MORAL REALISM AND INFINITE SPACETIME IMPLY MORAL NIHILISM

by Quentin Smith

1. INTRODUCTION

I argue that if the future is infinite, as contemporary astronomers believe it is, then moral nihilism is true if both moral realism and aggregative value theory is true. Usually, moral nihilism is defined as meaning nothing has value. But I am a moral realist, indeed a global moral realist, since I believe everything has value.  I argued that everything is intrinsically valuable in my 1997 Ethical And Religious Thought In Analytic Philosophy of Language. Nonetheless, I believe the recent astronomical discovery that future time is infinite implies that it does not morally matter what we do. This is what I mean by moral nihilism. It does not matter what actions humans or other agents perform. My derivation of moral nihilism has as one of its premises that moral realism is true. So this is a different approach than emotivists such as A,J. Ayer or relativists such as Nagel, Nietzsche and Sartre, who derived moral nihilism from moral anti-realism

The summary of my argument has three premises. My argument is

1. Necessarily, global moral realism is true.
2. Necessarily, aggregative value theory is true.
3. Contingently, it is true that future time is infinite.

Therefore,

       4. Moral nihilism is contingently true.

For those interested in the philosophy of religion, I will later show that this argument implies that God does not exist. It may be of interest to note that this is a new kind of argument for atheism. Usually, atheists argue that the arguments for theism are unsound and that the argument from gratuitous evil is sound (whether this be spelled out in terms of the probabilistic argument from evil or the deductive argument). But I argue from moral nihilism to the nonexistence of God. A further interesting twist is that I reverse the usual argument for nihilism. Traditionally, it is argued that nihilism is true because God does not exist. I argue the converse; God does not exist because nihilism is true.

To make my argument precise, I first need to define the relevant expressions.         

D1: Moral Nihilism is true if and only if, for any empirically possible action A, it is morally indifferent if A is performed or not performed. 

The performance of an action is morally indifferent if and only if the performance of that action neither increases nor decreases the amount of value in the universe. An action is empirically possible if and only if it is consistent with the boundary conditions (intuitively, the arrangement of particulars) and the laws of nature in the actual world.

Moral realism is true if and only if particulars possess value nondependently upon whether conscious organisms believe they have value. 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. I believe global moral realism is a justified belief on the basis of the several arguments I gave for it in my 1997 book Ethical and Religious Thought in Analytic Philosophy of Language. I have not argued elsewhere that the aggregative value theory is true, but I believe the arguments that other thinkers, both philosophers and economists, have provided sound arguments that just the belief in aggregative value theory. (As a scientific aside, I would note that (in addition to a massive amount of other, older evidence) the most crucial, new discovery that has convinced previously uncertain astronomers that future time is the 1998  observations of  the recession velocity of distant supernovae indicate the universe has an expansion rate that will ensure it will not contract but expand for an infinite amount of time. For a non-technical but accurate discussion of this new evidence, see the January 1999 issue and the January 2001 issue of Scientific American. It was the 1998 observations of the supernovae that provided the evidence that moral nihilism is true.

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. There is a massive body of literature both explaining and justifying aggregative value theory and I shall here merely explain the minimal amount necessary to understand my argument.

First, I will simplify my argument my using only type of aggregative value theory, namely, additive value theory, where the units of value are called “locations”. Each location a finite 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. Some, such as Vallentyne and Kagan, even define locations in terms of topological regions.

 The future is infinite if there are aleph-zero number of equal lengthened temporal intervals of some length, such as an aleph-zero number of hours. For the sake of familiarity, I will not use my theory that the past is infinite as well, but will use the more familiar theory that time began about 15 billion years ago with the big bang (my theory is that the familiar, so-called “scientific theory” that past time is finite is based on a metaphysical theory of time that includes a number of false metaphysical assumptions and invalid inferences). According to the astronomical observations, our universe is hyperbolic, which implies in big bang cosmology that at each time space is infinite, e.g., that there are aleph-zero, non-overlapping, equal sized cubes of space. 

I believe global moral realism and aggregative value theory are necessary true and the infinitude of the future is contingently true. Thus, I believe that moral  

nihilism is contingently true. In another possible world, where the universe is finite, moral nihilism is false.

2. THE MORAL INDIFFERENCE OF EVERY EMPIRICALLY POSSIBLE ACTION

A necessary condition of a person being morally obligated to engage in an action is that the performance or consequence of the action either increases positive value or prevents the decrease of positive value. If the future is infinite, it is impossible to increase or decrease the amount of value, since there are aleph-zero hours and each hour includes at least one unit of value (even if all that is valuable is matter or energy, or slices of space, or intervals of time). 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

Each time has at least one unit of value. Since there are an infinite number of times, say hours, ordered in the order of the positive integers, omega, the A-history and B-history both have the same number of units of value, aleph-zero. But this is wrong, since space is infinite at each time and each cube of space of any given size has some value. Thus, at time t₁, there are infinitely many equal-sized and non-overlapping cubes of space. Each cube has some value, even if it has the minimal unit of value, one, by virtue of being a cube of empty space (assuming a cube of

space can exist that is empty of everything whatsoever, including quantum fields or fluctuating quantum vacuums or the gravitational energy that is represented on the left hand size of the Einstein equation). Thus at time t₁, there is a difference in value of the cube of space that includes action A and in the (counterfactual) cube of space that does not include action A. Let us call this cube, which is located at a certain region on the planet earth, the cube c₁. Now at time t₁, the A-universe has cubes of space that extend infinitely in both directions along the dimension of length (as well as other dimensions). Each cube has some value. The cube c₁ that includes the action A has two more units of value, let us say, than does this cube in the merely possible universe that does not include A

The A-Universe at time t₁:

- c₃     - c₂      - c₁      c₀      c₁       c₂       c₃

               2        2         3        7       6       7        2

The Not-A universe at time t1:

- c₃     - c₂      - c₁      c₀      c₁       c₂       c₃

               2        2         3       7        4       7        2 . . .

Now we seethe problem. Time t₁ includes aleph-zero units of value, since t₁ includes an aleph-zero number of valuable cubes of space of the size c. Thus the correct history of the two universes is represented as:

History of A-Universe

t₀                           t₁                t₂                   t₃                  t₄

aleph-zero    aleph-zero   aleph-zero    aleph-zero     aleph-zero

The same holds for the not-A universe. Since aleph-zero plus aleph-zero equals aleph-zero, there are aleph-zero units of value throughout the infinite future of both our A-universe and the not-A universe. The number of units of value in both the A-history and the B-history is aleph-zero. This number is the number of the union of the units of value at each of the infinitely many times. Further, at each time in the history of each universe, the number of units of value is aleph-zero, since at each time the universe is spatially infinite.

Now it follows that I cannot increase the value of the universe at time t₁ by performing action A, since aleph-zero + 2 = aleph-zero. 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.

An example of how to apply these ideas to a specific ethical theory is act utilitarianism. On this theory, an action is morally permissible if no alternative leads to a better or more valuable world (one with a greater total utility sum). Given global moral realism and a spatiotemporally infinite world, it follows that every act is morally permissible, since no act can make an infinitely valuable world have a higher utility sum, and thus no act is better or worse than any other act.

3. SOME CONSEQUENCES OF MORAL NIHILISM IN A  SPATIOTEMPORALLY INFINITE UNIVESE

3.1 Each person’s death is more valuable than their life

One interesting consequence is that my entire life is less valuable than the entire state of my being dead (which may be identified with the continued existence of the matte and energy that composed my body at the time of my death, even if this matter and energy no longer constitutes a corpse and breaks down into separated and distant atoms). My life can add up only to a finite number of units of value. But my state of being dead lasts for an infinite amount of future time. Even if my state of being dead at each time has the minimal value, say one (the value of the members of the set of particles that composed my body at the time of my death), my state of being dead will have aleph-zero units of value. My state of being dead is infinitely more valuable than my state of being alive. The same is true for any human and for any living thing.

3.2 The futility of each person’s life

A second interesting consequence is that the value of all my acts and conscious states, and physical states, does not increase at all the value of the universe. For the value is finite. Further, 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. My life is futile if there is nothing at all I can do to increase the total amount of positive value in the universe.

3.3 Nobody has a right to life

Nobody has a right to life, or a right to own property, a right to engage in free speech, a right to be free rather than enslaved, a right not to be bodily harmed, or any other right. Some alleged right R is a right only if a violation of R decreases the amount of positive value in the universe. But no murder, theft, suppression of free speech, enslavement, torture or rape decreases the amount of positive value in the universe. Even if an act of this sort 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. Thus (ironically), I realized I did not have the right to argue for the truth of moral nihilism simultaneously with my realization of the truth of moral nihilism.

3.4 Persons have no intrinsic dignity

Nobody has an intrinsic (special sort of) dignity by virtue of the fact that she or he is a person. Somebody has the dignity of personhood only if deliberately harming the person for the sake of personal pleasure decreases the total amount of value. But it does not, since such an act of harming is a “location” in the sense of aggregative value theories and has only a finite negative value, which subtracted from an aleph-zero amount of positive value leaves the same amount of value, and thus does not decrease the total amount of value.

4. CONSEQUENCES IN THE PHILOSOPHY OF RELIGION

 If moral nihilism is true, then so is atheism (at least the disbelief in the “god the of the philosophers”, the perfect being with the omniattributes, omniscience, omnipotent, perfectly good, free, a creator of the universe, etc. The interesting consequence is that “classical theism” as this word is now used (a usage stemming from Plantinga’s writings) implies that persons have rights. For example, I implies that each person has the right to worship God. But moral nihilism implies that there are no rights and thus that we have no right to worship God. A second respect in which moral nihilism counts as a distinct “argument for God’s nonexistence” is that it implies that no creatures are moral agents. Somebody is a moral agent only if it makes a moral difference which action she chooses to perform. But it makes no moral difference, so theism is false. All such arguments can be summarized in the general argument:

1. Moral realism is true

       2. The universe in which we live is infinite.

       3. At least one relevant version of an aggregative theory of values is true.

4. Therefore, God does not exist.

Despite appearances, this argument is valid, since the seemingly “suppressed premises” are implied by the stated premises and thus do not need to be added as separate premises. Even if there is no gratuitous evil, the moral situation of our universe implies that God does not exist.

5. OBJECTIONS TO THE ARGUMENT FOR MORAL NIHILISM

5.1 First Objection

The most commonly made objection is always the most obviously invalid objection. The objection is that this theory of moral nihilism allows anybody to do any bad thing and that this bad consequence of the theory shows the theory should be rejected. This objection is largely emotional and I can empathize with it. But it is an informally invalid argument, a petitio principii. It assumes the very thesis it wants to proof, namely, that there are such things as morally bad acts. At this point, the woman or man in the street will likely say they would prefer to reject reason or logic than to accept this theory, and that they disbelieve this theory because it is an emotionally unpleasant theory. Philosophy professors would not make this objection, since they know that rejecting logic is self-referentially false, but it is worth noting that philosophy professors count as a tiny minority in this regard. Most everybody I know who is not an academic responds that they reject logic rather than accept moral nihilism. Of course, if they reject the law of non-contradiction, then they have no response to the assertion that they both believe and do not believe moral nihilism, other than another self-contradictory response, but they prefer such a state to accepting both logic and moral nihilism.

5.2 Second Objection

Philosophers will be more interested in “academic objections”, such as the following objection. They can respond that they reject either or both moral realism and aggregative value theories, and/or the theory that the universe is spatiotemporally infinite, and thus can in this way avoid the conclusion that moral nihilism is true. But this is not an objection to any argument I have put forth in this paper. I have argued that the conjunction of the propositions, (i) global moral realism is true, (ii) aggregative value theories (at least in one relevant version) are true and (iii) the universe has an infinite future and is spatially infinite, imply moral nihilism. Rejecting the premises is not rejecting my argument, which is that the premises imply moral nihilism. Nonetheless, rejecting the premises is not so easy. Rejecting moral realism implies a state of total apathy (as I have argued elsewhere) and leaves one no better off than being in the state as moral nihilism. And I believe it is very hard to reject every version of the aggregative theory of value; it seems obvious that killing all humans is or results in a state of affairs that has a greater amount of negative value than one human stubbing their toe. It seems evident that some events or things are more valuable than others, that there is such a thing as the relation “is better than” and “is more valuable than” and once we admit this, we admit items that can enumerated, even if only approximate, as in the case of most measurements

in the sciences. To say that “is more valuable than” is a qualitative and non-quantative relation, is in fact to say that it is epistemically indeterminate to some degree how much more valuable something is to something else. For example, it may be somewhere between twice as good and ten times as good. If we deal with approximations, which is done uniformly in the physical sciences, then the arguments still go through, but without the exact numbers being known.

5.3 Third Objection

There are more technical objections, which is where the theoretical interest lies. It can be objected that my argument is invalid since it is possible that the universe has an infinite amount of negative value and a finite amount of positive value. In this case, increases in the universe’s positive value are possible and, indeed, happen every day. The response is that the universe contains an infinite number of  positively valued locations, in the sense of aggregative theory of values. Global moral realism implies that everything has some value, even if minimal. A cube of space of some size has intrinsic positive value, i.e., has positive value has an essential property and independently of A spatially extended existent, a cubed region, has value just by virtue of being a spatially extended existence. This global moral realism is an extension of environmental ethics in the same way  that environmental ethics is an extension of human ethics; we extend the range of the kind of things that have value, and (in most cases) recognize that the kinds of things in the new area of the extended range have less intrinsic positive value than those in the old area (bluebirds are less valuable than humans, roses are less valuable than bluebirds and, on global realism, stones, electrons, and parts of space and time, are less valuable than roses, even though all have some intrinsic positive value. Many objections can be brought against global moral realism, but I believe these can be answered[1]. Accordingly, 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.

5.4 Fourth Objection

There has been some very fruitful discussion of an issue related to the theory I am putting forward. These discussions seem to be based on the tacit assumption that

moral nihilism is false, and therefore if any “infinite value” problems appear in a theory, that shows the theory should be rejected or modified. The theories in question are economic theories, act utilitarianism[2], finite additive theories of value[3] and related theories. The discussion involves how to best change the theory in question so the “infinite value problems” go away, the shared assumption always being that if the problems cannot be solved, then theory must be false (rather than it being the case that both the theory and moral nihilism are true).

Peter Vallentyne states that traditional act utilitarians face a problem with an infinite future due to the fact that actions may produce an infinite amount of utility. Traditional act utilitarianism holds that an action is permissible just in case it produces as much aggregate utility as any alternative. Thus, if most actions produce an infinite amount of utility, most actions are permissible. Vallentyne endeavors to show there is no genuine problem here. Before I address his ideas, I would note that the apparent problem that faces traditional act utilitarianism is of much narrower scope than the one I am discussing. I am talking about values, no utilities. For example, a length of time, such as a year, is not a utility that can be produced by any action, and yet on global moral realism it has value. Further, even if we stipulated (for purposes of argument) that there are no utilities (or anything of value) produced by actions, the infinite value problem still remains. An infinite number of material particles or stars, or an infinite number of stages of an endlessly expanding universe, provides infinite value. Moreover, if we stipulate that the consequences of acts have no value, and thus cannot produce an infinite value problem there still would remain the fact that each act is equally valuable, since at the time the act is performed, there simultaneously exist an infinite number of “locations”, or units of value, in which case no act could increase the amount of value of the universe any more than any other act.

            If we take a preference satisfaction utilitarianism[4] we may say that the utility of an act is determined by the extent to which its outcome satisfies the preferences of those alive at the time of the choice. If people assign a finite utility to infinite futures, and there are only a finite number of people, then the aggregate utility will be finite. My response to this theory is that global moral realism implies there are many more kinds of  items that are valuable than the satisfaction of preferences and thus if the universe has an infinite future, there will be an infinite number of states at which there exist material particles or at least units of energy (or 3-dimensional spatial slices of the universe) and these have infinite value. The same response may be given to any ethical theory that restricts, by definition, value to a small number of kinds of things that can be finitely additive in an infinite spacetime. Such theories would require us to believe that the existence of an infinite number of stars is of no more value than nothingness, i.e, the nonexistence of any universe, the value being zero. But it is hard to believe that an infinite universe of stars has no more value than nothingness.

            Perhaps the most widely discussed objection is based on a principle discussed by economists such as Koopman and independently rediscovered by Mark Nelson,[5] Peter Vallentyne,[6] Segerberg[7] and perhaps earliest of all by Frank Ramsey in the 1920s. An interesting sidelight of this multiple, independent discovery of the same theory by thinkers working in the same field is that each theoretical field is now

developing so fast that even full-time specialists in the field cannot hope to known all or even most of the literature. A positive epistemic consequence is that several thinkers independently discovering the same theory increases the degree of justification of the theory (but by no means entails it is true or is even probably true). If  several people independently hit on the same solution on the problem, that provides some sort of reason to have a degree of confidence in the solution.

            However, their solution is not a solution, but a mistake, as I will now show. The philosopher who has discussed and defended it the most is Peter Vallentyne and I shall use his formulation. But we must keep in mind that his discussion is confined to one type of ethical theory, traditional act utilitarianisms The principle is known as PMU* (“producing more utility”) and reads:

PMU*: An action, A1 produces more utility than action A2 if and only if there is a time t such that for any later time t’ the cumulative account of utility produced by A1 up to t’ is greater than that produced by action A2 up to t’.

For example, engaging in warfare (A1) produces more utility than engaging in a negotiated compromise (A2), then there is a time, say the year 1999, such that for any later time (say the year 2060), A1 produces more utility between 1999 and 2060 than A2, and the same holds for 1999 and any later time, such as ten trillion years from now. Can this principle, or some generalization of it, be used to block the argument for moral nihilism?

First, I will show this does not even suffice for the more limited purposes for which it was introduced, namely, to preserve the traditional act utilitarian theory. An action can produce more utility than another action only if it produces more utility all things considered, which in the case of act utilitarianism means “produces more utility all consequences taken into account”. But if the actions have an infinite number of consequences that are utilizes, then we have to take all of these consequences into account. This implies that action A1 produces the same amount of utility as A2, namely, an infinite amount. The principle PMU* is not a solution of the problem of infinite value, but a mere stipulation that is introduced to avoid having to face the fact that it has no solution. The insoluble problem is avoided by simply stipulating that we not take it into account, i.e., that we not take into account the infinite amount of utilities of actions. We pretend to solve the problem by choosing to take into account only a subset of the set of utilities produced by an action. This contradicts the basic axiom of act utilitarianism, than an act’s value is determined by assessing the total amount of utilities that it produces.

            But even if we allow that this principle is true, it will not help solve the argument from global moral realism. How much value does each consequence of acts A1 and A2 have at each time? That is depends in part on how much value it contributes to the universe as a whole at that time. Does consequence C1 increase the total value of the universe at time t more than does consequence C2? No, since the total value of the universe at time t is infinite and thus neither increases the total value to a greater amount than the other. James Cain (1995) has given two further, independent arguments against the principle, based instead on act utilitarian premises, in his 1995 article in Australasian Journal of Philosophy. In the same issue of this journal, Luc Van