• Banno
    26.2k
    And so to section Three.

    It seems, therefore, that all that Anselm’s proof requires is that modicum of rationality which is needed to understand a simple descriptive phrase, to reflect on what the description implies, and to conclude to these implications concerning the thought object one has in mind as a result of understanding the description.

    So this section takes the previous argument as valid and sound. Perhaps seeing that it is not sound requires more than a modicum of rationality?

    So to the second of Anselm's proofs.
    If you understand the phrase “something which cannot be thought not to exist”, you have to think of something which cannot be thought not to exist. But what cannot be thought not to exist is certainly greater than anything that can be thought not to exist. So, if that than which nothing greater can be thought of were something that can be thought not to exist, then something greater than that than which nothing greater can be thought of could be thought of, which is impossible. Therefore, that than which something greater cannot be thought of cannot be thought not to exist.

    The change here is in emphasis rather than form. Much the same problems can bee seen as in the first argument. There might simply not be a “something which cannot be thought not to exist”, despite our being able to think about it, just as there is no greatest number, despite our being able to think about a greatest number.

    The argument also depended on the ill-conceived notion of "necessary existence". How one is to make sense of a something that supposedly exists in every possible world is contentious. In particular, in S5, if something exists necessarily, then everything exists necessarily, and the distinction between the possible and the necessary collapses. See Modal Collapse.
  • Janus
    16.8k
    Just like Zeus, eh? Btw, do you stop to think about what omnipotent means and implies? Is omnipotence the greater thing?

    Then there is the question of what, exactly, a thought object is, and if it is of a being than which & etc., then what do we know about the idea? And in particular how that idea, or any idea about the idea, becomes constitutive of anything "existing in reality"?
    tim wood



    Omnipotence is the greatest power. It doesn't follow it is the greatest good or knowledge. God is traditionally conceived as being the greatest everything, so all other things being equal and omnipotent God would be greater than a God whose powers were limited.

    That said, I am an atheist, in the sense that I don't possess a belief in God and am only considering the logic of the ideas of degrees of goodness, power and knowledge.

    I suppose there are those who think that because we can conceive of the ideas of God, eternity and infinity that they must actually exist. I think that is really the thrust of the Ontological Argument. I can't see how it could be a matter of logic—I think it must be counted as a matter of faith.
  • Count Timothy von Icarus
    3.2k


    Edit: This is also a reply to ↪Count Timothy von Icarus. The non-theist need not maintain that the various notions of "unlimited being" are unintelligible, but can agree that it may be intelligible to some degree while maintain that it has not been demonstrated that this "unlimited being" is the same as say the Christian god, or indeed any god

    Sure, but the rejection of particularly Christian revelation doesn't affect the ontological argument at all.
  • Banno
    26.2k
    Sure, but the rejection of particularly Christian revelation doesn't affect the ontological argument at all.Count Timothy von Icarus

    What's your point here? Neither does the price of tea in Patagonia.

    That there is stuff may be a mystery, but there is no need to prefer the answer supposedly given by the ontological argument, especially since that argument is fraught with problems.Banno
  • Count Timothy von Icarus
    3.2k


    Arguably, the argument simply proves that the atheist cannot deny God (i.e. the being greater than which no being can be thought) without affirming a contradiction. So, it shows that we should affirm the existence of God, on pain of being fools or misologes.

    However, this itself does not prove "that God exists." We could consider here Brouwer and other's objections to the use of proof by contradiction in existence proofs in mathematics. So, there is a possible distinction here. And perhaps, having taken the conclusion in this way, we could dismiss some of the criticisms re "proofs cannot demonstrate existence," (what about existence theorems?) or "existence simpliciter must somehow be assumed somewhere in the premises" (I think it's fairly obvious that it isn't in Anselm's formulations though). I suppose the difficulty is that this only eliminates those fairly weak objections though.
  • Leontiskos
    3.8k
    On the argument, there seems to be a few issues. The first is "greater than."Count Timothy von Icarus

    I don't find this controversial when applied to existence. See my reply to Wayfarer:

    To contradict this is to say that a thought object is not thought to be greater in virtue of its being thought to exist. Or simplified: fiction is as good as the real thing - a fiction that is in fact realized is no greater than an unrealized fiction (where both are thought objects).Leontiskos

    -

    But we might suppose that such a concept is hard to fully take in.Count Timothy von Icarus

    Is the concept of (1) "unlimited"? Not per se. And are you pointing to instances of "unlimited" that would not be considered great or even good? Because if so, then that kind of unlimited would not filter through the ampliated (1). If someone is thinking of a form of unlimitedness that they don't take to be great, then they aren't really engaging (1). Or at least it seems so to me.

    that the argument could suffer from a premise that is not as well known as its conclusionCount Timothy von Icarus

    This is an interesting objection, and one which Klima does not canvass. But if you are depending on the notion of infinity/unlimitedness then I'm again not sure it necessarily filters through (1). Nevertheless, separated from that dependence the objection could still have merit.

    This is relevant in that infinite, unlimited being is often called upon to ground metaphysics. The claim that this is "unintelligible" while putting forth "it just is, for no reason at all" as the root explanation for everything is more than a little ironic, particularly when the ad hoc appeal to brute fact is paired with eliminativism or deflationism re causes, such that everything "just is" and explanation seems to be little more than a hallucination resulting from inexplicable constant conjunction in the first place (isn't this just epistemic nihilism with extra steps?)Count Timothy von Icarus

    Sure. A lot of people are bringing up more general arguments for or against God, and if "unlimited" detaches from the first premise then this would be an instance of that. I am trying to stick close to the paper at least until we've finished the final section. But maybe "unlimited" does derive from the first premise and I'm just not seeing it. For me (1) does bring with it the, "si enim comprehendis, non est Deus" (which is why Banno's "objection" that there might be something greater than what is thought is so poorly aimed). And there is a component of unlimitedness in that, albeit of a particular variety.
  • Banno
    26.2k
    Arguably, the argument simply proves that the atheist cannot deny God (i.e. the being greater than which no being can be thought) without affirming a contradiction. So, it shows that we should affirm the existence of God, on pain of being fools or misologes.Count Timothy von Icarus

    The argument professes to prove that; but it doesn't succeed, for the reasons given.

    Are you able to back up your claim?
  • Leontiskos
    3.8k
    Omnipotence is the greatest power. It doesn't follow it is the greatest good or knowledge. God is traditionally conceived as being the greatest everything, so all other things being equal and omnipotent God would be greater than a God whose powers were limited.Janus

    Well this is related to what said about the notion of unlimited (although it is more precisely about power than general unlimitedness). Do we think that a being which is omnipotent is greater than a being that is not? Because maybe someone would say, "If it is an evil being then the omnipotence would make it lesser, not greater." And of course no one thinks it is greater to be evil than to be good, so presumably it would not be an evil being, but the idea brings out your difference between moral (?) goodness and and a form of greatness which prescinds from the moral.

    But I tend to think that (1) produces the thought of an omnipotent being, and presumably we are agreed on that?

    ---

    Just like Zeus, eh? Btw, do you stop to think about what omnipotent means and implies? Is omnipotence the greater thing?tim wood

    Do you think it isn't? Do you think premise (1) does not bring with it omnipotence?

    (This subject is interesting because a lot of new forms of theism reject omnipotence. But does that mean they would find Anselm's first premise incompatible with their God?)
  • Wayfarer
    23.6k
    existence simpliciterCount Timothy von Icarus

    An oxymoron.
  • Leontiskos
    3.8k
    Arguably, the argument simply proves that the atheist cannot deny God (i.e. the being greater than which no being can be thought) without affirming a contradiction. So, it shows that we should affirm the existence of God, on pain of being fools or misologes.Count Timothy von Icarus

    That's a fair and interesting way of reading it. :up: I need to think a bit more about section 3. I'm just trying to catch up on some replies.

    However, this itself does not prove "that God exists." We could consider here Brouwer and other's objections to the use of proof by contradiction in existence proofs in mathematics. So, there is a possible distinction here. And perhaps, having taken the conclusion in this way, we could dismiss some of the criticisms re "proofs cannot demonstrate existence," (what about existence theorems?) or "existence simpliciter must somehow be assumed somewhere in the premises" (I think it's fairly obvious that it isn't in Anselm's formulations though).Count Timothy von Icarus

    Right, I am following what you are saying here. But the difficulty is that affirmation of existence separates from existence, or something like that. Right? If the argument proves that we should affirm the existence of God without proving that God exists, then how does that work? Or do we want to take a half-step back and say that it proves that the atheist cannot deny God without proving that we should affirm the existence of God? (But that seems to fall away from Anselm.) So how would we address these difficulties?

    "existence simpliciter must somehow be assumed somewhere in the premises"Count Timothy von Icarus

    I said this earlier:

    The wonder of Anselm's proof is that it does something that we think it should not be able to do, and it is very hard to say why it is wrong, or at least to say why rigorously. At this point the argument looks to be sound. It is valid and there are no premises that are clearly or demonstrably false.Leontiskos

    So I don't see that objection as necessarily weak, but it is not a "close argument." If the strongest arguments attack a premise or an inference, then this sort of argument does not meet that criterion, and is a form of begging the question. So I guess it is weaker than an argument which actually addresses the proof itself, but it isn't irrational. I definitely think this form of begging the question will need to be considered at some point, perhaps as we move away from more precise critiques.

    (I should note here that all of @Banno's attempts have been of this "weaker," question-begging variety. His claims that he has addressed or disproved premises are simply false. He himself knows that the conclusion he seeks to prove is that (1) involves a contradiction, and he also knows equally well that he has not produced that proof. In my opinion Gaunilo's island objection comes much closer to doing this than Banno's arguments have.)

    I'm going to have another look at section 3 and the Proslogion.
  • Banno
    26.2k
    So I am happy to play the recalcitrant fool. Anselm’s second conclusion denies the obvious, namely that God can be thought not to exist.

    Contrary to the suggestion in the article, what is juxtaposed here is not theist and atheist. A reasonable theist might accept the issues give so fat and yet not be moved to reject their theism. The argument supposedly shows that all rational folk must agree that god exists; showing it to be wrong does not lead to the conclusion that god does not exist. This is not a debate "between the theist and the atheist."

    If the argument is to hold, the it must not be possible for it to be in error. Accordingly it is not incumbent on the fool to show that one of the premisses must be false; but only that it might be false. So indeed, there is a clear way in which one can supose “something which cannot be thought not to exist", and understand that such a thing entails a contradiction. “something which cannot be thought not to exist" may well occupy much the same space as "a number greater than any other" or "A triangle with four sides" or even "The present king of France"; there may be no such thing.

    If the argument is to hold, the theist must show that “something which cannot be thought not to exist" is not of this sort.

    But notice that even if the argument turns out to be unproven, it can still serve as the sort of "intellectual prayer" mentions.

    Next we might begin to look at the place of reference and language generally.
  • Leontiskos
    3.8k
    Part 3. The Atheist, Who is Not a FoolLeontiskos

    As I read it, this section is meant to drum up the possibility of a dialogical impasse between the atheist (who opposes Anselm's proof) and the theist (who accepts Anselm's proof). Towards the beginning of the section Klima writes:

    Anselm’s retort, that the Fool’s denial was possible in the first place only because he is truly a fool, thoughtlessly mumbling words he himself does not understand, leads us directly to the crux of the very possibility of a dialogue between the Saint and the Fool, or put in less biased terms, between the theist and the atheist.Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding - Section 3

    He then tries to develop "requirements of rationality" that could "avoid a complete breakdown of communication." Then at the end of the section he caps the tempest in the teapot so that it might retain its potency:

    But even without these moral implications, it seems that the theist now may justifiably claim that, as a result of his denial, the atheist just rendered himself unable to think of a humanly otherwise thinkable thought object. By denying the existence of God the atheist will never be able to think of the same God as the theist, whose conception of God logically implies the existence of God, as Anselm’s proof shows.Gyula Klima, St. Anselm's Proof: A Problem of Reference, Intentional Identity and Mutual Understanding - Section 3

    (I have noticed an underlying theme in some of Klima's work, namely an attempt to make commensurable what others view as incommensurable.)

    The dialogical impasse is as follows, in the form of, "One man's modus ponens is another's modus tollens":

    For the theist/proponent:

    • If Anselm's thought is thought, then God exists
    • Anselm's thought is humanly thinkable
    • Therefore the atheist (who can think this thought) is unwilling to think it

    For the atheist:

    • If Anselm's thought is thought, then God exists
    • God does not exist
    • Therefore, Anselm's thought cannot be thought (because it is not humanly thinkable)

    (We could also phrase this in a more subjective way as intimates, by making the first premise, "If Anselm's thought is thought, then God must be acknowledged to exist.")

    In Klima's own words, the conclusion of the theist's modus ponens is this, "it seems that the theist now may justifiably claim that [...] the atheist just rendered himself unable to think of a humanly otherwise thinkable thought object."

    Notice that if the atheist is unable to think Anselm's thought, then there is an infinite gulf of a sort. The theist and the atheist cannot help but talk past one another because they cannot think the same thought, and for Anselm this is the atheist's fault because the atheist is stubbornly refusing to think a humanly thinkable thought.*

    I think this is the shape of section 3, but obviously I skimmed over the entire body of the section, which is where some of the more concrete wrestling between the theist and the atheist takes place. I want to look at that tomorrow since it so closely resembles some of the argument that occurred earlier in this thread.


    * This charge from Anselm may seem outlandish, but I think it does happen quite commonly in everyday life. Namely, people will intentionally misunderstand so as to avoid an undesirable conclusion, and oddly enough this can even go on below the level of the conscious mind. So I don't think the charge is crazy. But in order for Anselm's charge to hold up at a philosophical level we would have to say that every atheist is intellectually dishonest in this manner, and that is much harder to sustain. We might then say that Anselm's charge is possible but implausible, considered as a categorical claim.
  • Count Timothy von Icarus
    3.2k


    The argument professes to prove that; but it doesn't succeed, for the reasons given.

    Sure, I am pointing out that the conclusion can be given a different interpretation, and according to published responses to the article it may need to be given this interpretation to avoid problems.

    That said, the argument looks ok at first glance. I agree with this response:

    The formally regimented argument is pretty clearly valid, and none of the premises of which it is alleged to be a formalization is obviously objectionable. The first premise simply articulates Anselm’s conception of God as the thought object than which no thought object can be thought greater.5 The second premise is just the reductio assumption that God is a mere thought object. As for the third premise—the claim that thought objects that can be thought to exist in reality can be thought to be greater than mere thought objects—one might allege (as Klima himself does) that it is analytic by virtue of the meaning of ‘greater than’. Finally, one might convince himself of the truth of the fourth premise—the claim that God can be thought to exist in reality—by introspection. So Klima’s claim that these premises ‘have to be accepted as true’ is initially plausible.


    Tony Roark - Conceptual Closure in Anselm’s Proof

    I think this gets to "it is unclear that the reductio premise is the one that needs to go."

    The most common way to attack this sort of argument has been to deny that God actually can be conceived of (or for modal formulations, that God is possible). Plantinga's version has been vetted for 50 years now, has been overwhelmingly seen as at least valid, and this is widely agreed to be the weak part.

    But I think it is at least prima facie plausible that God can be conceived of in this manner because, as I said, disparate philosophies across the world have conceived of this same thought object and because atheist and agnostic scholars of relevant areas seem to have no trouble conceiving of such a being.

    Perhaps other problems remain. There are arguments that omnipotence is contradictory because it implies the ability to become not omnipotent. Plantinga has done a lot of work on this, e.g. showing that "God cannot create a stone that He cannot lift," is equivalent with "God can lift all stones." However, I am not convinced that "absolute power" or "absolute freedom" doesn't result in what are essentially paradoxes of self-reference, at least on some naive conceptions.

    Potentially more problematic are claims that perfect justice is in contradiction with perfect mercy, etc. Yet these don't seem relevant to the argument. For, the "being greater than any other that can be thought" need not have all the properties allocated to the God of revelation. Perfect mercy and perfect justice seem like they could be bracketed out so long as omnipotence, omnibenevolence, etc. are included.

    Of course, responses to Plantinga focus on the question: "is such a being is possible?" due to the modal formulation of his argument. St. Anselm's formulations deal with thinkability. I am not sure what important differences this could yield in attacks on the opening premise (i.e., the thinkability or possibility of God).

    Roark has his own critique. I would have to look at it more, but on first glance his main counter seems too strong. He argues that the atheist should be happy to allow that they are only engaged in parasitic reference because the theist's definition requires a framing that at least allows for the possibility of liar's type paradoxes. However, showing the mere possibility of paradox is far weaker than demonstrating a paradox.

    At any rate this counter would seem to lead to the conclusion that all sorts of people, not just atheists, should refuse to engage in anything but parasitic reference in a huge variety of cases. In particular, they should refuse to engage in anything but parasitic reference when it comes to liar's paradoxes. Yet, if someone took this line as a counter to logical pluralism or arguments against LEM, as opposed to God, I doubt it would pass the smell test. And it seems possible to push it farther, into a prohibition on accepting arguments in natural language, which would be absurd.



    If the argument is to hold, the it must not be possible for it to be in error. Accordingly it is not incumbent on the fool to show that one of the premisses must be false; but only that it might be false. So indeed, there is a clear way in which one can supose “something which cannot be thought not to exist", and understand that such a thing entails a contradiction. “something which cannot be thought not to exist" may well occupy much the same space as "a number greater than any other" or "A triangle with four sides" or even "The present king of France"; there may be no such thing.

    Can one ever totally eliminate the possibility of error? Is "error is possible," without pointing out any clear error a good counter to other demonstrations?

    This counter seems too strong, because it would seem to apply, in some sense, to skepticism vis-a-vis all demonstrations.



    Well this is related to what ↪Count Timothy von Icarus said about the notion of unlimited (although it is more precisely about power than general unlimitedness). Do we think that a being which is omnipotent is greater than a being that is not? Because maybe someone would say, "If it is an evil being then the omnipotence would make it lesser, not greater." And of course no one thinks it is greater to be evil than to be good, so presumably it would not be an evil being, but the idea brings out your difference between moral (?) goodness and and a form of greatness which prescinds from the moral.

    Right, and this perhaps touches on the theological concerns that came to the fore during the Reformation, that only doing what is best would somehow be a limit on divine sovereignty and power. I personally think this sort of concern doesn't hold water. Defining freedom in terms of potency leads to contradiction (e.g. the demonstrations at the opening of Hegel's Philosophy of Right) and so the notions that lead to a renewed salience for Euthyphro dilemmas in the early modern period seem to simply be flawed. This is relevant inasmuch as people claim that God is "unthinkable" due to these supposed "paradoxes."

    Right, I am following what you are saying here. But the difficulty is that affirmation of existence separates from existence, or something like that. Right? If the argument proves that we should affirm the existence of God without proving that God exists, then how does that work? Or do we want to take a half-step back and say that it proves that the atheist cannot deny God without proving that we should affirm the existence of God? (But that seems to fall away from Anselm.) So how would we address these difficulties?

    I'll have to think about it more. It is indeed strange. I do think intuitionist mathematics maybe offers some guidance here. To use an analogy that might be a bit weak, it seems obvious that something like a constructive proof of God cannot exist.

    We could also consider abductive arguments. There, we might have strong reasons to affirm the existence of something. It would be unreasonable to deny it. And yet this is also not a demonstration that it exists.

    At any rate, this outcome seems theologically preferable in some ways. For, if the demonstration was of existence, then it would be a demonstration that God exists in the manner of all other ens reale—of trees, stars, man, etc. But this is often explicitly denied. Dionysius the Areopagite writes:

    "It is wrong to say God that God exists. It is wrong to say that God does not exist. But it is more wrong to say that God does not exist...

    [God] is not a facet of being, but being a facet of Him. He is not contained in being but being is contained in Him. He does not possess being, but being possesses Him. He is the eternity of being, the measure and source of being. He preceded essence, being, and eternity. He is the creative source, middle, and end of all things."

    Indeed, we might say that a demonstration that shows that God exists in the same manner as both our conceptions of God's existence and the real existence of all other things would be guilty of equivocation. Ens reale and ens rationis can sit together on a Porphyrian tree, but God cannot.
  • tim wood
    9.4k
    Do you think it isn't? Do you think premise (1) does not bring with it omnipotence?Leontiskos

    Omnipotence is the greatest power. It doesn't follow it is the greatest good or knowledge. God is traditionally conceived as being the greatest everything, so all other things being equal an omnipotent God would be greater than a God whose powers were limited.Janus

    My point is that God is usually held to be perfection perfected (this definitely not the God of the Bible). If it be insisted that He is omnipotent, that implies that He can do anything, implying that there are things to be done, implying that of the things to be done, they are at present in an unperfected state needing to be perfected, implying God a kind of glorified maintenance man obliged to go about perfecting what needs to be perfected. Omnipotence, then, straight out implies an imperfect God and an imperfect creation, contradicting any notion of a perfect all-everything being.
  • Leontiskos
    3.8k
    - Great post. :up:
    Hopefully Roark's response can serve as an additional sounding board as we move along.

    Can one ever totally eliminate the possibility of error? Is "error is possible," without pointing out any clear error a good counter to other demonstrations?Count Timothy von Icarus

    Right.

    Right, and this perhaps touches on the theological concerns that came to the fore during the Reformation, that only doing what is best would somehow be a limit on divine sovereignty and power. I personally think this sort of concern doesn't hold water. Defining freedom in terms of potency leads to contradiction (e.g. the demonstrations at the opening of Hegel's Philosophy of Right) and so the notions that lead to a renewed salience for Euthyphro dilemmas in the early modern period seem to simply be flawed. This is relevant inasmuch as people claim that God is "unthinkable" due to these supposed "paradoxes."Count Timothy von Icarus

    Yes, and the claim is a little bit odd insofar as it involves the idea that "greatest" entails contradiction via two or more contradictory attributes. That is of course arguable, but it doesn't strike me as a promising approach.

    This is related to your point about unlimitedness, at least in the case of bad forms of unlimitedness. For example, if to be unlimited is greater than to be limited, then Anselm's thought must be unlimited. But if certain forms of unlimitedness are not greater, then we arrive at a similar paradox.

    We could also consider abductive arguments. There, we might have strong reasons to affirm the existence of something. It would be unreasonable to deny it. And yet this is also not a demonstration that it exists.Count Timothy von Icarus

    Yes, and I think we also want to draw a conceptual distinction between the natural language formulation and the quantification theory reductio formulation. A reductio is intrinsically less constraining than a simple demonstration.

    Indeed, we might say that a demonstration that shows that God exists in the same manner as both our conceptions of God's existence and the real existence of all other things would be guilty of equivocation.Count Timothy von Icarus

    Yes, interesting point. The first response might simply say that an analogical notion of existence is available here. But in the second place, the proof itself will mandate the level of existence-univocity in play. So for example, if Anselm's reply to Gaunilo's island objection succeeds, then the form of existence at stake in Anselm's proof is sui generis (i.e. it applies only to the greatest thing, and not to e.g. the greatest island).

    (But I am not going to delve too deeply into strictly theological objections such as this until we have finished the paper.)
  • Leontiskos
    3.8k
    I want to draw some connections between section 3 and what has already occurred in this thread (note that I did not read section 3 beforehand, and was not manipulating the thread to achieve these overlaps). Taking section 3 in chronological order:

    Choosing the first alternative would amount to claiming that God’s concept is contradictory. [...] In any case, in Anselm’s argument the concept of God to bevemployed is adequately specified by the first premise, and the atheist would probably be hard pressed to show that the description “that than which nothing greater can be thought of” is self-contradictory.Gyula Klima, St. Anselm's Proof - Section 3

    See 's post for this notion of contradictory concepts; see my replies pointing out that no contradiction has been shown/proved (, ).

    At this point, however, the atheist may shift the burden of proof by saying that even if this description does not seem to contain any prima facie contradiction, it may well be contradictory. By way of analogy, he may bring up the description: “the greatest prime number”, which, on the face of it, does not appear to be contradictory, so it seems to refer to the greatest prime number. But, as we know from Euclid, the assumption that there is a greatest prime number leads to contradiction, so the description cannot refer to anything.Gyula Klima, St. Anselm's Proof - Section 3

    Banno has been engaged in this "shifting of the burden of proof" all along, and has directly parallel to the argument from the greatest prime. Perhaps the clearest attempt to shift the burden of proof was , "Accordingly it is not incumbent on the fool to show that one of the premisses must be false; but only that it might be false." Banno's posts have been entirely dependent on this notion of possibility, e.g. "Might be wrong," "May be wrong," "No guarantee."

    , , and make similar arguments against the concept, having to do with omnipotence or unlimitedness.

    Second, he can say that a contradiction, if derivable at all, could be derived from this description only with the help of other assumptions, just as in the case of the greatest prime. But, unlike the case of the greatest prime, these auxiliary assumptions probably need not be accepted as true.Gyula Klima, St. Anselm's Proof - Section 3

    I made this move in contending that the greatest prime number (or real number) has no clear parity with Anselm's first premise, as I think the may/might's also indicate ( and elsewhere).

    Finally, concerning Anselm’s argument one can also say that the premise attacked by the atheist does not even require that Anselm’s description should be free from such implied contradictions. For the premise requires only that one can think that God (under Anselm’s description) exists, which one can do even with the greatest prime, until one actually realizes the implied contradiction. So the burden of proof falls back upon the atheist, if he wishes to challenge this premise.Gyula Klima, St. Anselm's Proof - Section 3

    This occurred in of mine and explicitly in its final paragraph.

    ---

    So, since [the atheist] denies that the description applies to any thought object he can think of, he just does not have such a thought object in his mind, while he perfectly understands what is meant by this description.Gyula Klima, St. Anselm's Proof - Section 3

    This is an interesting idea that stays very close to Anselm, and it also bears on Quine. Namely, if one is to say, "X does not exist as a concept," then what is being referred to by X? Is it possible to understand a description without having such a thought object in one's mind? This goes back to my .

    This also highlights the way that Klima differentiates objections to premise (1) from objections to premise (2). The idea is that the atheist might say that even if (1) manages some kind of quasi-concept, that concept is never really or fully present in the intellect a la (2).

    ---

    2. There is a sleight of hand from ens rationis to ens reale, somewhat hidden here but brought out in Free Logic by the invalidity of a move from Ti to E!i.Banno

    If one reads the first section one sees that such objections have been preempted. See:

    We actually saw this play out two days ago in the midst of a discussion on Mario Bunge, who admits of conceptual existence and who treats existence as a first-order predicate. A response was as follows:

    [...]

    That is, the assumption is that Bunge must be working with two mutually exclusive subclasses, at least "in effect." This is the sort of objection that Klima has in his sights. How does he address this objection?...
    Leontiskos

    -

    4. The argument relies on a substitution within an intensional context, at line (5), that is not justified.Banno

    This is an assertion, not an argument.

    ---

    If it be insisted that He is omnipotent, that implies that He can do anything, implying that there are things to be done, implying that of the things to be done, they are at present in an unperfected state needing to be perfected, implying God a kind of glorified maintenance man obliged to go about perfecting what needs to be perfected. Omnipotence, then, straight out implies an imperfect God and an imperfect creation, contradicting any notion of a perfect all-everything being.tim wood

    I think the error is, "He is omnipotent, which means he can do anything, which means there are things to be done, which means that he is obliged to do them." Those last two (bolded) interferences both look to be false, and particularly the last one.
  • Banno
    26.2k
    ...the argument looks ok at first glance.Count Timothy von Icarus
    Well... not so much. The definition (1) supposes that there is a greatest thing, which, even if we assume that "greatest" works in this way, is what is in question when we ask if there is a god. In combination with the other premises the argument is circular. That's not OK. But of course the argument has to be circular in order to be valid.

    If the point is to convince the fool of the error of their thinking, then it will not do to only be "at least prima facie plausible that God can be conceived of in this manner". And frankly the attempts to keep the various traditional properties of God consistent have the look of post-hoc bandaging.

    Can one ever totally eliminate the possibility of error?Count Timothy von Icarus
    Perhaps not, but here the error is set before you.

    There is more to be said here yet about the theory of reference being used, which seems to me to be quite problematic. Leon asked us to go slowly, so let's do as he suggests, and plod on. We should be reasonably clear as to what Klima is claiming about reference before we go on to critique it.

    Added: We might agree that one of the issues with the argument is that it treats god's being as on a par with the being of the more familiar stuff around us. I made this point previously, in pointing out that he does not carry his notion of ampliation into the argument proper.
  • Leontiskos
    3.8k
    Roark has his own critique.Count Timothy von Icarus

    Roark is getting into complicated questions of whether Klima's quantificational formulation accurately represents Anselm's proof. This is somewhat important because in order to understand that formulation one must understand that Klima is attempting an accurate representation of Anselm's proof. On the other hand, assessing the interpretation can quickly become overly complicated. Sticking for the moment to section 3, Roark's critique has to do with the - exchange, namely with sub-inference (a):

    (4) R(g)
    ____(a) M(g)(g)............................[2,3,4, UI, &I, MP]
    ____(b) (∃y)(M(y)(g))....................[a, EG]
    (5) (∃y)(M(y)(ix.~(∃y)(M(y)(x))).....[1,b, SI]

    Without closely reading Roark's lengthy assessment, my sense is that the logic here is attempting to indicate that the suppositional (2) is at the nub of the problems in (a), (b), and (5). Or rather, (a) and (b) are an extension of the problems with (5) (and (2)). It is possible that Roark draws the same conclusion but at the same time argues that this way of looking at it deviates from Anselm's original. In any case, he clearly thinks there is a coherent interpretation.

    These sorts of wrinkles are why we want to also keep an eye on the natural language version.

    (Note that Roark's page numbers refer to the book chapter version, linked in the OP.)
  • Banno
    26.2k
    I'll not reply to this directly. From past experience, including on this very thread, I do not regard Leon as an honest respondent. If any one else thinks there is anything of merit in Leon's post, let me know and I may reply.

    Or PM me, as some have already.
  • Leontiskos
    3.8k
    I'll not reply to this directly.Banno

    That's pretty much par for the course, as all you've managed in responses to criticisms is, "I won't repeat myself." Clarifying one's argument is dangerous, after all. Better not to say too much.

    Perhaps not, but here the error is set before you.Banno

    No, it's not. The possibility of error is set before you. That was the whole point.

    You are equivocating between things like error and possibility of error, or between a proof of a contradiction and a gesturing towards a contradiction. This bears on the "honesty" you just spoke of.
  • Banno
    26.2k
    Klima offers the fool a rhetorical exit - perhaps he has misunderstood the language involved in the argument, in the way of someone not understanding that "triangle" means "shape with three sides". What's salient here is the use of "I mean" in explaining the discrepancy between fool and saint.

    There are those who think that what a word means is what the speaker intends it to mean, and nothing more. So if the fool intends "four sided shape" by "triangle", then that's an end to it, and communication simply fails.

    This speaks to the poverty of this view of meaning. If the meaning of "square" is only what we each intend, then there can be no justification for supposing that you and I mean the same thing when we talk of squares. But of course there is such a justification, which can be seen in the ongoing conversations and interactions amongst us; when I order a square table, that's what you provide, not a triangular one; when someone talks of the three sides of a triangle, we question them; and so on.

    Language is inherently social. The meaning of a word is not given by speakers intent alone.

    Does Klima hold such a view? Read on.
  • Leontiskos
    3.8k
    Klima offers the fool a rhetorical exitBanno

    He is summarizing the Anselm-Gaunilo exchange, and this is transparent in the paper.

    There are those who think that what a word means is what the speaker intends it to mean, and nothing more. So if the fool intends "four sided shape" by "triangle", then that's an end to it, and communication simply fails.Banno

    Except that's not what Anselm or Klima say at all, so this looks to be another strawman from someone who has been desperate to cast aspersions from their very first post. :roll:

    But of course there is such a justification, which can be seen in the ongoing conversations and interactions amongst us;Banno

    Which is exactly why Anselm uses an ongoing conversation to clear up the equivocal term, and why Klima summarizes the same move.
  • Banno
    26.2k
    At this point, however, the atheist may shift the burden of proof by saying that even if this description does not seem to contain any prima facie contradiction, it may well be contradictory. By way of analogy, he may bring up the description: “the greatest prime number”, which, on the face of it, does not appear to be contradictory, so it seems to refer to the greatest prime number. But, as we know from Euclid, the assumption that there is a greatest prime number leads to contradiction, so the description cannot refer to anything.

    In response, the theist first of all can point to the whole tradition of rational (as opposed to mystical) theology showing how apparent contradictions concerning God’s nature are resolved.17 Second, he can say that a contradiction, if derivable at all, could be derived from this description only with the help of other assumptions, just as in the case of the greatest prime. But, unlike the case of the greatest prime, these auxiliary assumptions probably need not be accepted as true. Finally, concerning Anselm’s argument one can also say that the premise attacked by the atheist does not even require that Anselm’s description should be free from such implied contradictions. For the premise requires only that one can think that God (under Anselm’s description) exists, which one can do even with the greatest prime, until one actually realizes the implied contradiction. So the burden of proof falls back upon the atheist, if he wishes to challenge this premise. Therefore, he has to turn to the other premise anyway, asking whether he has to admit God as at least a possible object of thought.
    Here he offers three replies to the fool. The first is that theology has shown that the concept of god can be made consistent; of course, the fool will disagree. The second, that any contradiction must be derived from auxiliary assumptions; but the problem is not one of contradiction, it is of circularity and ambiguous definition. The third, the familiar insistence that all that is assumed is that one can conceive of god; ignoring premise 3.
  • Banno
    26.2k
    He is summarizing the Anselm-Gaunilo exchange, and this is transparent in the paper.Leontiskos
    Yep.

    Sure. Let's see.
  • Leontiskos
    3.8k
    The first is that theology has shown that the concept of god can be made consistent;Banno

    Well, no. He says that one could point to the tradition "showing." Obviously such arguments need to be shown to one who has never seen them. Klima does not think the atheist possesses arguments he has never encountered.

    The third, the familiar insistence that all that is assumed is that one can conceive of god; ignoring premise 3.Banno

    I have no idea where you find that idea in the quote. He is saying that even if contradiction is granted for the sake of argument, this still does not undermine premise (1), and in that case we would have to move to premise (2) (because that is where a contradiction becomes uncontroversially problematic). As I said:

    This occurred in ↪this post of mine and explicitly in its final paragraph.Leontiskos
  • Banno
    26.2k
    In response to this question the atheist now may claim that the way Anselm wishes to force him to think of God will not make him admit that God is even in the intellect, at least, in his intellect, despite the fact that he understands very well what Anselm means by his description, which may not be contradictory after all. For understanding this description does not require him to believe that it applies to anything, so understanding this description will not make him think of anything that he thinks to be such that nothing greater than it can be thought of. So, since he denies that the description applies to any thought object he can think of, he just does not have such a thought object in his mind, while he perfectly understands what is meant by this description.
    Taking the example from the text, one can clearly conceive of a greatest prime, and then look to see if such a thing makes sense. One can proceed, as has been done, to show that it involves a contradiction, thereby showing that a greatest prime does not exist.

    Let's use this analogy to look at one misunderstanding of what the fool is suggesting.

    Supose the theist were claiming that they have a proof of the existence of a highest prime. The proof in part claims that since we can conceive of a highest prime, one must exist. The fool does not need to demonstrate that there is no highest prime in order to show that the theist is mistaken. They only need to show that it does not follow from our being able to conceive of a highest prime, that such a thing exists.

    The fool does not need to show that god does not exist in order to show that the argument that he does exist is flawed. "...understanding this description does not require him to believe that it applies to anything".

    But here the theist swoops down: of course, the atheist is just a fool! Indeed, a wicked fool, who, only because of his insistent denial, admits to be simply unable to think of the same thought object that I think of, that is, God. With this last move the atheist just revealed himself for the miserable fool he is, for in order to maintain his untenable position he simply gives up his otherwise natural human ability to think of God, that than which nothing greater can be thought of. As Saint Bonaventure put it: “the intellect has in itself [...] sufficient light to repel this doubt and to extricate itself from its folly. Whence the foolish mind voluntarily rather than by constraint considers the matter in a deficient manner, so that the defect is on the part of the intellect itself and not because of any deficiency on the part of the thing known.”18
    And here, the fool is "simply unable to think of the same thought object" as the theist. The thought in the theists head is different to the thought in the fools's head, and never the twain; together with as much disparaging of the fool as can be mustered.

    Part of what is going on here is a bit of theatre, an attempt to avoid considering the fool's account by simply denigrating it. Hence "But even without these moral implications..."; the fool is evil for not thinking in the same way as the theist.

    This is not an argument, but a call to the faithful to pull together and reject anything Other. And the rejection of this painting of the fool as "other" occupies much of the remainder of the paper.

    (I'm essentially setting out my own notes on the article for my own purposes, which is enough for me. If there is anyone apart form Leon reading on, which I doubt, I apologise for plodding.)
  • Banno
    26.2k
    So on to Part Four.

    There's a description of the intentional theory of reference, allowing for successful references even when descriptions are inaccurate or fictional and so enables speakers to refer to objects based on shared intentions, even when the referent is not directly known or believed to be true. And then this:
    But throughout this process, the questioner thinks of the same thought object as the answerer, without knowing under what description or name the answerer identifies this thought object.
    The issue here is clear enough: how could we know that "the questioner thinks of the same thought object as the answerer"? And further, how can the "thought-object" in the mind of the saint be said to be the same as the "thought-object" in the head of the fool - and indeed, how could they be said to be different?

    And here again we bump in to the lack of extensionality. Two sets are said to be extensionaly equivalent when they contain the very same members. But infamously, there is simple no way to verify that the thing in the mind of the saint is the same as the thing in the mind of the fool - and indeed, every reason to doubt it.

    Now this is apparently recognised by Klima in the next paragraph. But rather than drop the very idea of thought-objects as a useful notion, as the fool might, he suggests:
    Accordingly, if one mind entertains a thought object under some particular description, another mind may make what I would call parasitic reference to the same thought object, by merely intending to refer to the same thought object that the first conceives of, but not conceiving it under the same description, indeed, sometimes even denying that the description in question in fact applies to this thought object.
    Intending to refer to the same thought-object but under a different description. "I'll have what she's having", involving some sort of telepathy, perhaps.

    This is the sort of thing attributed to the fool. But of course there is a much simpler response that can be made, that the idea of reference to some imagined thought-objects is misguided. A better approach would be to reject the picture of reference as being about latching onto pre-existing "objects" in thought at all. Instead, reference is a practice embedded in linguistic and social interaction, where success isn't a matter of mental duplication but of communicative coherence. In that case, the fool's response is not just simpler but arguably the only coherent one.

    And it avoids the lack of transparency that plagues talk of intensional references.

    Notice that this is very much the approach taken by Quine and Davidson, amongst others.

    So at the end of Part Four, the fool may on this account discuss the concept of god had by the saint, and see how this leads to the saint's belief that god exists, while consistently maintaining there own account of god in which god need not exist.
  • Leontiskos
    3.8k
    So on to Part Four.Banno

    Are you trying to take over the thread entirely? No, we will open part four tomorrow. You can remove your post or I will appeal to the mods.
  • Banno
    26.2k


    I flagged your post for you, so no need for you to draw their attention.

    You need not respond to my post if you do not wish to, and can proceed at whatever pace suits you. For my part, I've addressed the thread at length in detail and in sequence, and am preparing my comments on part five. That is were I am up to.

    ( I suspect it's only you and I who are paying this thread much attention, so the point is probably moot.)
  • kazan
    338
    Learning without participating is possible by paying (much) attention, perhaps?

    quiet smile
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