When Absence of Evidence is Evidence of Absence

There is a popular and catchy saying which I myself have been caught repeating in the past, but which, for all its intuitive appeal, is false; namely, that the absence of evidence isn’t evidence of absence. Many a new-atheist has repeated the mantra that there is no evidence for God’s existence, insinuating thereby that this absence of evidence is good evidence for atheism. William Lane Craig, a noted philosopher, theologian and tireless Christian apologist has responded as follows:

[Atheists] insist that it is precisely the absence of evidence for theism that justifies their claim that God does not exist. The problem with such a position is captured neatly by the aphorism, beloved of forensic scientists, that “absence of evidence is not evidence of absence.” The absence of evidence is evidence of absence only in cases in which, were the postulated entity to exist, we should expect to have more evidence of its existence than we do.1

He has reiterated as much more informally (but more elaborately) on his podcast, ReasonableFaith, where he says:

The absence of evidence will count as evidence of absence when if the thing existed, then having surveyed the grounds, so to speak, we would expect to see evidence of their existence, and we don’t see it. And so, for example, in the case of fairies, if they existed then we ought to be able to find traces of their existence – their dead bodies when they die, their carcasses, other sorts of remains, little clothing factories where they build their clothes, and we ought to detect them flying about just as we detect dragon flies and bumblebees – but we don’t. So this would be a case where I think the absence of evidence would count as evidence of absence.”2

On this view, the absence of evidence only counts as evidence of absence when we have some reason to expect to see the evidence ex hypothesi. This has enormous intuitive appeal; consider the hypothesis that there is at least one tiger in India. Can the fact that I, sitting in Canada, currently see no tiger really count as evidence that there is not at least one tiger in India? Surely not; presumably because that evidence isn’t expected on the assumption of the relevant hypothesis’ truth. Elliott Sober, reflecting on absence of evidence, notes that in the case of arguments from absence “it is easy to see how each can be turned into a valid argument by adding a premise. The arguments have the form:

I do not have any evidence that p is true.
p is false.

Just add the premise

(P1) If p were true, then I’d have evidence that p is true.”3

This further highlights the fact that it is natural for us to think that absence of evidence is evidence of absence only when we expect the evidence ex hypothesi.

For years I found this response intellectually satisfying, but in recent years I have come to think that it is woefully mistaken. It is true that my failure to observe a tiger in Canada provides no evidence against there being at least one tiger in India, but it is not because I wouldn’t have anticipated seeing a tiger in Canada given that there is at least one tiger in India. All my affection and respect for Craig notwithstanding, if Craig means that absence of evidence E for hypothesis H is only evidence of absence (i.e., not-H) when the probability of E on H is greater than 0.5, then he is, I think, incorrect. In what follows I will try to explain why, as well as explore what to me seem interesting corollaries of Bayesianism.4

John Hawthorne, speaking about probability theory and the fine-tuning argument at a conference back in 2015, warned:

“Human beings, even intelligent human beings, are terrible at reasoning about probabilities. There’s enormous empirical evidence that human beings are terrible at reasoning about probabilities, and so we have to proceed with care.”5

Playfully picking on (presumably) a student in the audience, Hawthorne says: “Justin gave us the kind of awesome sounding principle… [that] if you don’t see something then that can be evidence of its absence only if you expect that you would get evidence were the thing there.”6 Not the cleanest off the cuff articulation, but clearly Hawthorne had in mind the principle for which W.L. Craig advocates. He continues; “that’s wrong… and I can prove to you that it’s wrong.”7 He proceeds to give an illustration using a hypothetical creature he calls a Dynx, where he stipulates that 75% of Dynx are invisible to the naked eye, and the probability that there is a Dynx in a box placed before us is 50%. We open the box, and we see no Dynx. The probability that there is no Dynx given our background knowledge and this new piece of information (namely that we do not see any Dynx) is approximately 57%. You can satisfy this for yourself by simply dividing up the space of possibilities (i.e., ‘seeing a Dynx in the box,’ ‘not seeing the Dynx in the box,’ and ‘there being no Dynx in the box’), eliminating the possibility of ‘seeing a Dynx in the box,’ and then expressing your updated probability assessment accordingly. So, even though we ought not to expect to see a Dynx in the box if there is one in the box, our failure to observe one is still evidence for their being no Dynx. This simple illustration (and others like it) seems to be entirely compelling. What, then, is the genuinely Bayesian determination of evidence?

On the Bayesian theory of confirmation,8 some evidence E will count as evidence for some hypothesis H (given background knowledge B) just in case E (conjoined with B) raises the (prior) conditional probability of H. To put it more formally, E will count as evidence for H just in case: P(H|E&B)>P(H|B). However, [P(H|E&B)>P(H|B)]⊃[P(~H|~E&B)>P(~H|B)]. In other words, if E provides any evidence for H, then ~E provides some evidence against H. It needn’t, of course, be the case that E provides as much evidence for H as ~E does for ~H, but it strictly follows from Bayesianism itself that ~E would be evidence against H just in case E would be evidence for H.

To illustrate with an example, let us take a hypothesis H1: “that aliens exist,” and evidence E1: “I am being abducted by aliens.” Obviously P(H1|E1&B)>>P(H1|B). What is not so obvious is that P(H1|~E1&B)<P(H1|B). The reason it isn’t so obvious is that ~E1 provides negligible evidence for ~H1 (even though E1 would provide compelling evidence of H1). If aliens abduct me, that’s really good evidence that they exist. If aliens do not abduct me that’s really poor evidence that they don’t exist. It may be some evidence, but it isn’t very much evidence.

Not only can the absence of evidence be negligible evidence of absence while the presence of that evidence would be altogether compelling, but the absence of evidence can even be inscrutable evidence of absence while the presence of evidence is scrutable and enormously supportive of the hypothesis in question. Take the example of a miracle, and for simplicity let us use the miracle of the bodily resurrection of Jesus of Nazareth. The bodily resurrection of Jesus, if it did occur, would be relatively good evidence for God’s existence; P(G|R&B)>>P(G|B). However, if Jesus had not been raised from the dead, would that provide any evidence against God’s existence? According to Bayesianism it would, but it seems like it would be not only negligible evidence, but even inscrutable evidence. There is no way one could put a figure (with any justification) on how much more confident it should make us in atheism that some miracle, like Jesus’ resurrection, did not occur. If we could give any estimate of what the probability is that God would perform a miracle when called upon to do so, for instance, then we could make some predictions about how many hospitalized people with terminal diseases (according to medical diagnosis) under observation get better when prayed for. We can’t make these predictions not because there is no actual probability of God doing a miracle, but because we aren’t at an epistemic vantage point from which we can assess that probability with any level of confidence at all.

Further, the evidence may not be merely negligible, but can in special instances be literally infinitesimal (an infinitesimal is a non-zero infinitely small quantity). Consider Hempel’s paradox9 for a moment; any observation of a pink shoe provides some evidence for the hypothesis that all ravens are black. The hypothesis that all ravens are black is logically equivalent to the statement that all non-black things are non-ravens. It follows, therefore, that any observation of a black raven is evidence that all non-black things are non-ravens, and any observation of a non-black non-raven is evidence that all ravens are black. An observation can’t be evidence for one without being evidence for the other precisely because they are logically equivalent statements, at least interpreted at face value; this is just what Hempel called “the equivalence condition.”10 However, it seems as though there are potentially infinitely many things which are non-black non-ravens which, at any moment, we will fail to observe. If this is so, then each of these instances of absence of evidence will count as instances of infinitesimal evidence of absence (or, at least, infinitely many of these instances will count as instances of infinitesimal evidence of absence). One thinks of the infinitely many miracles God could have performed at any given moment (e.g., growing a lost limb, bringing a dead child back to life, parting the Atlantic ocean); is it really the case that every instance of a miracle not happening provides some evidence against God’s existence? If so, and if there are infinitely many opportunities for God to perform a miracle of some kind (in infinitely many of which God decides to perform no miracle), does that not entail that the probability of theism is literally infinitesimal, or else that each instance (or, at least, infinitely many instances) of a non-miracle provides at most infinitesimal evidence against theism? This gets a little tricky, of course, because Bayesian theory isn’t really equipped to deal with cases of what we might call ‘transfinite probabilities,’11 but if we take its implications seriously even in such cases we will plausibly think that at least some things provide literally infinitesimal evidence for a conclusion or hypothesis.

An interesting objection to this suggests that there is not, even potentially, an infinite number of unobserved observables. Given the limited bandwidth of the human body as a kind of measuring apparatus,12 there may be infinitely many different but observationally indistinguishable events. Imagine, for instance, two pairs of pink shoes whose colours or sizes differ by so little as to make it impossible for any human being to tell the difference between them. For any of the attributes assessed by the five senses, there will be limited empirical bandwidth given the human body as a tool of observation. What this seems to entail is that there is not a potentially infinite number of different possible observations, in which case we needn’t concede the absurdity of infinitesimal probabilities. This objection is appreciably practical, but I’m not entirely confident that it settles the matter. After all, I can imagine a human being with “electron-microscope eyes”13 or with any number of other physical alterations which would allow them to observe an apparently potentially infinite number of different events. For any such alteration, I can imagine God miraculously bringing it about that observer S has precisely the alterations necessary to observe some miracle M1 which would have previously been indistinguishable from miracle M2, but is not now indistinguishable from M2 for S. Moreover, I’m not convinced that observational indistinguishability is terribly relevant; there are infinitely many possible pink shoes which I could now be observing, but am not, and even if infinitely many of them would be indistinguishable to me, failing to observe any one provides some evidence against the hypothesis that all ravens are black. So it seems to me that we’re stuck with conceding that at least some things provide literally infinitesimal evidence.

In summary, I think we have seen why the absence of evidence is evidence of absence in all cases except those in which the presence of so-called evidence would do nothing to raise the conditional probability of the hypothesis in question. Thus, my failing to observe a tiger in Canada provides no evidence against the hypothesis that there is at least one tiger in India not because I wouldn’t expect that evidence if there were at least one tiger in India, but because even if I were observing a tiger in Canada it would provide no evidence that there is at least one tiger in India.14 We have also seen that even when absence of evidence is negligible evidence of absence, or inscrutable evidence of absence, or infinitesimal evidence of absence (or any combination of those three), it will still provide some evidence of absence; if E would have been evidence for H, then the absence of E provides evidence against H.

Post Scriptum: I want to thank Tim Blais, Cale Nearing and Sean Boivin who provided me, in discussions subsequent to the original article, with food for thought without which I would never have made the improvements I have lately introduced above.

1 William Lane Craig, “Theistic Critiques of Atheism” The Cambridge Companion to Atheism. Edited by Michael Martin (Cambridge University Press, 2006): 70.

3 Elliott Sober, “Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads,” in Philosophical Studies 143, no. 1 (2009): 64.

4 As a cautionary caveat lector; though I’m pretty confident that what I’m about to say is correct, I have not taken any class on probability theory (yet); if anyone thinks there’s some subtle mistake somewhere, they are encouraged to share it. I am more than open to updating my views.

8 Elliott Sober, “Absence of Evidence and Evidence of Absence: Evidential Transitivity in Connection with Fossils, Fishing, Fine-Tuning, and Firing Squads,” in Philosophical Studies 143, no. 1 (2009): 66.

9 James Fetzer, “Carl Hempel,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, (Spring 2017 Edition), accessed April 2, 2017. https://plato.stanford.edu/archives/spr2017/entries/hempel/

10 James Fetzer, “Carl Hempel,” in The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, (Spring 2017 Edition), accessed April 2, 2017. https://plato.stanford.edu/archives/spr2017/entries/hempel/

11 If one dislikes this term because they think that probabilities can be no higher than 1, which makes them finite, I would suggest they think about how the conditions I just stipulated could imply that some hypothesis H is infinitely likely without having probability 1. However, if that doesn’t mollify the critic, I could agree to change the term to ‘non-finite’ probabilities.

12 I borrow here from Bas C. van Fraassen, who notes insightfully that “the human organism is, from the point of view of physics, a certain kind of measuring apparatus.” See: Bas C. van Fraassen, The Scientific Image, (Oxford: Clarendon Press, 1980), 17. 

13 Bas C. van Fraassen, The Scientific Image, (Oxford: Clarendon Press, 1980), 17.

14 If one thinks that observing a tiger somewhere raises the conditional probability that one may be observed anywhere then one will reject this conclusion, but they needn’t, in so doing, reject the principle this example is being employed to illustrate.


Does Micro-indeterminism entail Macro-indeterminism?

A professor of mine, with whom I habitually disagree (much to his pretended ‘chagrin’ and our mutual amusement), has argued previously, and again recently, that even if indeterminism were true at the micro-level, for instance at the level of quantum mechanics, that would do nothing to make macro-determinism infeasible, where macro-determinism means something like: for every macro-physical event E, either (i) there is always exactly one macro-physical event E* from which E followed deterministically, or at least (ii) E, if it is not preceded by any physical events, deterministically entails all proceeding macro-physical events. I have previously expressed my skepticism about the thesis that if quantum indeterminacy were really true, then it would yield no consequences for the thesis of physical determinism on the macro (i.e., ‘observable’) level. It seemed to me that if quantum indeterminacy were really true, then it would always in principle be metaphysically and even nomologically possible for some macro-physical event of type E (which, with law-like regularity, causally brings about some subsequent macro-physical event type E*), to obtain without E* subsequently obtaining. To fail to recognize this, I thought, was just not to take quantum indeterminacy seriously. Even if the probability that macro-physical event E occurred without bringing it about that E* occurred is vanishingly small, so small as to be reputed practically impossible (say something in the order of, or less than, one chance in ten to the power of fifty, or something like that), it would still be physically possible for E to occur and E* not to occur. I argued that although there are some properties for which it is false to say ‘if one part of a whole has property P, then the whole has property P’ – for instance, if a song on an album has the property of being under three minutes long, it does not follow that the album has the property of being under three minutes long[1] – there are other properties for which it is true to say that ‘if one part of a whole has property P, then the whole has property P.’ For instance, suppose one part of a whole has the property of being extended in space; it does clearly follow from that that the whole has the property of being extended in space.[2] We call it a ‘fallacy’ because the inference from part-to-whole isn’t always and everywhere truth-preserving, but that doesn’t entail that it is never anywhere truth-preserving, and it is intuitively obvious that it is an inference immune to the problem of truth-preservation in at least some instances. Thus I argued that the property of being indeterminate was one of these instances, so that if some part of a whole (say, where the ‘whole’ is the continuous space-time, and the part in question is the quantum foam) has the property of being indeterminate, then the whole has the property of being indeterminate.

However, more recently I had been considering revising my view, and in trying to revise it I had to think through some of the considerations which I want to explore in this article. I will, here, lay out a case for defending my professor’s contention, and then subsequently argue that while I can imagine a possible world in which micro-indeterminism and macro-determinism were both true, such a world is not part of the set of physically possible worlds. What has to be denied, in order to reconcile micro-indeterminism and macro-determinism is, I think, too much.

First, the case in defense of the thesis that micro-indeterminism does not entail macro-indeterminism could go something like this: there is some finite set of possible and indeterminate quantum mechanical events [Q1, Q2,… Qn], and nothing determines which of these events will occur. This is sufficient for micro-indeterminism. Now suppose that each member of the set [Q1, Q2,… Qn] would either (i) (along with the set of macro-physical events preceding it) bring some macro-physical event P about necessarily, or else (ii) at least would do nothing to impede P’s coming about deterministically from some set of antecedent macro-physical events. So, on the first story Q1 ⊃ P, and Q2 ⊃ P, and so on, so that (Q1 v Q2 v … Qn) ⊃ P. On the second story there is causal closure of the macro and/or micro physical levels, so that each of these levels is entirely causally autonomous from the other. If either of these two stories worked, then one could safeguard macro-determinism even while conceding micro-indeterminism.

Do either of these stories work? I was, for a time, tempted to think that the first one could work in principle. After all, it seemed logically possible. The second is a little more queer because it is hard to imagine that micro-physical events could be called genuinely ‘physical’ events if they were not in any sense causally connected to the observable physical realm – what would it mean to call them ‘physical’ if they were not part of one single physical plenum? However, maybe the second story deserves more sympathy than that. Perhaps the word ‘physical’ has a wider use, so that we can even refer to universes in a multiverse ensemble (if such an ensemble exists) as physical, and the events occurring in them would be genuinely physical events, even if they were causally sealed off from our observable physical world. However, something is obviously wrong, in fact, with both of these stories, as I intend now to illustrate.

Suppose that there is a macro-physical brain-state event B1 which is caused by some ‘observation’ of an (indeterministic) quantum mechanical event (of course this wouldn’t be direct observation, but just suppose that all the appearances where such that, given my scientific paradigm, it appears to me that some quantum mechanical indeterminate micro-physical event has occurred – i.e., I can ‘detect’ it). Suppose that the set of all macro-physical events prior to B1 is symbolized by ‘S’, where each event in S is either entailed by all the events prior to it, or at least, if there is a ‘first event’ in the set, that it will entail all of the events subsequent to it in the set. Let this world with S & B1 be symbolized as W. Now, there is a logically possible world W’ which is maximally ‘close’ or ‘near’ to W, in which S obtains, but B1 does not obtain. Instead, S obtains along with B2, where B2 is the observation of a different quantum mechanical event (or none at all). Here, since both B1 and B2 are macro-physical events (i.e., observable brain states), it seems as though micro-indeterminism has led to macro-indeterminism. Notice that our logically possible worlds (W: [S&B1], and W’:[S&B2]) are both metaphysically possible, and nomologically possible given our currently best understanding of physics (at least to the best of my knowledge, and accepting for the sake of argument that an indeterministic model of quantum mechanics is correct insofar as it is indeterministic).

Consider the fact that observable brain states can be caused by (indeterministic) quantum mechanical events – if this is true, then neither of the stories we told work in fact. Quantum mechanical events, if they are really indeterminate, and if they really can, under certain conditions, cause different brain-states to actualize, and the actualization of brain-states is a macro-physical event, then clearly micro-indeterminism of the kind attested to in the standard Copenhagen view of quantum mechanics really can (and necessarily can) bring about some macro-physical observable event which would otherwise mutatis mutandis not have occurred. (I should add here a quick caveat lector: I do not endorse or believe in indeterminism of this kind, I mean only to accept that there is such indeterminism for the sake of argument – to see what would follow). For either story to work, we need micro-physical indeterminacy to be in principle undetectable to science. So, we can conclude that if detectable micro-physical indeterminacy exists, then micro-indeterminacy does entail macro-indeterminacy. In other words: detectable micro-indeterminacy entails macro-indeterminacy. Even in a world where micro-indeterminism were true and macro-determinism were never observationally disconfirmed, macro-determinism would, given ‘detectable’ micro-indeterminism, not in fact be true.

This same conclusion could be derived if we accepted the doctrine of mereological supervenience, according to which, as Jaegwon Kim explains, “[the] properties of wholes are fixed by the properties and relations that characterize their parts.”[3] If the set of properties and relations which characterize the physical world at the most basic level include indeterminacy then it seems to follow from mereological supervenience that the properties of the observable physical world include indeterminacy, even if nothing we bear witness to on the observable level would lead us to suspect its indeterminacy.

The intuition of my professor, I assume, is something like this: whatever happens at the quantum level, if we suspend an 18-wheeler 30 feet off the ground and then let it go, it will fall; come what may on the quantum mechanical level, that 18 wheeler is necessarily going to fall to the ground. Is this true? I’m not sure. I can imagine a set of quantum mechanical events all conjunctively occurring (however unlikely) such that the truck just disappeared, but this might just be my failure to distinguish science from science fiction.

Macro-physical determinism (Macro-determinism for short) is true if and only if every single macro-physical event either follows deterministically from others, or else at least deterministically entails all successive macro-physical events. If micro-physical events are indeterministic and observable or detectable by creatures whose brain-states are macro-physical, then macro-determinism is false. Even in a world where there are no observers at all, if there are indeterministic events which, counterfactually, would be observable were an observer appropriately situated, then that world is (macro-)indeterministic. The difference between the micro- and the macro- physical, after all, is purely anthropomorphic. There just is, in reality, no causal separation between events which are not observable to us, given the human organism as, in the words of Bas C. van Fraassen, “a certain kind of measuring apparatus,”[4] and those events which are observable to us. Our being organisms for whom some physical events are directly observable, and for whom others are merely detectable, does not give us any reason at all to think that unobservable physical events have no causal efficacy for bringing about macro-physical events. The atomic bomb is evidence enough of that. The idea is that the world really is a causal plenum. Imagine, by analogy, that each event in the physical world hooks up to all other physical events so as to make the whole aggregate different then it otherwise would have been without it, in the same way that the meaning holist thinks that each belief in a web of beliefs determines the character of all of the beliefs in that particular web.

This seems to settle the case pretty definitively, since a difference in the brain states of some observer can plausibly bring about a very different causal chain of macro-physical events. Thus, even if there is a logically possible world in which both micro-indeterminism and macro-determinism are true, it certainly isn’t our world, nor any worlds near enough to ours where there are detectable indeterministic events of any kind.

Is there a way out of this? Perhaps; for one thing, all somebody needs in order to claim that micro-indeterminism does not entail macro-indeterminism is that there be some logically/metaphysically possible world in which micro-indeterminism and macro-determinism are both true. I can imagine somebody arguing that when an observer ‘observes’ (mediately) a quantum mechanical event, the observer determines (by observing) what would otherwise have been an indeterminate event. Here the suggestion is that observation has the effect of making a macro-physical event deterministically cause a micro-physical event, but that no unobserved micro-physical events ever bring about a different macro-physical event. Is this possible? We are putting to one side the question of whether this gets the science right (I make no pretensions to understand the dynamics of quantum theory, since I am a philosopher and adamantly not a physicist); the question is rather ‘if this did get the science right, if this were really how the world were, then would it follow that micro-indeterminism could be conjoined with macro-determinism?

This would have to deny Heisenberg’s uncertainty principle, the cornerstone of chaos theory (which, contrary to folk-science, is actually a deterministic theory). The intuition behind chaos theory in general is just that every event, no matter how seemingly insignificant, has an impact on the whole causally-continuous world. A butterfly flaps it’s wings twice, as opposed to once, within some finite span of time, in central park, and a hurricane is set to hit the shore of Australia where it otherwise (keeping all else besides the extra butterfly-wing-flap the same) would not have. However, that’s no surprise – after all, chaos theory is built on the assumption that the world is a causal plenum, and this is perhaps the very thing being denied. If one is sincere in her commitment to the indifference micro-indeterminism makes for macro-(in)determinism then it seems there has to be causal closure of the micro-indeterminate level, such that no micro-physical event can even in principle bring about an observational difference, which would mean that no indeterminism could, in principle, be observed. If it were observed, (at least if it were observed by physical creatures whose brain states could be observed) then by that very fact it would have caused a macro-physical event.

It would have to be that the micro- and macro- levels were causally sealed off from each other, or causally indifferent to each other; at least that either the indeterminacy of the one was causally impotent with respect to the other, or that the determinacy of one was causally indifferent to the indeterminacy of the other. To be truly indifferent, though, the indeterminacies would have to be in principle unobservable – or at least they could not be observable/detectable in principle by beings whose observational apparatus was significantly physical. This, however, raises a troubling conundrum for the philosophy of science. Since the range or set of nomologically possible worlds is determined by our best scientific theories, and since those are birthed by methodologically empirical observation, it seems odd, and perhaps even incoherent full stop, to say that there is a nomologically possible world where physical events occur in such a way that they could not, in principle be detected or figure into our theories born of empirical observation. Perhaps there is a metaphysically possible world where materialism/physicalism is correct, and this case-scenario obtains, but it would not be a nomologically possible world. In fact, it seems a necessary truth that such a world would not be nomologically possible!

Is it metaphysically possible to have a causal quarantine of the micro-physical indeterminate level? If it is, then micro-indeterminism does not strictly entail macro-indeterminism. Moreover if that kind of quarantine is possible, then why not a quarantine of a certain set of macro-physical events? Maybe there are some macro-physical events which are deterministic in the sense that they will follow each other ‘come what may’ elsewhere (even come what brain-state events may). For instance, if the universe is expanding at escape velocity and thus faces imminent heat-death, then (plausibly) no combination of quantum mechanical events (or macro-physical brain-state events), however unlikely, will steer the universe clear of this apocalyptic course. This kind of macro-determinacy would be weaker than the macro-determinacy we have had in mind (pace the definition I offered above), but it would still be some kind of macro-determinism.

Therefore, micro-indeterminism nomologically entails macro-indeterminism just in case both (i) micro-indeterminism is observable in principle by creatures whose brain-states are macro-physical, and (ii) no set of macro-physical events is causally quarantined from the rest of the macro-physical order. The cost of denying (ii) is no less than the presumption that the world is a causal plenum (an assumption upon which some of our scientific theories, like Chaos theory, are built), along with mereological supervenience. The cost of denying (i) is to abandon the view that the range of nomologically possible worlds is set by what would be in principle empirically verifiable by observers situated appropriately/idyllically  in the logically possible world in question. Maybe this second option isn’t as bad as it looks; perhaps we can imagine, given our best science, a logically possible world within the range of nomologically possible worlds set by our best science, where the same regularities held in fact, and where we would only ever and always observe (even in principle, we could only ever and always observe) phenomena which would proscribe the construction of our best scientific model(s). Whether it is coherent to talk about nomologically possible worlds where no observers idyllically situated could in principle, using the scientific method, come to apprehend the nomic regularities which held in fact is an issue which I will leave for further exploration another time, when/if I decide to dig deeper into the relationship of modal discourse and the philosophy of science.

To recapitulate, so far I have argued that the ‘fallacy of composition’ objection against inferring macro-indeterminism from micro-indeterminism doesn’t seem to work, just as it doesn’t work to object that way to the inference from some thing’s part being extended in space to the thing as a whole being extended in space (note that having the property of being extended in space as a whole does not imply that there is nothing more to a thing than it’s spacial extension). This argument is tenuous though, as it will rely in part on one’s intuitions, and could in principle be defeated given a better understanding of the science involved. I argued that the cost of denying the legitimacy of this inference would be (no less than) the doctrine of mereological supervenience, and the doctrine that the physical world is a causal continuum from top to bottom. I also argued that there cannot in principle be a nomologically possible world were observers with a physical apparatus could not in principle detect indeterminacy if indeterminacy were a nomic reality. This is because it seems to me that to say that something is undetectable to physical science in principle is plausibly just to say that it is not physical. I have also conceded, however, that perhaps there is a more modest form of macro-determinism, call it weak macro-determinism, according to which there is some subset of macro-physical events which follow deterministically from each other come what may elsewhere. The universe’s facing heat death is one example of something which, come what brain-states may, seems physically inevitable. This, however, is not strong enough for macro-determinism as such, and thus has nothing, or in any case very little, to do with the present discussion. If observers can in principle stand in a ‘detecting’ relation to nomic indeterminacy (whether of the macro or micro variety), then macro-indeterminism follows of nomological necessity.


[1] I am here adapting an example I first read here: Is The Universe Contingent? (http://www.philosophyofreligion.info/theistic-proofs/the-cosmological-argument/the-argument-from-contingency/is-the-universe-contingent/)

[2] I gave this example previously on my Undergraduate Blog, in an article called: The Fallacy of “The Fallacy of Composition” Objection (http://thirdmillennialtemplar.wordpress.com/2013/02/03/the-fallacy-of-the-fallacy-of-composition-objection/)

[3] Jaegwon Kim, Mind in a physical world: An essay on the mind-body problem and mental causation. (MIT press, 2000), 18.

[4] Bas. C. van Fraassen, “Empiricism and Scientific Realism” in Philosophy of science: The central issues. Second Edition, edited by Curd, Martin, and Jan A. Cover. (WW Norton, 1998): 1070.