I’d like to try out this small argument for substance dualism. Let a quasi-miracle be a sequence of events that is both (i) remarkable and (ii) extremely improbable. Flipping a fair coin 1,000,000 times and its landing heads 1,000,000 constitutes a quasi-miracle. A chimpanzee at a typewriter producing a 950-page dissertation on anti-realism is another quasi-miracle.

Our world is indeterministic, and improbable events occur often. But quasi-miracles do not occur, and certainly do not occur regularly. Suppose you perform some action A and claim that A was done freely. For instance, let A be some deliberate and serious action such as swearing to tell the truth. Now suppose you are asked whether you did in fact act freely in swearing to tell the truth. You answer yes, or you type Y on your computer. I ask you again whether you acted freely in swearing to tell the truth, and again you type Y.

Since our world is indeterministic, there is always some small chance that any physical event fails to occur. But I claim that no matter how many times you were asked whether the action A was done freely, you would answer Yes. The resulting sequence of physical events would be both remarkable and extremely improbable. It would take the form Y,Y,Y,Y,Y,Y,Y,Y ….. oo. So if every instance of your answering Yes was nothing more than a physical event, there would be lots of quasi-miracles occurring, or we could easily make lots of quasi-miracles occur. But, by definition, we cannot make lots of quasi-miracles occur. Therefore, it is false that every instance of your answering Yes is purely a physical event. But this is just to say that some non-physical events occur. But then dualism is true.

Here’s another way to put the argument.

1. Indeterminism is true. Fact

2. Quasi-miracles do not occur (or almost never occur). Fact

3. For each agent S and free action A, S can affirm indefinitely that S performed A freely. Fact

4. If physicalism is true, then for each agent S and free action A, S can bring about a quasi-miracle.(from 3 and Def. quasi-miracle).

5. Physicalism is not true. From 2,4.

6. :. Dualism is true. From 5, and reasonable assumptions about idealism.

*An indeterministic process may create mechanism that could yield the kind of sequences you mention.*

It could not yield them with the kind of regularity with which they occur. Nor, frankly, do I see how quasi-miracles might be semi-regular. I don’t deny that there are regular occurences of sequences that are as improbable as the ones I descibe. But not ones that are improbable and remarkable: that’s why the problem of luck looms so large for libertarians. I’ll check out the Lycan paper. Thanks.

Mike

Interesting argument. Questions/comment for qualification. How is 3 like the examples of quasi-miracles you gave above? Does the person know that she is going to affirm S each time or is she ‘surprised’ by her response each time she gives it? It seems to me that if she knows that she is going to affirm S each time then she is not performing a quasi-miracle as you describe them above which I take it involves some element of surprise.

John,

The question you ask is an empirical one. What in fact does happen when you ask someone, “did you do that freely?”. In fact, they are not surprised by their answer. The answer yes all the way up or they answer no all the way up. Since the sequence is YYYYY, it resemble tossing a fair coin and it coming up HHHHHH. Both are quasi-miracles as they approach a certain level of improbability.

Ted notes that an indeterministic process might be able ot produce such a mechanism. But what an indeterministic process cannot do is generate a deterministic mechanism. So, we are still going to get quasi-miracles happening all of the time.

Jacob,

I mean free as opposed to unfree. People disagree about what would make an action less than free, but I suppose most would make it a necessary condition on free action that it is not determined. So, one answer to your question is free from causal determination.

Even if indeterminism and physicalism are true, that doesnât mean that everything physical is entirely indeterministic; it just means that everything physical is not entirely deterministic. So, even if indeterminism and physicalism are true, we can build, for example, a machine which *always* says âdetectedâ when it detects a specific object. So it does not seem to me surprising that S in your example always says âyesâ indefinitely.

Another minor point: you might need to amend premise 1 and 2 so that they focus only on physical events? Otherwise, there is no connection between premise 1 and 2, on the one hand, and 4, on the other. Your current formulation allows us to construct a parallel argument against dualism as well.

*Even if indeterminism and physicalism are true, that doesnât mean that everything physical is entirely indeterministic*

I don’t see where I made any of those assumptions. What does “entirely indeterministic” mean? I’m guessing it means perfectly random: but I make no such assumption. I said quasi-miracles do not happen, not that nothing is highly predictable in indetermnistic worlds. Of course things are not perfectly random; nor are they perfectly predictable. I’m assuming only that each event has some chance of not occurring, and chance matches frequency, and those are facts in our indeterministic world. On that assumption I can show that physicalism is true only if (per impossibile) we can make quasi-miracles occur.

*So, even if indeterminism and physicalism are true, we can build, for example, a machine which *always* says âdetectedâ when it detects a specific object. So it does not seem to me surprising that S in your example always says âyesâ indefinitely.*

I think it should surprise you. First, I said nothing about anything occurring indefinitely. Indefinite events can occur three times and stop. What will happen with your machine is that the frequency of saying ‘detected’ will match the chances of saying ‘detected’. So, there is no quasi-miracle there. What, I assure you, you cannot do is build a machine in which the chances of saying ‘detected’ are far smaller than the frequency of doing so. With human beings there is supposed to be some chance of denying that you acted freely when asked. But that chance never gets reflect in the frequency of affirming that you acted freely. You yourself can make the frequency of affirming outstrip any chance that one can imagine of doing so consistent with indeterminism. Since that can’t happen, the chances of you affirming that you acted freely are certainty. But, given indeterminism, that is inconsistent with physicalism.

Not sure I understand your argument yet. Let event type E = I drop a rock off a cliff. (Assume nothing intercepts the rock, no wind suddenly picks up, etc.) Let Y = “the rock falls toward the earth” and N = “it’s not the case that the rock falls toward the earth.” Given indeterminism, the probability P of Y/E is nearly, but not quite, 1. If I understand you correctly, then if we were to repeat an E event X times (for very large X), we should count it as a quasi-miracle if the relative frequency of Y “outstrips” P (which, recall, is very nearly 1). We should count it as remarkable and highly improbable if there weren’t occasions in which N follows E (as X gets larger). So far so good?

If so, then I don’t see what evidence you have for your premise 3. I imagine the physicalist will want to simply deny it, and affirm instead that we should expect – very, very rarely, but not never – that the agent eventually fails to answer ‘Y’ (in the same way that eventually we should expect the rock to fail to fall toward the earth). What’s the argument for denying this possibility? Why think the sequence will/would be an unbroken chain of Ys? Is this supposed to be something that falls out of the concept of agency?

Hi Brian, you write,

*Given indeterminism, the probability P of Y/E is nearly, but not quite, 1.*

I doubt it is nearly 1, since (for various reasons) only necessary truths get probablity 1.

*If so, then I don’t see what evidence you have for your premise 3. I imagine the physicalist will want to simply deny it, and affirm instead that we should expect – very, very rarely, but not never – that the agent eventually fails to answer ‘Y’ (in the same way that eventually we should expect the rock to fail to fall toward the earth).*

I take the argument for (3) to be empirical. Incidentally, (3) should not be a claim about indefinitely replying Y (apologies to Yujin(!), this is what you were alluding to). It should be that S will without exception affirm Y. You can run the test another way. Ask someone whether he can say affirm without exception as many times as asked. Make it much less likely: ask them whether they can affirm on every other odd minute on the clock. My claim is that, as a matter of empirical fact, virtually anyone can do this. But such a sequence is not possible under indeterminism and physicalism.

I’d also like to point up that there’s no reason to believe that the chances should be as small as you suggest. Why should we expect it to be very, very rare, that I answer N under physicalism? Unless we are *very, very well designed* to say yes under such circumstances, and no physicalist (ok, almost no physicalist) wants to say that.

Does that help?

Can you help me see how 5 follows from 2 and 4? The consequent in 4 appears to be a modal claim, but 2 does not appear to be the denial of a modal claim. Is 2 supposed to be modal, something like, quasi-miracles cannot happen, or many quasi-miracles cannot happen?

You claim that’s true by definition. Since clause (b) in your definition doesn’t seem to entail that many quasi-miracles can’t occur, it must be clause (a). But I’m not sure how that’s supposed to work. Couldn’t there be lots of remarkable series of events?

Won’t you also need premise 4 to say that if physicalism is true, every (or many) agents could *simultaneously* perform a quasi-miracle?

I was reading it like Yujin was. So what you’re saying is that we all have this intuition that we would produce this infinite sequence of Ys, and this intuition is incompatible with that response being indeterminate? This does leave unanswered whether or not we actually could produce that infinite sequence, and I imagine that a physicalist is just going to say that the intuition is wrong.

It also seems to me that an indeterminate system could easily produce this sort of sequence. You’re assuming, I think, that these responses are like coin flips – that they’re independent of each other. But if I’m listening to you answer this question again and again, then, at least in terms of my epistemic probability, P(Y) keeps increasing. It seems plausible that the factual probability of undetermined answers could also do this (it’s at least possible).

So suppose that the probability that the person will answer Y the nth time the question is asked is (1-b^n), where b is some very small number. Then the probability that the person can produce an infinite sequence of Ys in response to these questions is actually quite large (1-b-b^2, as near as I can tell). Depending on the value of b, you wouldn’t actually have a quasi-miracle until an impossibly large number of agents could produce sequences like this. But b could easily be so small that we’ve simply never encountered the agent that would fail. It could also be so small that it’s reasonable for every agent to expect that they could produce the infinite sequence if required, in the same way that they expect that all of the molecules in their glass of water won’t suddenly move three feet to the right, which would make just asking people whether they can produce the infinite sequence useless.

Hi Jonathan,

Yes, right, your suggestions are on tightening up the argument, which it surely needs. But it seems clear the way to go. It is not that a quasi-miracle cannot happen in the sense that it is metaphysically impossible. The claim is that no one is able to make them happen regularly. That is a modal claim too, of ocurse, but a much weaker one.

I did try to strengthen the argument in ways that I find pretty persuasive. Set aside the sequence of YYYYY, and consider virtually any remarkable sequence you like. Take the sequence of affirming (that you acted freely) on every other odd minute and in every other even hour beginning at noon. I take it that for something that is not designed to do this sort of thing (and I’m certainly assuming that we are not so designed) the chances of success ought to be pretty low. But, I submit, it is easily achieved, and its achievement would constitute a quasi-miracle, were the events purely physical ones.

Does that make better sense?

Hi Billy, you write,

*So what you’re saying is that we all have this intuition that we would produce this infinite sequence of Ys, and this intuition is incompatible with that response being indeterminate? This does leave unanswered whether or not we actually could produce that infinite sequence, and I imagine that a physicalist is just going to say that the intuition is wrong*

No, my claim does not appeal to intuition. I claim that we can actually perform quasi-miracles, if our actions/choices are purely physical events. You do not have to go to infinity, which is good news. As I mentioned to Jacob, just take an event that is sufficiently specific to increase its chances of not occuring. There is no question that, for any possible event e, the chances of e occurring are greater than the chances of e at t in C occurring. So consider not merely affirming that you acted freely, but affirming that you did so on every odd minute of every even hour. My claim (it’s verifiable) is that this is easily achieved. And you would not have to do to infinitely to make the sequence a quasi-miracle.

*But if I’m listening to you answer this question again and again, then, at least in terms of my epistemic probability, P(Y) keeps increasing*

That could be right. But why would epistemic probability matter here? I’m talking about chance.

*So suppose that the probability that the person will answer Y the nth time the question is asked is (1-b^n), where b is some very small number.*

I’m not sure I follow that. Suppose there is a genuine chance of answering yes when prompted, and it is p. Why would the (objective) probability of answering yes again on the nth occasion be anything like (1 – p^n)? That is the objective probability of not answering yes on all occassions in that sequence to n, as far as I can see.

Notice that your argument entails that quasi-miracles could not occur. Suppose you start flipping what is in fact a fair coin. After n (far before 1,000,000) flips of heads your epistemic probability that it’s fair is going to be very low. So, you are not going to be surprised at 1,000,000 heads in a row. That’s true in all cases where an alleged quasi-miracle occurs. But quasi-miracles are defined in terms of chance or objective probability, not in terms of epistemic probability.

On the other hand, I agree that, in general, your epistemic probability is compelling reason never to believe that what just happened (the answering of YYYYY… or the 1,000,000 landings of heads) was a quasi-miracle.

Finally, how did you arrive at (1-b-b^2)?

Sorry, remarkable and improbable events happen all the time. You’re just using an ad hoc and highly convenient definition of “remarkable.”

Right, well, this is not my definition of ‘remarkable’. The definition is due to David Lewis, ‘Counterfactual Dependence and Time’s Arrow’ and John Hawthorne, ‘Chance and Counterfactuals’. Similarly for the defnition of ‘quasi-miracle’.

I don’t understand this argument at all. A free agent consistently affirming Y would be what you’d expect. The probability of such an agent failing to affirm Y is going to be extremely low. There’s nothing surprising that a person would affirm Y each time on any reasonable time span. It’s more like a sequence of HHHHH with a weighted coin than with a fair coin.

Now it does seem entirely possible that if you actually asked someone to affirm something on every odd minute of every even hour, once in a while that person might get confused, or distracted and not affirm Y. I don’t see why indeterminism would lead you to expect anything more.

Hi Eric. you write,

*I don’t understand this argument at all. A free agent consistently affirming Y would be what you’d expect. The probability of such an agent failing to affirm Y is going to be extremely low.*

In a sense, what you say is true. But under indeterminism and physicalism, this is not what you would expect. You’d expect that since each affirmation (suitably described to ensure its improbability these assumptions) has a chance of not occuring, the sequence of affirmations (far less than an infinite sequence) is highly improbable and remarkable, or, a quasi-miracle. Of course, if the person falls asleep, the sequence will be stopped temporarily. But this is not to the point; it’s not an endurance test. Just as with the coin, you can stop flipping for a while, so long as when you do flip, it keeps coming up heads.

Mike,

You say: “So if every instance of your answering Yes was nothing more than a physical event, there would be lots of quasi-miracles occurring, or we could easily make lots of quasi-miracles occur. But, by definition, we cannot make lots of quasi-miracles occur.”

I find the second sentence here puzzling. By definition, a quasi-miracle is a sequence of events which is remarkable and highly improbable. But, this definition doesn’t say anything about human beings and what they are able to do. So, the second sentence above seems false. We need an argument for it. I wonder whether you haven’t supplied us with an argument against it.

Mike, thanks for your response.

Perhaps you’re using indeterminism as a term of art that I just haven’t encountered before. You say,

*You’d expect that since each affirmation (suitably described to ensure its improbability these assumptions) has a chance of not occuring, the sequence of affirmations (far less than an infinite sequence) is highly improbable and remarkable, or, a quasi-miracle.*

I think you’re too quick to move from “Event A has a chance of not occurring” to “a sequence of event A is highly improbable and remarkable.” This is certainly true with a fair coin, since the chance of H not occurring is fairly high at 50%. But if the coin were weighted so the chance of H not occurring were .00001%, then a sequence would be neither improbable nor remarkable. You have to consider how likely A’s failure to occur is before you can make an assertion about how improbably a sequence of As is.

In your example, I would say the probability of and agent failing to affirm Y at any given time is extremely low. The lower that probability is, the longer your sequence of affirmations would have to be before it becomes a quasi miracle. That makes a difference, since you can imagine a number of low probability events that would cause someone to fail to affirm Y (for example, the atoms in the agent’s brain spontaneously rearrange themselves and alter the agent’s memory). For a large enough sequence, then, 3 isn’t true. For a shorter sequence, 4 isn’t true.

But again, I may have simply misunderstood indeterminism here.

*By definition, a quasi-miracle is a sequence of events which is remarkable and highly improbable. But, this definition doesn’t say anything about human beings and what they are able to do. So, the second sentence above seems false.*

Ryan, if quasi-miracles are highly improbable and remarkable, then nothing can make them happen with a high frequency. Frequency and chance go hand in hand, except in the case of a Molinist God. If we could make quasi-miracles happen frequently, they would lack the chanciness of such miracles. Hence, we are bot able to do this.

*I think you’re too quick to move from “Event A has a chance of not occurring” to “a sequence of event A is highly improbable and remarkable.” This is certainly true with a fair coin, since the chance of H not occurring is fairly high at 50%. But if the coin were weighted so the chance of H not occurring were .00001%, then a sequence would be neither improbable nor remarkable*

Well, sure, for events that have a high chance of occurring, it takes a lot for frequency to outstrip chance. Agreed. But, first, why assume that the free actions of human beings, whether A or ~A, have a high chance of occurring? Odd that this should even be an issue, since everyone is quick to point out that libertarianism suffers from a perenial problem of chancy action! So, that is the first thing. Second, if you claim that free action, on each occasion of choice, whether A or ~A is performed, always has a high chance of occurring, you seem to be saying something inconsistent. If A is highly probable, then ~A isn’t. So, if your argument is, oh well, a large sequence of Y’s is no big deal, really, and not even improbable, I’m happy to switch to N’s. The same person can disaffirm as easily as he can affirm in very larger sequences. One of those sequences has to be improbable! Third, I’ve been urging that the action be described in detail (such as affirming on every odd minute on each even hour). That is much more chancy (assuming that physicalism and indeterminsim is true) and yet it too is easily achieved.

No, I’m not using ‘indeterminism’ stipulatively. I mean what you mean by the word. I understand it in terms of genuine chance (not epistemic probablity), as I assume you do. Each event that does occur had some positive objective probablity (less than certainty) of not occurring.

*So consider not merely affirming that you acted freely, but affirming that you did so on every odd minute of every even hour.*

I’m reading this as “I affirm that I acted freely” on every odd minute of every hour (as opposed to I affirm that “I acted freely on every odd minute of every hour”).

I don’t see that this is much less probable than just producing those affirmations when prompted. Affirmations of free action don’t just spontaneously occur; an affirmation one way or the other is generated in both scenarios in response to a prompt. The probability of affirming that one acts freely at any arbitrary time is very small, but if you’ve asked someone whether or not they’ve acted freely, the probability of an affirmation in some range of time is really quite high. If you don’t tell someone to affirm on every odd minute, then P(Y) would be very low, but we also don’t expect that they actually would affirm on every odd minute (they wouldn’t even think about it). If you tell them to affirm on every odd minute, you’ve drastically increased P(Y) in some range of time about each odd minute. Without implying a designer, time-appropriate response to stimuli is exactly what we *are* designed to do. Also, I bet that, as a matter of fact, you won’t have to wait very long before your test subject misses an odd minute, unless you give him some sort of alarm clock (in which case this is just a special case of asking repeatedly where the questions occur with some regularity).

My mention of epistemic probability was just to illustrate that there was a sense in which P(Y) was definitely increasing with each Y given. I then supposed that the increasing epistemic probability reflected an increasing objective probability. There are plausible reasons for why this might be so – as a matter of psychology, perhaps we become more sure of claims as we affirm them, perhaps our brains build pathways to make repeated successes easier and more likely, etc. You’re right it’s possible that a fair coin could produce so many Hs that I end up concluding that it’s not fair, but it’s possible that a fair coin isn’t a good model for a human brain doing a repetitive task (even under physicalism).

So it’s possible that the objective probability P(Y) on occasion n is smaller than P(Y) on occasion n+1. You’re looking at these affirmations as independent trials with P(Y) = (1-b) so that 1 – (1-b)^n would be the probability of answering N just once in a long series (which limits to 1). But if they’re not independent, perhaps P(Y) on the nth occasion is actually some function of n, such as (1-b^n) (provided all previous responses are Y, but those are the only cases we’re interested in). That is, P(YYY) could be (1-b)*(1-b^2)*(1-b^3), and the probability of an infinite sequence of Ys is (1-b)*(1-b^2)*…*(1-b^n) as n goes to infinity. Expanding this out, you get (1-b-b^2 + A), where A is an alternating series of higher order terms starting at b^5 that clearly converges.

Mike,

It’s not chancy if the agent has decided she is going to perform that action, since it is not difficult for the agent to do that. In other words, once the agent has chosen to attempt to affirm Y at every odd minute of every hour, the probability of the agent’s performing that action is extremely high.

If, on the other hand, the agent hasn’t decided to affirm Y at every odd minute of every hour, then I agree that the sequence has a low probability of occurring. But saying an agent who hasn’t decided to do that “can” do it nevertheless is just like saying a fair coin could have a long string of H’s.

I guess it comes down to what you mean by the word “can” in 4. Do you mean it’s possible that an agent perform a quasi miracle by pure chance? If so, 4 is true but can’t lead to 5. Do you mean an agent can choose to perform a quasi miracle? Because I don’t think that’s true. Once the person has chosen to do something that would produce the sequence, then the chances of the person producing the sequence are high, and the sequence wouldn’t be a quasi miracle.

*I don’t see that this is much less probable than just producing those affirmations when prompted. Affirmations of free action don’t just spontaneously occur; an affirmation one way or the other is generated in both scenarios in response to a prompt*

I don’t see how that claim is not question-begging, under the assumption of physicalism and indeterminism. As I say above, if the chance of Y at t is high, then the chance of ~Y at t is not. Yet, the fact is that a sequence of ~Y,~Y,~Y is just as easily realized as a series of Y’s. Or, an alternating series featuring the less probable action at each time. Take any series you like of Y’s and ~Y’s, and these are all as easily realizable as any other, no matter how improbable is each Y or ~Y.

*The probability of affirming that one acts freely at any arbitrary time is very small, but if you’ve asked someone whether or not they’ve acted freely, the probability of an affirmation in some range of time is really quite high.*

Yes, of course, I’ve been claiming this. This is just what is not consistent with indeterminsim and physicalism. Highly specific actions should have a sufficiently low probablity that the sequence is highly improbably and remarkable. The observation that people affirm easily does nothing to help physicalism.

* If you tell them to affirm on every odd minute, you’ve drastically increased P(Y) in some range of time about each odd minute.*

This seems confused. We agree that the observation is that if you ask someone whether he can complete the sequence, he can easily. My claim is that this observation is inconsistent with physicalism and indeterminism. You assert without argument that the observation is what we would expect on physicalism and indeterminism. You say something about being designed without a designer, but this is not coherent (or I can’t make it so). If you want to tell a story about how evolution selects for such ability, you’ve got a very long and difficult story to tell, since it has to explain how we can easily realize virtually any sequence with ease. It won’t do to explain how indeterminism might spring forth a mechanism that yields Y’s to prompts about Y’s, though even that is really hard to do (witness Dawkins’ speculative difficulties in explaining the simple case in another context).

But even setting all of that aside, the main point is that the chances of any long sequence of chancy and remarkable events (these events, independent or not, will not move to 1 in an indeterministic world) has to decrease as the sequence gets longer. I claim that we can make the frequency of answering Y outstrip any chance of answering Y. I realize that’s an empirical claim. I predict that it will work out as I suggest, but it can be tested.

*My mention of epistemic probability was just to illustrate that there was a sense in which P(Y) was definitely increasing with each Y given. I then supposed that the increasing epistemic probability reflected an increasing objective probability*

Objective probability does not follow from epistemic probability, at best, a rational person will take information about chances and make his epistemic probability fit the objective probability. But that requires knowing what the objective probabilities are.

*It’s not chancy if the agent has decided she is going to perform that action, since it is not difficult for the agent to do that*

The very problem is that it *has to be* chancy under physicalism, the action description, and indetermnism. This part is not in question, really.

That can’t possibly be correct. The probability that a person will affirm Y on every odd minute of every even hour is very high if that person decides she is going to do that. There’s still some small probability that she won’t, but it’s not a quasi miracle if she does, except for extraordinarily long sequences. Once a person chooses to do something, that changes the probability of that thing happening.

I’m sorry to belabor this discussion, but I simply don’t understand what I’m missing here.

*That can’t possibly be correct. The probability that a person will affirm Y on every odd minute of every even hour is very high if that person decides she is going to do that.*

I think we’re talknig past one another. I agree that *The probability that a person will affirm Y on every odd minute of every even hour is very high if that person decides she is going to do that*. I deny that the probability that a person will affirm Y on every odd minute of every even hour is very high if that person decides she is going to do that, ON THE ASSUMPTION THAT PHYSICALISM AND INDETERMINISM ARE TRUE. So what we are observing re a person’s ability to affirm Y in a variety of sequences is incompatible with indeterminism and physicalism being true. That’s the argument.

I am not sure I believe 3. After you asked me the same damn question a hundred times, I am pretty sure I would stop answering you seriously.

(I once took a phone survey that asked me my preferences in cream cheese. The surveyor began going through every brand and flavor of cream cheese on the market. I interrupted and said, “I buy Philadelphia light cream cheese.” She continued her questions, as she had to, and I repeated, “I buy Philadelphia light cream cheese.” A few more occasions of this, and I hung up the phone.)

Thanks for your clarifications; I’m afraid I’m still either failing to understand parts of your argument, or just disagree. Take my “drop rock off the cliff” case. First, you’re right that the probability of Y on E (i.e. the probability that the rock falls toward earth, given that one has dropped it off the cliff) is nowhere near unity; but it is if we hold fixed the laws of nature and the actual past. So hold them fixed; but we allow for an indeterministic universe. I maintain that the chance of Y on (E & actual past & actual laws) is very nearly 1. You will fail to get Y after E in our indeterministic world only very, very rarely. I very much doubt, in fact, that as a practical matter we humans beings could ever observe a single counterexample (again, ruling out fluke winds, obstructing objects, etc.). Does it sound right to you, so far, to say that the probability of the rock falling toward earth given that the rock is released from a cliff, on the assumption of physicalism and indeterminism, is very high?

If so, then we have a case of a sequence whose probability, even given physicalism and indeterminism, is very high. Only if the sequence in the very long run turned out never to have exceptions would we conclude that a quasi-miracle has occurred; but this would have to be a very, very long run indeed.

Now turn to your case. Assume physicalism and indeterminism. You say that there is a certain sequence, given those assumptions, should *not* be highly probable, even though (we know) it *is* highly probable. That sequence is a certain sequence of responses by an agent to a prompt. I still don’t understand why you think the first conjunct is true (that this sequence, given physicalism and indeterminism, will not be highly probable). It can’t be because of a commitment to a *general* claim that no physical, indeterministic sequence can be highly probable, unless you think that the “rock falls when released, given the past and laws” sequence is not highly probable. That makes me think it’s because of some other concept involved – perhaps the fact that free agency is involved? But I thought we weren’t talking about the original action, A, of the free agent – where the agent freely swears to tell the truth. I thought we were talking about the distinct actions (call them Bs) in which the agent answers the prompt about whether they did A freely. Are you thinking that each instance of B-type actions (1) are free actions, and (2) (therefore?) do not have a high probability of being answered a certain way, given physicalism and indeterminism? Why couldn’t the physicalist-indeterminist simply say that B-sequences of YYYY… are as probable as the YYYY… sequence of the rock-falling-off-cliff case? Or am I confused again about your position?

*I am not sure I believe 3. After you asked me the same damn question a hundred times, I am pretty sure I would stop answering you seriously.*

Heath,

I think that’s likely in most cases. The question is whether someone can reply Y consistently, and I think the answer is obviously yes.

Mike, thanks for continuing to clarify.

I think I’m still having the same problem Brian has. Since the sequence you postulate doesn’t seem difficult for any person to do, that suggests to me that it is not improbable that the sequence could arise, and I don’t understand why physicalism and indeterminacy suggest otherwise. Phyiscalism and indetermanism allow many long sequences of events. Perhaps you could clarify what it is about the action you are suggesting that makes the sequence of affirmations improbable. Is there some part about physicalism and indetermanism that claims the probability of an event is the same whether or not a person has decided to bring about that event?

Also, because I’m concerned that we may still be talking about different cases, is your position that a person can choose to bring about a quasi miracle, or instead that a person has the potential to unknowingly bring about a quasi miracle?

*First, you’re right that the probability of Y on E (i.e. the probability that the rock falls toward earth, given that one has dropped it off the cliff) is nowhere near unity; but it is if we hold fixed the laws of nature and the actual past.*

That’s not so, it is still not near 1. This is what indeterminsicm entails, that the history and laws prior to events does not determine them to occur. Now, maybe you want to say that the laws make it very probable that the rock falls. That is true in some cases and I’m happy with that in this case. But you don’t want to say that the rock’s falling is nearly as probable as 2+2=4. It’s not. But I do not deny that it is very probable.

Setting that issue aside, the falling rock case might be helpful to illustrate the position I’m taking. Suppose you take the view that YYYYYY is just like dropping the rock several times in sequence and it falling each time. So, big deal, he says yes, just like, big deal, the rock falls to earth. Ok, but what about the sequence of the rock not falling to earth each time? That must be very low on your account, no? And analogously, it would be very low on saying No, or not saying yes (whichever you like). But the fact is that the sequence of NNNNN is also easily achieved. There is simply no difficulty at all in realizing this (on your account) extremely improbable sequence. In fact, suppose we take a series of possible sequences of Y’s and N’s, S0, S1, S2, . . .,Soo. And suppose you use a randomizer to choose a sequence from the series. And suppose we use a randomizer to choose a person P to realize a sequence. For any person P and sequence Sn in the series, P can easily realize the sequence. This cannot be true on indeterminism and physicalism.

Does that help you?

*I think I’m still having the same problem Brian has. Since the sequence you postulate doesn’t seem difficult for any person to do, that suggests to me that it is not improbable that the sequence could arise, and I don’t understand why physicalism and indeterminacy suggest otherwise*

See my response to Brian. I claim (and it is certainly true) that YYYYY is highly probable only if NNNNN (or ~Y~Y~Y~Y) is not. But the fact of the matter is that both are easily realizable. That is not consistent with indeterminism and physicalism.

I agree that NNNNNN is not highly probably *once a person has decided to answer YYYYYY*. So again I have to ask whether the actor is supposed to be choosing to realize the sequence. You seem to think this does not make a difference, but I don’t see how that could be so. The probability changes after the choice to affirm Y is made. And if the person then changes her mind and decides to affirm ~Y, the probability changes again. There’s no case where your agent can choose a sequence without thereby making the sequence more probable.

Eric,

There’s really nothing left to say. As I noted above, let L be a series of possible sequences of Y’s and N’s, S0, S1, S2, . . .,Soo. Use a randomizer to choose a sequence Sn from the L. Let G be a set of people P. Use a randomizer to choose a person P from G. For any randomly chosen person P in G and any randomly chosen sequence Sn in the series L, P can easily realize S. This cannot be true on indeterminism and physicalism. What are the chances under indetermisnism and physicalism that any randomly chosen sequence of physical events can easily be realized in any randomly chosen material being P? It’s highly improbable. Yet it is true. Hence physicalism or indeterminism is false. Hence physicalism is false.

If that has no intuitive pull for you at all, then either you don’t follow the argument or you are simply unmoved by it. In either case, I think we’re done.

Mike:

Surely the thing to say is this: Yes, you can say “Yes” infinitely many times, but the probability of your doing that is zero, because (as Heath notes) you are more and more likely to get bored, or because each time you do this, you are making a free choice whether to say “Yes” or to lie and you have some non-zero probability of lying each time, or because indeterministic events in your brain might simply cause you to non-freely say “No”. So, the probability of saying “Yes” infinitely many times is zero, and that matches the physical probabilities.

Now, you will say: But it’s remarkable, and hence a quasi-miracle. True, but an indeterministic coin-flip process run for an infinite amount of time *can* produce quasi-miracles as well. (It is just as possible for it to generate HHHHHH… as any other sequence.) Of course, it is very unlikely to do so, but likewise you are very unlikely to say “Yes” each time, unless you are in heaven and hence can no longer lie. So I guess the argument does show that materialism is false in heaven–an interesting point!

*Ok, but what about the sequence of the rock not falling to earth each time? That must be very low on your account, no?*

Correct, given the actual conditions specified in my example (releasing the rock off a cliff, holding fixed the laws, etc.)

*And analogously, it would be very low on saying No, or not saying yes (whichever you like).*

This would be true only if the agent P has not decided to always answer N. If the agent has decided always to (attempt to) answer N, then the sequence NNNN… is highly probable. Of course, holding *that* antecedent fixed (that the agent has decided always to answer N), then the sequence YYYY… will be improbable. But I thought we were conditionalizing our probability, in the case of the agent, on something like the agent’s decision or desires, just like in the case of the rock, we were conditionalizing the probability of a certain sequence of outcomes on certain antecedent circumstances (holding laws and past fixed, having no tornadoes nearby, etc.). The agent’s YYYY sequence is highly probable if *and only if* the agent has decided (or would decide, upon being prompted) to answer YYYY.

*But the fact is that the sequence of NNNNN is also easily achieved.*

It is easily achieved by the agent *only if* it’s not the case that the agent has decided to answer YYYY. Prob(YYYYY/(Agent decides to answer YYYYY)) = high. But then holding fixed that on which we’re conditionalizing, Prob(NNNNN/(Agent decides to answer YYYYY)) = low; so the latter sequence is not “easily achieved” unless we reconditionalize. But then we’ve changed the case.

*In fact, suppose we take a series of possible sequences of Y’s and N’s, S0, S1, S2, . . .,Soo. And suppose you use a randomizer to choose a sequence from the series. And suppose we use a randomizer to choose a person P to realize a sequence. For any person P and sequence Sn in the series, P can easily realize the sequence. This cannot be true on indeterminism and physicalism.*

Why couldn’t the physicalist respond as follows:

We could easily build a set of devices (e.g. computers) that would display a sequence of Ys or Ns on its screen. We could program it to display whichever sequence was scanned in on a scanner connected to it. Suppose we use a randomizer to choose one of the devices, D, from this set. For any device D and any sequence Sn in the series (that you describe above), D can easily realize (i.e. display on its screen) Sn. (That is, the probability of D realizing Sn will be very, very high.) This can be true (indeed, *is* true of many actual analogous devices that exist) on indeterminism and physicalism.

The physicalist will want to say that feeding Sn via scanner to the device D is relevantly analogous to “giving” the agent P some sequence Sn. After all, if we don’t “give” Sn to P, it’s plainly false that the probability that P subsequently produces Sn is high (correct?) To make Prob(Agent realizes Sn) = very high (or “easily realized”), we need to conditionalize: Prob(Agent realizes Sn / Agent is shown, prompted with, given, Sn) = very high.

But then I don’t see why physicalism and indeterminism rule out the possibility of D-type devices that can do the same thing. And then of course I don’t see why the physicalist couldn’t consistently claim that human agents are relevantly similar to D-type devices…

Again: I agree that there’s a sense of “can” that makes it true that an agent P “can easily realize” either YYYY or NNNN, or any other sequence of responses. But it seems obvious that, even given physicalism and indeterminism, we could create (indeed, have created) physical devices that “can easily realize” some randomly selected (and prompted!) sequence as well.

Hopefully I’m narrowing down where we’re talking past one another…

*It is easily achieved by the agent only if it’s not the case that the agent has decided to answer YYYY.*

That’s just question begging. The device response is not relevant, since you assume design.

*Surely the thing to say is this: Yes, you can say “Yes” infinitely many times, but the probability of your doing that is zero*

This is like objecting to the claim that a coin can be flipped heads infinitely many times because you’ll get tired of flipping. That feature is irrelevant. The point is that the sequence of flips be heads each time, no matter how much rest you take in between and no matter how many times you put the coin down out if boredom.

Second, my claim is not about infinitely many trials, which is far more than necessary for a quasi-miracle. A large finite number–1,000,000 say–is far more than enough.

Third, we have moved past affirming Y’s. It’s now the chances that, for some randomly chosen person P and randomly chosen remarkable sequence S, P can realize S. My empirical hypothesis is that P can do this for any such S, despite the fact that physicalism and indeterminsim predict that S cannot. I’m prepared to take all bets on this.

Fourth, all I’ve seen so far are bald assertions that the probability is high for P to realize S *if P is prompted*. But there is not a single argument in the comments that indeterminism and physicalism predicts this, which is the very point at issue. But aside from the question begging, I’m happy to select the promptings randomly too. We’d get the same result.

Mike,

You say “if quasi-miracles are highly improbable and remarkable, then nothing can make them happen with a high frequency. Frequency and chance go hand in hand, except in the case of a Molinist God. If we could make quasi-miracles happen frequently, they would lack the chanciness of such miracles. Hence, we are [n]ot able to do this.”

Isn’t this true only on a Lewisian style (i.e., frequentist) account of chance? On his view, the frequencies can diverge a bit from the chances, but not by too much!

But if, say, a propensity account of chance is correct, then the frequencies *can* diverge, even radically, from the chances.

So perhaps the thing to say is that if you’re a physicalist *and accept a frequentist account of chance*, then….

*Isn’t this true only on a Lewisian style (i.e., frequentist) account of chance? On his view, the frequencies can diverge a bit from the chances, but not by too much! But if, say, a propensity account of chance is correct, then the frequencies *can* diverge, even radically, from the chances.*

I’m not sure the latter is possible in the sense I’m talking about. Agreed, it is logically (and metaphysically) possible. But I don’t think it is something that I am able to bring about.

There are divergencies too for Lewis, I think. What is true is that over the long-term frequencies will reflect chances. In the meantime I think we’re supposed to adjust our credences about whether we have the chances right.

Mike,

*My empirical hypothesis is that P can do this for any such S, despite the fact that physicalism and indeterminsim predict that S cannot.*

Perhaps you could explain why you believe that physicalism and indetermanism predict S cannot do this. It seems like I can fulfill your example by having a random number generator make sequences of digits and then have a random person read them. Is it really your position that physicalism + indetermanism predicts that is impossible?

Hi Mike,

An indeterministic process may create mechanism that could yield the kind of sequences you mention. By the way, have you seen Bill Lycan’s article “Giving Dualism its Due”? It’s out in AJP. It’s probably the best article I’ve read in a long time.