Spatial inconsistencies

Consider a society S₁ which constructs the fact D₁ that dinosaurs existed in the Mesozoic era, and another society S2 which constructs the fact D2 that dinosaurs never existed, but that the numerous skeletons of huge reptiles were deliberately buried in the earth by God to make S₂’s denizens believe that dinosaurs existed. BothD1 and D2 have been constructed so that, according

to MC, they are facts about the world. Obviously, they contradict each other.

To be clear, the issue is not about two distinct societies having contradictory beliefs about paleontology, but about two societies constructing incompatible facts. How is constructivism supposed to cope with this incompatibility?

A relevant discussion of this problem is offered by Nelson Goodman (1978).

Goodman is well-known as a fervent promoter of ontological relativism, the doctrine that entities exist only relative to one version of reality as expressed in some symbolic system, but not relative to some other version of reality.

The notion of aversion of reality designates all those classes of entities whose existence is required to make the use of a certain system intelligible.

To display the relevance on SMC of a discussion on ontological relativism, we merely need to accept that SMC entails ontological relativism (the converse need not be true: one can be ontologically relativist without being construc-tivist.) Hence, any knock-down objection against ontological relativism will knock down SMC as well. This is not the place to deal in detail with Good-man’s views about ontological relativism. It suffices to say that his answer to the aforementioned inconsistency is straight and clear: incompatible facts may both be true if they are facts about different worlds. Thus, society S₁ lives in world W1 in which D1 is true, whereas society S2 lives in world W2

in which D2 is true. As Goodman phrases it, ‘contradiction is avoided by segregation’ (Goodman 1996: 152). Different civilizations could thus construct realities thoroughly foreign to each other.

How does Goodman support his position? We’ll discuss two of his lines of argument. First, he argues that there are conflicting truths that cannot be accommodated in a single world:

Some truths conflict. The earth stands still, revolves around the sun, and runs many other courses as well at the same time. Yet nothing moves while at rest. (Goodman 1996: 151)

The natural response to this is that the sentences ‘The earth is at rest’ and ‘The earth moves’ should be understood as elliptical for ‘The earth is at rest accord-ing to the geocentric system’, and respectively, ‘The earth moves accordaccord-ing to the heliocentric system’. But Goodman tells us that this is a wrong answer.

He analogizes with the following two historiographical sentences: ‘The kings of Sparta had two votes’ and ‘The kings of Sparta had only one vote’. There is an inclination to understand these sentences as ellipses for ‘According to Herodotus, the kings of Sparta had two votes’, and ‘According to Thucydides, the kings of Sparta had only one vote’. But obviously, these sentences do not tell us anything about Sparta. They only tell us about what Herodotus and Thucydides said about Sparta. It is clear that Herodotus’s and Thucydides’s versions cannot generate anything but self-descriptions, not descriptions of the

world. It is true that ‘According to Herodotus, the kings of Sparta had two votes’, even if they actually had no vote, or had three votes. The same about the relativizations to the geocentric and the heliocentric systems: it is true that the earth is at rest according to the geocentric system, but that still does not inform us about the world.

Merely that a given version says something does not make what it says true; after all, some versions say the earth is flat or that it rests on the back of a tortoise. That the earth is at rest according to one system says nothing about how the earth behaves but only something about what these versions say. What must be added is that these versions are true. But then the contradiction reappears, and our escape is blocked.

(Goodman 1996: 151)

Though subtle, Goodman’s argument is based on a spurious analogy. On the one hand, Herodotus’s version of the history of Sparta cannot possibly contain more than a finite list of permissible assertions about Sparta. On the other hand, the fact that the earth moves according to the heliocentric system allows an indefinite number of possible assertions which are not all of them constrained by the stipulations of the system. After all, the heliocentric system merely requires that the sun be in the center of the solar system.

The relative positions of the planets might have been fixed relatively to the sun. But even if the motion of the earth is made in this system a matter of definition, there are indefinitely many observational facts that cannot be obtained by stipulations about the constitution of the solar system. Think of the gravitational deviation by the sun of the light rays emitted by distant stars;

that is a fact about the world which is not entailed by defining a heliocentric system thought the stipulation that the earth revolves around the sun. It is thus clear that not every sentence which is relativized to a world-version is only about that version.

Goodman can do more of the same: he can make any new fact a fact about the system. The move would not seem entirely ad hoc if one looks at Goodman’s story about how world-versions are formed through the transfor-mation of other world-versions by the operations of composition, decomposi-tion, weighting, deledecomposi-tion, supplementadecomposi-tion, deformadecomposi-tion, and so on. Yet such a strategy should remind us of our previous discussion about semantic con-structivism’s slide into irrationalism. The same threat ought to be a sufficient ground to dismiss Goodman’s first attempt to tackle the spatial inconsistency of ontological relativism.

His second attempt to avoid the contradiction, quite surprisingly for an ontological pluralist, is an argument from parsimony. Goodman’s reasoning takes again a surprising direction. For him, the tolerant realist view that a

plurality of worlds can be versions of unique underlying world is nothing but the addition of an useless concept. To make this point clear, it needs to be emphasized that according to Goodman, only the accessible counts as real – a contentious assumption, no doubt, but one which will not be discussed here.

Since what is accessible is relative to versions, he concludes that what is real is relative to versions. Therefore, Goodman firmly opposes the concept of an independent world underlying the many world-versions. Even if its idea is intelligible, he maintains, such a world would be inaccessible, and thus of no philosophical avail. As Goodman urges,

Shouldn’t we stop speaking of right versions as if each were, or had, its own world, and recognize all versions of one and the same neutral and underlying world? The world thus regained is a world without kinds or order or motion or rest or pattern – a world not worth fighting for or against. (Goodman 1978: 20)

But if he conceded indeed, even if only for the sake of the argument, that the underlying world exists, why should it be entirely featureless? Why should the whole realm of properties be relegated to the world-versions and no bit of it to the world itself? Again, a way to understand this might be offered by SMC, which claims that all facts about the world (apart from the world of brute facts itself) are constructed. But this does not explain why Goodman holds the concept of a world to be theoretically useless.

Besides, there is at least one good reason for adopting this concept even if it has no specifiable properties: it allows the shunning of a fundamental inco-herence. After all, even Goodman must recourse to this world lacking “kinds or order or motion or rest or pattern”. We saw earlier that it is incoherent to talk about constructed world-versions unless one assumes that there are brute facts out of which constructed facts are made – apart from the event where one is a radical metaphysical constructivist, which certainly is not Goodman’s case.

We can now turn to another argument against Goodman’s strategy of avoiding inconsistency by segregation. Following Kukla (2000), we label it the argument of the interparadigmatic lunch. The argument goes against Good-man’s rebuttal of representing the universe in terms of a spatio-temporal con-tinuum. Instead, the suggestion is that we give up any representation of an all-encompassing space-time continuum:

The several worlds are not distributed in any space-time. Space-times of different worlds are not embraced within some greater space-time. (Good-man 1996: 152)

I do not see logical inconsistencies in this suggestion and shall not search for any other shortcomings. Suffices it to notice, together with Carl Hempel

(1996), that advocates of different versions can debate about their world-versions even though they are supposed to be living in different worlds. As Hempel phrases it,

If adherents of different paradigms did inhabit totally separated worlds, I feel tempted to ask, how can they ever have lunch together and dis-cuss each other’s views? Surely, there is a passageway connecting their worlds; indeed it seems that their worlds overlap to a considerable extent.

(Hempel 1996: 129–30)

I take it that this objection is decisive against the model of the unconnected spatio-temporal continua.

True, Goodman does not plead for a model of unconnected continua. In fact, he does not plead for anything specific. He merely objects to the repre-sentation of an all-encompassing space-time. Given his incomplete ontological proposal, we cannot conclude that it is incoherent. Nevertheless, we cannot infer that Goodman’s proposal stands as an adequate reply to the objection that the worlds constructed by different civilizations fight for the same space.

Therefore, we are warranted to infer the spatial inconsistency of SMC.