The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  Here is a simple, “toy” example of what we have in mind. Suppose that the world consists of 1000 marbles, each of which is either black or white. We have observed 30 of them, and all of the observed marbles have been black. By induction, we conclude that nearly all of the world's marbles are black. However, there is only one possible world in which all 1000 marbles are black. In contrast, there is an astronomically high number of worlds in which the first 30 marbles are black and the rest are half black and half white.

  If we don't suppose that we have been interacting with a mechanism that provides us with a random sample of the marbles, the 30 black marbles give us virtually no reason for thinking that most of the rest are black. But Neo-Humeists have no right to talk about “mechanisms” here, since such talk implies the existence of powers and propensities as fundamental realities, exactly the sort of thing Neo-Humeists deny.

  Here's another example. Suppose that we have observed a simple pattern, repeated trillions of times over: an event of type X followed by an event of type O, followed in turn by another event of type X. There is one possible world where this same pattern is repeated throughout the history of the world, including all of the so-far-unobserved times. There is an astronomically large number of alternative worlds, where the pattern is violated some, many or all the time beyond the window of observation. The existence of an astronomical number of “anti-inductive” possibilities seems to give us a good reason not to jump to the usual inductive conclusion. This worry is based on the following version of the Principle of Indifference:

  Principle of Indifference. If the number of possibilities consistent with available data that contradicts a certain guess is known to be astronomically larger than the number of possibilities consistent with the data that fit it, then it is prima facie unreasonable to be certain that the guess is true.

  The best Neo-Humeist response is simply to insist that reasoning inductively is part of what we mean by ‘being rational’. Despite the large number of complicated worlds agreeing with observed data, it is always most “reasonable” to be confident that we in fact occupy a relatively simple world. It's just a fundamental axiom of reason to do so, in need of no justification and in danger of no refutation. Once again, this response comes at some cost. The Neo-Humeist must treat induction as a brute requirement of reason, without further justification. This can be done, but it must be counted as a cost of adopting the theory, in light of the first corollary of Ockham's Razor (PMeth 1.1), which requires that we minimize rational postulates.

  There is an alternative solution that is somewhat less attractive. Neo-Humeists could suppose that what it is rational to believe depends on what is true. In that case, it might be reasonable to believe that our world is governed by simple worlds, so long as it actually is. The skeptic would have to prove that the world is not simple in order to prove that we are unreasonable in thinking that it is. The drawback to this proposal is that it violates a plausible constraint on rationality, namely, that what is reasonable must be to some extent independent of what is true. It must be possible to reasonably believe something false and to unreasonably believe something true.

  Do Strong Nomism or Strong Powerism have an advantage here or is induction equally a problem for all? Armstrong and Tooley cautiously argued that Nomism does have some advantage. For Nomists, the problem is not to assign probabilities to possible mosaics of qualities (as it is for Neo-Humeists). Instead, Nomists can simply assign probabilities to each possible law, where the truthmaker for a law is a nomic-necessitation relation among certain universals. If we are considering whether or not there is a law that entails that all F's are G's (e.g., all ravens are black), it seems that we could give each possibility a prior probability of 50%. If we then observe many black ravens and no non-black ones, the probability that it is a law that all ravens are black should go up, approaching 100% in the limit.

  There are two problems with this rosy assessment of the rationality of Nomist induction. First, each possible law will be in logical conflict with a large number of competing laws. For example, that all ravens are black is in conflict with the law that all ravens smaller than 5 kg are black and the rest are white. In fact, there are an infinite number of possible laws in conflict with the law that ravens are black, and so it seems that each possible law must begin with an infinitesimally small prior probability. These tiny priors would constitute a probability trap from which the laws cannot escape, no matter how much data we collect.

  Second, this argument for induction works only if we assume that we already know in advance which universals exist and which do not. However, Armstrong and Tooley (at least) believe that we discover the universals that exist empirically, by discovering that they play a role in actual laws of nature. If the world is infinitely large, then there would be infinitely many possible universals to consider and so once again an infinite number of competing laws over which to distribute our finite prior probabilities. (It is a law of the calculus of probabilities that each set of incompatible hypotheses must have a total probability that is no greater than 1.)

  Powerist theories of induction will face exactly the same problems, with one important difference. For Powerists, the laws of nature are metaphysically necessary. Hence, there really are no “chaotic” worlds in which the actual laws of nature are violated. These chaotic scenarios are conceivable and can't be ruled out a priori (prior to empirical investigation), but Powerists don't have to concede that they are really possible, and they can claim that experimentation suffices to rule them out (as we will argue in the next chapter). Hence, Powerists are under no pressure to concede that we are unreliable or merely lucky in our inductive reasoning. That is, the Principle of Indifference cannot be used against Powerists because they do not concede that we know that there are a large number of chaotic possibilities. In fact, they can claim that we know that there are no chaotic possibilities at all. However, Powerists do share with the other theories the problem of the existence of an infinite number of possible hypotheses, all of which are compatible with the evidence so far collected.

  So, is the situation a symmetric one? Might no account of powers and laws have a solution to the problem of justifying induction? Not really. There is a difference between the challenge faced by both Neo-Humeists and Nomists and that faced by Powerists. Powerists have no simple solution to offer that explains why inductive inference is reasonable. However, they don't face a positive argument that seems to show that, if their theory is true, induction must be unreasonable. In contrast, Neo-Humeists and Nomists do face such an argument, based on the Principle of Indifference, since their account of possibility entails the real existence of large numbers of chaotic worlds that are really possible and fully compatible with observed data. They have the burden of explaining how induction could be reliable under those circumstances.

  Notes

  1Tooley and Armstrong also argue that Nomism provides a solution to the problem of induction, the problem of justifying the inference that unobserved cases are like observed ones. We'll examine this further in the section on neo-Humeism.

  2Could the Nomist suppose that there is a higher-order law, constraining the lower-order laws to connect only simple properties? Perhaps, but this also comes at the price of additional complexity in the theory.

  3Neo-Humeists differ from Hume himself in three ways. First, they are concerned with metaphysical issues of fundamentality and truthmaking, not with the psychological question of what our concepts of power and law may be. Second, Neo-Humeists do not deny, as Hume occasionally did, that it is true that there are powers and real lawful connections between things. Finally, Neo-Humeists offer a new account of the distinction between laws and accidental generalizations, as we discuss in the following paragraphs.

  6

  Powers and Properties

  We turn, finally, to Strong Powerism. Strong Powerists believe that attributions of power are fundamental. Laws of nature are merely expressions of the powers possessed by various kinds of
things, and counterfactual conditionals are grounded in the powers and tendencies of the entities involved in the counterfactual supposition together with their counterfactual surroundings.

  As we have defined them, powers and dispositions are properties of things. It seems natural to assume that there are other properties besides powers. If so, we can ask about the relationship between those properties that are powers and those that are not.

  There are two versions of Strong Powerism. One takes the truthmakers for causal laws to be universals (a “Realist” version). The second takes the truthmakers for causal laws to be the particulars that fall under the laws (a “Nominalist” version). We will explore the Realism-Nominalism controversy in more detail in the following chapter (Chapter 7). In the present chapter, we will ignore this distinction, instead focusing on how Powerism compares to other views about the laws.

  6.1 Advantages of Strong Powerism

  6.1.1 Causal connections and causal direction

  Powerists believe in real causal connections between things, causal connections that are not reducible to the Neo-Humeist's mosaic of qualities in spacetime. Instead, Powerists can rely upon the existence of causal processes, temporally extended things that unite cause and effect into a single, undivided whole. When one thing exercises an active causal power, introducing a process of change in a patient, there exists a single process that begins with the agent's active power at the time of the action and that includes the subsequent process of change in the patient (for more details on this issue, see Chapter 28). Where there is symmetric overdetermination (whether deterministic or probabilistic), the question of which potential cause is a real cause is simply the question of which potential agent is actually connected, by a real process, with the effect. This may be impossible for us to determine empirically, but there will always be a fact of the matter in the things themselves.

  Similarly, Powerists can appeal to the intrinsic nature of processes to fix the direction of causation. The exercise of an active power is always found at the beginning of an appropriate process in the patient, never at the end. That is, agents with appropriate active power are always joined to a process of an appropriate kind in the patient at the beginning of that process. Which terminus of the process counts as the beginning and which the end is also fixed by the nature of the active and passive powers involved. So, for example, since fire has the power to heat water, exposure to fire will typically be found at the beginning of a process of the water's becoming hotter, that is, at the terminus of the process with the lowest water temperature. We learn whether a power is one of heating or cooling by interacting with its bearer in well-designed experiments.

  6.1.2 Strong powerism and scientific knowledge

  We have considered objections to both Neo-Humeism and Strong Nomism based on the fact that they could not explain either the rationality or the reliability of our inductive and scientific methods. Do Powerist views fare any better in this regard?

  First, as we gestured toward in the last chapter and as will become clear below, the causal laws of nature turn out to be metaphysically necessary on standard Powerist accounts. In addition, these are not “brute” necessities because the causal laws are manifestations of the intrinsic natures of powers. This opens up the possibility of a purely rational, a priori component to our knowledge of the laws of nature, a component that might reliably and rationally guide us to the simplest of the empirically adequate theories (see Ellis 1999 and 2001).

  Second, since the causal laws are necessary, there are no worlds in which the same properties occur but obey different laws. Hence, we have no reason to think that there are any worlds that agree with our world in the distribution of properties in the observed zone but deviate from it in the unobserved zone. Thus, we lack any argument (any ‘undercutting defeater’) against the rationality of induction, in contrast to Neo-Humeism and Nomism.

  However, the critic could charge that there a large number of conceivable and epistemically possible scenarios in which things are chaotic in the unobserved zone, even if there aren't any really possible worlds like that. Doesn't the existence of such counter-inductive scenarios provide an equally good defeater to the rationality of induction?

  The simple answer is, No. Strong Powerists believe that we gain knowledge about the natures and powers of things through scientific investigation. This knowledge enables us to rule out those otherwise-conceivable scenarios in which things act contrary to their actual natures. For example, before we understood the nature of water (that it is composed of H2O molecules, each with a certain quantum-mechanical structure and associated powers), we might have thought it was possible for ice to exist at high temperatures. Now, we see that that conceivable scenario is just not possible.

  As Nancy Cartwright (1983, 1994), Judea Pearl (2009), and Alexander Bird (2010), among others, have noted, Powerism better accounts for our actual scientific practice than does Neo-Humeism. We don't simply consider a passively received set of observations and reason inductively. Instead, we actively isolate and manipulate things in order to better understand their causal powers and propensities. For example, in order to understand the causal powers and propensities of electrons and magnetic fields, we create carefully constructed experiments in which we expose electrons to magnetism while isolating them from other influences and interferences. We force the electrons to start with a variety of speeds and directions, and we use electrons produced by a variety of sources. We change the intensity and orientation of the magnetic field, noting how these changes affect the electrons' accelerations. These active interventions give us knowledge of natures that enable us to exclude certain conceivable scenarios from the realm of real possibility.

  This is not to say that Powerism has no epistemological vulnerabilities relative to Neo-Humeism. The Powerist has to admit that our ability to observe or detect real powers through experimental interaction is fallible. There is always the possibility that we have misidentified the samples we are probing (e.g., we're trying to study water but accidentally obtain a sample of hydrogen peroxide instead) or that we have failed to identify and neutralize all interfering factors in the environment. In addition, if we are trying to measure something's propensity to cause or to undergo certain effects, we may unluckily observe a frequency that deviates from the true objective propensities. Our empirical investigations of powers can never attain certainty, and this opens the door to the skeptic, who worries that we can never rule out the possibility that we are wrong. However, the Powerist can plausibly respond that it would be unreasonable to be paralyzed by mere possibilities of error, without specific reason to suspect that we are in error in this particular case. In addition, Neo-Humeists face similar skeptical challenges, since our observations of the categorical qualities of things are also fallible.

  Can the Powerist explain our preference for simple laws of nature? Is this theory vulnerable to the same objection we ran against Nomism—that it makes preference for simplicity a brute fact? The simplicity of the laws of nature would be a consequence of which properties are actually instantiated in our world. In other words, the simplicity of the laws is a function of the complexity of the essences of instantiated properties. The Powerist could perhaps appeal to God's preferences for simplicity as an explanation for the simplicity of the essences of instantiated properties. The Nomist has no such move.

  6.2 The Individuation of Properties

  It also seems natural to suppose that the connections between non-powers and powers are sometimes internal relations. That is, we might suppose that in some cases there is a property that is not a power, F, and a power, P, such that it is a matter fixed by the intrinsic characters of F and P that everything that has F also has P. In such a case, we could say that P is part of the ‘causal profile’ of F, or, to put it in abbreviated form, that F has P as one of its powers. For example, suppose that the property of being fire is such that, by virtue of its intrinsic character, anything that has the property of being fire also has the power
of heating proximate things. If so, we could say that the property of being fire itself has the power of heating proximate things.

  Def D6.1 Conferring a Power. A property F confers power P if and only if there is an internal relation between F and P of such a kind that anything that has the property F also has the power P.

  In particular, we can ask whether a property is ‘individuated’ by the powers it confers. Is it possible for two distinct properties P1 and P2 to confer exactly the same powers? If not, then the powers conferred by properties individuate them.

  Def D6.2 Property Individuation. A property P is individuated by the features in set A if and only if A is a minimal set with the following property: necessarily, any property having all of the features in the set is identical to P itself. In other words, if and only if A is a set having that property, and no proper subset of A has that property.

  6.1T Causal Individuation of Properties (Weak Thesis). Some fundamental properties are individuated by the set of powers they confer.

  6.1A Sicceity Theory. No fundamental properties are individuated by the set of powers they confer.

  If a property P1 is not individuated by its powers, then it would be possible for there to be a second property P2, such that P1 and P2 are distinct properties that confer exactly the same powers. If P1 and P2 are distinct but confer the same powers, it seems that there must be something that makes them distinct properties. At the very least, P1 has the property of being identical to P1, a property not shared by P2. The property of being identical to P1 is an example of what have been called ‘thisnesses’ or ‘haecceities’ (see Chapters 7 and 9), in this case the thisness of a property. We don't want to assume that properties are particular things, so we will use a different term than ‘haecceity’ in this case. Some contemporary metaphysicians, including John Hawthorne (2001) and Jonathan Schaffer (2005), have used the term ‘quiddity,’ but this choice is inappropriate, since the word ‘quiddity’ (or ‘quidditas’ in Latin) has a long history of use in medieval and early modern philosophy with an entirely different meaning. For this reason, we prefer ‘thusness’ or ‘sicceity’ (‘sic’ is Latin for ‘thus’ or ‘so’, pronounced ‘sick-say-ity’). If P1 and P2 are distinct properties, then the being-so that corresponds to P1 is different from the being-so corresponding to P2. In other words, they have different thusnesses or sicceities.