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# Probability, Possibility, and Conceivability

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I've recently found that Pascal's Wager is more influential than I had thought. My professor who is teaching probabilities, as well as several undergrads, all seem to be impressed by the argument even though I doubt any of them are religious. So below I'll lay out Pascal's Wager, and below that I'll criticize it.

Pascal's Wager wasn't a very clear argument for Pascal--he wrote it out several times, each time with significantly different wording, and never as a core topic in his writings but just in passing and in letters. The main thrust, though, is: There are two possibilities for god's existence, that he exists or doesn't. Likewise there are two possible believes, that he does exist or doesn't. The reward for believing when he does exist is infinite happiness; for believing when he doesn't is some finite reward or consequence (presumably negative); for not believing when he does is infinite sadness; and for not believing when he doesn't is some finite reward of consequence (presumably positive). Today we could express this as expected utility: Expected utility is the probability that an event will happen multiplied by the reward expected. So if the reward for rolling a 2 on a six-sided die is \$4, then expected utility is \$4/6 or \$.33. Expected utility represents the exact amount of money you should bet on an event so that, as you play more and more times, your reward tends toward zero. If you bet less for the same reward, then as you play more and more times, you will gain money; and the opposite for betting less. Thus, if someone offers you \$4 if you roll a 2 on a six-sided die, but to take up the bet you must pay .32--then assuming you want money and playing the game is of no cost to you, it is a rational bet. Assuming a very large pool of money from which you can keep paying the "entrance fee" for the bet, your reward will grow over time. Applied to Pascal's Wager, if the reward is infinite and the probability of the event finite, then expected utility is infinite and no matter how much is the entrance fee for the wager, it is always rational to bet that god exists.

My criticism here is that we don't have a clear rubric for what is possible! I don't grant that the idea of infinite happiness is contradictory, or that all conceptions of god are contradictory (I know that's a point some here will argue, but I'm not interested in that argument). But to assert that god is possible, or that one particular kind of god is possible, is not yet established. Point in case, I am very amused that Pascal himself was first a Catholic, then a Jansenist, then a Jesuit. I take it that each change was from one religion to another which he had previously thought would send him to hell. In fact, looking at the number of Protestant religions, all of which are mutually exclusive and the infinity of conceivable religions, it seems that the possibility of any given religion tends toward zero. A result like this should at least look metaphysically suspicious. Is something possible just because we can posit its existence, that is, just because we can think it? When we calculate the toss of a coin, we are right when we say that it is (roughly) 50:50. Yet we could posit all kinds of outcomes. It could land on its edge. We could toss the coin and then a lion eats it. We could toss the coin and then all of the sudden it disappears. It would be ridiculous, though, to factor these into our probability calcuations. So we need a good standard to judge what is genuinely possible and what is merely conceivable.

In the case of religion, this is even more clear where you could fathom literally countless, each of which will tell you that anybody in any other religion is going to hell. The conclusion is not that the probability of a given religion is very small, for then Pascal's Wager would be good decision theory. You just pick one religion, it doesn't matter which. The conclusion is that the probability is infinitely small or, just as well (I think), it is zero. Now that I get to thinking about it, you don't even need to choose a religion. Maybe you'll get infinite happiness by being an atheist--maybe you'll get infinite happiness by killing people. There's no way to know which action actually gets you infinite happiness, unless there's some independent proof for it. So to talk about probabilties in this case would be absurd because we don't know what to admit as possible and impossible.

The point of the post isn't to rail, though. I was wondering, given this, does anybody know of some published material that talks about the difference between conceivability and possibility in just this way?

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When dealing with what may happen, I tend to break things down into three Ps. Possibility, Plausibility, Probability.

Possibility - Can it happen?

Plausibility - Could it happen?

Probability - Will it happen?

In other words, is an event physically possible at all, are the conditions realistically possible, and how likely is it to meet these conditions? Most intenerations of God do not pass the first hurdle, so there is very little point in dwelling upon attaching mathmatical value to the probability of an arbitrary concept.

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I've not read Pekioff's article, "What if you're wrong?" but it seems to be right up this alley. He's talking about Descartes' issue with 'error' that since you've been wrong in the past, you might be wrong now - therefore, assume you're wrong. Essentially this is the same thing. Certain things have happened in the past; other things could have happened; different things could happen in the future; therefore, there are only possibilities of what might happen, no certainties.

But, when you say something is probable, you are declaring certain evidence or knowledge by which you reached that guess. Also, to claim something is probable or possible, is to say that there are other things which are definite. 'Probability' is a statistical fraction of absolute (Objective, not omniscient) certainty and so you must know the absolute, or at least, how to attain it, before you can speak of a fraction of it and how to attain that.

From Peikoff's article as presented on the Lexicon:

"It is possible, the skeptic argument declares, for man to be in error; therefore, it is possible that every individual is in error on every question. This argument is a non sequitur; it is an equivocation on the term “possible.”

What is possible to a species under some circumstances, is not necessarily possible to every individual member of that species under every set of circumstances. Thus, it is possible for a human being to run the mile in less than four minutes; and it is possible for a human being to be pregnant. I cannot, however, go over to a crippled gentleman in his wheelchair and say: “Perhaps you’ll give birth to a son next week, after you’ve run the mile to the hospital in 3.9 minutes—after all, you’re human, and it is possible for human beings to do these things.”

The same principle applies to the possibility of error."

Ignore the extra stuff about 'error' there, and just focus on possibility, and you'll find quite a succinct little excerpt on what you're looking for.

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If you ask me what the probability of God's existence is, I would have to ask you: What evidence, or reasons to believe he exists, do you have?

Since the answer is none, the probability of God(PG) is zero.

So no matter how high a happiness-coefficient (HHC) this product of fantasy called eternal soul in heaven would have, the net after death benefit(NADB), measured in degrees of happiness, of you pretending that there's a God would be: NADB=PG*HHC= 0*HHC=0.

Of course if you decide that the HHC=infinite, then the whole story starts over again: what evidence do you have that there is something called infinite happiness, which multiplied by zero would produce something other than zero? None, so the probability of its existence is zero, therefor it is pointless to discuss the possibility. Our only option is to assume that HHC is a very high number.

The point of the post isn't to rail, though. I was wondering, given this, does anybody know of some published material that talks about the difference between conceivability and possibility in just this way?

Try OPAR (the first part). Objectivist metaphysics states that reality is independent of consciousness. The fact that something is conceivable does not have any bearing on whether it is possible, or on how probable it is.

So to talk any further about the mathematical relationship between what is conceived and what is possible is completely pointless. (though I'm sure people nevertheless do all the time) Mathematics is a product of reason. You cannot apply it to fantasy, or any form mystical revelation (such as the idea of God).

Edited by Jake_Ellison
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I've recently found that Pascal's Wager is more influential than I had thought. My professor who is teaching probabilities, as well as several undergrads, all seem to be impressed by the argument even though I doubt any of them are religious. So below I'll lay out Pascal's Wager, and below that I'll criticize it.

George H. Smith, who years ago wrote, "Atheism, the Case Against God," gave a talk on defending atheism, and at the end of the talk he offered a counter argument or wager to Pascal's, "Smith's Wager." You might find it interesting: http://www.infidels.org/library/modern/geo.../defending.html. Scroll down towards the end, looking for the paragraph that begins, "As one final argument or satire on an argument, you may have heard of Pascal's wager at some point."

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When dealing with what may happen, I tend to break things down into three Ps. Possibility, Plausibility, Probability.

Possibility - Can it happen?

Plausibility - Could it happen?

Probability - Will it happen?

This should be better clarified:

Arbitrary--a claim for which there is *no* perceptual evidence.

Possible--a claim for which there is at least *some* perceptual evidence.

Probable--a claim which *most* of the perceptual evidence supports.

Certain--a claim which *all* the contextually available perceptual evidence supports.

Insofar as Pascal's wager is concerned, its major root fallacy is that it requires the equivocation between the arbitrary and possible. If its intended victim doesn't pretend that the *arbitrary* is the equivalent of the *possible*, then the entire argument collapses--*if* god exists, then consider this statistical nonsense and the threat of eternal damnation in hell (another arbitrary claim). Pascal's wager first requires the misidentification and misintegration of the arbitrary and the possible before one can even consider the so-called wager. This misidentification and misintegration is *prior to* the actual wager. In other words, one first must accept the implicit assumption that an arbitrary claim (god's existence) is in the realm of the possible. Without this implicit assumption, Pascal's wager is pure rationalistic nonsense, on par with Descartes' evil demon.

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• 2 weeks later...
"It is possible, the skeptic argument declares, for man to be in error; therefore, it is possible that every individual is in error on every question. This argument is a non sequitur; it is an equivocation on the term “possible.”

What is possible to a species under some circumstances, is not necessarily possible to every individual member of that species under every set of circumstances. Thus, it is possible for a human being to run the mile in less than four minutes; and it is possible for a human being to be pregnant. I cannot, however, go over to a crippled gentleman in his wheelchair and say: “Perhaps you’ll give birth to a son next week, after you’ve run the mile to the hospital in 3.9 minutes—after all, you’re human, and it is possible for human beings to do these things.”

Peikoff is not offering a satisfactory answer to skeptical claims here, mostly because of his absurd misreading of skeptical argumentation. If you look to Descartes, he's not saying that because one person can be in error, all of them can be in error - which is what the example from Peikoff about the crippled guy seems to point at. He's not even saying that because error is possible in one circumstance, it's possible in all circumstances (which is maybe a more charitable reading of Peikoff on this point). Rather, Descartes says:

All that I have, up to this moment, accepted as possessed of the highest truth and certainty, I received either from or through the senses. I observed, however, that these sometimes misled us; and it is the part of prudence not to place absolute confidence in that by which we have even once been deceived. (from the first meditation)

There's two premises. Your senses sometimes mislead you. You shouldn't trust absolutely that which has deceived you even once. The argument does not rely on generalization to every instance of a species as some kind of logical truth as per Peikoff's reading, but rather on the strength of that second premise.

There are definitely strong replies to Descartes on this point (you can just deny one of the premises), but Peikoff's is just silly.

And since nobody actually answered the OP's real question:

YES. There's a huge literature on possibility and conceivability, going back centuries. Some crucial issues in contemporary philosophy of mind hinge on this question. Here's some places to start if you want to check out some of the lit:

Chalmers has an interesting paper: http://consc.net/papers/conceivability.html

Frege famously argues for the claim that the impossible is conceivable in "On Sense and Meaning"

Just check the works cited in all of these if you want more.

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No, cmdownes, you've got it wrong. That's not the totality of Peikoff's argument. It's just a pithy application of a more general point which he's making overall, which is that Descartes tries to claim the following:

I accept my senses as self-evidently reliable;

But so do mad men, who think their senses convey the truth, when they think they have a glass-head or some such;

But I can have dreams where, upon reflection, my senses evidently are not telling me about real things;

This could be happening all the time;

Therefore, I cannot say with certainty that I can trust me senses as a standard of knowledge.

You can argue against Descartes' premise that you shouldn't trust something which has deceived you once, but I happen to side with Descartes here, that if something is not certain, then it cannot be a standard of knowledge. As does Peikoff. It's an argument you can make, but it does not make the argument that Peikoff makes any less valid.

Peikoff, and myself, accept Descartes premises, that we can be misled as to whether we are actually having a real sense perception, or whether we're dreaming, but we do not accept the leap that Descartes' makes, that this automatically classifies it as part of the field of things which cannot be a certain standard of knowledge, the very reason being that if we can tell we are in error about our senses, then we have some surer sense of reality. The ability to tell that something is a dream, always presupposes a surer, certain standard by which to tell the fact.

Descartes wants to say that because it's possible we've been in error, we could always be in error, but he misses the point that to be in error means to have certainity about what not being in error means. As Peikoff rightly calls out, this is the very meaning of a stolen concept.

So yes, you can make your argument against Descartes (though everyone I've read fails), but it makes Peikoff's no less valid and no more silly.

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You can argue against Descartes' premise that you shouldn't trust something which has deceived you once, but I happen to side with Descartes here, that if something is not certain, then it cannot be a standard of knowledge.

If you agree with his major premise that "it is the part of prudence not to place absolute confidence in that by which we have even once been deceived", then this commits you to the view that we are never deceived by our senses. Your (and Peikoff's, presumably, though like you I haven't read the article in question) reply then seems to hinge on this notion that our post-hoc ability to distinguish dream states from non dream states means that dreams aren't genuine instances of being deceived by our senses. But then I don't know what to make of this pair of claims:

Peikoff, and myself, accept Descartes premises, that we can be misled as to whether we are actually having a real sense perception, or whether we're dreaming...

...if we can tell we are in error about our senses, then we have some surer sense of reality. The ability to tell that something is a dream, always presupposes a surer, certain standard by which to tell the fact.

You concede that there are cases where we can't distinguish dreams from reality. But then you use as a premise the claim that we CAN tell if we are in error about our senses - that is, that we are dreaming.

And Descartes anticipates something like this line anyways, when he says that, "...the occurrences in sleep are not so distinct as all this. (But) I cannot forget that, at other times I have been deceived in sleep by similar illusions; and, attentively considering those cases, I perceive so clearly that there exist no certain marks by which the state of waking can ever be distinguished from sleep...". You can disagree with the claim about phenomenal experience here, I guess, and just say that we can always retrospectively distinguish dream experiences from waking experiences, but that seems plainly false. I can think of a number of instances when I couldn't recall if a given conversation I remembered had actually happened or had been a dream.

Descartes wants to say that because it's possible we've been in error, we could always be in error, but he misses the point that to be in error means to have certainity about what not being in error means. As Peikoff rightly calls out, this is the very meaning of a stolen concept.

This seems like a distinct argument from what you've outlined so far. One need not know the necessary and sufficient conditions for being in error to be able to identify instances of being in error - much less just to acknowledge the possibility of being in error. I'm not sure which of these two you mean by "having certainty about what not being in error means". But the claim that "to be in error means to have certainity about what not being in error means" is just false. I obviously don't need a rigorous understanding of what mathematical error is to, for instance, fail my calculus final today. I can do that just fine without any additional philosophical equipment.

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• 4 weeks later...

Sorry it's taken me so long to reply to this post. I couldn't think of a good response. I've now thought it through and am prepared to respond:

You take my position to be the following...

this notion that our post-hoc ability to distinguish dream states from non dream states means that dreams aren't genuine instances of being deceived by our senses

Let me first be clear on my terms, because I use two different terms in my argument.

Perception - I think you know what I mean by this. We're talking about the direct communication from reality. The point at which what you're perceiving is the world *out there*.

Real Sense Perception - I use this in contrast to, say, a memory of a perception, or something that seems like a perception, but which is then later proved not to be a perception. It seems like a direct communication, but it's not. The contrast would be a Fake Sense Perception (for now on, I'm going to call it a Fake Perception; the word 'sense' adds nothing in this context).

So, I contend that the post-hoc ability to tell a dream from a reality is evidence that we are not deceived by our senses. At least, it shows that since we are able to tell the two apart, 'perceptions' from 'fake' perceptions (in a very odd turn of a phrase, 'images' of perceptions), the real perceptions must exist. If we can, after having had a dream, tell the dream from real perception, then we must have a sense of real perception. An analogy would be that to tell that some food is rotten, we must know what non-rotten food must look like. I'm pretty sure you understand what I mean here, I'm just trying to make sure we're absolutely clear.

You then point out that I also accept, that we can be aware of a fake perception, such as a lucid dream, where we actively think, "This is fake, I know it's fake, but I'm still experiencing it". Not only this, we can have a fake perception and NOT be aware of it. We can have a dream and not know we're dreaming. We can be fooled into thinking the fake perceptions are real perceptions.

Now, let me be clear about how I come to my next premise, that if we are indeed having a fake perception, then we must have some way of knowing it. What I mean here, is that to call something a fake perception, we must have reference to a true perception. I cannot call this or that piece of art work a forgery unless I know what the real piece is as a standard to prove that the forgery is not this real piece. It lies in the arbitrary to consider things which are not, and cannot be, proved. My point is not that:

we can always retrospectively distinguish dream experiences from waking experiences

My point is that if one wants to state that everything we are experiencing right now is a dream, then he must damn well have some proof that this, right now, is a dream. It's not enough to state, 'Well, we have had dreams before'. That is not evidence. He has to have proof that right now, what we are experiencing could be a dream, and to do that, he must provide the real standard of perception, the one to which we have occasionally 'woken up', as it were. If you don't understand why this is necessary, then I urge that you go back to OPAR and read the section on Proof, specifically, that of the arbitrary. Arbitrary claims are not evidence of anything - they are just that, arbitrary.

May I finally rebut one more point you make. You challenge my claim that error presupposes an understanding of correctness/certainty/truth (I can't think of the right synonym for 'error'), with your example of the calculus final. You state that you don't need an understanding of calculus to know whether or not you failed the exam. This is egregious dropping of context. You're substituting an understanding of correctly answering calculus sums for an understanding of reading a slip of paper that says, 'You failed' (and I assume you know the difference already between passing and failing). But perhaps I'm being too harsh. Perhaps what you mean is that you don't need to know any calculus to know that what you're writing is the incorrect answer. You don't need a prior knowledge of calculus to know that you're not going to pass. I think you're still missing the point, then. You'd be ignoring that you know there are certain things expected of you to correctly fill out a calculus paper. You know that they expect certain answers on the answer sheet. You know those answers must be numerical. You know that to answer them would require a knowledge of calculus. You know what it would take to pass this exam, to know that you could answer the questions: studying. Supposing a direct, positive relationship between study and passing, you know that some level of studying will equal passing to some degree. You know what success requires, and you know how to be in error for this exam, even without any knowledge of calculus itself.

I hope I have presented this argument clearly, and that, incidentally, you didn't fail your calculus exam.

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I was wondering, given [this discussion of Pascal's Wager], does anybody know of some published material that talks about the difference between conceivability and possibility in just this way?

I assume, since this is an Objectivist forum, that you're interested in sources from the Objectivist corpus. Peikoff's article "The Analytic/Synthetic Dichotomy," printed in the second edition of ITOE, discusses the notion of concievability versus possibility (albeit in a slightly different context). Specifically, the section "Logic vs. Experience" has a nice discussion of why conceiving a proproposition does not constitute evidence of that proposition-- it contains his pithy summary: "Fantasy is not a form of cognition."

Personally, it's a pet peeve of mine when people start misapplying the theory of probability in contexts like this. The first time I ran into it was in a philosophy of science class, where a professor gave us an article discussing at length the notion of "the probability that the theory of evolution is true." I never received an answer as to what that meant or how to calculate it as a number that wasn't ultimately picked out of the air or an implicit postulation of some sort of useless metaphysical "many-worlds" hypothesis.

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Nate, could you expand on exactly what this professor was claiming this article showed? Do you have any sort of link to the article?

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Nate, could you expand on exactly what this professor was claiming this article showed? Do you have any sort of link to the article?

I'm afraid not-- that was several moves ago and I don't remember most of the other details of the article. I believe the article was about Bayesianism, though, if you're looking for substantiated instances of people abusing probability in the way I mentioned.

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Ah, cheers! It's not quite as bad as this guy high up in the Department of Philosophy here. He does the reverse - he holds anything highly possible to be the exact same thing as true (I mean, he doesn't just say, "Well it's as good as true", he means it's literally true). Likewise, he thinks anything highly unlikely is false, so that if he enters the lottery, he 'knows' he's going to lose.

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Ah, cheers! It's not quite as bad as this guy high up in the Department of Philosophy here. He does the reverse - he holds anything highly possible to be the exact same thing as true (I mean, he doesn't just say, "Well it's as good as true", he means it's literally true). Likewise, he thinks anything highly unlikely is false, so that if he enters the lottery, he 'knows' he's going to lose.

Um ... wow. Any chance he's the one in your sig?

But yeah, I don't think my prof was actually trying to argue that we should cast things in terms of, e.g., "the probability that Newton's laws are valid"-- it's just that we wasted a whole class discussing that article based on the idea when no one couldn't even tell me what it meant; I think that's what left a big impression on me.

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