LA EXPANSIÓN Y APERTURA DESMEDIDA DE ESCUELAS DE POSTGRADO:

11.1. Universe growing in size.

Structurally, this argument is almost perfectly analogous to Shoemaker’s argument for the possibility of time without change. There is a world comprised of three inhabited regions

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which exhaust this world: A, B and C. Region A grows in size by 1 unit every three years; region B by 1 unit every four years; region C by 1 unit every 5 years. Given the observed regularity of these changes in size, the inhabitants of this world infer the same pattern will continue into the future, and hence that the sixtieth year will be one in which the whole world grows by 1 unit (for all and only multiples of sixty are multiples of all three numbers, 3, 4 and 5 (Oppy 2004, section 1.2)65. As with time without change, the global growth cannot be directly observed, for since all regions would grow together by an equal amount, there is nothing in the world that could be held up to measure the growth. That’s not yet to say that the global growth is non-relational, for, on the assumption that a global growth takes place, the whole world will be a greater size that it was before; hence the inference to a global growth does not directly contradict relationism about size. It does however mean that there could be changes in size that are not observable.66,67 _{It thus seems that relationism about size}

and the view that there can be no concrete differences that are not in principle observable (a view which provides some motivation for relationism) come apart.

11.2. Earth and the Aleph.

65 _{Oppy’s (2004) argument proceeds from local doublings to a global doubling, but the numbers don’t add up in}

such a way that would make for a sixtieth year where all three regions grow by the same amount. For consider that, since region A is meant to double every three years, by the sixtieth year it would have doubled 20 times; but region B would have only doubled 15 times in that same period, and region C 12 times. Having the regions all grow by one unit each time, instead of doubling, remedies this by ensuring that each would grow by the same amount as the other in the sixtieth year (even if the different regularities of growths in the different regions is such as to render them all different sizes as time progresses).

66 _{This assumes Euclidean space (Oppy 2004, footnote 4; Dainton 2010, Chapter 14.1).}

67 _{In my exposition I referred to the local doubling in size of the regions, and this seems to suggest that they are}

growing with respect to some others. But a region can become double the size of another in virtue of the

shrinking of the other. Indeed, for a relationist about size, these are different descriptions of the same occurrence. Thus the relationist can describe the local doublings in size in two ways: for example, take the twelfth year, in which regions A and B both double in size relative to region C. Observing this, the inhabitants might say that A and B have grown to double the size of region C; but they might also say that region C has shrunk to half the size of A and B. For the relationist, the difference is only at the level of description. Therefore, the relationist must separate the concept of doubling from that of growing, and that of halving from that of shrinking.

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Josh Parsons offers an argument from possible evidence to suggest that it is possible for an object to be a proper part of itself, based on a variation of J.L. Borges’s story “The Aleph” (2000; originally published in 1949). In Borges’s story, an object, the Aleph, in Beatriz Viterbo’s house, is described as containing the whole universe; which is to say, it is a part of itself.

Suppose that, prior to the events of Borges' story, Beatriz Viterbo discovered the Aleph for herself. Looking at her cellar staircase through a powerful electron microscope, she finds a tiny apparent replica of the Earth among the microscopic constituents of the 19th step. Looking closer, she sees an even tinier apparent replica of herself in her house, looking into a tiny electron microscope. Zooming out, she sees that the tiny Earth is surrounded by a Solar System, and indeed by a tiny apparent replica of the entire known universe, all forming a microscopic part of the 19th step. Looking into the sky with a powerful radio telescope, she sees that what she thought was the universe is in fact a part of a gigantic intergalactic replica of her cellar, as seen from the 19th step. Being a parsimonious reasoner, she concludes that the apparent replicas are one and the same thing – that the Earth she found in her staircase is the Earth she lives on; that the gigantic step in the sky is the one in her house. (Parsons 2013, 1)

Parsons ultimately uses this story as a springboard for a mereology according to which the proper part relation is not transitive. I’m not concerned here with his further arguments for that claim; but it is worth noting that Parsons is explicitly (Parsons 2013, footnote 6) making a Shoemaker-style argument. Parsons goes on to say:

I am not just asking you to consult your intuitions to decide that a work of literature is internally consistent. The story also describes a way in which a clearly consistent set of evidence could favour a scenario in which there is a mereological circularity. But scenarios cannot be favoured by evidence unless they are consistent. (Parsons 2013, 2-3)

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These last remarks are acknowledgment that appeal to possible evidence can be more powerful than appeal to intuitions, particularly given that different theorists may hold contrary intuitions. An argument along these lines is also the best bet for a conclusion such as the one drawn by Viterbo; conjuring up the imagery given in the story is not enough to determine whether what is being imagined is a mereological circularity, or a Russian doll universe containing parts that, while qualitatively exactly similar, are distinct. That is, as we saw above, such imagery can underdetermine the world imagined, giving rise to the problem of adjudication. Where intuitions among different theorists differ, Viterbo’s appeal to parsimony can be brought in to help adjudicate.

11.3. The Turing test. Turing (1950) famously proposed a test for the presence of mind, thought or intelligence in machines.

I believe that in about fifty years' time it will be possible to programme computers, with a storage capacity of about 109, to make them play the imitation game so well that an average interrogator will not have more than 70 percent chance of making the right identification after five minutes of questioning. … I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted. (Turing 1950, 442)

Putting aside the correctness of Turing’s predictions, and the demandingness of the test he proposes, he is effectively presupposing something like my modal principle: given that a computer could convince us – the average interrogator – that it is human more often than not, we should conclude that it is possible for machines to think. While Turing is perhaps more

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concerned about what will be the case, than he is about what could be the case, there seems to be a more general principle underlying his test: if there is a possible world in which the observable facts make it objectively reasonable to believe/conclude that p, then we should grant that p is possible.

12. Concluding remarks.

Appeal to possible evidence can help make progress on a debate concerning a certain possibility claim where differing claims about what can be imagined would have left the dialogue at a stalemate. Where one side in the debate has a principled reason for why a certain scenario is beyond justification by imagination (as I suggested would be the case for time without change if the Dependency Thesis is correct), then imagination of course cannot be appealed to in order to justify the possibility of that scenario. By illustrating how PEP might be appealed to, my aim has been to show that possible evidence can in principle

provide one with justification for a claim that lies beyond possible experience and beyond sensorial imagination. In this sense, PEP can be seen as expanding a scientific realist stance to the modal realm, with potentially surprising results.

I hope that the cases provided also show how one might go about justifying a possibility claim using PEP. Of course, it is open to anyone to disagree on what the observable facts in a given world make reasonable to conclude (perhaps by disputing one theory’s claim to be the most virtuous explanation of the possible phenomena, just as one might reject an actual inference to the (purported) best explanation, by pointing to the virtues of an alternative explanation). This was Warmbrod’s (2004) tactic, to rebut Shoemaker’s argument for the possibility of time without change. But, as I suggested in my discussion of Warmbrod’s

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critique, such a tactic seems to grant the general capacity of possible evidence to provide evidence of possibility.

However, the reader will have noticed that I have only provided a route to possibility claims. In the next chapter, I will explore the capacity for a consideration of possible evidence to lead to necessity claims.

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