Does Moral Realism and Infinite Spacetime Entail Atheism?
Vlastimil Vohánka send me an email recently asking for my thoughts on the following reconstruction of an argument recently proposed by Quentin Smith.
1. Necessarily, global moral realism is true (everything, or rather, every physical entity, has a positive amount of value). PremiseThe gist of the argument is that if something exists that is infinitely valuable, if some such thing would exist regardless of what we do, and if our contributions are at best finite, then nothing we do makes any real difference to the aggregate value of what exists (since ∞ + 1 = ∞). Hence, nothing we do really matters.
2. Necessarily, aggregative value theory is true (each physical location has a finite positive amount of value; a location can be a person, any other animal, a plant, a particular of matter or energy, a point of space or time, or some larger complex of particulars of these kinds, for example, a forest, an orchestra or an hour of time; values add up). Premise
2*. Necessarily, the performance of an action is morally indifferent iff the performance of that action neither increases nor decreases the amount of value in the universe. Premise, or from (2)
3. Contingently (and according to contemporary physics), spacetime is infinite, both temporally -- there are infinitely many non-overlapping future hours --, and, more controversially, spatially -- at each time there are infinitely many non-overlapping, equal sized cubes of space. Premise
3*. Necessarily, every human action has only finite effect on the amount of value in the universe. Premise
3**. Necessarily, neither any finite addition to nor any finite detraction from an infinite amount of value neither increases nor decreases the amount of value. Premise
4. Moral nihilism is contingently true (it does not morally matter what humans do, it does not matter what actions humans perform). From (1)-(3**)
5. Humans have no intrinsic dignity (from 1-3**); humans have no rights (from 1-3** or from 4); human life has no meaning (from 1-3** or from 4); every human's life is less valuable than the entire state of his being dead (from 1-3**).
5*. God (at least as traditionally conceived) does not exist. From (4) or (5)
Now, I think that premise (3) of this argument is particularly questionable. I don't think there are any empirical results from physics that establish or that even could establish the existence of an infinite spacetime. But the argument could be reconstructed without that premise. For example, instead of infinite spacetime, we could start from the assumption that God necessarily exists and has infinite value. The result, if the rest of the argument is sound, would be a reductio ad absurdum of theism.
If there's a fundamental flaw in the argument, it has to do with its assumptions about the nature of value. There are several that I find particularly questionable.
I'm skeptical about (1). If all that ever existed was a diffuse cloud of hydrogen, would it have positive value? I'm inclined to think not. I suggest, rather, that there may be no value that is not value to someone or, more broadly, to some sentient being. This is reflected in the notion of the good as that which is desirable, a notion that has no application apart from beings capable of desiring.
I'm also skeptical about (2). Can values simply be added up? Not if there are incommensurable kind of value. It may well be that there is no common currency in which all values can be "cashed out" and then added up.
Finally, I'm skeptical about (3*). Why think that human actions have only a finite effect on the amount of value in the universe? Suppose, for example, that there is an afterlife and that one of the possibilities is heaven (infinite positive utility). Well, if I by my own choices and the grace of God can enter the kingdom of heaven, then haven't I done something that contributes infinite value? Or if inspire others to lives of virtue and godliness so that they enter the kingdom of heaven, then haven't I done something that contributes infinite value?
posted by Alan Rhoda @ 2:25 PM
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18 Comments:
Yes, value is only value for someone at a specific moment. Value is subjective *and* it can change with changes in the environment (including time). I would have thought this obvious :)
Thanks, Alan.
As for (1), cf. pp. 160ff here: http://qsmithwmu.com/ethical_and_religious_thought_in_analytic_philosophy_of_language_contents_page.htm . Basically, (1) says that organisms, inanimate mass, energy, space and time, and states of these, have value independently upon whether conscious organisms believe they have value. Don't you, as a Christian, accept this? Cf. Gn 1 with the repeated "He saw it was good." Further, don't accept that ens et bonum convertuntur?
I've got hard times understanding the concept of incommensurable goods; though I know Pruss, Grisez and Finnis defend it. Anyway, thanks for the hint.
Thanks also for the hint concerning (3*). But how does it adrress the problem already stated by you?: "start from the assumption that God necessarily exists and has infinite value. The result, if the rest of the argument is sound, would be a reductio ad absurdum of theism."
As for Marcel's comment, I don't take it as "obvious" at all. Neither Smith (see the first link in my comment) nor Vallicella (http://maverickphilosopher.powerblogs.com/posts/1199732298.shtml ). Further, as there are (or could be) n-ary and n-minus-m-ary predicates of, say, causation (interest-relative vs. context-independent causation) and belief (belief de dicto 2-place vs. belief de re 3-place), so there could be an n-ary (3-or-more-place) predicate of value (X is valuable for S at t) and at the same time unary predicate of value (X is valuable, period). What do you think, Alan?
See also M. Almeida at prosblogion.ektopos.com/archives/2009/01/quentin-smith-o.html
As you see, these days I've drawn attention of several philosophers to QS's argument which seems to me as a sporadic attempt at making a popular line of thought, famously formulated by T. Nagel, more rigorous. Cf.: "According to Nagel, we are capable of comprehending the world from a variety of standpoints that are either internal or external. The most internal perspective would be a particular human being's desire at a given instant, with a somewhat less internal perspective being one's interests over a life-time, and an even less internal perspective being the interests of one's family or community. In contrast, the most external perspective, an encompassing standpoint utterly independent of one's particularity, would be, to use Henry Sidgwick's phrase, the "point of view of the universe," that is, the standpoint that considers the interests of all sentient beings at all times and in all places. When one takes up this most external standpoint and views one's finite—and even downright puny—impact on the world, little of one's life appears to matter. What one does in a certain society on Earth over an approximately 70 year span just does not amount to much, when considering the billions of years and likely trillions of beings that are a part of space-time." http://plato.stanford.edu/entries/life-meaning/#Nih
Note, however, that Nagel, contrary to QS, rejects (1).
"What one does in a certain society on Earth over an approximately 70 year span just does not amount to much, when considering the billions of years and likely trillions of beings that are a part of space-time."
True, and yet totally irrelevant. You must be an engineer :) One's weight does not amount to much compared to the weight of the Sun. Does that mean "damn, this guy is fat" is a meaningless statement? No, it expresses a SUBJECTIVE opinion. Yes, from the point of view of the universe, our acts are almost (or even exactly) zero. So what? Neither of us is the universe, so why is that relevant in any way for human beings?
Value is subjective. Until you grok that you will reach nonsensical conclusions like "it does not matter what humans do". (This philosophy is self-refuting.)
Vlastimil,
Regarding the relation of denying (1) to Christianity and, in particular, Genesis 1 and "ens et bonum convertuntur", I don't see the problem.
"And God saw that it was good" may suggest that creation possesses intrinsic value, as opposed to both instrumental value ("value for" something else) and subjective value ("value to" someone). But I suggest that perhaps the value God sees value in creation is a reflection of an antecedent subjective valuing by God in the course of deciding whether and what to create. (Is that too voluntaristic? Maybe. I'm not completely wedded to this line of thought, mind you.)
As for "ens et bonum convertuntur", I agree that these are at least extensionally equivalent, but I don't think even that would be true if there were no God. The interconvertibility of the transcendentals - being, truth, goodness, unity - is a consequence of theism, not a metaphysical datum that would hold in any world, even a naturalistic one.
I agree with you, however, that Marcel's point is not as obvious as he initially claimed, though neither do I think it obvious that there is a unary predicate "is valuable". It seems plausible to me that all such locutions are elliptical for "is valuable to".
What about God himself? Here's a Euthyphro-type question: Is God valuable because he values himself, or does he value himself because he's just plain valuable? Perhaps neither is right. Perhaps the distinction between value simpliciter and value to God breaks down. Perhaps being of value to God just is being of value.
"I agree with you, however, that Marcel's point is not as obvious as he initially claimed"
It might be the influence of the Austrian school of economics :) but I cannot see value as anything but subjective. If value were an objective property, what would its measurement unit be? Its composition? What would "a / some value" look like outside someone's mind? The impossibility of conceiving of such a notion is why I consider that my point is obvious :)
Alan,
Thanks.
Do you accept that that organisms, inanimate mass, energy, space and time, and states of these, have value independently upon whether conscious ORGANISMS believe they have value? I think you do. Then you accept (1).
Secondly, suppose that being of value to God just is being of value. A nice hint. But how do you solve the problem that given the existence of God with infinite value, every human action is morally indifferent?
Vlastimil,
Assuming that by 'organisms' you mean physical beings, I answer your first question with a qualified 'yes', qualified because I don't think that all of the items in your list are proper objects of value - space and time, for instance. I don't, however, see how that commits me to (1).
To your second question, I say two things. First, if human actions are of significant value to God, then they have significant value simpliciter. Second, according to non-standard analysis, ∞ behaves just like an ordinary finite number. Hence, ∞ + 1 ≠ ∞.
Alan,
Thanks again.
First,
if
(A) ens et bonum conventuntur
or
(B) God believes that (A) (which seems to be supported by Gn 1:10),
then
(C) organisms, inanimate mass, energy, space and time, and states of these, have value independently upon whether conscious (physical) organisms believe they have value.
Right? But you accept (A) or (B), don't you?
I admitt that (1) is stronger than (C). (1) = Necessarily, (C). Nevertheless, (C) is enough for QS's argument.
Secondly,
you wrote:
"if human actions are of significant value to God, then they have significant value simpliciter."
How would you justify the antecedent? Given the existence of God with infinite value, QS would contend, every human action is morally indifferent and insignificant to God.
As for the non-standard analysis, yes. QS seems to me to assume standard analysis.
I am an utter amateur in this field, but nevertheless I submit this.
First, I agree that Q's argument breaks down the moment beings with eternal life enter the picture - and I notice one of his express assumptions is a finite life of humans. Oddly, I don't even think heaven / perpetual bliss needs to be assumed for this objection to work. Say we either have a dualistic afterlife or a material resurrection, such that our acts not only accomplish certain finite goods (say, helping someone who is hurt) but also condition us towards future goods (building up the habits of helping those who are hurt). If that's true, then any individual human is or may be working towards adding infinite value in the aggregate. Just 'eternal life' is enough to put one heck of a spin on the question, even if it's vastly different from the traditional religious concepts. That goods can beget goods and continue into the future also seems to throw a wrench into what's being envisioned here.
Second, I think there's some confusion going on about human actions being valueless due to their significance to God. One biblical/classical thought of God seems to be that God needs nothing. Humans doing evil does not hurt Him, humans doing good does not help Him. So nothing humans could do could 'matter' to God in that sense - and that doesn't seem to 'disprove the God of classical theism'. (Actually, is it right to label arguments like this as entailing atheism? If a Calvinist argues with an Armenian, would they argue that an offered argument entails atheism?) It therefore seems strange to measure value in terms of 'whether or not it affects an infinite God'. Stranger still to argue against God (even the traditional conception of God, which always seems to me as a vaguer idea than presented) based on problems with this scheme.
Third, I'd agree that the nature of value is what's really at issue here. Trying to reduce value, rights, and meaning to numerical measures in a theoretical/mathematical plane is fraught with problems, as is trying to equate values in an absolute sense. I think the flaws in play are most apparent when looking at QS's conclusion - his conclusion assumes finite human life, finite effects of human endeavors (partly as a result of compartmentalizing 'value' to specific acts, regardless of the fact that consequences of acts continue), etc. It seems to me that far too much has to be unjustly assumed about reality and measures of value for his conclusion to go through.
All,
First,
After rethinking QS’s argument, now I think my own (and also QS’s) formulation of (1) and (2) is muddy. There should have been (leaving the modal operators aside) rather something like these:
(1’) Every location, that is, every organism, inanimate mass, energy, space and time, and state of these, have some positive amount of positive value independently upon whether conscious organisms believe they have value. Premise
(2’) There is some unit of positive value U+ such that every vacuous metric cube of space and every hour of the existence of vacuous space is such that its overall amount of value is at least one U+.
Premise; or from (1’) and some auxiliary premise like: If (1’), then there are some units of positive and negative value expressing total amounts of positive value, total amount of negative value, and overall amounts of value of all locations.
(2’’) The overall amount of value of the collection of all empty metric cubes of space is at least the sum of all their overall amounts of value. The overall amount of value of the collection of all hours of the existence of vacuous space is at least the sum of all their overall amounts of value. Premise
(2’’’) The total amount of positive value of the universe (comprising past, present, and future) is greater than or equal to the total amount of value of the collection of all empty metric cubes of space. The total amount of positive value of the universe (comprising past, present, and future) is greater than or equal to the total amount of value of the collection of all hours of the existence of vacuous space. From (2’) and (2’’)
But according to QS (see the premise no. 3), there are at least aleph-zero of metric cubes of space (because the universe has hyperbolic topology) or at least aleph-zero of hours of the existence of vacuous space (because the universe will expand forever and disintegrate, getting darker, colder, and more and more gauzily).
***
Secondly,
Roger’s and Alan’s objection to (3*) is good.
Currently, however, I also think QS inserts neither (3*) nor (3**).
He rather inserts something like these:
(3’) No action of a human (and of any collection of humans) alters the overall amount of value of the collection of all empty metric cubes of space. No action of a human alters the overall amount of value of the collection of all hours of the existence of vacuous space. Premise
(3’’) Every action of a human (and of every collection of humans) which adds some U+’s to the the total amount of positive value of the universe adds at most aleph-zero U+’s. Premise
(3’’’) In Cantorian arithmetic, for any non-negative number n which is at most aleph-zero, aleph-zero + n = aleph-zero. Premise
(3’’’’) No action of a human (or of a collection of humans) alters the total amount of positive value of the universe. From (2’’’), (3), (3’), (3’’), and (3’’’)
(3’’’’’) The overall amount of value of the universe equals the total amount of positive value of the universe minus the total amount of negative value of the universe. Premise (Isn‘t the overall value of any entity captured by the sum of its positive value minus the sum of its negative value?) Premise
(3’’’’’’) But in Cantorian arithmetic, both subtracting from positive transfinite numbers and adding to negative transfinite numbers is disallowed/not defined. Premise
Therefore,
(3’’’’’’’) No action of a human (or of a collection of humans) alters the overall amount of value of the universe. From (3’’’’), (3’’’’’), and (3’’’’’’)
***
Ad (3’’’’’’) and (3’’’’’’’)
QS, p. 50: "... since there are infinitely many intervals of space, intervals of time, particles, and maybe infinitely many organisms, there are aleph-zero units of positive value. There could also be aleph-zero units of negative value; perhaps there are infinitely many intelligent organisms who engage in infinitely many moral acts. There could be infinitely many acts that are unjust or unfair. If so, there are aleph-zero units of negative value and aleph-zero units of positive value. This implies that the number of units of negative value can neither be increased nor decreased and that the number of units of positive value can neither be increased or increased by morally relevant acts or "locations" (something with a finite amount of value). Thus, the response to the objection is that the conjunction of the two premises, global moral realism is true, and the universe is spatiotemporally infinite, imply (given the aggregative theory of values) that there cannot be merely a finite number of units of positive value."
QS's assumption is the claim that at each time there are at least aleph-zero non-overlapping metric cubes of space, each with one unit of positive value. But he also takes for granted that the infinite amount of positive value of all the space-cubes could not be canceled or made finite by the the infinite amount of negative value of all unjust acts, and vice versa. Why? I guess because he assumes Cantorian arithmetic.
In Cantorian transfinite arithmetic, subtracting from aleph-zero is not allowed. I admit the rationale for disallowing subtraction and division, which I read in W. L. Craig's book The Kalaam Cosmological Argument (1979, pp. 80ff), seems somewhat arbitrary.
In sum, the rationale is that
{1, 2, 3, ...} - {1, 2, 3, ... } = { },
{1, 2, 3, ...} - {2, 3, 4, ...} = {1},
so,
aleph-zero - aleph-zero = zero, and at the same time
aleph-zero - aleph-zero = one.
But that cannot be.
And for every positive real number n,
n * aleph-one = aleph-one, and aleph-zero * aleph-one = aleph-one,
so,
aleph-one/aleph-one = n, and at the same time
aleph-one/aleph-one = aleph-zero.
But that cannot be.
That's how Craig explains why subtraction and division cannot be performed in Cantorian transfinite arithmetic.
Of course, one naturally asks: if the Cantorian allows other weird statements (as well-defined), like aleph-zero + one = aleph-zero and, at the same time, aleph-zero + two = aleph-zero, then why does not he allow (as well-defined) also the weird statements above?
***
An objection to QS: as already said, isn‘t the overall value of any entity captured by the sum of its positive value minus the sum of its negative value?
If so, isn’t in Cantorian transfinite arithmetic, likely embraced by QS in his paper, both subtracting from positive transfinite numbers and adding to negative transfinite numbers disallowed/not defined?
If so, however, then the overall value of the infinite universe is not allowed/defined (in Cantorian arithmetic). Because what else would be the overall value of the universe than the sum of its positive value minus the sum of its negative value?
Even if so, however, QS still could change his argument, in the following way:
The overall amount of value in the universe is not defined.
An action is morally different only if it makes a difference to the total value of the universe whether that action is performed or not.
So,
No human action is morally different.
***
Roger,
I wrote:
“Given the existence of God with infinite value, QS would contend, every human action is morally indifferent and insignificant to God.”
I did not mean to imply something like affecting God by creatures. If it’s still puzzling, delete “and insignificant to God” and add: “because an action is morally different iff the action neither increases nor decreases the amount of value of the whole reality.”
As for “the traditional conception of God”, you can change it for “every conception of God which entails some human right or some moral difference”.
Vlastimil,
Thanks for the clarification. Makes a little more sense to me that way, though I still don't see the connection between perceived aggregate values and human rights, etc.
I still question the ability to translate values the way that seems necessary here, such that giving food and water to one homeless person is equal to holding open the door for someone carrying heavy packages 17.3 times, etc. Or so it seems implied to me.
Another reason, which I think is highlighted somewhat by Mike Almeida: It's a mistake to judge a universe in terms of normalized aggregate value, because it leads to scenarios where W and W' are classed equally despite one clearly being better than the other.
Another consideration on those lines: Any choices made in a person's life will change the aggregate composition (put value aside for now) of a universe even when we're considering the infinite totality. If we have universe 1 and 2, and the sole difference is that in universe 1 at point X I paid someone a sincere compliment while in universe 2 I paid someone a sincere insult, it establishes a difference in composition between those universes. Argue the value is the same in totality, but there still seems reason to choose one universe over the other (just as there seems reason to choose W over W'). So one universe is more valuable despite their values being equal? Something isn't right.
I think this point gets compounded once you work in eternal life - because, if eternal life is true, then every act I and others take not only affect my life at the moment, but can affect my life infinitely since said acts will affect future acts/states of the universe. On that assumption acts have tremendous value subjectively (because I'm going to have to experience some/all fallout of said acts eventually because my life is eternal) and objectively (because my acts will change the composition of the universe both at the moment and when considered in totality - ie, by making choice X at time A in the universe, I have forever established a difference between universe 1 and universe 2.) No matter how much time passes in the aggregate, no matter how many acts build up in the aggregate, the differences will remain. So under that perspective, any act I undertake has eternal consequences for an infinite universe, no matter how small.
I think the upshot here is that we have very good reasons to believe that assigning value and meaning under QS's scheme to either individual acts or aggregate totals doesn't work for a number of reasons. First because it assumes utter mortality which has tremendous subjective/objective ramifications. Second because using the sort of value in the way QS assigns leads to universes of equal 'value' yet one is clearly better than the other. Third because it ignores that any distinguishing act between two universes changes the composition of an infinite totality (which is an important perspective, because it seems that a large part of the currency in QS's scheme here is the emotional response of performing an act which adds value 1 to an infinite total.) That's just to begin with, but - again, I speak as an amateur here - I think that's enough to sink the scheme.
Thanks, Roger. Very good comment.
Yes to the 2nd point. As for the 1st and the 3rd pont, QS would say that even if we are eternal and/or every our action have an infinite positive (or negative) consequence both in the compostion of the universe history and in the amount of value contributed to the universe history, it still holds that no action of a human (or of a collection of humans) alters the overall amount of value of the universe. Cf. especially (3’), (3’’), and (3’’’’’’).
A TENSION IN QS?
1. QS, p. 45:
"Suppose, for example, that there is an action A that has two units of value and that there is a possible history of a universe that is exactly like our universe except for the fact that action A is not performed at the time t1 when it is actually performed (and all the future consequences of the nonperformance of this act). Let us suppose the nonperformance of this action at time t1 implies that no units of value have been added at this location but that two units would have been added at this location if the action were performed. Then, if time begins at t0, we have two endless histories of the universe that differ in value at least at time t. Action A, we shall say, contributes to the overall value of the universe at time t, making this value consist of 800 units. The not-A universe differs at t by having only 798 units of value and (if the action has consequences whose units of value make the not-A history differ at every time later than t), we may represent the two histories as follows:
The A-history of the universe:
t0 t1 t2 t3
200 800 860 920 . . . .
The not-A history of the universe:
t0 t1 t2 t3
200 798 840 600 "
That suggests not to insert (3*). That our actions can have both positive and negative infinite impact is not ruled out, given such scenarios. But, then, if subtraction from transfinite numbers is allowed, how to reach the conclusion that we cannot alter the overall value of the universe?
2. Now cf. pp. 46f and 50:
"I am obligated to perform an action only if the performance of that action increases the total value more than not performing that action increases that action. But this condition is not met by any action any human could undertake. It follows that there is no action that any human is obligated to undertake. It also follows that there is not act that is morally impermissible. An act B is morally impermissible only if it decreases the amount of value in the universe. But aleph-zero minus any finite number is aleph-zero. Therefore, every act is morally permissible. Further, no act is better or worse than any other act. An act C is better than another act D only if C increases the value of the universe more than does act D. But no finite amount of value added to aleph-zero results in a greater amount of value. Further, no act E is worse than any other act F, for E is worse than F only if E decreases the value of the universe. But a finite number of units subtracted from an aleph-zero number of units still results in an aleph-zero number of units of value. ... There could be infinitely many acts that are unjust or unfair. If so, there are aleph-zero units of negative value and aleph-zero units of positive value. This implies that the number of units of negative value can neither be increased nor decreased and that the number of units of positive value can neither be increased or increased by morally relevant acts or "locations" (something with a finite amount of value)."
This suggests to insert (3*) and to allow subtraction from transfinite numbers. As I've said already, if we do allow subtracting from positive transfinite numbers or adding to negative transfinite numbers, what what would be the total value of this universe? Zero? That would seem like a natural answer. But then it still holds that no FINITE human action (no action of a human or of a finite human population) can alter the sum of positive value, the sum of negative value or the total value (which are all infinite).
But, again, how to defend (3*) and rule out that our actions have both positive and negative infinite impact? By the saying that the universe will expand forever and disintegrate, dead, darker, colder, more and more gauzily, and ultimately dead? That does beg the question against human immortality. (But I suppose QS is happy to do so.)
In fine, if QS assumes (3*), it is not clear how he would defend it. If he does not assume (3*) and allows the subtraction, it is not clear how to derive the conlusion. So, a new twist: it seems QS assumes (3*), but it is not very clear why, and that he allows the subtraction.
Sorry for these quandaries of mine. I hope they are instructive, in a way. :-)
It also follows that there is not act that is morally impermissible.
Interesting. 1 Cor 6:12
"Everything is permissible for me" — but not everything is beneficial. "Everything is permissible for me" — but I will not be mastered by anything.
Re: Does Moral Realism and Infinite Spacetime Entail Atheism?
Marcel,
I think St. Paul's statement has an implicit qualifying clause. Not so the one by QS.
Other parts where QS does not assume (3*) and allows the subtraction.
P. 47:
"... if there are an infinite number of consequences of my acts with positive values, my actions plus their consequences still do not increase the value of the universe. For aleph-zero plus aleph-zero equals aleph-zero."
I don't get this. Why assume the universe is modeled by the formula aleph-zero + aleph-zero (or aleph-zero + aleph-zero + aleph-zero + ...)? Why not rather aleph-zero - aleph-zero - aleph-zero + aleph-zero ...?
P. 48:
"Even if an act ... has an infinite number of consequences, each with a negative value, this still does not decrease the amount of positive value in the universe. For an aleph-zero number of integers (e.g. all the negative integers) can be removed from the set of all integers […-2. –1, 1, 2…] and the amount of positive value in this set will remain the same, namely aleph-zero."
I get this neither. Isn't the overall value equal to the sum of positive value minus the sum of negative value? So, allowing the subtraction, what equals aleph-zero - aleph-zero? Presumably zero, doesn't it?
Let's have a 4 seconds long process with 8 units of positive value and 3 units of negative value, represented by the series: [-2, -1, 3, 5]. What's the overall value? Presumably 5+. And it does not seem relevant to say that all the negative integers can be removed from this series and the sum of positive value will remain the same. Or am I missing something?
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