Wednesday, November 10, 2010

An Ontological Argument Based on Providence

Providence, roughly stated, is power over all things. It is slightly different than omnipotence in that providence specifies an actual causal relationship between the agent with providence and all existing, and all possibly existing, things.

Take the following axioms:

1. If X is a great-making property, then ~X is not a great-making property.

2. Being a necessary condition is a great-making property.

3. Having providence is a great-making property.

Now, the argument:

4. A provident agent is not possible. (Premise)

5. If a provident agent is not possible, then every existing thing has the property of not being provident. (Premise)

6. If every existing thing has the property of not being provident, then not being provident is a necessary condition. (Premise)

7. If not being provident is a necessary condition, then not being provident is a great-making property. (From 1 and 2)

8. Not being provident is not a great-making property. (From 1 and 3)

9. Hence, a provident agent is possible. (From 5 - 8)

10. Therefore, a provident agent exists. (From 9 and S5)

63 comments:

  1. I like it (though, it seems to me, 5 and 6 are both logical implications of 1-4 and premises of 7).

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  2. I like it Doug! Is it original? I think that most people who would have qualms about it would be concerned both (as traditionally) with the notion of a great-making property and perhaps with utilizing the the S5 modal system. What is your defense of S5, if you don't mind?

    RR

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  3. Upon considering other possible objections I find among them: opposition to the classical law of non-contradiction (per axiom 1). That is a rather hot issue, however. It seems that the only cases where the LNC breaks down are in ascribing it to approximate descriptions of actual states; as in: a property/state is either great-making or not great-making. Could it not be the case that the nature of the numinal aspects of instances of great-making properties is such that things can be 'somewhat great-making' or 'partially great-making', etc.?

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  4. There is, of course, a difference between denying the law of non-contradiction itself and denying that it applies in a particular case.

    BUT, anyone who denies the law of non-contradiction itself has already marked himself as willfully irrational. And you cannot argue with a crazy man.

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  5. Thanks for the comments, guys. Rigelrover, the argument is only semi-original. I was inspired by Maydole's modal perfection argument. The differences include my preference of S5 as opposed to the Barcan Formula, as well as a focus on a specific great-making property (providence). In defense of S5, I would point to the fact that what is necessary does not vary from world to world. We are able to conclude that square-circles do not exist in any world simply because they are logically impossible in the actual world. To be necessary in one possible world (possibly necessary) thus implies necessity in all possible worlds.

    Examples of "partially great-making properties" would have to be given before I could comment any further.

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  6. Walter Van den AckerNovember 12, 2010 at 3:48 AM

    I'm sorry, but the argument, like most onyological arguments, is question-begging.
    Let me explain.
    8 only follows from 3 if having providence is possible and that is what you want to prove. If having providence is not possible, then of course having providence is not a great-making property and not having providence is a great-making property jus because it is, in this respect, the only possible property.

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  7. Ilion and Doug,

    Though I am certainly not advocating for it here myself, the suggestion was the mere objection to excluding a middle for designating a great-making property (and not denying the prolific power of the LNC or the law of the excluded middle themselves); in that sense suggesting that someone might claim that some property can be both great-making and not great-making.
    Without seeing an example, Doug, you might at least suggest that if something could be considered only 'partially great-making' then it is not really great-making at all. This is most likely what the definition of a great-making property would entail; something that is only maximally great (so 'partial providence' does not entail greatness in this sense).

    Another objection to the notion of 'great-making properties' might be that they are demonstrably epistemically indeterminate. That is: what may seem to be great-making, from our point of few, is not necessarily but maybe only possibly great-making. This might be akin to claiming that 'great-making' is a subjective notion, and a demonstration would entail saying something about all such qualitative claims.

    So if one were to say that providence is such a thing he would have to qualify the claim by not only systematically ruling out all other possibilities, but by first knowing all of the possibilities.

    My feeling about this is that the same might be said of whole class of taxonomic properties, and that the pragmatic way of handling knowledge claims is to assume that we only must deal with possibilities that have been made explicit.

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  8. That last point would also include the property of being 'necessary' in the same way.

    We have evidently seen strong objection to the notion of a necessary beginning of the physical universe (in time and space), for example, in that people people have posited many many possible cosmological scenarios involving the steady state universe instead of simply accepting that a priori demonstration of the necessity of a beginning. It seems that they, and perhaps in general: we, are not quite comfortable with strictly designating a ontological fact of this sort merely based on scholastic demonstrations, but rather need to search the domain of possible scenarios first, and even more: be sure that they have exhausted all the possible scenarios, before accepting the original demonstration.

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  9. BTW, Ilion, if there is at least one example where the LNC doesn't hold, then the LNC as a universal notion is false. That is not to say that it couldn't be modified to account for particular exceptions; but then it would not be the strong version. It would be hard not to go crazy if one wanted to deny both the LNC and the principle of sufficient reason which suggests that there would need to be a reason for the LNC not holding in particular cases. So your assessment might be more apt than you know! :)

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  10. One of the problems I see with positing an exception to the LNC is that it would be impossible to affirm such an exception. If X is a violation of the LNC, then presumably ~X (the affirmation of the LNC) is also veridical in the same instant and sense.

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  11. Walter, thanks for the comment. An argument is only question-begging if there is no reason to affirm one or more of the premises other than to affirm the conclusion. If your analysis is taken to its logical implication, that would mean there are no sound deductive arguments, which I assume is not what you intend to say. As for the argument in question, I figured (8) would be one of the least controversial premises. If we isolate (8) from the rest of the argument, the point becomes more apparent. Which is more rational to believe: that providence is a great-making property or that non-providence is a great-making property?

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  12. Rigelrover: "Though I am certainly not advocating for [denial of the law of non-contradiction] here myself ..."

    I understood that.

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  13. Sorry, I didn't mean to imply that you didn't...

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  14. Walter Van den AckerNovember 12, 2010 at 8:37 AM

    Hi Doug

    I didn't know this was supposed to be an inductive argument.
    Anyway, whether it begs the question or not, the fcat remains that (3) is only true if the conclusion of your argument is true. if having providence is not possible, then (3) is obviously false and so is (8).
    This is a formal argument and you cannot just isolate one of the premises. And if you don't isolate(8) it is certainly not obvious that not having providence is a great-making property.

    So, the argument as it stands, is only convincing to someone who already believes that providence is possible, something I of course don't believe.

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  15. It's a deductive, not an inductive, argument. The point is that if your objection were to be taken to its logical conclusion, then all deductive arguments ought to be dismissed.

    Also, one can accept (3) and still reject the actual possibility of a provident agent. The formality of the argument aside, any one of the premises may be isolated from the rest.

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  16. Actually, (3) is a tautology, it's a truism; it follows from the given definition of 'providence:'

    "Providence, roughly stated, is power over all things. It is slightly different than omnipotence in that providence specifies an actual causal relationship between the agent with providence and all existing, and all possibly existing, things."

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  17. You're right about that, Ilion. (3) is listed as an axiom. I didn't expect anyone to be skeptical about it, tautological or not. Good discussion.

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  18. Walter Van den AckerNovember 12, 2010 at 10:20 AM

    Yes,I meant a deductive argument of course, and a deductive argument is what it is, an argument which can be convincing or not and my point is, yours isn't convincing because I don't accept (8)for the reason I've stated.
    I don't think one can reject the actual possibility of a provident agent if one accepts (3) because (3) entails the actual possibility of providence. Something that doesn't/cannot exist cannot be great-making.
    You could of course state (3) as a conditional: "if providence exists, it is a great-making property." This does not entail that non-providence is not a great-making property, so (8) would still not follow.
    I have also an objection to (1). If X is a great-making property then ~X is not a great-making property is only true if ~X is the opposite of X.
    If being a genius means that you will succeed, not being a genius does not mean that you will fail, but being a complete moron will probably mean you will fail.
    The way you state it, nothing other than X can be a great-making property, because ~X can be read as 'anything that is not X'.

    And we cannot isolate (8) because as it stands there is no reason to think that non-providence is not a great-making property. Since I don't believe in provident agents, to me of course non-providence is a great-making property, if great-making properties exist, which is a different issue of course.

    Anyway, these are some of my objections. I'll leave it at that, because I don't want to get into a long discussion.

    Regards

    Walter

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  19. You're definitively saying, then, that non-providence is a great-making property? I want to make sure I understand you correctly.

    By the way, ~X isn't the same as "anything that is not X." ~X is the negation, or contradictory, of X.

    Why does (3) entail the actual possible existence of a provident agent?

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  20. Walter Van den AckerNovember 12, 2010 at 12:12 PM

    Well, I was going to leave this discussion, but since you ask

    Firstly: yes, I am saying that non-providence is a great-making property. If providence does not exist, then this is a logical conclusion.If there is such a thing as a great-making property, of course.

    Secondly if providence is 'the power over all things' then non-providence does NOT mean 'the power over nothing'. Any power that is not over ALL things would qualify as non-providence. So, a very powerful being that can do anything but lift a stone of more than 1000 kg is non-provident under your definition and so is an inert elementary particle and everything that lies in between.

    Thirdly: if providence does not exist then it is a non-existing property, IOW not a property at all and certainly not a great-making property.
    I'll illustrate this with an analogy in which I use something that is obviously false.

    1. If X is a great-making property, then ~X is not a great-making property.

    2. Being a necessary condition is a great-making property.

    3. Being able to create square circles is a great-making property.

    Now, the argument:

    4. An agent capable of creating square circles is not possible. (Premise)

    5. If an agent capable of creating square circles is not possible, then every existing thing has the property of not being capable of creating square circles . (Premise)

    6. If every existing thing has the property of not being capable of creating square circles , then not being capable of creating square circles is a necessary condition. (Premise)

    7. If not being capable of creating square circles is a necessary condition, then not being capable of creating square circles is a great-making property. (From 1 and 2)

    8. Not being capable of creating square circles is not a great-making property. (From 1 and 3)

    9. Hence, an agent capable of creating square circles is possible. (From 5 - 8)

    10. Therefore, an agent capable of creating square circles exists. (From 9 and S5)

    You could object that the ability to create square circles is not a real ability, and in this case it is obvious, but if providence is a non-existing property, then it would be the same as in my square circle example.

    Regards


    Walter

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  21. DB: "You're right about that, Ilion. (3) is listed as an axiom. I didn't expect anyone to be skeptical about it, tautological or not."

    I don't use 'tautological' as a deprecation. But, I realize that many people do, so I clarified which sense of the word I meant: that given the definition of 'providence,' axiom (3) is a truism.

    You could have use nonsensical words for 'omnipotence' and 'providence' and 'great-making' and the *form* of the axiom would still be a truism, given the form of the definition.

    ====
    Shoot, my quibble would be with the modal logic, as I'm not sure I trust it to be *real* logic.

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  22. Walter, I'm adding asterisks to your premises in order to distinguish them from the premises of the original argument. The culprit in your counter-argument is both (3*) and the inference from (9*) to (10*). In fact, even if we grant that (3*) is coherent, and it doesn't appear to be, the use of S5 isn't applicable. After all, there is no hint of necessary existence in the counter-argument.

    As for (3*), the contradiction in creating a square-circle is manifest, whereas providence cannot be so easily dismissed. If there is an incoherence in providence, then it would have to be implicit, which is a disparity given that square-circles are explicitly contradictory. I would have to ask: what is the contradiction inherent in the concept of providence?

    It would be too hasty to conclude that if providence does not exist, then neither is providence a great-making property. That would be much like inferring that since there are no unicorns, then unicornness is not the property of being a magical horse with a horn.

    You stated, "Secondly if providence is 'the power over all things' then non-providence does NOT mean 'the power over nothing'."

    This is true, but surely it misses the point that power over all things is greater than power over some, but not all, things. Nobody would say that the ability to lift 300 lbs is greater than the ability to lift 400 lbs.

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  23. Walter Van den AckerNovember 13, 2010 at 2:08 AM

    The culprit in my argument is not 3*. My whole argument is set up to show that your argument does not work if providence is not possible, therefore I'm using something that most people already agree is not possible.
    If we treat 'square circles' as possible, my argument proves the possible existence of a square circle creating agent. Whether we can use S5 to go from possible to necessary here is a different matter, but your argument does not hint at necessity either. Your inference form 9 to 10 is also inapplicable unless we already assume the possible necessity of a provindent agent. Now, we can just as well assume the possible necessity of a square circle maker, because if making square circles is possible (as the argument presupposes)then this is a case of "super-providence".This agent , on top of the power over all things,also has the power over logic.
    It is not a matter of saying where the contradiction in a provident agent is, my argument shows that your argument can be used to prove the existence of clearly non-existent beings.
    In fact, all your argument says is that if it's possible that provident agents exist, it is possible that provident agents exist (and by S5 that they do existà. The real issue is somehow proving that provdence is actually possible, which you haven't done.
    You also say that nobody would say that the ability to lift 300 lbs is greater than the ability to lift 400 lbs. That is correct, but my point is: if the ability to lift 400 lbs. does not exist, then the ability to lift 399 lbs. is the only great-making property, just as the ability to create everything + square circles would be greater than the ability to create everything except square circles, but since square circles are not possible, the ability to create everything except SC's is the only great-making property, porvided this said ability is possible.

    Now, this is my opinion, I think I have made it as clear as I can. I'm not planning on using this blog as a discussion board. I just wanted to pop in to say hello, but it's turned out a bit longer than I had expected. So long, Doug. It's been a very interesting discussion.

    Regards

    Walter

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  24. Feel free to pop in whenever you want, Walter. I will reply to your latest response, though.

    You will recall that the definition of providence that I provided includes power over all existing, and all possibly existing, things. This would indeed imply necessity, so the inference from (9) to (10) is justified under S5.

    There is some confusion about what a great-making property is. The ability to lift 399 lbs wouldn't be a great-making property in lieu of the fact that there is (hypothetically) no possible ability of lifting 400 lbs. All that would show is that there is no great-making property in the ability to lift objects whatsoever.

    It should also be reiterated that square-circles are explicitly contradictory. One would be hard-pressed to find any explicit contradiction in the concept of providence.

    More importantly, though, I do maintain that this is a good argument for the possibility premise of the ontological argument (which, of course, turns out to be the key premise). There's no circularity, and our intuitions (theist and atheist) generally admit that providence is a coherent concept. One might think of providence in an analogous sense. The governor of each district has power over his/her respective districts, but surely it is logically coherent to postulate a ruler over the entire nation. What, then, would prevent us from concluding that an entity with power over all things (generally-speaking) is logically possible?

    Take care, my friend.

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  25. Walter Van den AckerNovember 14, 2010 at 8:07 AM

    I'm sorry to trouble you again, Doug, but it's obvious from you latest reply that you don't quite understand my objection, so I want to make something clear.
    Yes, your use of S5 is justified by the implication of providence, but suppose I were one of those people who believe that God's (super-) providence includes the ability to create square ciroles (I'm sure you know, there actually are people who believe that.)
    Then, to prove my point, I use your argument, and it proves the existence of a provident agent who can create square circles.
    Are you now convinced that God can create square circles? If you aren't, there is clearly a fatal flaw in your argument.
    The fact that square-circles are contradictory does not help your case, because you claim (3) does not entail the possible existence of provident agents, so whether there is an implicit or an explicit contradiction shouldn't matter.
    So, in reality, your argument does hinge on whether or not (3) provides an actual possibility or not.
    So, I'm afraid that, if we remove all the cosmetics from your argument, you are stuck with a circular argument. If providence is actually possible, then it is actually possible, just as if square circles are actually possible, they are actually possible.
    There are some other problems with your argument, but I'm not going to delve into them here.

    Regards

    Walter

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  26. Commenting on my blog is no trouble at all, Walter. It's what bloggers want. :)

    Substituting one premise for another doesn't make the original argument unsound. The point is that (3*) can be rejected outright, not just because there is no actual possibility of a square-circle, but because the very notion of a square-circle is contradictory. Lack of contradiction doesn't entail that something is actually possible. So, one can consistently affirm (3) on its own and also reject the actual possibility of a provident agent. It's just that this becomes absurd in light of (1) and (2).

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  27. It seems to me that if there is a weakness in the argument, the weakness is grounded in the lack of definition for "great-making property."

    And, if there is a flaw in the argument, a point of attack it which it may all fall down, it seems it must be at (2) [for even lacking the definiton of "great-making property," I'm not sure (2) is properly phrased], which leads directly to (6) and especially to (7).


    I think perhaps (6) might be rationally denied (I'm not sure).

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  28. Walter Van den AckerNovember 14, 2010 at 11:27 PM

    It does not matter whether 3* can be rejected outright or not. In fact, I agree the concepts of square circles can be rejected outright, nevertheless, your argument proves they do (possibly exist, so your argument is flawed. The argument in fact not only proves the (possible) existence of super-providence, but also disproves the possible existence of ordinary providence.
    So, if we use something impossible in the original axioms, the argument proves the existence of an impossible thing.

    As it stands now, it does not ,because super-providence is actually impossinle (and we now this because , as you say, it contains a contradictory notion.)
    Now if the existence of ordinary providence is not possible (for whatever reasons), then of course (3) does not make sense either. Something impossible cannot be a great-making property.

    I don't know whether providence is actually possible or not, I have very seriouss doubts, but if it isn't actually possible, it is impossible that a sound argument would prove it is.

    We can also consistently affirm 3* (if we use super-providence instead of merely square-circle making)and reject the actual possibility of a super-provindet aganet, but the argument would still prove the possible existence of super-providence. Which would be impossible if the argument were sound.


    Regards

    Walter

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  29. What do you mean that (2) might not be properly phrased? It seems that potential problems could be that "condition" and "property" are not compatible. Or, it could be that a person could be concerned about the universal claim about necessary conditions. If someone would like to be concerned about this part of (2) she would only have to produce one example of a necessary condition which which is strictly not possibly great-making (for any generously broad definition of 'great-making').

    I have been trying to think of examples of necessary conditions that would fit the bill, but the only thing that I run into, again, is the problem with ascribing 'necessary conditions' (as in "how can I know that something is necessary") rather than any possible examples that would contradict (2).

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  30. Walter, the argument couldn't be used to prove the existence of super-providence for the reasons I've already given - most notably, that we know (3*) to be necessarily false. (3*) cannot just be substituted for (3) in order to disprove the soundness of the original argument. That's not how counter-arguments are meant to be effective, especially when the counter-argument contains axioms and/or premises that are known to be false. The argument I have presented doesn't prove that square-circles are possible; in fact, it doesn't even begin to suggest that such things are even coherent. On the other hand, (3) should be granted regardless of whether providence is actually possible or not.

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  31. Walter Van den AckerNovember 15, 2010 at 10:20 PM

    I'm not going to repeat myself over and over again, Doug. Your argument can be used to prove known absurdities, so it is unsound. Of course we knwo 3* to be necessarily false, but if we use it, your argument works. So if your 3 is false, then your artgument would still work.
    But there is a much simpler rejection of your argument.
    If square-circles are impossible, then every exiting thing (and every possible thing) has the property of not being able to create square circles, so not being able to create square circles is a necessary condition, and, by your definition, a great-making property. Which means that, regardless of providence or whatever, every (non-provident or alleged provident) thing has a great making property. If providence is actually impossible, then still, non-providence is a great-making property.

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  32. Repetition is a common practice on internet forums, which is one reason I'm no longer posting on them. You haven't given a good counter-argument to my point that (3*) should be rejected outright, so you can repeat yourself all you want, but it won't invalidate the argument.

    Since the ability to create a square-circle is meaningless, so is the inability to create one. Therefore, neither is a great-making property. Great-making properties, and all properties for that matter, have to incorporate meaningful referents.

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  33. In other words, if (3*) is to be rejected, and it is, then any argument that necessitates the use of (3*) will be invalid and/or unsound. In fact, the more I think about it, the more your objection resembles Gaunilo's Island. The problem with the latter objection is that the notion of a maximally great island is incoherent, so it doesn't constitute a good counter-argument. One cannot just assume that if a counter-argument leads to an absurdity, then the original argument does as well.

    To emphasize again, my argument cannot be used to prove absurdities. The counter-argument demonstrably uses a false axiom, whereas the original argument does not.

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  34. Walter Van den AckerNovember 16, 2010 at 10:43 AM

    The inability to create square circles is, by your definition, a great-making property.

    But, it's clear that you do not understand my argument, so I'm not going to say much more about it

    Just this. As for Gaunilo's island, (or Dawkins greatest stinker), the reason why it is generally rejected is because it is completely misunderstood. When understood properly it is, in fact, a very good objection against the ontological argument.

    And if 3* is to be rejected, that would mean the argument may be unsound, but it is most certainly valid (if yours is of course)because there is no formal difference between the two.

    Regards


    Walter

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  35. It's entirely possible I don't understand your argument. I very much doubt it, though. There's a reason why even atheistic philosophers today reject such parodies.

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  36. Walter Van den AckerNovember 16, 2010 at 12:39 PM

    As with all arguments, some philosophers accept them and others reject them. That's partly because philosophy isn't an exact science.And BTW the parody was not the only argument I presented.
    But I see you have posted a new argument, so I won't bother you with this one any longer.

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  37. You cite Dawkins who, while very intelligent, isn't a philosopher. I know you offered other arguments, and I responded to each of them.

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  38. Everyone is a philosopher (though, not necessarily a "lover of wisdom"), just as everyone is a theologian, in the sense that everyone has some theory of the divine.

    =====
    Ilíon "It seems to me that if there is a weakness in the argument, the weakness is grounded in the lack of definition for "great-making property."

    And, if there is a flaw in the argument, a point of attack it which it may all fall down, it seems it must be at (2) [for even lacking the definiton of "great-making property," I'm not sure (2) is properly phrased], which leads directly to (6) and especially to (7).
    "

    Rigelrover "What do you mean that (2) might not be properly phrased? It seems that potential problems could be that "condition" and "property" are not compatible. Or, it could be that a person could be concerned about the universal claim about necessary conditions. If someone would like to be concerned about this part of (2) she would only have to produce one example of a necessary condition which which is strictly not possibly great-making (for any generously broad definition of 'great-making').

    I have been trying to think of examples of necessary conditions that would fit the bill, but the only thing that I run into, again, is the problem with ascribing 'necessary conditions' (as in "how can I know that something is necessary") rather than any possible examples that would contradict (2).
    "

    If the argument is to be attacked in a rational and logical manner, the attacker must do one of two things:
    1) deny that the conclusions logically follow from the premises;
    2) deny one of more of the premises.

    I'm not really sure what a "great-making property" is. But, for the validity of the form of the argument, that's not important.

    Premise (2) is: "Being a necessary condition is a great-making property."

    Since the term "great-making property" can be substituted without affecting the form of the argument, so as to set aside that potential confusion, change that to: "(2*) Being a necessary condition is a Z property" or even "(2**) Being a necessary condition is a Z*".

    Now, what does "being a necessary condition" *mean* -- is that phrased well? is it phrase in an imprecise manner? worse, it is it phrased in an ambiguous or confusing manner?

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  39. Ilion, I agree with your sentiment that everyone is a philosopher in some sense. I just mean that Dawkins isn't a professional philosopher - that is, he doesn't have any formal background in academic philosophy.

    The best route for the skeptic to take, in my opinion, is to question the meaningfulness of great-making properties. Parodies and other counter-arguments just don't appear to be at all compelling. So, what is a great-making property? It's hard to define it in simpler terms, but one may provide synonyms, e.g. "perfection." What this ontological argument assumes from the outset is some form of axiological realism, which is the commonsensical view. Of course, that doesn't automatically make axiological realism true, but the intuition at least lends itself toward the argument's rational acceptability. Additional reasons for accepting axiological realism will only bolster the acceptability of the argument.

    One may show what a necessary condition is by providing examples. The conclusion that "Socrates is mortal" has at least two necessary conditions in order for said proposition to be true: a) that all human beings are mortal, and b) that Socrates is a human being.

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  40. "So, what is a great-making property? It's hard to define it in simpler terms, but one may provide synonyms, e.g. "perfection.""

    Ah: "great(est)-making property" ... "the property of being in a state of wholeness/completeness/integrality" ... and that's how I understood it all along.

    But, from his posts, it seemed to me that Walter Van den Acker was taking it to mean something very different ... essentially as "great(er)-making property;" such that if X is greater (in some property) than Y, then X possess a "great-making property."

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  41. Yes, that's the impression I get from him as well.

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  42. This is a form of the objection that I suggested above, then. I think we already decided that something cannot be 'partially/somewhat or greater-making'.

    I think that Walter may be arguing from non-cognitivism, though. He (Walter: you) seem(s) to be suggesting that "providence" in the sense of complete agency may be non-nonsensical or impossible. If so then it seems that that is exactly what (4) entails. You would have to go further and say that (4) is also non-cognitive as well. If not, then given that the rest of the argument has a valid form we find that it is not possible to hold (4) along with (1-3).

    The second bit of his (your) argument seems to be that Doug's is circular in that in order to deny (4), one must first adopt (3), but one cannot adopt (3), he (you) say(s), unless a provident agent is already possible. In this I think there is a potential defeater on the surface, but Doug points out that you can take any proposition you want as an axiom/premise, so unless the premise (3) is being denied (8) follows, and so then does (9). I think that that he (you) have confounded the non-cognitivism and the circularity argument where they are in fact not co-dependent.

    Better luck denying (3) by trying to claim that 'great-making properties' are meaningless, I think.

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  43. What about the property of existing? Is that a "great-making property"?

    Is that a necessary property? -- that *is* a serious question, at least in the context of this thread.

    Consider:

    "6. If every existing thing
    has the property of not being provident, then not being provident is a necessary condition. (Premise)
    "

    versus

    "6*. If every existing thing has the property of [existing], then [existing] is a necessary condition. (Premise)"

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  44. Walter Van den AckerNovember 16, 2010 at 11:12 PM

    Rigelover

    Thanks for your comments.
    Yes, I take a non-cognitivist approach with respct to (3), in that, I think, (3) should be read as "We do not know if providence is possible or not, but if it is possible, it is a great-making property."
    (4) Then is a premise and assumes for the sake of the argument that, in fact, (3) entails that "Providence is impossible, but if it were possible, it would be a great-making property.
    We can leave (5)-(7)
    5. If a provident agent is not possible, then every existing thing has the property of not being provident. (Premise)

    6. If every existing thing has the property of not being provident, then not being provident is a necessary condition. (Premise)

    7. If not being provident is a necessary condition, then not being provident is a great-making property. (From 1 and 2)
    Now (8) has become a non-sequitor because we have established that being a non-provident agent is a great-making property in vitue of its being a necessary condition, and of course, not by virtue of its being "perfect" (as Doug suggests), although we can still argue that non-providence is a perfection in that perfection in this domain (providence) does not exist. Thus, non-providence really is as far as one can logically get.
    So, either, the argument already assumes from the outset that perfection (in the domain of providence) is possible, and then it works but is clearly circular, or it doesn't, which means that the argument does not show its possibility.
    Ans, as you say, we can go further and say that the argument presupposes the possibility of perfection in other domains too, IOW it presupposes the possibility of great-making properties.
    I do not think perfection is possible, so, while I agree that Doug or anyone else can take anything they like as an axiom, the fact that I don't take this as an axiom, means that I don't think the argument proves the existence of a provident agent.
    What my parody attempts to show is that if we use a slightly different axiom (in this case a known impossibility)we can prove the existence of impossible entities, so if (3) is also taken to be impossible, (8) does not follow anymore.

    Regards


    Walter

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  46. Walter, everyone can make up his/her own mind about whether your parody would work. I've made my case that it doesn't. (8) isn't a non-sequitur - it follows the laws of negation and modus tollens. A great-making property is a perfection, simply as a matter of identity.

    Ilion, I'm not sure if existence is a great-making property or not. Necessary existence is, but existence itself? I'm not sure. Even if existence is a great-making property, that would only mean that all existing things possess one great-making property. There are other great-making properties to consider, such as providence, which only one existing thing could possibly have, e.g. God.

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  47. Walter Van den AckerNovember 17, 2010 at 1:10 AM

    Ilion said

    "But, from his posts, it seemed to me that Walter Van den Acker was taking it to mean something very different ... essentially as "great(er)-making property;" such that if X is greater (in some property) than Y, then X possess a "great-making property." "

    Doug said
    "Yes, that's the impression I get from him as well. "

    Well, to be clear, I do not take great-making to mean what Ilion thinks. I take great-making to mean a perfection.
    But, it seems that at least in some domains, perfection is logically impossible. There is no highest natural number e.g., so we can say that great-making property is incoherent in this domain.
    But consider providence, defined as 'the power over all possible things' and let's say for the sake of the argument that power over 100% of possible things is impossible, it's only logically possible to have power over 99.999...% of possible things.
    From Doug's definition, power over 99.999...% of possible things is not providence. Does that mean there is no great-making property in the category of providence, or can 99.999...% be considered a great-making property because it is the greatest possible property? In that case, (8) is a non-sequitur and if 99.999...% of providence is not great-making (and 100% is impossible), then a non-provident agent has a great-making property in virtue of a necessary condition and (8) is still a non-sequitur because, since providence is impossible, it cannot be a great-making property.
    X cannot be great-making property, so ~X can be a great-making property.

    The only way to get out of this would be to insist that an impossible condition can be great-making. But I think that is contradicted by (2).

    Regards


    Walter

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  49. There is no highest natural number, yes. But, we're talking about qualitative perfections. A highest natural number would constitute something quantitative, and it's difficult to see any parity between this example and providence.

    In any case, power over all things (providence) should be considered greater than power over some, and not all, things (non-providence). This is true regardless of whether providence is possible. Now, you continue to call (8) a non-sequitur, but (8) isn't even a conditional statement. We just know that all power is greater than some power, regardless of actual possibility.

    You say, "let's say for the sake of the argument that power over 100% of possible things is impossible, it's only logically possible to have power over 99.999...% of possible things."

    But, this is a conclusion, not a premise that you would need for your counter-argument to work. (9) is a conclusion - namely, that a provident agent possibly exists. You're reading (9) back into (3), and then turning possibility into impossibility. But, that's not what (3) is getting at, so I'm afraid you have (unintentionally) misinterpreted the argument.

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  50. Walter Van den AckerNovember 17, 2010 at 3:14 AM

    So, in your opinion, Doug, an impossible condition is greater than a possible condition or even a necessary condition?

    BTW, what I say is not a conclusion, it's a premise that is justified because, as you claim, (3) does not entail the possibility of providence. So, I see no reason why I couldn't use it as a premise. In fact, it's just the same as (4), just with a little more detail.

    And how is 'the power over all things' not quantitative? If there are 1000 possible things, then providence means the power over all 1000 and non-providence means the power over 999 or less. I agree it may also be qualitative, but it most certainly is quantitative too, isn't it?
    And I am not trying to find a parity between natural numbers and providence. I'm saying that, while it is clear that in the case of natural numbers, there is no great-making property, it isn't so obvious that there cannot be one in the providence domain. And a great-making property could perhaps be 'the greatest logically possible property'.

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  51. "Ilion, I'm not sure if existence is a great-making property or not. Necessary existence is, but existence itself? I'm not sure. Even if existence is a great-making property, that would only mean that all existing things possess one great-making property. There are other great-making properties to consider, such as providence, which only one existing thing could possibly have, e.g. God."

    Well, isn't God "existence itself?" Or is that the wrong way to put it (the correct way being "God is being itself")? – Some have argued that “being” and “existing” are not the same thing.

    But yes, definitionally, only one being can be provident.


    "Ilion, I'm not sure if existence is a great-making property or not. Necessary existence is, but existence itself?"

    But, doesn’t that raise some sort of question about the structure, or even the validity, of the argument?

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  52. 99.999... is equal to 100, unless a distinction is being made about a actual limiting procedure. I just thought that I would point that out, though you could have just said 99% instead.

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  53. I didn't say one condition would be greater, but that one property would be greater. More importantly, though, you cannot assume from the outset in (3) or (3*) that providence is possible/impossible. That's not what the axiom is getting at.

    You are making a conclusion first, since a thing's possibility/impossibility is what is determined by the time we get to (9). (4) is just the beginning of a reductio ad absurdum and (3) has nothing to do with possibility.

    Power over all things may be quantitative, but the key is that it's also qualitative - that is, it's better to have all power than only some. But, in the series of natural numbers, is 1,000 really a "better" number than 999? I doubt it.

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  54. Ilion: "Well, isn't God "existence itself?" Or is that the wrong way to put it (the correct way being "God is being itself")? – Some have argued that “being” and “existing” are not the same thing."

    I would use "existing" and "being" synonymously. Yes, God is existence itself, but God's existence is necessary and perfect, whereas the existence of everything else is contingent and imperfect given the composition of potentiality.

    Ilion: "But, doesn’t that raise some sort of question about the structure, or even the validity, of the argument?"

    I don't think so. The argument's use of "providence" entails not only existence, but necessary existence.

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  55. Walter Van den AckerNovember 17, 2010 at 3:03 PM

    Doug said

    "I didn't say one condition would be greater, but that one property would be greater."

    Indeed, you did, so I'll have to rephrase my question. So, in your opinion, Doug, an impossible property is greater than a possible property or even a necessary property?

    "More importantly, though, you cannot assume from the outset in (3) or (3*) that providence is possible/impossible. That's not what the axiom is getting at."

    I don't assume from the outset that providence is possible or impossible, but the axiom only leads to your preferred conclusion if providence is possible

    "You are making a conclusion first, since a thing's possibility/impossibility is what is determined by the time we get to (9). (4) is just the beginning of a reductio ad absurdum and (3) has nothing to do with possibility."

    (4) is the beginning of a reductio , yes, and I've only added some details, instead of just saying as a premise that a provident agent is impossible, I say that power over 100% of possible things is impossible, it's only logically possible to have power over 99.999...% of possible things, which is nasically the same as your premise, so I'm definitley not making a conclusion.
    And I'm sure you really believe that (3) has nothing to do with possibility, but you are wrong, unless you believe that an impossible property can be greater than a possible one.

    Let's take a closer look at your first axioms

    1. If X is a great-making property, then ~X is not a great-making property.

    2. Being a necessary condition is a great-making property.

    Now, just let X = "being a necessary condition", then you get
    1'. If being a necessary condition is a great- making property, then not being a necessary condition is not a great-making property.

    Now if we look at (3)
    3. Having providence is a great-making property.
    For 3 to be true, "Having providence" must be a necessary condition

    So, if we take (4),
    4. A provident agent is not possible. (Premise)
    This entails that having providence is not a necessary condition, so (3) isn't true.

    That's all.

    So, as I've been saying all along: if we don't assume the possibility of providence in (3), the argument does not lead to your conclusion. Therefore, the argument is circular.

    To Rigelrover
    "99.999... is equal to 100, unless a distinction is being made about a actual limiting procedure. I just thought that I would point that out, though you could have just said 99% instead."

    Yes, you are right in that 99.999... equals 100. I should have used 99, but I wanted to stress the fact that even if an agent has power over everything but a very tiny proportion, the agent cannot be provident.



    Power over all things may be quantitative, but the key is that it's also qualitative - that is, it's better to have all power than only some. But, in the series of natural numbers, is 1,000 really a "better" number than 999? I doubt it.

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  56. Walter: "Indeed, you did, so I'll have to rephrase my question. So, in your opinion, Doug, an impossible property is greater than a possible property or even a necessary property?"

    Possibility doesn't even enter into the equation in (3), so you're knocking down a straw man.

    Walter: "I don't assume from the outset that providence is possible or impossible, but the axiom only leads to your preferred conclusion if providence is possible"

    The consensus here seems to be that it doesn't. Either way, (3) only necessitates that providence be greater than non-providence, regardless of whether providence is actually possible.

    Walter: "(4) is the beginning of a reductio , yes, and I've only added some details, instead of just saying as a premise that a provident agent is impossible, I say that power over 100% of possible things is impossible, it's only logically possible to have power over 99.999...% of possible things, which is nasically the same as your premise, so I'm definitley not making a conclusion."

    How is that not a conclusion, again?

    Walter: "And I'm sure you really believe that (3) has nothing to do with possibility, but you are wrong, unless you believe that an impossible property can be greater than a possible one."

    How about non-providence being greater than providence? If you really believe that, then okay. Nothing requires more faith than that.

    Walter: "Now if we look at (3)
    3. Having providence is a great-making property.
    For 3 to be true, "Having providence" must be a necessary condition"

    This is an invalid inference. Providence is a great-making property, and being a necessary condition is a great-making property, but from those two axioms it doesn't follow that providence is a necessary condition. That's a lot like saying that since dogs are animals, and cats are animals, then dogs are cats.

    Walter: "So, as I've been saying all along: if we don't assume the possibility of providence in (3), the argument does not lead to your conclusion. Therefore, the argument is circular."

    It's demonstrably not circular. (9) isn't used to support (3), regardless of how many times one says it is.

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  57. Walter, I still think your beef with this argument centers on a misconception about the formal logic.

    Doug's reductio requires what is sometimes called (by another Doug...Hofstadter) the 'fantasy rule'. That is if Y can be derived when X is a theorem (even if Y and/or X aren't decided/decidable) then X => Y is a true proposition. Let X be (1)^(2)^(3) and Y be ~(4) then by (5-8) we see that X => ~(4) or X => Y, so (1)^(2)^(3) => ~(4) is a true proposition; that is if we assume (1-3) to be true, then ~(4) is also. This is what Doug's argument demonstrates. You don't have to believe that (3) is true for the argument to be sound, but it you do believe (3) & (1) & (2) (and you like to maintain that formal logic is an acceptable way to arrive at truth) then you should also believe ~(4), i.e. (9) (and what follows from it by S5 if you are ok with S5).

    This is, of course, setting aside the gap between belief and truth (that is why I said "should also believe"). You can believe what you like about any part of any of the argument.

    Like Doug says then, (9) isn't support for (3) (or (2) or (1)), it just follows from them formally. It seems that you have said that in order to believe (3) one must believe a priori in (9). But this is simply not the case as (I think) has been demonstrated.

    But you then seem to say that in order for (3) to be cognitive both "providence" and "great-making" must be meaningful concepts. Now this is a separate argument. Clearly if I wanted to believe the proposition that 'All Bips are Boops' I could do so regardless if Bips and Boops are fictions. I think that the underlying axiom in your assertion, then, is that meaningfulness entails possibility.

    I think that this is a much deeper philosophical issue and a defense of it would require taking many schools of thought into consideration. Is this, in fact, the critical point that you are arguing from? If so, maybe someone should start a new blog post about it, and we can carry on the discussion there.

    RR

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  58. Rigelrover, I especially agree with you that meaningfulness does not necessarily entail possibility. That's why I claim that (3) doesn't entail that a providence agent is possible. Elsewhere I have argued that conceivability doesn't necessarily entail possibility, so it seems we're on the same page on this issue.

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  62. Just a couple things before I close this post again. Walter, if you're reading this, your latest responses were filtered out as spam. I think this is because you are not a registered user with blogspot, and that happens from time to time as a result. I'm not publishing any more comments post-Nov. 19 or so partly because this has become too lengthly, and I want to move on to other subjects.

    I do want to make one correction. You are right to infer that being provident would be a necessary condition via (1) - (3). I misunderstood the implications of what you were saying at first. Nevertheless, what you said here needs refurbishing:

    Walter: "So, if we take (4),
    4. A provident agent is not possible. (Premise)
    This entails that having providence is not a necessary condition, so (3) isn't true."

    First, (4) isn't known to be true, and it cannot be asserted to be true on pain of circularity. As a result, (3) couldn't be rejected by merely asserting the truth of (4). More importantly, (4) doesn't entail that providence is not a necessary condition. "Necessary condition" doesn't imply anything about possibility. It's just that if there were such a thing as providence, it would be a necessary condition. Notice that in order for your objection to work, (3) would have to entail something about possibility, so it turns out that your own objection hinges on a circularity.

    Mainly I just wanted to make the above correction so you wouldn't think I was ignoring any of your points.

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