Quentin Smith (cf. ‘Moral Realism and Infinite Spacetime Imply Moral Nihilism’, in Dyke, Heather (ed.), 2003, Time and Ethics: Essays at the Intersection, Kluwer Academic Publishers, pp. 43-54) has an ingenious argument for moral nihilism that he derives from global moral realism and value aggregation. Assume global moral realism is true,
GMR. Global moral realism is true if and only if all organisms, inanimate mass and energy, and space and time, and states of these entities, have value nondependently upon whether conscious organisms believe they have value.
GMR is an odd moral view, since it entails that even empty spaces have positive value. He does argue for that view elsewhere (cf. his Ethical and Religious Thought in Analytic Philosophy of Language. New Haven, Yale University Press, 1997) but I’m not sure such a position could be made plausible. Assume value aggregation is true,
VA. Aggregative value theory is true if and only if units of value can be totalised in some way, either by adding them, averaging over them, measuring the equality of their distribution, measuring the minimum, etc.
- The universe (past, present & future) contains infinitely many (at least aleph-null) locations of value (e.g. infinitely many non-overlapping equal sized cubes of space).
- The total amount of value in the universe is infinitely large. from 1, GMR, VA
- An action is morally indifferent if it makes no difference to the total value of the universe whether that action is performed or not.
- Every possible action is morally indifferent. from 1,2,3
According to Smith’s version of moral nihilism, “… this is what I mean by moral nihilism. It does not matter what actions humans or other agents perform”.
/:. Moral nihilism is true. from 4
Here is an argument that (4) does not validly follow from (1)-(3). For the purposes of this argument, I will simply concede that (1)-(3) are all true, as I do the rest of Smith’s assumptions.
1’. Assume that the actual world W0 has infinite positive value: at each of the infinitely many locations of value, there is at least one unit of positive value, L+.
2’. Assume there are infinitely many people, each of whom can change L+ to L-, or leave L+ as it is.
3’. According to Smith, it makes no difference to the overall value of the world if person P1 changes L1+ to L1-. Smith’s argument, as we might expect, is that no finite negative or positive amount of value can make any difference an infinite total value.
4’. For each person Pn, let Pn change Ln+ to Ln-.
5’. The value of W0 = the value of W1 (where W1 is exactly like W0 except that L1+ is changed to L1- in W1).
6’. V(W1) = V(W2), same reason as in (5’).
7’. V(Wn) = V(Wn+1) for all n, same reason as in (4’) and (5’)
8’. V(W1) = V(Woo), by the transitivity of ‘equal in value to’.
9’. ~(V(W1) = V(Woo)), obviously the value of W1 is positive and infinite, the value of Woo is negative and infinite. Contradiction!
All we can do is either deny that ‘equal in value to’ is transitive, when it obviously is, or deny that each action of changing Ln+ to Ln- is morally indifferent.
10’. Smith’s premise (4) is therefore false. It is false that every possible action is morally indifferent.
Hey Mike,
To say that that's an interesting argument is an understatement. Quick question about GMR. I would have thought that on the natural reading of it (or a natural reading of it), the view was committed to saying that:
(x)(x has value --> x's value is non-subjective)
Not:
(x)(x has value & x's value is non-subjective)
The first doesn't support Smith's argument. But, it's his thesis so he can mean whatever he likes I suppose.
I worry about the truth of (3) since it implies that my punching someone in the nose is morally indifferent if it were the case that had I refrained that person's nose would be struck with the same impact by a falling apple. But, I suppose that's no fun. And, if we reformulate the argument in terms of value rather than moral difference making properties it's still troubling.
I have a question about your response. Does it imply that if you had infinite wealth, I'd leave you worse off if I stole a penny?
A much, much better version of this argument has been considered and answered (and a small literature developed around the answer) by Vallentyne and Kagan.
Kagan, S. & Vallentyne, P. 1997. "Infinite Utility and Finitely Additive Value Theory," Journal of Philosophy 94: 5-26.
I suspect one could deny that "equal in value to" is transitive. They could deny this and point out that it is transitive when its relata are finite quantities, but not when they are infinite quantities. We mistakenly infer that it is always transitive, with respect to both finite and infinite quanities, since, as it happens, we only apply it in finite cases and generalize to all cases. But infinite cases are simply different.
Mike,
Thanks for this!
Is this an argument from mathematical induction?
(W0, W1, W2, ...) is an infinite series of possible worlds. I guess I am not supposed to take Woo as the last member of this series. The series has no such a member. Rather, I should take Woo as the world with ALL L+'s in W0 changed into L-'s. Am I right?
Now consider this objection: for every natural number n (that is, for every number like 0, 1, 2, 3, ...), (7') holds. But oo in (8') is not a natural number. Note that oo has no immediate predecessor (a number n different from oo and such that n + 1 = oo). So, why accept (8')?
***
Clayton,
QS understands (1) rather the 2nd way. His argument for this premise is at http://qsmithwmu.com/ethical_and_religious_thought_in_analytic_philosophy_of_language_contents_page.htm , pp. 160 ff.
***
A minor comment
As far as you change only a finite collection of L+'s (for L-'s), the value of the resulting W remains infinitely positive.
If you change an infinite collection of L+s, the value of the resulting can, but doesn't have to, be not infinitely positive positive. If you change ALL L+'s, the resulting value is infinitely negative. If you change all EVEN L+'s (L2+, L4+, L6+, ...), the value of the resulting world is BOTH infinitely positive and infinitely negative.
Cf. 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 natural 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?
Nevertheless, given the aleph-zero amount of positive value in the universe (due to the value of aleph-zero metric cubes of space in the universe; which, at least hypothetically, can be accompanied by the aleph-zero amount of negative value in the universe, due to aleph-zero unjust acts in the universe), and given the Cantorian background, all actions of a human, though they have some finite amount of value, cannot alter the total amount of value in the universe (which is at least aleph-zero positive -- or at least aleph-zero positive and at the same time at least aleph-zero negative). To repeat myself, as I understand it, in Cantorian arithmetic, subtracting is allowed only from FINITE numbers.
Christian,
QS addresses Vallentyne and Kagan at section 5.4 of the given paper.
http://qsmithwmu.com/moral_realism_and_infinte_spacetime_imply_moral_nihilism_by_quentin_smith.htm
Hi Clayton,
Quentin clearly means the second version, strange as it is,
(x)(x has value & x's value is non-subjective)
Yes, I think I have two options, deny transitivity for equality, which cannot rationally be done, or hold that the loss of a penny is a loss of 1/ooth of my total wealth.
A much, much better version of this argument has been considered and answered (and a small literature developed around the answer) by Vallentyne and Kagan.
I'd hardly call the Kagan argument an "answer", unless we're using that term non-normatively. In any case, Quentin is denying that the peculiarities of infinite value can be resolved in the way Kagan suggests.
I suspect one could deny that "equal in value to" is transitive. They could deny this and point out that it is transitive when its relata are finite quantities, but not when they are infinite quantities.
The relata in my case are finite quantities, so I don't see the advantage to taking that position. Aside from that 'equality' is transitive, if any relation is.
What's with 2? If we totalize by averaging, rather than adding, there's no reason to think the total value of the universe is infinitely large.
(W0, W1, W2, ...) is an infinite series of possible worlds. I guess I am not supposed to take Woo as the last member of this series. The series has no such a member. Rather, I should take Woo as the world with ALL L+'s in W0 changed into L-'s. Am I right?
Now consider this objection: for every natural number n (that is, for every number like 0, 1, 2, 3, ...), (7') holds. But oo in (8') is not a natural number.
It don't think that will help. Take the infinite series of worlds, W0, W1, ...Woo. Obviously, oo is not a natural number, so strictly there is no world Woo. It's just a stand in for the claim that there is no terminating world in the sequence. According to Smith's argument, every world in that infinite series is equal in value: all have infinite positive value. That claim is plainly false. There must be worlds in that infinite sequence that are worse than W0.
What's with 2? If we totalize by averaging, rather than adding, there's no reason to think the total value of the universe is infinitely large.
Heath, right. Smith believes, in addtion, they there are infinitely many locations of value (each of which contains at least a single unit of value) that can be summed to an infinite total value. I'm just conceding all of that, though, as I say, I don't think the claim about every particular being valuable can be made plausible.
(W0, W1, W2, ...) is an infinite series of possible worlds. I guess I am not supposed to take Woo as the last member of this series. The series has no such a member. Rather, I should take Woo as the world with ALL L+'s in W0 changed into L-'s. Am I right?
Now consider this objection: for every natural number n (that is, for every number like 0, 1, 2, 3, ...), (7') holds. But oo in (8') is not a natural number.
Vlastimil,
It's also possible to base my objection on a supertask that involves changing, in a finite time, all of the denumerably many Ln+ to Ln-. And I think the case is even clearer under this assumption, assuming supertasks of this sort are coherent.
Surely the weakest premise in QS's argument is 3). You'd think that some such principle as the following would hold:
P) If an action results in the obtaining of some instance of value that did not previously obtain, then that action is not morally indifferent.
And P) entails the falsity of 3).
This allows you to sidestep all the tricky questions about infinite cardinalities and suchlike.
The relata in my case are finite quantities, so I don't see the advantage to taking that position.
But look at premise 8.
8’. V(W1) = V(Woo), by the transitivity of ‘equal in value to’.
Aren't the relata worlds that have infinite value? You said:
1’. Assume that the actual world W0 has infinite positive value: at each of the infinitely many locations of value, there is at least one unit of positive value, L+.
Maybe you could say more about how the quantities are finite. And I didn't mean to imply that Kagan and Vallentyne solved the problem. I just think their presentation of the problem is vastly superior to Smith's. I like quite a lot of Smith's work, this particular paper is likely my least favorite of his. That's neither here nor there, I suppose.
But look at premise 8. 8’. V(W1) = V(Woo), by the transitivity of ‘equal in value to’
But that's the conclusion. I don't assume that V(W1) = V(Woo). It follows that V(W1) = V(Woo) on the assumption of every finite equality. But set that aside, we can derive a simpler contradiction. Suppose that somewhere in the sequence is a world W in which every even numbered location is positive Ln+ and every odd numbered location is negative Ln-. In W it is true that the total of positive locations LL+ + LL- = LL+, so the world is overall good. But it is also true at W that LL- + LL+ = LL-, so the world is overall bad. The order in which you add affects the result of the addition. So the world is both overall good and overall bad. Contradiction.
I like that quicker argument alot. Seems right. But it's seems, at first blush anyway, to be an objection to premise 2 of Smith's argument. Or do you think it's an objection to a different premise, or to it's validity?
Heath and Mike,
How would the totalizing by averaging, as opposed to the totalizing by adding, look like? What would be the averaging formula? How would it help?
Using adding, the total amount of value of the universe-history (past, present and future) is the sum of all amounts of value of all locations of value in the universe-history. Given there are at least aleph-zero future hours, each with at least one unit of positive value, or at least aleph-zero metric cubes of space at each time, each cube which with at least one unit of positive value, the total amount of positive value of the universe-history is at least aleph-zero.
Using averaging, is the total amount of value of the universe-history (past, present and future) equal to (the sum of all amounts of value of all locations of value in the universe-history / the number of all locations of value in the universe-history)? Given the assumptions just mentioned, the total sum of positive value is at least aleph-zero and the total number of locations of value is at least aleph-zero, too. But, first, division of transfinite numbers is not allowed in Cantorian arithmetic (which I take to be QS’s background). And, secondly, if it is allowed, what is the result of aleph-zero/aleph-zero, and how is the result relevant for QS’s argument?
***
Mike,
I wanted to ask this before, as an addendum, but my comment did not appear. So, here it is again:
how, exactly, does (4) contribute to deriving the contradiction? (4) is not mentioned in your (1')-(9') reductio.
Secondly, in your first reply to my objection to (8'), you say that "According to Smith's argument, every world in that infinite series is equal in value: all have infinite positive value." This is not clear to me. I hope the following remarks are relevant.
As I wrote already, it seems to me that according to Smith, as far as you change only a finite collection of L+'s (for L-'s), the value of the resulting W remains infinitely positive.
(If you change an infinite collection of L+s, the value of the resulting can, but doesn't have to, be not infinitely positive positive. If you change ALL L+'s, the resulting value is infinitely negative. If you change all EVEN L+'s (L2+, L4+, L6+, ...), the value of the resulting world is BOTH infinitely positive and infinitely negative.)
Let's have the set S of individuals {a0, a1, a2, a3, ...}. For any NATURAL NUMBER n and any set S' constructed by deleting n members from S, |S'| = |S|. It does not follow that for the set S* constructed by deleting ALL members from S, |S*| = |S|. Further, for any natural number n, any natural number n', any set S' constructed by deleting n members from S, and any set S'' constructed by deleting n' members from S', |S''| = |S'| = |S|. And it does not follow that for the set S* constructed by deleting all members from S, S' or S'', |S*| is equal to |S|, |S'| or |S''|.
In the second reply to my objection, you say allude to a „supertask that involves changing, in a finite time, all of the denumerably many Ln+ to Ln-“, suggesting that „the case is even clearer under this assumption, assuming supertasks of this sort are coherent.“ Well, not clearer to me. I don’t see how the supertask helps. Mea culpa, probably.
Finally, you replied to Clayton, „Yes, I think I have two options, deny transitivity for equality, which cannot rationally be done, or hold that the loss of a penny is a loss of 1/ooth of my total wealth.“ I believe oo/1 is not allowed in Cantorian transfinite arithmetic. See my minor comment above. Is 1/oo allowed?
Blip,
"You'd think that some such principle as the following would hold:
P) If an action results in the obtaining of some instance of value that did not previously obtain, then that action is not morally indifferent."
Thanks for that hint. "Instance of", yes, that seems relevant.
One correspondent wrote similarly to me:
"Suppose that universes can have infinite value. If I make two universes, then I have two things of infinite value. While there is a sense in which the sum of the two universes has no more value than either one of the universes -- since, ex hypothesi, the value of the sum, and the value of each of the individuals, is infinite -- it is nonetheless the case that there is also a sense in which my holdings are more valuable in the case of the sum than in the case of either of the individuals. For, if I have *two* universes, then I can lose one, and still maintain an infinite holding. (I assume that universes are indivisible: you cannot hold half a universe.) Now, suppose instead that I have two things, only one of which is of infinite value. By the same kind of reasoning, I'm better off with the sum of the two things than I am with just the infinite one."
Another correspondent very generally: "... I do not accept (Cantorian) cardinality the appropriate measure of ... size ... I accept something like a range theory or a topological approach. I wish I could try to explain more what that is, but just consider that a circle and an inscribed square have the same cardinality of points within their bounds, but we can still say that the circle has a larger area. Cardinality does not capture the size of the area. I think sets are like that too. There is very little written on this unfortunately."
Mike,
„... LL+ + LL- = LL+, so the world is overall good. ... also ... LL- + LL+ = LL-, so the world is overall bad.“
1. But do you really capture the overall value by ADDING? Isn‘t the overall value of any entity captured by the sum of its positive value MINUS the sum of its negative value?
2. 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, and so neither LL+ - LL-, nor - LL- + LL+ is allowed/defined?
3. If so, however, then the total (overall) value of the world W is not allowed/defined (in Cantorian arithmetic). Because what else would be the total value of the world W than LL+ - LL- or - LL- + LL+? But then (2) is not true.
4. If so, however, QS still could change his argument by changing (2) and (3), in the following way:
(2‘‘) The total amount of value in the universe is not defined. from (1), (GMR), (VA)
(3‘‘) An action is morally different only if it makes a difference to the total value of the universe whether that action is perfmormed or not. premise
So,
(4‘‘) No possible (human) action is morally different. from (2‘‘) and (3‘‘)
What do you think?
5. If you accept my point 1, but don’t accept the point 2 and allow subtracting from positive transfinite numbers or adding to negative transfinite numbers, what equals LL+ - LL- and - LL- + LL+? 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 LL+ or LL- (which are infinite in value).
The transitivity of a relation R says that if xRy and yRz, then xRz. It says nothing about the case of an infinite chain of R-relations. In general, if x(1),x(2),... is a sequence, and R is a transitive relation, it can be true that x(n)Rx(n+1) for every n, but x(1)Rx(infinity) is false, where x(infinity) is some kind of a limit of the x(n). For instance, "equal in cardinality" is transitive. Let R be this relation. Let N={1,2,3,...}. Let x(1) be the set N-{1}. Let x(2) be the set x(1)-{2}. And so on. Then, x(n)Rx(n+1) for every n. But the natural limit of the x(n) is the empty set. And it is false that x(1)Rempty.
You're right that Smith's argument (at least as you give it) is invalid. It needs an auxiliary premise, such as that no action affects more than a finite number of locations, or that every location necessarily has positive value, or the like.
Then, x(n)Rx(n+1) for every n. But the natural limit of the x(n) is the empty set. And it is false that x(1)Rempty.
Right, this is why I suggested (among other possibilities) supertasking. Let W+ be a world with all L+. Let God supertask the change of all L+ to L-. The resulting world W-, achieved in a finite amount of time, is one in which all locations have negatvie value L-. Though it is true that for each world actualized in that finite time between the actualization of W+ and the actualization of W-, W+1 = W+2 (where '=' is now 'equal in value'), it is false that W+ = W-.
The transitivity of a relation R says that if xRy and yRz, then xRz. It says nothing about the case of an infinite chain of R-relations.
Can that be quite right? It does follow by transitivity that every world Wn in the infinite sequence has the same value, and so all are equal in value to W0 (the first world in the sequence).
Mike,
By transitivity it follows that every Wn in the infinite sequence has the same value, and so all are equal in value to W0. But what does not follow is that Winfinity has the same value, unless you add the auxiliary premise that value is a continuously varying function (so lim Value(w_n) = Value(lim w_n)) in an appropriate topology. The value continuity claim, though, is in general false, I think.
The supertask case does, however, succeed in showing Smith's argument is is invalid, if undertaking a supertask counts as a single action. If it doesn't, then you have the situation that each part of the supertask makes no difference to value, but the supertask as a whole does make a difference. That is odd, but not contradictory. In that case, though, Smith has to grant you that while single actions perhaps have no moral significance, sequences of actions do have moral significance.
In any case, we agree: his argument is invalid. But an invalid argument can always be made into a valid one by adding a premise. So now the question is whether there is some reasonable premise that Smith might have implicitly had in mind which would rescue his argument. I would suggest something like the following:
(*) No action either changes infinitely many locations from having positive value to having non-positive value or makes an infinite change in what locations there are.
And when one confines oneself to human actions, (*) is very plausible.
Actually, even that is not enough. For we could use nonstandard arithmetic to get out of the problem.
Moreover, I think (3) is clearly false, so the argument is unsound. An easy counterexample to (3) is this. You have a world where an infinite number of people is tortured and an infinite number of people is not tortured. You save one of the tortured people from torture. The total value remains unchanged. But, plainly, the world is better by the following clearly true domination principle:
(D) If world w2 strictly dominates w1, then making w2 actual instead of w1 is morally significant.
Here, w2 strictly dominates w1 provided that locus of positive value that is in w1 exists in w2 and has at least as positive a value in w2 as it does in w1, and there are no loci of negative value in w2 that are not also in w1 with at least as negative a value, and either some locus of positive value in w1 has a greater positive value in w2, or some locus of negative value in w2 has a more negative value in w1, or there is a locus of positive value in w2 that is absent in w1.
I agree with Alex's criticism, but I don't think (D) is enough to solve the problem.
Suppose the loci of value in w1 and w2 are different. Suppose there are the same number of people in w1 as there are in w2, but they are all different people. Then (D) does not apply. But also suppose that everyone in w1 has +1 units of welfare and everybody in w2 has +2 units of welfare. Intuitively, w2 is better than w1 and making w2 actual instead of w1 is morally significant. This is so even if the loci of positive value between worlds are different. Another way to put the point: we a dominance principle that doesn't require the same loci of value between worlds.
A different way to deny premise 3 of Smith's argument is to say that it is the causal consequences of one's actions that are relevant to whether it is morally significant, not simply the value of the world in which those consequences exist. If the value of he consequences of our actions is finite, then this is enough to show that (3) is false. The action can be significant not because it makes the world better, but because its consequences are better.
You have a world where an infinite number of people is tortured and an infinite number of people is not tortured. You save one of the tortured people from torture. The total value remains unchanged. But, plainly, the world is better by the following clearly true domination principle: (D) If world w2 strictly dominates w1, then making w2 actual instead of w1 is morally significant.
I agree that there are dominance arguments which seem to show that (3) is false (I've given arguments of this sort against the randomizing "solution" to no best world; Pollock offers similar criticism to the problem of "everbetter wine"). There are also the appeals to intuitive differences in value that you mention. Still, there is something fishy about the claim that (4) every possible action is morally indifferent. I think the problem with (4) is shown in supertask (I actually think it is enough of an argument against (4) to reach the conclusion that every world in the infinite sequence is equal in value).
I think one can think of a good number of reasons why (4) does not follow from 1,2,3.
If an action would destroy the universe and create a universe with the same value as the old one, but negative, that would make a difference.
There could be infinitely many spacetime-cubes with negative value, which could balance the value of the universe to zero.
An action that would abrogate moral realism would also make a difference. Moral nihilism would be true after that action, but not before that action.
K. Parsons' comment to QS's argument here:
http://secularoutpost.infidels.org/2009/01/atheism-and-meaning-of-life.html
A paraphrased quotation (names of premises and sub-conclusions altered):
"It uses extremely dubious premises to reach a highly counterintuitive conclusion, in fact, a conclusion (4) that everybody, including Quentin Smith, knows to be false. Each premise could be cogently challenged, but I shall just consider (3):
(3) 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. ...
This is not only not necessarily true, it is clearly false. Even if we concede GMR and VA (which I don't), and the spatial and temporal infinity of the universe (spatial infinity, at least, is highly questionable), then (3) does not follow. Even if the total value in the universe is infinite, so that actions performed by human beings neither increase nor detract from the total value in the universe, particular slices of space/time can (and do) have finite amounts of value that can be significantly increased or decreased by human action. Human history is possibly, indeed, very probably finite. Let's assume that it is. In this case, the sum total of moral value or disvalue created by human beings will be finite. Therefore, increasing or decreasing the amount of moral value can add to or detract from the total moral value in that portion of space/time encompassing human history. If human beings have value (and the argument assumes that they do), then, what matters for human beings matters, period. If the amount of moral good in human history matters for human beings (and, of course, it does) then the creation of moral value or disvalue in human history matters. Can Quentin Smith, or anyone, really expect us to believe that it does not matter for human beings whether or not there is more or less torture, genocide, holocausts, Gulags, or despotism? Again, if it matters for human beings, it matters."
I think that QS would say that "if it matters for human beings, it matters" begs the question against (3). Cf. section 5.4 of his paper.
Alex,
You wrote:
"(*) No action either changes infinitely many locations from having positive value to having non-positive value or makes an infinite change in what locations there are.
And when one confines oneself to human actions, (*) is very plausible."
I wonder whether one could fine a serious argument against (*). What do you think?
Outside philosophy, St. Catherine of Siena, for instance, implies that some human deeds have infinitely positive or negative value: "Do you not know, dear daughter, that all the sufferings, which the soul endures, or can endure, in this life, are insufficient to punish one smallest fault, because the offense, being done to Me, who am the Infinite Good, calls for an infinite satisfaction? However, I wish that you should know, that not all the pains that are given to men in this life are given as punishments, but as corrections, in order to chastise a son when he offends; though it is true that both the guilt and the penalty can be expiated by the desire of the soul, that is, by true contrition, not through the finite pain endured, but through the infinite desire; because God, who is infinite, wishes for infinite love and infinite grief." http://www.ccel.org/ccel/catherine/dialog.txt
Similarly (?) CCC, 311: "... moral evil, incommensurably more harmful than physical evil, entered the world.." (Lat.: "... malum morale, sine comparatione gravius quam malum physicum, mundum est ingressum.") http://www.vatican.va/archive/ENG0015/__P19.HTM But it seems that these claims are derived from the assumption of the existence of Christian God.
A. Rhoda suggested this line of thought:
"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?"
http://www.alanrhoda.net/blog/2009/01/does-moral-realism-and-infinite.html