Intrinsic maxima and omnibenevolence

INTRINSIC MAXIMA AND OMNIBENEVOLENCE

Some philosophers have objected to the Ontological Argument for God's existence by claiming that the concept of a greatest possible being is incoherent. C. D. Broad, for example, suggests that the phrase 'most perfect being' might mean the same as 'a being which has all positive powers and qualities to the highest possible degree'. Broad then claims that the suggestion

that each positive property is to be present in the highest possible degree...will be meaningless verbiage unless there is some intrinsic maximum or upper limit to the possible intensity of every positive property which is capable of degrees. With some magni- tudes this condition is fulfilled. It is, e.g., logically impossible that any proper fraction should exceed the ratio l / i ; and again, on a certain definition of 'angle', it is logically impossible for any angle to exceed four right angles. But it seems quite clear that there are other positive properties, such as length or temperature or pain, to which there is no intrinsic maximum or upper limit of degree?

If having length or having temperature are, as Broad seems to suggest "positive properties," then it's clear that the greatest possible being need not possess a// positive properties to the highest possible degree. But a restricted version of Broad's criticsm would perhaps be correct if such great-making properties as being knowledgeable, being power- ful, and being benevolent do not have intrinsic maxima. In this paper I shall suggest a way of thinking of the intrinsic maximum of a property. I shall then suggest a strategy for trying to show that a given property has an intrinsic maximum, or, as I prefer to say, has an intrinsic maximum which is possibly exemplified. Finally, ! shall construe a definition of omnibenevolence proposed by William Mann -"

C.D. Broad. "Arguments for the Existence of God" in Religion, Philosophy and Psychical Research (London, 1953): 179ff.

William E. Mann, "The Divine Attributes" American Philosophical Quarterly 12 (1975): 151-159.

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as an attempt to apply the strategy. I shall conclude that this applica- tion is unsuccessful.

Broad's talk of possessing a property "to the highest possible degree" suggests that intrinsic maxima are had by degreed properties. A degreed property might be taken to be a property which can be had to various degrees. I do not find this way of thinking of the matter con- genial. The reason is that it would seem that if two individuals each possess the same property to some degree, then either they possess the property to the same degree or one individual possesses the property to a greater degree than the other. But insofar as the concept of a degreed property is intuitive, I do not find it intuitive that this condition ob- tains. For example, if the property of being squat is equivalent to (in the sense of being necessarily co-extensive with) the property of being short and thiekset, then two individuals can be squat without being equally squat and without one being squatter than the other, if one is shorter and the other is more thickset. But the property of being squat does seem to be degreed in the sense that if someone is squat then it is possible that there is someone who is more squat. This suggests that we should avoid, if we can, explicit commitment to degrees of properties. Perhaps we can explain the notion of a degreed property by the following two schemata (where ' 2 ' is replaceable by any English predicate and for each such predicate, 'P' is replaced by a name of the property expressed by that predicate):

1) x has P in a world W to a greater degree than y has P in a world W' = df. x i s C 2 i n W a n d y i s 2 i n W ' a n d x i s m o r e ~ i n W than y is in W';

2) P is a degreed property = dr. there is a possible world W in which there is an individual x such that in W x has P and is such that there is some world W' in which there is an individual y such that y has P in W' to a greater degree than x has P in W.

As an instance of (1) we have

l a) George has squatness in W to a greater degree than Bill has squatness in W" -- dr. George is squat in W and Bill is squat in W' and George is more squat in W than Bill is in W'.

In case we are interested in comparing existing individuals with respeci: to properties they actually possess, the references in (1) to possible worlds may be eliminated. They were included primarily for the

INTRINSIC MAXIMA AND OMNIBENEVOLENCE 43

sake of (2). (2) may appear to be overly complex. It is designed to accomodate the possibility that some properties which can be had by at most one thing in a given world are, nevertheless, degreed. An example of such a property might be being Lipkie's second daughter and intelligent.

A limi.tation of the approach I am recommending is that the key notions are defined only for properties expressible by English predicates. But there are more properties than that. For every real number r, there is the property being less than r. So there are non-denumerably many properties. No natural language, however, has more than denumerably many predicates. Nevertheless, I do not believe that this is a serious limitation. Any property we are interested in discussing will presumably be expressible--either by a stock predicate or an in- vented one.

We can also define what it is to have a degreed property to the intrinsic maximum.

3) x has P to the intrinsic maximum in W = df. P is a degreed property and x has P in W and there is no world W' in which there is an individual that has P in W' to a greater degree than x has in W.

If we want to say what an intrinsic maximum is, we seem to be faced with a choice. Either we could say that a property has an intrinsic maximum just in case it is possible that something have the property to the intrinsic maximum, or we could admit that every degreed property has an intrinsic maximum. I am inclined to favor the second alternative. If we think of being a large integer as a degreed property, then it is plausible to think that being the largest integer is the intrinsic maximum of that property. Of course, it's not possible that anything have the property of being the largest integer, but it is easy to say what property it is. It's the property of being the unique integer which is large and such that no integer is larger. More generally,

4) Necessarily, if P* is the intrinsic maximum of P then P is a degreed property and P* is a property an individual x has in a world W if and only if in W x has P and is such that there is no world W' in which there is an individual y that has P in W' to a greater degree than x has in W.

(4) gives only a necessary condition for being the intrinsic maximum


of a property; it does not give a sufficient condition. For a given property P, the consequent of (4) will not specify a unique property P*. It will, however, determine a set of logically equivalent properties, one of which is the intrinsic maximum. In what follows I shall speak as though (4) defines unique properties, since what I say can be re- formulated more carefully as talk about sets of equivalent properties.

In accordance with (4), we can say that the intrinsic maximum of the property of being knowledgeable is the property a thing has just in case it's knowledgeable and such that it's not possible that anything be more knowledgeable than that thing is in fact. The interesting question now will be not whether various degreed, great-making properties have intrinsic maxima--for on:'this account all degreed properties have intrinsic maxima but whether,the intrinsic maxima of these properties are possibly exemplified. And it's not in general easy to see how to answer this question.

The property of being knowledgeable might provide us with some insights, however. We have said that its intrinsic maximum is the property a thing has just in case it's knowledgeable and such that it's not possible that anything be more knowledgeable than that thing in fact is. Perhaps it is not obvious that this property is possibly exem, plified. But perhaps it is plausible to think that this property is just the property of being omniscient. Now if it is also plausible to think that omniscience is the property of knowing every true proposition and that this property is possibly exemplified, then we have found a reason for thinking that the intrinsic maximum of being knowledgeable is possibly exemplified.

This suggests a strategy for deciding whether the intrinsic maxima of various great-making properties are possibly exemplified. Rather than pondering for some property P, whether being P and such that it's not possible that anything is more P is possibly exemplified, it might be more fruitful to try to define directly the intrinsic maxima of the properties we are interested in. By "defining directly" I mean defining in a way that does not appeal to such corresponding com- paratives as, for example, being more knowledgeable than, being less knowledgeable than, or similar variations. This approach will be successful if it's clear that the defined property is possibly exemplified and if it's clear that the defined property is the intrinsic maximum of the property in question.

This is perhaps the approach adopted by William Mann, who claims,


in effect, that the property of being benevolent has an intrinsic maxi-

mum which is possibly exemplified? Mann proceeds by offering a definition of omnibenevolence, and although Mann does not explicitly argue that omnibenevolence is possibly exemplified and that it is the intrinsic maximum of being benevolent, I think that he believes that these claims are clearly true. In the remainder of this paper, I propose

to examine Mann's attempt. Mann's definition of omnibenevolence relies on a number of techni-

cal concepts, and so before we can state his definition, we must first look at those other concepts. First, a bundle of an object x in a possible world W is the aggregate of intrinsic goods and evils which x has in W. And a value structure of a world W is the set of all bundles of individuals existing in W. Next, Mann introduces the concept of a Bruno improvement.

W is a Bruno-improvement of W' if and only if for each individual bundle, bk, in the value structure V' of W' there is a distinct bundle, bs, in V of W such that b~ is equal to or greater than bk, and if W has more individuals in it than W', all the bundles in V not correlated by the above procedure with bundles in V' are such that they contain a sufficient amount of intrinsic goods on balance relative to W so that it is not the case that it would have been better for the individuals having these bundles had they never existed. (p. 156.)

This definition presupposes that it makes sense to say of an individual that it would have been better off had it not existed. 4 But ignoring this

difficulty, I think that the notion of a Bruno-improvement is relatively clear. One world W is a Bruno-improvement over a world W' just in

Op. cit. 4 We might try to understand

a) S would have been better off if S had not existed roughly along the lines proposed by Lewis and Stalnaker as

b) In the worlds most like the actual world but in which S does not exist, S is better off than S is in the actual world.

But if, as I believe, nothing can have a property in a possible world without existing in that world, (b) is necessarily false, for any person S. Accordingly, if the correct analysis of (a) is (b) or something like it, (a) is also necessarily false, for any person S. So it looks as though the second condition in the definition is vacuous. Cf. David Lewis, Counter/actuals (Oxford: Blackwell, 1973)and Robert Stalnaker, "A Theory of Conditionals" in N. Rescher, ed., Studies in Logical Theory (Oxford: Blackwell, 1968).


case there is a one-to-one function J from the value structure V' of W '

into the value structure V of W such that for every bi ~ V', ] (b) ~ >/ b i and such that for every bi ~ V but not in the range of J, the individual associated with b i would not have been better off never having existed.

We are now in a position to state Mann's definition of omnibene-

volence. Mann gives two variations, but for our purposes it will be sufficient to look only at what he calls "a utilitarian conception" of omnibenevolence.

(I) x is benevolent to the intrinsically maximal degree if and only if for any possible worlds W and W', if x believes that W is a Bruno-improvement over W', then x prefers to see W actualized over W', and if x believes that except for his own case, W is a Bruno-improvement over W', then x prefers to see W actualized over W', provided that x believes that the absolute magnitude of the increase of intrinsic goods to others in W as compared to W' exceeds the absolute magnitude of the decrease of intrinsic goods to x in W as compared to W'. (p. 157.)

For a number of reasons, I believe that this definition is unacceptable. In the first place, if the conditionals in the definiens of (1) are inter- preted as material conditionals, then they are trivially true for all, or almost all, human beings. Mann allows (p. 159) that it is possible for human beings to be omnibenevolent in the sense defined in (I). But a definition according to which we are all omnibenevolent is surely wrong. Let me try to say why I think that Mann's definition has this consequence. For simplicity, let's just consider the first conjunct of the definiens, which says that for any possible worlds W and W', if x believes that W is a Bruno-improvement over W', then x prefers to see W actualized over W'. Now I think that hardly anyone has any de re

beliefs with respect to a pair of possible worlds to the effect that one is a Bruno-improvement over the other. There are two reasons for thinking this. The first is that it seems unlikely that someone could believe one world to be a Bruno-improvement over another without having the concept of a Bruno-improvement. But since the concept of a Bruno-improvement is an unusual, highly technical concept, it seems likely that only a very few people have that concept. So any person who lacks the concept and, hence, lacks beliefs about certain worlds being Bruno-improvemenCs over others, will trivially satisfy the condi-


tion that for any worlds W and W', if he believes that W is a Bruno- improvement over W', then he prefers to see W actualized over W'. Similar considerations apply to the second conjunct of the definiens.

There is a second reason for thinking that most, if not all, of us trivally satisfy the definition. It is that the definition is in terms of beliefs de re with respect to worlds. But I think that no human being has any de re beliefs with respect to any world other than the actual world. A necessary condition of having a de re belief with respect to a thing is that the person having the belief be able to uniquely identify the thing, in some way or other? I 'm not sure of exactly what should count as uniquely identifying a thing, but I am inclined to be generous. Thus, a thing may be picked out, for example, by providing a definite description true of it, by perceiving it, by remembering to have per- ceived it, or, perhaps, in the case of some abstract entities, by directly apprehending it. I think it is clear, however, that no matter how tolerant we are in allowing something to count as uniquely picking out a thing, we are unable to uniquely pick out any world other than the actual world. The actual world we can pick out, for example, with the description, 'the actual world'. But I think that we do not perceive

possible worlds, and hence, also, we do not remember perceiving them. Furthermore, we do not directly apprehend possible worlds. And finally there is no description we can give that uniquely picks out a world other than the actual world. For whatever we try to say about such a world will be true of infinitely many worlds. I may believe that a world as much like this world as possible in which I am independently wealthy would be a Bruno-improvement over this world, but there is no such world of which I believe that it is a Bruno-improvement over this world. So if no human beings have de re beliefs about possible worlds other than the actual world, there is no pair of distinct possible worlds of which any of us believes that the first is a Bruno-improvement over the second. And so, with an exception to be noted below, every human being trivially satisfies the condition that for any worlds W and W', if he believes that W is a Bruno-improvement over W' then he prefers to see W actualized over W'. Again, similar considerations apply to the second conjunct of the definiens.

It might be thought that this objection could be avoided by strength-

For a discussion of various conceptions of de re belief see Roderick Chisholm, "Knowledge and Belief 'De Dicto' and 'De Re'" Philosophical Studies 29 (1976) : 1-20.

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ening the conditionals in the definiens. Thus, the clause we've been examining might be replaced by the condition that for any worlds W and W', it's necessary that if x believes that W is a Bruno-improvement over W', then x prefers to see W actualized over W'. Since many of us who don't presently have de re beliefs about worlds and Bruno-improvements might well have had such beliefs without preferring the Bruno-improvements, it will not be true that in every world in which one of us has the right beliefs, that person has the right preferences. So on this stronger version, those who fail to have the appropriate beliefs won't trivially satisfy the definition, as long as it's possible for them to have the appropriate beliefs without having the requisite preferences. The trouble with this suggestion, however, is that it would require that we say of someone who in fact has the right beliefs and the right preferences but who could have had the right beliefs and wrong preferences, that such a person is not omnibenevolent. But it seems exceedingly harsh to denigrate someone for attitudes he might have had. The trouble with this suggestion, in other words, is that it doesn't allow us to distinguish between omnibenevolence and essential omnibenevolence.

The exception, mentioned one paragraph back, to the suggestion that every human being trivially satisfies Mann's definition arises as follows. Since the relation of being a Bruno-improvement of is re- flexive, every world is a Bruno-improvement of itself. A person might thus believe of the actual world that it is a Bruno-improvement of itself without preferring that the actual world be actualized rather than the actual world. In fact it is hard to imagine how a person could reason- ably prefer that a given world be actualized over itself. So anyone who believes of the actual world that it is a Bruno-improvement of itself without preferring that the actual world be actualized over itself won't trivally satisfy Mann's definition. The feature of Mann's definition that insures reflexivity is that one world is a Bruno-improvement over a second if there is a function that maps bundles of the value structure of the second world to bundles of the value structure of the first world which are greater than or equal to the bundles of the second world. This feature also gives rise to the following objectionable consequence. Consider two distinct worlds with the same value structure, for example, worlds in which Smith and lones exchange bundles. Clearly such worlds will be Bruno-improvements over each other. But Mann's definition requires that in order to be omnibenevolent, a being


who recognizes that such worlds are Bruno-improvements over each

other will have to prefer each of them over the other. But that is to

have contradictory preferences. (Mann allows, as this objection requires, that distinct worlds can have the same value structure (p. 156).

But then his claim that the relation being a Bruno-improvement of is

anti-symmetric in the set of worlds (p. 157) is mistaken.) ~ The objections I have raised so far might be thought to be objec-

tions merely to specific formulations of a definition of omnibenevolen-

ce in terms of the concept of Bruno-impovement. I want to suggest next

a reason for thinking that no definition of omnibenevolence solely in

terms of the notions of Bruno-improvement and preference is likely

to be successful. As Mann notes, the relation of being a Bruno-improvement o] is not connected in the set of possible worlds (p. 157).

For example, consider a world in which one person has a vast amount

of pleasure (derived from torturing others) and in which everyone

else has a vast amount of pain, and compare such a world with one

in which the same individuals all have a moderate amount of

pleasure7 Clearly, neither world is a Bruno-improvement over the

other. For, the first world has only one bundle as large or larger than

the bundles in the second world, and the second world has no bundle

as large or larger than the torturer's bundle Jn the first world. More-

over, it is clear that the second world is preferable to the first. But

now it is compatible with the definition of Bruno-improvement that someone have all the right preferences for worlds one of which is a

Bruno-improvement of the other, but have wrong preferences in the

case of worlds not related by the relation of Bruno-improvement. In

A way of avoiding this objection would be to change the definition so that W is a Bruno-improvement over W" just in case there is a one-to-one function f from the value structure V' of W' into the value structure V of W such that for e v e r y b i E V', f(b i) is strictly greater than b i and such that for every b i ~ V but not in the range of J, the individual associated with b i would not have been better off never having existed. A result of making this change would be that a world in which one person's bundle remained the same (sup- pose that bundle is very large) but in which everyone else's bundle were doubled, would fail to be a Bruno-improvement over this world. Yet clearly such a world would be an improvement over this world. I shall argue below that it is a defect of Mann's definition of omnibenevolence that the relation of being a Bruno-improvement of is not connected in the set of possible worlds. But the effect of making the suggested revision in the definition of 'Bruno- improvement' would be to make the relation even "less connected." 7 By giving an example involving pleasure and pain, I do not mean to suggest that pleasure is the only thing of intrinsic value and pain the only thing of disvalue.

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particular, someone could have the right preference with respect to worlds one of which is a Bruno-improvement over the other, but prefer, in the example above, to see the world with the torturer actualized over the world in which everyone has a moderate amount of pleasure. A person with these preferences would certainly not be omnibenevolent. So it seems reasonable that any definition of omnibenevolence solely in terms of a person's preference with respect to Bruno-improvement will be defective.

In conclusion, then, I think that trying to find a property which is possibly exemplified and arguing that it is the intrinsic maximum of a particular property is an intriguing method of trying to show that Broad's objection to the concept of the greatest possible being is mistaken. I do not think, however, that Mann has succeeded in finding a property which it is plausible to think is the intrinsic maximum of benevolence.S

s For much helpful discussion I am indebted to Richard Feldman and Del Ratzsch.

Edward WIERENGA,

University oJ Rochester.

Intrinsic maxima and omnibenevolence

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