PMeth 1.5 Fifth Corollary of Ockham's Razor. Other things being equal, adopt the theory that attributes the fewest ambiguities to natural language.
There is no evidence, independent of the theory of Actualism and Possibilism themselves, that these expressions are ambiguous. This is a clear advantage to Meinongianism, which can treat all such expressions, whether referring to possible or impossible things, in a perfectly uniform matter. Nonetheless, although this is certainly an advantage, it is not an absolutely decisive one.
12.1.3 Exportation and the Barcan Formula
As we have seen, Actualists take definite descriptions to be quantifiers rather than referring expressions. They can also interpret ordinary proper names in much the same way. For example, if we consider the sentence ‘Austin is a city’, we could interpret ‘Austin’ as a quantifier. ‘Austin is a city’ then says that there is one and only one thing named ‘Austin’, and everything named ‘Austin’ is a city. (Importantly, other things might have names that look and sound just like this one, but those are in fact different names.) In this way, Actualists can handle empty proper names. To assert the sentence ‘Santa Claus does not exist’ is to say that the name ‘Santa Claus’ does not name anything.
If definite descriptions and proper names are quantifiers, then every use of these expressions has to be assigned a definite scope within the sentence in which it occurs. Suppose, for example, that a sentence contains an operator, an expression that operates on one sentence to produce another. Some common operators are ‘It is necessary that…’, ‘It is possible that…’, ‘S believes that…’, and ‘It is not the case that…’. If we combine operators with quantifiers (including Russellian definite descriptions and names), we can produce two kinds of sentences, those in which the quantifier has wide scope over the operator, and those in which the quantifier has narrow scope within the operator. Consider, for example, (13–18):
(13) It is possible that the F is G.
(14) The F is possibly G.
(15) Something is possibly G.
(16) Sam believes that the F is G.
(17) The F is something Sam believes to be G.
(18) There is something that Sam believes to be G.
The transition from (13) to (14) and from (16) to (17) is exportation. Actualists deny that exportation is generally valid. They will insist that (13) can be true, although (14) is false, and that (16) can be true even if (17) is false. For example, Actualists might say that it is possible that something is a golden mountain, but that there is nothing that is possibly a golden mountain. Similarly, it may be that Sam believes that an elf lives at the North Pole, even though there is nothing about which Sam believes that it is an elf living at the North Pole. It is invalid, in general, to export a quantifier from a narrow scope position, like (13) and (16), to a wide scope position, like (14), (15), (17), and (18). The invalidity in these cases mirrors the invalidity of exporting the existential quantifier (‘something’) through these same operators, as in (19–22):
(19) It is possible that something be a golden mountain. (Narrow scope quantifier)
(20) There is something that is possibly a golden mountain. (Wide scope quantifier)
(21) Sam believes that something is a jolly man at the North Pole. (Narrow scope quantifier)
(22) There is something that Sam believes to be a jolly man at the North Pole. (Wide scope quantifier)
In contrast, Possibilists and Meinongians should insist that exportation of this kind is always valid. If (19) and (21) are true, then so must (20) and (22). They need not accept the exportation of all quantifiers, but they will accept the exportation of names, definite descriptions, and existential quantifiers through modal and intentional operators.
The logical transition from (19) to (20) corresponds to a formula of modal logic known as ‘Barcan's formula’ (after the logician Ruth Barcan Marcus). The Barcan formula states that we can always export an existential quantifier through the possibility operator. This formula is logically valid in those modal logics that assume a fixed domain of quantification in all possible worlds. That is, those logics that validate the Barcan formula are logics where the answer to the question—What exists?—doesn't vary from possible world to possible world. Such logics would be embraced by Possibilists and Meinongians but rejected by Actualists.
12.1.4 Arguments for Actualism
We will look briefly at five arguments for Actualism. The first appeals to Ockham's Razor (PMeth 1). The second raises problems for attributing properties to non-existent things. The third raises problems concerning the identity and distinctness of non-existent things. The first stems from the best interpretation of true statements in natural English. And the fifth stems from Truthmaker Theory (2.1T/2.1A.1T/2.1A.1A.1T).
1. Ockham's Razor. Possibilism and Meinongianism require more entities than Actualism, so Ockham's Razor gives us reason to prefer Actualism. But does Ockham's Razor apply to non-existent entities or does it merely enjoin us not to posit the existence of things needlessly? Possibilists and Meinongians do not do the latter. They posit exactly the same number of existing things as do Actualists, and they do not assign existing things to more fundamental kinds or categories than do Actualists.
However, it does seem that Possibilists, and a fortiori Meinongians, are doing something extravagant, ontologically speaking. They take the class of things (whether existing or not) to be much larger than do Actualists. Even if they resist saying paradoxical things like ‘There exist some things that don't exist’, they must agree that some things don't exist, and the class of possible values of the phrase ‘some things’ includes for Possibilists and Meinongians many more things, like golden mountains, than it does for Actualists. This should count, at least to some extent, against Possibilism, and even more so against Meinongianism, which includes impossible things).
This isn't a knockdown argument for Actualism, since Ockham's Razor only proscribes multiplying entities needlessly. Possibilists can argue that both common sense and an adequate interpretation of many ordinary assertions demand the additional entities. As we've seen, this claim is disputed by Actualists. We will return to this issue in Chapters 14 through 16, on modality.
2. Attributing properties to non-existent things. Possiblists and Meninongians claim that there are non-existent things. Presumably, these non-existent things will have certain properties. But it is difficult to say what properties they do and don't have. Did Sherlock Holmes live in London or in a fictional city called ‘London’? Was Queen Victoria (the real Empress of India) acquainted with him? Was he left-handed? Did he ever live in Shropshire? Does he inherit all of the properties attributed to him in the stories? (What about existence? He exists in the Conan Doyle stories.) Is he an incomplete object, neither left-handed nor not left-handed? What happens if the Conan Doyle stories are logically inconsistent, if for example the stories imply both that Watson was and was not married in 1889? What then? These puzzles given us some reason to prefer Actualism, if Possibilists and Meinongians cannot supply principled answers.
Assuming that we have given up the Characterization Principle, these questions must be sorted into two kinds. First, there are questions about how a non-existent thing is conceived of, and second, there are questions about how a non-existent thing really is. If we ask whether Sherlock Holmes, as he is portrayed in the stories, is right- or left-handed, the answer is simply, Neither. We are not violating any principle of logic (like the Law of Excluded Middle, either p or not-p, which will we discuss later in this chapter) in recognizing that stories and other mental pictures are often incomplete. In contrast, if we ask whether Sherlock Holmes is really right- or left-handed, the answer again is Neither, but for a different reason. Sherlock Holmes has in reality no hands at all—he is neither left-handed nor right-handed in the same way that a rock is neither. The only properties Sherlock Holmes really has are either modal (possible or impossible, actual or not actual) or intentional (thought of by Conan Doyle, loved by many re
aders, widely imitated). Further, inconsistent stories pose no special problems. We do not contradict ourselves by asserting that the Conan Doyle stories represent Watson as both married and not married during a certain period of time.
3. Identity and distinctness. Quine (1953/1980) argued that the merely possible entities of Possibilism behave very badly with respect to identity, distinctness, and number. He worried that Possibilists could provide no sensible answer to the question of how many possible fat men are standing in the doorway or whether the possible fat man in the doorway is identical to or distinct from the possible bald man standing there. Similar worries arise concerning fictional characters. Does the same Sherlock Holmes inhabit each of Conan Doyle's stories? Did he add properties as new stories were written? Can the very same individual appear in new stories?
Possibilists have offered answers to these questions, or have offered explanations of why we don't know the answers. The answers to many of these questions turn on details about the structure of possibility and of its relation to the actual world, as well as metaphysical doctrines concerning the grounds of identity and distinctness for individuals. Some of these questions are as hard for Actualists to answer as they are for Possibilists.
Where fictional or mythical individuals are concerned, there are cases in which it seems that we do have good grounds for making judgments about identity or distinctness. In fact, it seems pretty clear that one and the same Sherlock Holmes appears in all of Conan Doyle's stories. Peter Geach (1967) introduced a relevant thought experiment involving two peasants, Hob and Nob, who erroneously believe that a witch exists who is blighting the village's crops. We can imagine a scenario in which it is plausible that Hob and Nob are thinking about and fearing the very same non-existent witch. (We'll consider the Hob and Nob case again, when looking at arguments against Actualism in Section 12.1.5.)
4. Interpreting statements in natural language. We tend to think that claims like (23–25) are true:
(23) Everything exists.
(24) Nothing is a golden mountain.
(25) There are no golden mountains.
This provides some evidence in favor of Actualism, since Possibilists and Meinongians deny all three. Possibilists can respond that these sentences reflect a well-known linguistic phenomenon, namely, the contextual restriction of the class of objects relevant to the truth of a particular quantified sentence. For example, one might truthfully say something like ‘All the students are here’, meaning that all of the students who are registered for this course are here. Similarly, it would be natural to restrict the relevant class in many cases to the class of actually existing things. Consider the following amendments to (23–25):
(23') Everything that exists exists.
(24') Nothing that actually exists is a golden mountain.
(25') There are no golden mountains that actually exist.
It is, therefore, unclear how much support (23–25) provide for Actualism.
5. Truthmaker objections to Anti-Actualism. Anti-Actualism is fully consistent with the weakest form of Truthmaker Theory, Truth Supervenes on Being (2.1A.1A.1T). Statements about non-existent things won't require any existing truthmakers. Consider, for example, (26):
(26) Golden mountains don't exist.
The truth of (26) supervenes on being, since in order to make it false, we would have to add golden mountains to the class of existing things. Intentional properties also seem to supervene on the conditions of actual beings. If it is true that Sherlock Holmes is RCK's favorite character, then making this proposition false requires a change in some existing thing, namely, RCK. Modal truths about the non-existent, like the possibility of golden mountains, are plausibly considered to be necessary truths, and all necessary truths supervene on each contingent truth, given the definition of weak supervenience (Def 3.1): you cannot change a necessary truth to a falsehood without some change in being, since you cannot change a necessary truth to a falsehood in any case!
However, Atomic Truthmaker Theory (2.1T.4) poses a set of serious challenges to Anti-Actualism. Consider, for example, (27) and (28):
(27) Native Martian organisms could have existed, although they do not in fact.
(28) Sherlock Holmes is my favorite fictional detective.
If (27) attributes a modal property (possibility) to non-existent Martians, then its truthmaker must be somehow connected, by its very essence, to those non-existent Martians. Similarly, if (28) attributes an intentional relation between Sherlock Holmes and me, then Sherlock must be somehow implicated in its truthmaker.
It is natural for Truthmaker Theorists to assume that a truthmaker for an atomic predication Fa or Rab must contain the subject or subjects (the entities a and b) of the predication as parts. It is also natural to assume the following Principle of Actual Parts:
Principle of Actual Parts. If something actually exists, so do its actual parts.
If we combine Anti-Actualism with both the Principle of Actual Parts and Atomic Truthmaker Theory, then the truthmakers for (27) and (28) would have to contain an actual native Martian and an actually existing Sherlock Holmes. Since neither native Martians nor Sherlock Holmes actually exist, this is a serious problem. In contrast, Actualists can provide truthmakers for (27) and (28) that include such actual entities as the property of being a native Martian or the property of being a brilliant detective named ‘Sherlock Holmes’.
Anti-Actualists have four options: (a) deny Truthmaker Theory altogether, (b) modify Truthmaker Theory in such a way that the merely possible existence of a truthmaker is sufficient for the truth of the corresponding proposition, (c) deny that the truthmakers for (27) or (28) need to contain the non-existent objects named by them or (d) deny or restrict the Principle of Actual Parts. Let's consider these one at a time.
a. Deny Truthmaker Theory altogether
Denying Truthmaker Theory altogether opens the door to extreme cases of metaphysical cheating. Indeed, if modal and intentional statements like (27) and (28) require no truthmaker, why think that their truth even supervenes on being? Leaving behind the Truthmaker Principle (2.1T) would be welcome to Presentists (20.2T.4, see Section 20.4) and to Hypotheticalists (4.1T, which we discussed in Section 4.2).
b. Modify Truthmaker Theory
Could Anti-Actualists respond by modifying Truthmaker Theory? Perhaps the attributions of possibility are made true by the possible existence of a truthmaker? There is a problem with this suggestion: it treats possible existence as a species of existence. That is controversial. It seems that possible existence is to existence as fake diamond is to diamond. To be merely possibly existing is not to exist at all, but to be something that could exist.
This option will help only with modal properties of non-existent entities, as in (27). It won't help with intentional relations to the non-existent, since non-existent objects need not have even possible existence, like RCK's favorite round square.
c. Truthmakers that are disjoint from the objects referred to
Anti-Actualists could deny that the truthmakers for (27) and (28) contain the non-existent objects they refer to. But then what connects these truthmakers to the proposition's subject or subjects? This would require brute necessary connections between separate or disjoint existences (that is, connections between the truthmakers and the relevant non-existent objects). These connections would not be grounded in any internal relation between the connected things. This is contrary to the Third Corollary of Ockham's Razor (PMeth 1.3). Therefore, Anti-Actualists should either give up on Truthmaker Theory entirely or bite the bullet by admitting actual things with actual but non-existent parts.
d. Denying the Actual Parts Principle
In the latter case, the truthmakers for (27) and (28) have non-existent objects as parts, even when the whole truthmaker exists. These would be weird entities, existing things with non-existent parts. However, Anti-Actualists can mitigate this drawback in two ways.
First, they could distinguish between more or
less fundamental truthmakers, with less fundamental ones grounded in more fundamental ones (this would have to be extra-conceptual grounding, to use the term introduced in Section 3.4). Truthmakers containing non-actual particulars are always grounded (directly or indirectly) in truthmakers that include only actual ones. For example, the intentional relations between Sherlock Holmes and RCK are grounded in psychological facts exclusively about RCK, facts involving relations between actual things, internal psychological activities, and RCK. The truthmaker for true propositions about RCK's attitudes toward Sherlock Holmes is not fundamental but is rather wholly grounded in facts about RCK's psychology. The Principle of Actual Parts applies only to the most fundamental truthmakers.
Second, Anti-Actualists could say that non-existent objects, as parts of existing facts, stand only in external relations. They stand in no internal relations or and have no qualities. They are super-thin, much more abstract than normal abstract objects such as numbers and sets. For instance, each set has some internal nature that grounds the fact that it has certain members. Non-existent objects have no such internal nature. They have only intentional and modal properties, grounded in the natures of actual things.
12.1.5 Arguments against Actualism
On the other side of the ledger, we examine four arguments in favor of Anti-Actualism. The first appeals to common sense. The second appeals to the need for intentional objects, that is, objects of certain mental attitudes. The third appeals to the need for fictional and illusory entities. And the fourth appeals to the need for non-existent things as constituents of certain merely possible situations.
The Atlas of Reality Page 43
