical to x, then it is definitely not identical to x.
Since it follows from the Law of Excluded Middle that either y is identical to x or y is not identical to x, we have proved that either y is definitely identical to x or y is definitely not identical to x. There can be no vague identity (assuming Real Ontological Vagueness).
Actualists have a simple argument for thinking that there can be no vague cases of existence. For any entity x, the existence of x can be defined (for Actualists) as the logical tautology x = x. Certainly, this logical tautology must be definitely true. Thus, every case of existence is a case of definite existence. Anti-Actualists, in contrast, treat existence as a property that does not belong, as a matter of logic, to every entity. So, Anti-Actualists can countenance vague existence.
12.3 Conclusion
We've covered two main topics in this chapter, both concerned with the scope of existence: are there non-existent or non-actual things, and are there vague objects? The No answers (Actualism and Epistemicism) seem the most conservative, from an ontological point of view. They certainly avoid multiplying objects. However, Anti-Actualists and defenders of Anti-Epistemicism (such as the Many Actual Worlds theory) insist that we have good reason for the multiplication.
The strongest case for Anti-Actualism appeals to the role of merely possible objects as objects of intentional attitudes like seeking, fearing or worshipping, and as constituents of the truthmakers of modal facts. To meet this case, Actualist
s must resort to ersatz entities, like haecceities or abstract representations. We will examine this debate in further detail in Chapters 14–16.
The positive case for Real Ontological Vagueness consists simply in the strong impression that many things lack definite boundaries or definite quantitative features. This positive case faces two challenges. One comes from Epistemicists, who insist that all apparently vague boundaries are merely projections of our own ignorance. The other comes from Multiple Meaning Theorists, who locate all vagueness in ambiguities in our language or our concepts.
13
Solipsism, Idealism, and the Problem of Perception
We've examined reasons for thinking that the world includes more than one particular. Now we can turn to questions about what those particulars are like. In subsequent chapters, we take up a wide range of such questions, including:
Do particulars change over time? Do they persist through time? Do they begin to exist or cease to exist?
What is it for particulars to be located in space? Are regions of space themselves particulars? If so, of what kind?
Do some particulars have other particulars as parts or are all particulars simple? When do some things compose a further, composite thing?
Do some particulars cause others? Does everything have a cause? What sorts of things can be causes or effects?
However, before taking up those questions, we should ask a more fundamental set of questions. We must consider whether the world really includes a host of physical objects arranged in space and time, as our sense experience suggests. We do not consider the possibility of an all-encompassing form of skepticism, that kind of skepticism according to which we know absolutely nothing, as was defended by the ancient New Academic school of philosophy. We assume that we know something about the world. However, we must consider the question of the relation between our minds and the world as it appears to us.
Historically, many philosophers have adopted one version or another of Idealism, the view that everything in reality is in some sense fundamentally mental, consisting entirely of minds and their dependent contents. Philosophers who have embraced some form of Idealism include George Berkeley, G.W. Leibniz, Immanuel Kant, J.G. Fichte, F.W.G. von Schelling, G.W.F. Hegel, F.H. Bradley, and Alfred North Whitehead. In modern times (since Descartes revived the problem of skepticism), many philosophers have been challenged by the need to prove the existence of the external world, of everything beyond one's own mind. Modern philosophy has thus been haunted by the specter of Solipsism, the view that only I and my experiences exist. At an even further extreme, George Santayana (1955) proposed (as a hypothesis) Solipsism of the present moment, the theory that everything that was, is, or will be is wholly contained in the contents of my own present state of consciousness. On this view, one must deny the reality even of one's own past or future.
At times, the threat of Solipsism has been taken as a challenge to the very possibility of metaphysics, as traditionally understood. How can one hope to describe reality in its most fundamental features if we can be certain of nothing beyond our own minds? It is better, however, to think instead of Idealism and Solipsism as metaphysical theories in their own right, to be evaluated just as we would evaluate other metaphysical theories.
We must make a sharp distinction between radical skepticism, which is an epistemological thesis, and Idealism or Solipsism, which are metaphysical theses. Radical skeptics deny that we can ever know or be certain about the existence of anything beyond our own minds. Solipsists adopt the metaphysical thesis that nothing exists beyond his or her own mind. One can be a skeptic about the external world without being a Solipsist. One might even think that the best metaphysical theory of the world includes the existence of other minds and of the physical world, while denying that we can know or be certain that this theory is true. In this chapter, we consider Solipsism as a theory about reality, not merely as a thesis about what we can know.
Of course, radical skepticism and Solipsism are connected. If one believes that one knows that the external world exists, then one cannot be a Solipsist. Conversely, if one thinks that one cannot know anything about the external world, then one will have to at least consider Solipsism as an initially attractive option, given its great economy.
13.1 Defining the Mental and the External
Idealism is the thesis that everything is mental. This raises the question of what it is to be mental.
Presumably, to count as mental in the appropriate sense is to be a thing all of whose intrinsic properties, or perhaps all of whose intrinsic and fundamental or natural properties, are mental. So, it would be helpful to have a clear conception of a mental property.
The mental should encompass two kinds of things: minds and the things that are parts, constituents, events or qualities of minds. The former are subjects of ideas, thoughts, experiences, beliefs, attitudes, feelings, and so on, while the latter are those ideas, thoughts, and so on, themselves.
We don't want to define mental properties in terms of those properties the having of which depends somehow on the existence of a mind, since this would make every variety of theism (the belief in the existence of a creator God) into a form of Idealism, on the assumption that God is a mind and that everything depends on God for its existence. Instead, we should focus on the nature of mental properties themselves.
We could proceed simply by listing some paradigmatic mental properties and then counting any property as mental if it sufficiently resembles those on the list. However, everything resembles everything, to some degree. To carry out this definitional strategy successfully, we should also have a list of paradigmatic non-mental properties, to serve as the contrast class. To be a mental property would be to resemble the first class more than the second. The latter task is difficult, since Idealists may claim that any property we could name is really a mental property. Certainly George Berkeley would have claimed this. Berkeley argued that what we might think of as paradigmatically physical properties, like mass, shape, and volume, are in fact only properties of our sensory ideas, and so covertly mental in character.
Another tack would be to attempt to define physical property, and then to identify the non-mental things as things having only physical intrinsic properties. Idealism could then be defined as the thesis that there are no non-mental things. However, this won't quite work, since some Idealists, Berkeley included, will insist that some ideas have only physical properties.
What we really need to do is to define first what it is to be a mind, a subject of thought and experience. We could then define a physical thing as something that is neither a mind nor a part, constituent, attribute, or event in the life of any mind.
Some mental properties are clearly subject-entailing, that is, they are the sort of properties that only minds or subjects can have. These include such properties as thinking, believing, experiencing, intending, and so on. Only minds or subjects can do those things. Now we can just use the sensible qualities themselves as the contrast class for the definition of ‘subject-entailing property’. Even Idealists will admit that there is a difference between the subject-entailing properties of the mind itself (thinking and so on) and the properties of the ideas or experiences in the mind (including their supposed sensible or even physical qualities).1
So, here is a suggested path:
Def D13.1 Sensible Property. A sensible property is a quality that things appear to have in our sensory experience (like colors, tastes, shapes, textures, etc.).
Def D13.2 Subject-Entailing Property. A subject-entailing property is a property that is more like believing, thinking, intending or experiencing than it is like any sensible property.
Def D13.3 Mind. A mind is a thing with at least one subject-entailing property, or the property of having the power or potentiality for a subject-entailing property (like the property of being able to think) that is essential to it.
Def D13.4 Mental Thing. A mental thing is either a mind or a part, constituent, attribute or event intrinsic
to the life of a mind.
Def D13.5 Mental Property. A mental property is a property the having of which entails being a mental thing.
Def D13.6 Wholly Mental Thing. A wholly mental thing is a thing whose only intrinsic or fully natural properties are mental properties.
Idealism can then be the thesis that everything is wholly mental.
13.1T Idealism. Every fundamental particular is wholly mental.
We can define a physical property as a perfectly natural non-mental property. Idealism entails that no physical property is instantiated, since it entails that all instantiated natural properties are mental properties. (An even stronger version of Idealism would entail that no physical property could be instantiated.) We also assume that if there are any instantiated physical properties, they are similar to the properties posited by our best physical scientific theories, including mass, charge, volume, baryon number, spin, shape, velocity, and so on.
13.2 Solipsism and Phenomenalism
As we said, Idealists suppose that everything in the world, including what appear to be ordinary physical objects, are in fact either minds or conscious aspects of minds. Solipsism is that form of Idealism that insists that only one mind exists.
13.1T.1 Solipsism. Every fundamental particular is wholly mental and part (or attribute or event intrinsic to the life of) of a single subject or mind.
Historically, Idealism and Solipsism were associated with Phenomenalism, the view that the things that appear to us in sense experience are in reality only mental phenomena.
13.2T Phenomenalism. Everything we are familiar with or that we have knowledge of, including apparently physical objects, is in reality wholly composed of or wholly grounded in wholly mental things.
Phenomenalism would have some plausibility for us if we accepted the Veil of Perception: