Goodness and Existence
So, I was trying to think of a way to show that the following claim is true.
(*) Necessarily, if something, x, is maximally good, then x exists necessarily.
Here's one (not unproblematic) way that I was considering.
First, consider the property of being morally good. That, I take it, is a better making property. That is, something that is morally good is better than something that is not morally good. And, something that is morally good to degree, n, is better than something that is morally good to degree n-1. So, the best thing (the thing that satisfies the antecedent of (*)(if there is such)) will be maximally morally good. That is, it will be good to degree, n, where there is no degree of goodness, m, which is such that m>n.
Say that something is durably morally good if and only if it is morally good to some degree, n, and, at the nearest possible worlds, it is morally good to at least degree n.
Durable moral goodness comes in degrees as well. My moral goodness might, for instance, be more durable than yours. This would be so if the space of possible worlds free of a world, w, such that my goodness is diminished at it is larger than the space of worlds free of a world, w', such that your goodness is diminished at it.
So, suppose that possible worlds are ordered in possibility space by a similarity relation. The closer a world, w, is to a world, w', the more similar w is to w'. Consider a series of concentric circles centered on the actual world in possibility space. If there is some world, w, such that your degree of goodness in w is less than your degree of goodness in the actual world, and the circular region of possibility space with the smallest diameter in which w is located has a smaller diameter than the circular region of possibility space in which a world where my degree of goodness is less than it is in the actual world can be found, then I am more durably morally good than you.
Say that something is maximally durably morally good (MDMG) if and only if it is durably morally good to degree, n, and there is no degree of durable moral goodness, m, such that m>n.
So, here's a quick argument for the claim that maximal goodness entails necessary existence.
1. Necessarily, if something, x, is maximally good, then x is MDMG.
2. Necessarily, if something, x, is MDMG, then x exists necessarily.
3. So, necessarily, if something, x, is maximally good, then x exists necessarily.
Why think one is true?
Here's an argument for one.
1'. Suppose, for reductio, that at some world, w, something, x, is maximally good at w, and not MDMG at w.
2'. If x is not MDMG at w, then x would be better by being more durably good.
3'. If x would be better by being more durably good, then x is not maximally good at w.
4'. So, for all worlds, w, it is not the case that something, x, is both maximally good at w and not MDMG at w.
Why think two is true?
Here's an argument for two.
1''. Suppose, for reductio, that at some world, w, something, x, exists contingently and is MDMG.
2''. If x exists contingently, then there is some world, w', such that x does not exist in w'.
3''. If there is some world, w', such that x does not exist in w', then x is less good in w' than x is in w.
4''. If x is less good in w' than x is in w, then x is not MDMG in w.
5''. So, for all worlds, w, it is not the case that something, x, exists contingently and is MDMG in w.
So, initially I thought this argument is good. I think it's probably not now.
What do you guys think?
(*) Necessarily, if something, x, is maximally good, then x exists necessarily.
Here's one (not unproblematic) way that I was considering.
First, consider the property of being morally good. That, I take it, is a better making property. That is, something that is morally good is better than something that is not morally good. And, something that is morally good to degree, n, is better than something that is morally good to degree n-1. So, the best thing (the thing that satisfies the antecedent of (*)(if there is such)) will be maximally morally good. That is, it will be good to degree, n, where there is no degree of goodness, m, which is such that m>n.
Say that something is durably morally good if and only if it is morally good to some degree, n, and, at the nearest possible worlds, it is morally good to at least degree n.
Durable moral goodness comes in degrees as well. My moral goodness might, for instance, be more durable than yours. This would be so if the space of possible worlds free of a world, w, such that my goodness is diminished at it is larger than the space of worlds free of a world, w', such that your goodness is diminished at it.
So, suppose that possible worlds are ordered in possibility space by a similarity relation. The closer a world, w, is to a world, w', the more similar w is to w'. Consider a series of concentric circles centered on the actual world in possibility space. If there is some world, w, such that your degree of goodness in w is less than your degree of goodness in the actual world, and the circular region of possibility space with the smallest diameter in which w is located has a smaller diameter than the circular region of possibility space in which a world where my degree of goodness is less than it is in the actual world can be found, then I am more durably morally good than you.
Say that something is maximally durably morally good (MDMG) if and only if it is durably morally good to degree, n, and there is no degree of durable moral goodness, m, such that m>n.
So, here's a quick argument for the claim that maximal goodness entails necessary existence.
1. Necessarily, if something, x, is maximally good, then x is MDMG.
2. Necessarily, if something, x, is MDMG, then x exists necessarily.
3. So, necessarily, if something, x, is maximally good, then x exists necessarily.
Why think one is true?
Here's an argument for one.
1'. Suppose, for reductio, that at some world, w, something, x, is maximally good at w, and not MDMG at w.
2'. If x is not MDMG at w, then x would be better by being more durably good.
3'. If x would be better by being more durably good, then x is not maximally good at w.
4'. So, for all worlds, w, it is not the case that something, x, is both maximally good at w and not MDMG at w.
Why think two is true?
Here's an argument for two.
1''. Suppose, for reductio, that at some world, w, something, x, exists contingently and is MDMG.
2''. If x exists contingently, then there is some world, w', such that x does not exist in w'.
3''. If there is some world, w', such that x does not exist in w', then x is less good in w' than x is in w.
4''. If x is less good in w' than x is in w, then x is not MDMG in w.
5''. So, for all worlds, w, it is not the case that something, x, exists contingently and is MDMG in w.
So, initially I thought this argument is good. I think it's probably not now.
What do you guys think?
posted by avwake at
10:23 AM
5 Comment(s):
I would be inclined to say that premise (3') is false. I don't think that the definition of MDMG is satisfied. So, insofar as I think it is possible for something to be maximally good, I am inclined to think that (3') is false. (However, I guess I am not inclined very far to believe that possibly something is maximally good.
I am also inclined to think that either (3'') or (4'') is false. I am not sure that a thing that fails to exist in some world is less good in that world than it is in any world in which it exists and is good. But, If I were to accept that, then I would be inclined to deny (4''). If you say that (4'') is entailed by the definition of MDMG, then I am even more inclined to deny a premise in the argument that supports premise (1) (probably (2').
By
Joshua, at 4/13/2007 7:01 PM
(2') looks solid to me, perhaps true by definition.
Same for (3')
I wonder if Joshua's doubts as to the possibility arise for the same reason's typically adverted to for denying that there is any best possible world. If I thought that, I'd deny (2') and (3') too, but I don't know why someone would want to think that.
By
Trent_Dougherty, at 4/13/2007 7:21 PM
Damn, strike that apostrophe, don't know what happened there.
By
Trent_Dougherty, at 4/13/2007 7:23 PM
I’m sorry it has taken me a while to respond to Trent’s comments. I’ve been sick for the past week and haven’t gotten up to date on all my work. I have realized that my initial post is rather vague and underdeveloped. Let me focus on one point that Trent made. He claimed that (2’) looks pretty solid, “perhaps true by definition”. I don’t think (2’) is “solid” but I will not defend that claim at the moment. Rather, I’d like to say that (2’) is not true by definition.
Andrew made the following (seemingly) stipulative definitions:
(MMG) x is maximally morally good at w iff x is good to degree n at w and there is no degree of goodness, m, which is such that m>n.
(DMG) x durably morally good at w iff there is an n such that x is morally good to degree n at w and, at the nearest possible worlds x is morally good to at least degree n.
Andrew noted that this comes in degrees as well. I think his suggestion is something like the following sufficient condition for a kind of relational durable moral goodness:
(RDMG) x is more durably morally good at w than y is at w* if the sphere of worlds around w at which x has at least the degree of moral goodness that x has at w is greater than the sphere of worlds around w* at which y has at least the degree of moral goodness that y has at w*.
I don’t know if Andrew intended the sufficient condition above to also be a necessary condition. But I will ignore this for now.
Notice that if this is what Andrew is thinking, then it is consistent with the condition given above that one thing be more morally good than another while being less durably morally good. Suppose that Small has a small degree of moral goodness at w, but he has that degree in a rather wide sphere of worlds. However, Big has a big degree of moral goodness but falls below that level at rather nearby worlds. In this case, Big is less durably morally good than Small. This follows from the sufficient condition indicated above. You might think that it’s just a metaphysical fact that if one thing has a greater degree of moral goodness at a world than another, then the first must be more durably morally good than the second. But I don’t know why someone would think this. In fact, it seems that for some individuals the opposite might be plausible. We might think that it is rather difficult for some people to retain a high degree of moral goodness. These people drop below the degree they actually have at nearby worlds; they are not very durably morally good given the sufficient condition above. Others might easily maintain a rather low level of moral goodness. This suggests that they might have a high degree of durable moral goodness. In any case, whether it is a metaphysical fact or not, it has no bearing on whether (2’) is true by definition.
Now Andrew also introduced the following definition:
(MDMG) x is MDMG iff x is durably morally good to degree n and there is no degree of durable moral goodness, m, which is such that m>n.
Unfortunately, we don’t have a principle that connects up the MDMG with the relation that one thing bears to another when the one is more durably morally good than the other. Presumably though, the following is supposed to be true:
(M-R) If x is MDMG at w, then there is no possible individual y and world w* such that y is more durably morally good at w* than x is at w.
This is the strongest principle that I think is suggested by Andrew’s passage. Let’s suppose that eachof these principles, even those that are mere sufficient conditions, are meaning principles in some sense. That is, each of them has something to do with the definitions of these various technical terms. This, I think, is giving a lot to the defender of the claim that (2’) is true by definition. Even granting all of this, though, I think we have no support for (2’) from these principle.
Here is a model that is consistent with all the definitions given above. There are only two possible individuals, Durable and Great. Durable has a low degree of moral goodness but has it in all possible worlds. Great has a high degree of moral goodness, but has it only in the actual world. Durable is more durably morally good than Great. This follows from (RDMG). Now it is consistent with the story and everything we have defined so far that Durable is maximally durably morally good and Great is maximally morally good. In fact this last claim might follow given (MMG) and the story (I have to admit that I am a bit unsure about how to understand (MMG) so I might be wrong about this). In any case, it is certainly a consistent story. What this shows is that if (2’) is true by definition, then it must be true by some other definitions than those given in the post.
If I have time later, I’ll try to clarify some of the other things that I said in my initial post. Maybe I’ll make good on my rather unsupported claim that (2’) is not solid.
By
Joshua, at 4/22/2007 8:46 PM
It exists as obligate that I propose that it seems Andrew is unquestionably consistent in all logical exercises employed in his proof save for those yielding (2') and (3"); (2') seems to be consistent when be there especial cognition deliberated unto the condition maximality implicates; (3"), though, seems to follow only from additional axioms not mentioned in the body of the proof, and thus begs further justification; if perhaps it was appended that a variable quality may have its specifying quantities related according to similarity to maximality thereof (that is, have specifying quantity n be related to specifying quantity m (both being of the same variable quality (ie moral goodness)) through, "n>m" if n is more similar to maximality of concerned variable quality (ie maximal moral goodness)); according to this having some possible world in which some agent does not exist might be considered less morally good than having zero possible worlds in which some agent does not exist as the latter case is more similar to maximal moral goodness, a condition (maximal moral goodness) entailing existence of a possible world in which moral goodness describes some maximally morally good agent; thus, this entailment being that presence of such in the intensities of both having possible worlds in which does not exist some agent and having possible worlds in which does exist some agent is that upon which is contingent the similarity between maximal moral goodness and having possible worlds in which does not exist some agent and upon which is contingent, as well, the similarity between maximal moral goodness and having possible worlds in which does exist some agent, from this additional given, it may be concluded that having possible worlds in which exist some agent is more similar to maximal moral goodness than having possible worlds in which does not exist some agent is, and thus for a contingently existing agent there exists a possible world such that an agent is more morally good at this possible world than it is at a possible world in which this agent does not exist; thus a contingent existent may not be maximally durably morally good; thus a contingent existent may not be maximally morally good (assuming veridicality of propositions consisting at least partially of attestation to this implication being implicated in what it means to be maximally morally good); and, indeed, if basic combinatorial algebra be employed to deduce that no other possible scheme of possible worlds exists for some agent x other than those which have x as contingent and those which have x as necessary and those which have x as impossible, than some maximally morally good agent x is either necessary or impossible; of course the modal condition of impossibility might preclude the maximality of moral goodness potentially to be said of this agent x, and thus it seems that the only possible modality to be correctly said of a maximally morally good agent x is that of necessity.
I respectfully ask that you excuse my lack of knowledge on this topic as may be most manifest in this post; I was just perusing this site when I came upon this topic which interested me sufficiently for me to compose this comment; please correct all my shameful demonstrations of ignorance.
By
Josh, at 12/04/2011 4:13 PM
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