In §8.1, I offer three scenarios where there fails to be a unique, ideal science. The first two types of scenario can be grouped, because they are both kinds of cases where there is a failure of consensus.
Neither kind of scenario is particularly implausible. In the first, there is a unique, closest best-world where a number of complete sciences are discovered. However, at this world, there is no consensus among scientists to adopt a unique theory. This could be the case if the different, complete sciences heavily overlap. If they overlap, there may be no particular need to decide upon one theory as
the theory of science.
In the second, there are multiple, closest best-worlds where complete sci- ences are discovered. Perhaps we can imagine that all the closest best-worlds are such that substantial, social pressure prompts scientists to agree on a unique theory. However, there is no reason to presume that consensus will not settle on a different ideal science at each closest best-world.
Hence, we cannot rule out these types of scenario as implausible or impos- sible. If things are optimal, then there is one closest best-world, and at this best-world, consensus leads scientists to adopt a unique, complete theory. This
8.3. NO UNIQUE CONSENSUS 99
provides a unique, ideal science. However, there is no reason to presume things are optimal as described.
On the other hand, I propose that Deflationary-Friendly Naturalness does at least as well as its rivals in these kinds of scenarios. To evaluate this, I consider a number of sub-scenarios, depending on how lucky we are regarding the complete sciences that are available at the closest best-worlds. In each sub-scenario, I argue that Deflationary-Friendly Naturalness does at least as well as Lewis’s interpretation of naturalness.
An important point running through this chapter concerns Lewis’s episte- mology for naturalness. As detailed in ch.6, Lewis treats fundamental physics as our guide to which properties are perfectly natural. He states that ‘physics is relevant because it aspires to give an inventory of natural properties – not a complete inventory, perhaps, but a complete enough inventory to account for duplication among actual things’ (Lewis 1983, 356-7). This suggests that a complete, fundamental physics would provide a complete inventory of perfectly natural properties.
Furthermore, insofar as our actual, fundamental physics is a guide to nat- uralness, this suggests that Lewis should be most interested in a complete, fundamental physics discovered at the closest worlds meeting our restrictions. If a complete, fundamental physics discovered at a very distant world provided the correct, complete inventory, Lewis would have little reason to think that our actual, fundamental physics is even a guide to naturalness. This is because our actual, fundamental physics may not at all resemble a complete, fundamen- tal physics at some distant world. By restricting our attention to the closest world – which also shares its best theories with our world – we focus on the same worlds that Lewis should be concerned with
Consequently, this suggests that Lewis should have similar concerns about which complete, fundamental physics are discovered at the closest best-worlds. I make use of this point in what follows.
We are Maximally Lucky
If we are maximally lucky, then there is a unique, complete science adopted by consensus of scientists at the closest best-world(s). This means that there is a unique, ideal science.
100 CHAPTER 8. THE UNIQUENESS OF IDEAL SCIENCE To assume that we are maximally lucky is to assume that the three scenar- ios laid out in §8.1 do not reflect reality. Hence, on the assumption that we are maximally lucky, Deflationary-Friendly Naturalness does not render nat- uralness relative to multiple theories. This avoids the problems discussed in §8.2.
Similarly, when we are maximally lucky, Lewis’s interpretation of natural- ness operates smoothly as well. If there is a unique, ideal science, then this is presumably the science that provides a complete inventory of the perfectly natural properties. This provides a clear extension for duplication and other concepts by the theoretical roles considered in ch.7.
Unfortunately, there is no guarantee that we are maximally lucky in the way described. We might be relatively lucky, or we might be unlucky.
We are Relatively Lucky
We might measure our luck as a function of various concerns. For example, it might be partly measured by the number of candidate theories that are adopted by consensus at the closest best-worlds, where the fewer the number, the luckier we are. Additionally, an important measure of our luck is how
similar the favoured candidates are, with respect to their ontology. If we are
relatively lucky, the ideal sciences will not say dramatically different things about what exists.
There are reasons to think that we might be relatively lucky. Given that we are restricting our attention to best-worlds, we are concerned with worlds that share best theories with our world. It is plausible that the ideal sciences at those worlds have very similar ontologies.
Suppose, then, that we are relatively lucky. There are not many ideal sciences, and they are very similar with regard to their ontologies. Lewis faces an epistemological problem of knowing which properties are perfectly natural, because he does not know which ideal science gives the correct inventory of perfectly natural properties. However, he may nonetheless know the extension of duplication. This is because distinct, ideal sciences can provide the same set of duplicates, but provide different reasons for why two individuals are duplicates.
Following an example given by Button (unpublished), suppose that we are relatively lucky, and the choice at all closest best-worlds is between two ideal
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sciences, RGB and HSL. Both theories agree that there are properties cor- responding to colours, that there are properties of Redness, Greenness and Blueness, and that there are properties of Hue, Saturation and Luminance. However, RGB treats the properties of Redness, Greenness and Blueness as perfectly natural, and HSL treats the properties of Hue, Saturation and Lumi- nance as perfectly natural.
Suppose we have what Button might call a ‘Rainbow World’, which consists just of spacetime points, each of which has exactly one colour. Suppose that spacetime points a and b are both in this Rainbow World, and are both a par- ticular shade of orange. They both exemplify the same properties of Redness, Greenness and Blueness. Further, they both exemplify the same properties of Hue, Saturation and Luminance.
According to RGB, a and b are duplicates because they exemplify the same properties of Redness, Greenness and Blueness. According to HSL, a and b are duplicates because they exemplify the same properties of Hue, Saturation and Luminance. The two theories disagree on why a and b are duplicates, but agree on the extension of duplication.
If we are relatively lucky, then the ideal sciences form this kind of case. On this assumption, the ideal sciences are definitionally equivalent, in the sense that the primitives of one theory can be defined in the other theory, and vice versa. They agree extensionally and intensionally, but differ hyperintension- ally. In this case, Lewis does not know which properties are perfectly natural – he does not know whether it is RGB or HSL that provides the correct in- ventory of perfectly natural properties – but he can give a definitive extension to duplication nonetheless. This situation is inherited across the theoretical roles that rely on Duplicates. If we are relatively lucky, the benefits of these theoretical roles are therefore preserved for Lewis.
However, the case is analogous with those adopting Deflationary-Friendly Naturalness. If we are relatively lucky, then the complete sciences that are adopted by scientists at the closest best-worlds are few in number, and all have very similar ontologies. Unlike with Lewis, this does not raise epistemologi- cal issues with naturalness, but instead renders naturalness relative to distinct theories. In the example given, and by Deflationary-Friendly Naturalness, nat- uralness itself is relative to our choice between RGB and HSL. On the other hand, as with Lewis, the deflationary-friendly interpretation offers a unique
102 CHAPTER 8. THE UNIQUENESS OF IDEAL SCIENCE extension for duplication. Duplication, relative to RGB or relative to HSL, has the same extension. This provides a unique notion of duplication that avoids the costs for Deflationary-Friendly Naturalness discussed in §8.2, a good state of affairs that is inherited across the theoretical roles that rely on Duplicates.
Consequently, when we are relatively lucky, the theoretical roles considered in ch.7 are preserved on any interpretation of naturalness. Both Deflationary- Friendly Naturalness and its rivals enjoy the same benefits from these theoret- ical roles. So far, my uncomplicated cost-benefit analysis is preserved.
We are Unlucky
However, we may not be relatively lucky either. If we are unlucky, the situation becomes disastrous for both Lewis and those adopting my deflationary-friendly interpretation.
Suppose that we are unlucky. The ideal sciences are many in number, and they present remarkably different ontologies.
If this is the case, then Lewis is not in a position to even guess at which of these theories provides the correct inventory of perfectly natural properties. It follows that he cannot even guess at which properties are perfectly natural. By Duplicates, this means that he cannot even guess at which individuals are duplicates.
The situation for those adopting Deflationary-Friendly Naturalness is not much better. If we are unlucky, then there are many ideal sciences with re- markably different ontologies. According to Deflationary-Friendly Naturalness, naturalness (and thus duplication) is relative to the choice of ideal science. This renders duplication and associated concepts highly relative. If there are enough ideal sciences, the extensions become so variable relative to theory that we might start to doubt that these concepts really form cohesive notions at all. I propose that this situation is disastrous for both Lewis and me, but in different ways. Those adopting my deflationary-friendly interpretation face a situation where they possess a concept of duplication, but its extension dif- fers wildly relative to a multitude of theories. In this case, we might think that Deflationary-Friendly Naturalness’s analysis of duplication is extension- ally inadequate. Hence, the theoretical roles of Duplication and its related roles are unsuccessful in these conditions, and confer no theoretical benefits to Deflationary-Friendly Naturalness.
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Lewis does not face this problem of extensional inadequacy when we are unlucky. However, he achieves this only at the cost of providing no real analysis of duplication at all. Duplication seeks to analyse duplication in terms of perfectly natural properties. However, when we are unlucky, Lewis cannot even guess at which properties are perfectly natural. Hence, the ‘analyses’ offered by Duplicates and its related roles are entirely uninformative. It follows that Duplicates and its related roles confer no theoretical benefit to Lewis’s interpretation of naturalness.
Lewis might object that Duplicates is not entirely uninformative when we are unlucky: it tells us that two individuals are either duplicates, or they are not duplicates, and there is no in-between. This might be important across other, related, theoretical roles. Consider Materialism. When we are unlucky, Lewis can nonetheless say that materialism is either true or false. It is just that whether materialism is true is unknowable. By contrast, Deflationary- Friendly Naturalness provides the result that the facts of the matter as to whether materialism is true are theory-relative. Further, it may be that some metaphysician can prove some important claim p from the assumption that materialism is true or materialism is false. This confers a substantial benefit for Lewis’s interpretation of naturalness.
However, we can challenge this point. Our considered metaphysician rea- sons as follows, when ‘M ’ expresses the truth of materialism, and ‘p’ is some important metaphysical claim:
1. M∨ ¬M 2. M→ p 3.¬M → p 4. p
However, the deflationist – relative to any ideal science – can simulate the same reasoning. Hence, the result that p can be agreed upon by everyone, non-relative to ideal science. With this in mind, it is not obvious that the relativisation to ideal science imposes any cost here.
Hence, we see that Deflationary-Friendly Naturalness and Lewis’s interpre- tation both meet with equal disaster – when we are unlucky. This preserves the cost-benefit analysis in favour of Deflationary-Friendly Naturalness, because,
104 CHAPTER 8. THE UNIQUENESS OF IDEAL SCIENCE if we are unlucky, Deflationary-Friendly Naturalness still enjoys all the same benefits as its rivals.
This completes my overview of the ways in which the first two scenarios can come about. Across them all, I argue that Deflationary-Friendly Naturalness does at least as well as Lewis’s interpretation. If we are lucky or relatively lucky, then Duplicates is successful on both interpretations. Otherwise, both interpretations face trouble. As noted earlier and in §6.3, a number of other theoretical roles for naturalness follow from Duplication. They inherit the same situation.