It's all about the deep questions.
Second Principle on the Structure of Possible Worlds: A Solution to Hume’s Problem of Induction
1. An Allegorical Tale
Imagine that you have been taken prisoner. The judge of this imaginary prison, however, decides that your fate will be decided by chance in the following manner. Every morning during your stay at this prison a card will be drawn from a hat. Within this hat, 100 cards are placed. Furthermore, you are told that 99 of them have the word “death” written on them while 1 of them has the word “life” written on it. If one of the 99 are drawn on a particular morning, you will be killed that morning. If the “life” card is drawn, you will be spared. Not surprisingly, the very moment that you are told this, you expect to die the following day. Luckily, you don’t. This doesn’t take away your dread, however. The rest of the day is just as nerve-wracking as the previous one. However, the next morning, you are spared again. This cycle of dread and redemption continues on for days, then weeks. Gradually, the feeling of dread begins to wane and subconsciously you begin to expect to live to another day. Moreover, this feeling is justified. As long as you were not 100% confident that the judge was telling the truth with respect to the hats contents, the more days you live the more confident you are licensed to believe that the probability distribution of cards in the hat is not 99% chance of death and 1% life, but something much more skewed in the direction of life (this can be argued mathematically with conditional probabilities and Bayes’ theorem). As the months approach a year, you begin to wonder if there were any “death” cards in the hat at all.
Let us first start with some definitions. Call a possible world a Reasonable World (RW) precisely when that world, loosely speaking, is governed by reasons. This can be fleshed out in a number of ways. RWs can be said to have a “causal structure” where causes can be justly inferred from effects because of some internal necessity between events. These RWs can be said to have natural laws or nomological facts. These RWs are precisely the kind of world that science is justified in extrapolating its results into the future. Alternatively, call a possible world an Unreasonable World (UW) just in case it is not an RW. Now intuitively, a world which is in actuality a UW may resemble a RW , at least in part, “accidentally”. That is, a world with no natural law and no causal structure, can, from the point of view of an observer, look and behave as if it were a world with a causal structure. For another definition, a UW is said to be isomorphic to an RW just in case it behaves in this way. For our purposes, we will also need to similarly say that a UWis isomorphic until time t to a RWjust in case these two are indistinguishable to an observer at time t and at all times prior to time t, and after time t they are distinguishable. (Technically, under the Humean picture UWs that are completely isomorphic to RWs just are RWs. However, I do not need the existence for UWs that are completely isomorphic to RWs for my argument. I just need those UWs that veer off from RWs after some time to be conceptually coherent.)
3. Setting up the Analogy
David Hume’s problem boils down to the fact that no amount of sensory experience seems to be able to justify that we are not living in an isomorphic UW up to the present moment to the RW that science describes by extrapolating it’s results into the future. Sensory experience can’t do this since, by definition, these worlds are, at least up to the present, isomorphic to the world we suppose we inhabit. Now the allegorical story comes up. We are in precisely the same position as the prisoner. Except worse. With our current philosophical understanding, the actual world may be the RW that science posits or any one of infinitely many different isomorphic UWs until the present time. In almost all of these UWs, I will not be alive in the next second. Since in UWs future time states are not in any way constrained by past time states (if we are living in an isomorphic UW, time t could be our world, time t+1 could be a world consisting only of one floating pebble, and time t+2 could be a world filled with exploding supernovas) the chance that the aggregate of molecules that is me will continue to exist with all of the memories intact for one more second (in which an infinity of instances have past) is, basically, zero (or a hyperreal away). In this picture, an event that is next to impossible happens every instant: the “judge” draws the “life” card (the RW that science posits) out of all of the other UW isomorphic worlds and the RW. What should we conclude? Our conclusion must make all of these troublesome UWs not be genuine epistemic possibilities for the actual world. How do we go about doing that? By not letting these UWs be metaphysical possibilities. Furthermore, it is not enough restricting them to some finite number since we are “drawing out of the judges hat” infinitely many times a second. If the probability of picking the RW world described by science “out of the judges hat” is anything less than one on each drawing, our state of affairs quickly turns into an impossibly lucky state of affairs. There are no UWs in the judge’s hat.
4. The Argument
- If UWs are metaphysically possible, a miracle (or a violation of the correct laws of nature) would have occurred sometime in the past minute.
- A miracle, or a violation of the correct laws of nature, did not occur some time in the past minute.
- Therefore, UWs are not metaphysically possible.
(Note: Under the non-humean conception of laws there is a fact of the matter as to what laws govern the world. Under the humean conception of laws, there is a fact of the matter as to which set of statements that accurately describe the world are the most simple, economical, elegant, etc. for some explication of simplicity, elegance, etc.)
This argument proves the Principle of Reasonable Worlds (PRW): only RWs are metaphysically possible. What this argument concludes is what is called a strong necessity in the philosophical literature (for example, David Chalmers in his book The Character of Consciousness discusses the possibility of strong necessities as relevant to his conceivability argument for dualism), or alternatively a fundamental law of metaphysics. It is a necessary principle that is not known aprioribut can only be known, if it can be at all, by partly a posteriori considerations. Strong necessities constrain the space of metaphysically possible worlds alongside logical considerations. It can be easily shown that strong necessities are brute facts about reality. If they were to have some grounding to them, it wouldn’t be anything contingent since a contingent fact can not ground a necessary fact. Necessary logical facts cannot entail strong necessities since if they did strong necessities would be knowable a priori, which by definition they are not. Of course, if we accept PRW as a metaphysically necessary principle, which the argument argues for, David Hume’s famous Problem of Induction that has been plaguing the philosophy of science for centuries will have been answered. In defending the argument, premise 1 is doing the most work. Although it is conceivable to hold a view that miracles occur all the time in this world, I take very few (at least nonreligious) philosophers to hold this view. In what follows I will give a brief recap of why premise 1 is nearly certainly true, and then I will answer some potential objections. Finally, I will consider some ramifications of the principle.
4.1 A recap for the motivation behind premise 1
Imagine the initial allegorical tale except that the current philosophical opinion says that there are infinitely many cards that say death on them (corresponding to isomorphic UW worlds) and the “life card” (corresponding to the RW world in which all of scientific law carries on as usual). Furthermore, drawings of the hat occur every instant, infinitely many times in the span of a second. Current philosophical opinion would say that we are just “lucky” that every single one of those cards turns out to be the life card. This amount of luck is, almost literally, impossible. If the prisoner is justified in believing the hats contents do not contain death cards, we should be justified in concluding that the metaphysical hat of all possibilities do not include UWs.
4.2 Objection 1: Are strong necessities impossible?
There is a strong tendency to shy away from strong necessities for understandable reasons. Up to now, no strong necessities have been recognized to be true. They are brute facts that constrain the realm of all possible worlds, and one would like to avoid brute facts whenever possible. However, strong necessities don’t seem to be epistemically impossible. After all, it is a substantive claim about reality that X, where X is some maximally consistent state of affairs, could have been the case. Put in other words, it is not analytically true that “For all maximally consistent state of affairs X, X could have been the case.” When we say something could have been the case we are saying something more than just X is logically consistent.
Another reason for thinking that strong necessities are epistemically possible is the epistemic possibility of Modal Deflationism. Modal Deflationism says that there is nothing in the world making it true that X, where X is a non-actual state of affairs, is metaphysically possible. So, strictly speaking, it is not the case that X is metaphysically possible under Modal Deflationism. Even the fact that intelligent philosophers can hold this claim to be true should make someone hold that “If X is logically possible, then X is metaphysically possible” with less than absolute certainty. For example, David Chalmers being able to entertain the possibility of strong necessities would be a reason for not holding that the existence of strong necessities have probability zero. Again, to be able to deny the argument, it is not enough to say that it is extremely unlikely that there exist states of affairs that are logically consistent but not metaphysically possible. One would have to hold this view with absolute certainty, with the same certainty as an analytic statement, for example. However, this view is not analytic.
What would an argument for the impossibility of strong necessities look like? Since neither any particular strong necessity or its negation follows from a priori logical considerations, and contingent facts in all likelihood do not bear on them, it is a similar brute fact about existence that there are no strong necessities (a brute fact similar to admitting that there are strong necessities). It would almost seem that the only way to avoid strong necessities is to posit a strong necessity barring all other strong necessities! In my opinion, there is no reason to believe that human beings have a sort of privileged access to the constraints of all causally detached metaphysically possible worlds, an access that is completely infallible. So, it is not surprising that some strong necessities may exist that are not self-evident.
Furthermore, we must weigh the epistemic considerations we have concerning the truth or falsity of PRW. On one side is the understandable reason to not admit brute strong necessities constraining possible worlds, but on the other side of the argument we literally have the most evidence possible for any non-tautological proposition. I personally think it is quite clear that the epistemic considerations in favor outweigh those against. Now, being a necessary principle, it either constrains all possible worlds or no possible worlds. Since the epistemic considerations for such a proposition is literally the highest which it can possibly be, we should believe in the metaphysical necessity of PRW, a claim that can be argued through Bayesian reasoning.
4.3 Objection 2: The argument is too ambitious in the scope of its strong necessity
Technically, this claim is correct. From the above considerations it does not immediately follow that I am entitled to claim that all UWs are metaphysically impossible. The problematic UWs are just those that are isomorphic to the RW that science attempts to describe. If those are metaphysically impossible and some others are, then that would be fine. Premise 1 should be revised to read “If isomorphic UWs to the RW that science describes are metaphysically possible,….”. The conclusion should then read “isomorphic UWs to the RW that science describes are metaphysically impossible.” Although strictly speaking this claim is true, the resulting strong necessity proven by the argument turns out to be somewhat awkward. The principle would rule out only those isomorphic UW with the actual world up to the present moment. The previously proposed principle, PRW, is much more unified, simple, and (if it counts for anything) philosophically elegant. Either way, however, the purpose of this paper is to solve the problem of induction, which either principle solves anyway.
4.4 Objection 3: Couldn’t you do this for anything that is improbable?
While it is correct to say that someone could do this procedure for anything that is improbable (i.e. banish the improbability by guaranteeing the improbable event in question with a metaphysically necessary principle), it wouldn’t be epistemically justified. The argument I have spelled out could be couched in terms of Bayesian reasoning. The crucial point is this: no matter what non-zero prior probability you assign to strong necessities, my argument would go through with absolute certainty (technically, a hyperreal away from that). It also has to be the right kind of an event. If infinite people played the lottery and Bob won, a strong necessity shouldn’t be invoked to guarantee this event since you didn’t predict before hand that he would win. All in all, however, I think it is an interesting question for further analysis when someone is justified in invoking strong necessities.
PSW, and more generally simply the existence of strong necessities, not only solves the problem of induction but it also significantly impacts several philosophical debates. Every argument that uses conceivability to entail possibility (i.e. arguments in the philosophy of mind for dualism) must acknowledge that the existence of strong necessities not knowable a priori leads to conceivable situations that are not metaphysically possible (UWs). Not surprisingly, the study of modality in general would be dramatically change. The question of modal epistemology would be much more salient. PSW is also eerily familiar to Leibniz principle of sufficient reason, which could breathe new life into the argument from contingency in the philosophy of religion. Perhaps most importantly it would open the road for the examination and discovery of other strong necessities, if any more exist.