Retired Boards (Archived)
Ontological Argument
Posted by: Arnold T. Guminski
« on: December 02, 2016, 08:01:36 PM »Re: ontologicalme's reply post of November 28:
ONTOLOGICALME: “Plantinga gives two final versions of the argument in one of them maximal greatness is not given in terms of maximal excellence, and the later is a necessary implication of the former, Maximal greatness entails necessary maximal excellence.”
COMMENT: This sentence is rather confusing. I take it that “Maximal” (appearing after “former,”) was intended to begin a new sentence. As to the purported sentence ending with “former”, ontologicalme does not provide any citation to Plantinga’s writings. One can hardly disagree with ontologicalme’s statement (i.e., “Maximal greatness entails necessary maximal excellence”). Plantinga put it this way: “The property has maximal greatness entails the property has maximal excellence in every possible world.” … Maximal excellence entails omniscience, omnipotence, and moral perfection. He noted that “a property P entails a property Q if there is no world in which there exists an object x that has P but lacks Q.” (The Nature of Necessity (1974), 214.)
ONTOLOGICALME: “In the final version, they are taken as equivalent, but, this is not to couch maximal greatness in terms of necessary maximal excellence, they are logically equivalent, nothing more follows from it.”
COMMENT: ONTOLOGICALME manages to obfuscate that maximal greatness is defined by Plantinga (and Craig) in terms of maximal excellence obtaining in every logically possible world. So necessary maximal excellence is the state of maximal excellence being exemplified in every logically possible world.
ONTOLOGICALME: “Furthermore, Maximal greatness in the MOA is a universal property, meaning if it is not co-exemplified it is necessary that it is not, and, if it is co-exemplified it is necessary that it is, It is this that is most fundamental when it comes to these concepts, the universality of the essential property of maximal greatness, thus, my comment on AP3 begging the question against necessary metaphysical or broadly logical truths.”
COMMENT: I have no problem with the proposition that a maximal excellence is exemplified in some possible world. I have a problem with those who claim that it is false to affirm that maximally excellence is not exemplified in some possible worlds. After all, I am just conforming to the rules pertaining to possible worlds semantics. Before you can coherently discuss whether maximal greatness is exemplified in some possible world you must first consider whether maximal excellence is exemplified in some possible world. Doing so leads to the conclusion that there are possible worlds in which maximal excellence is not exemplified. To first prematurely consider the former case (i.e., whether maximal greatness is exemplified in some possible world) ultimately compels (via legerdemain) the conclusion that maximal excellence is exemplified in all possible worlds. So I am not begging the question. I submit that ontologicalme is doing so.
ONTOLOGICALME: “Plantinga gives two final versions of the argument in one of them maximal greatness is not given in terms of maximal excellence, and the later is a necessary implication of the former, Maximal greatness entails necessary maximal excellence.”
COMMENT: This sentence is rather confusing. I take it that “Maximal” (appearing after “former,”) was intended to begin a new sentence. As to the purported sentence ending with “former”, ontologicalme does not provide any citation to Plantinga’s writings. One can hardly disagree with ontologicalme’s statement (i.e., “Maximal greatness entails necessary maximal excellence”). Plantinga put it this way: “The property has maximal greatness entails the property has maximal excellence in every possible world.” … Maximal excellence entails omniscience, omnipotence, and moral perfection. He noted that “a property P entails a property Q if there is no world in which there exists an object x that has P but lacks Q.” (The Nature of Necessity (1974), 214.)
ONTOLOGICALME: “In the final version, they are taken as equivalent, but, this is not to couch maximal greatness in terms of necessary maximal excellence, they are logically equivalent, nothing more follows from it.”
COMMENT: ONTOLOGICALME manages to obfuscate that maximal greatness is defined by Plantinga (and Craig) in terms of maximal excellence obtaining in every logically possible world. So necessary maximal excellence is the state of maximal excellence being exemplified in every logically possible world.
ONTOLOGICALME: “Furthermore, Maximal greatness in the MOA is a universal property, meaning if it is not co-exemplified it is necessary that it is not, and, if it is co-exemplified it is necessary that it is, It is this that is most fundamental when it comes to these concepts, the universality of the essential property of maximal greatness, thus, my comment on AP3 begging the question against necessary metaphysical or broadly logical truths.”
COMMENT: I have no problem with the proposition that a maximal excellence is exemplified in some possible world. I have a problem with those who claim that it is false to affirm that maximally excellence is not exemplified in some possible worlds. After all, I am just conforming to the rules pertaining to possible worlds semantics. Before you can coherently discuss whether maximal greatness is exemplified in some possible world you must first consider whether maximal excellence is exemplified in some possible world. Doing so leads to the conclusion that there are possible worlds in which maximal excellence is not exemplified. To first prematurely consider the former case (i.e., whether maximal greatness is exemplified in some possible world) ultimately compels (via legerdemain) the conclusion that maximal excellence is exemplified in all possible worlds. So I am not begging the question. I submit that ontologicalme is doing so.
Posted by: ParaclitosLogos
« on: November 28, 2016, 12:45:03 AM »Ontologicalme raises a couple of issues in his reply post. He writes:
AP3 begs the question against necessary truths, or/and it is a non sequitur, since it is true that possible worlds can be formed by the negation of different conjuncts in a maximal description, but this does not imply that it must be the negation of each and every conjunct, some conjuncts staty the same, while others are negated.
There is a possible world where 2+2=4 , but, possible worlds can be formed by the negation of different conjuncts in a maximal description, so it is possible that it is not the case that 2+2=4 .
What reasons are there to accept that it is possible that it is not the case that 2+2=4?
AP3 reads: "IIf a maximally excellent being exists in some possible world and since possible worlds can be formed by the negation of different conjuncts in a maximal description, then a maximally excellent being does not exist in some (other) possible world." I do not see why AP3 begs the question against necessary truths because, in the first place, the ontological argument concerns itself with concrete entities, and not with abstract entities (e.g., numbers) and their logical or mathematical relations. Moreover, while it is verbally possible to assert that the proposition that 2+2=4 is false in some logically possible worlds, Plantinga, Craig, and your truly would maintain that because this assertion is a negation of a logically necessary truth it is, therefore, logically necessarily false. Next, the notion of a maximally excellent being is patently logically coherent and is analytically prior to the notion of a maximally great being. The RF video fails to mention that Craig in his writings defines a maximally great being in terms of a maximally excellent being (i.e., that a maximally great being is a maximally excellent being that exists in all possible worlds). Finally, AP3 conforms to the definitions and basic rules pertaining to possible worlds semantics (as expounded by Plantinga and Craig), as the reader of my essay ("A Critique of the Plantinga Version of the Modal Ontological Argument" [available at http://infidels.org/library/modern/arnold_guminski/]).
Plantinga gives two final versions of the argument in one of them maximal greatness is not given in terms of maximally excellence , and the later is a necessary implication of the former, Maximal greatness entails necessary maximal excellence.
In the final version, they are taken as equivalent, but, this is not to couch maximal greatness in terms of necessary maximal excellence, they are logically equivalent, nothing more follows from it.
Furthermore, Maximal greatness in the MOA is a universal property, meaning if it is not co-exemplified it is necessary that it is not, and, if it is co-exemplified it is necessary that it is, It is this that is most fundamental when it comes to these concepts, the universality of the essential propery of maximal greatness, thus, my comment on AP3 begging the question against necessary metaphysical or broadly logical truths.
Posted by: Arnold T. Guminski
« on: November 27, 2016, 07:12:42 PM »Ontologicalme raises a couple of issues in his reply post. He writes:
AP3 begs the question against necessary truths, or/and it is a non sequitur, since it is true that possible worlds can be formed by the negation of different conjuncts in a maximal description, but this does not imply that it must be the negation of each and every conjunct, some conjuncts staty the same, while others are negated.
There is a possible world where 2+2=4 , but, possible worlds can be formed by the negation of different conjuncts in a maximal description, so it is possible that it is not the case that 2+2=4 .
What reasons are there to accept that it is possible that it is not the case that 2+2=4?
AP3 reads: "IIf a maximally excellent being exists in some possible world and since possible worlds can be formed by the negation of different conjuncts in a maximal description, then a maximally excellent being does not exist in some (other) possible world." I do not see why AP3 begs the question against necessary truths because, in the first place, the ontological argument concerns itself with concrete entities, and not with abstract entities (e.g., numbers) and their logical or mathematical relations. Moreover, while it is verbally possible to assert that the proposition that 2+2=4 is false in some logically possible worlds, Plantinga, Craig, and your truly would maintain that because this assertion is a negation of a logically necessary truth it is, therefore, logically necessarily false. Next, the notion of a maximally excellent being is patently logically coherent and is analytically prior to the notion of a maximally great being. The RF video fails to mention that Craig in his writings defines a maximally great being in terms of a maximally excellent being (i.e., that a maximally great being is a maximally excellent being that exists in all possible worlds). Finally, AP3 conforms to the definitions and basic rules pertaining to possible worlds semantics (as expounded by Plantinga and Craig), as the reader of my essay ("A Critique of the Plantinga Version of the Modal Ontological Argument" [available at http://infidels.org/library/modern/arnold_guminski/]).
AP3 begs the question against necessary truths, or/and it is a non sequitur, since it is true that possible worlds can be formed by the negation of different conjuncts in a maximal description, but this does not imply that it must be the negation of each and every conjunct, some conjuncts staty the same, while others are negated.
There is a possible world where 2+2=4 , but, possible worlds can be formed by the negation of different conjuncts in a maximal description, so it is possible that it is not the case that 2+2=4 .
What reasons are there to accept that it is possible that it is not the case that 2+2=4?
AP3 reads: "IIf a maximally excellent being exists in some possible world and since possible worlds can be formed by the negation of different conjuncts in a maximal description, then a maximally excellent being does not exist in some (other) possible world." I do not see why AP3 begs the question against necessary truths because, in the first place, the ontological argument concerns itself with concrete entities, and not with abstract entities (e.g., numbers) and their logical or mathematical relations. Moreover, while it is verbally possible to assert that the proposition that 2+2=4 is false in some logically possible worlds, Plantinga, Craig, and your truly would maintain that because this assertion is a negation of a logically necessary truth it is, therefore, logically necessarily false. Next, the notion of a maximally excellent being is patently logically coherent and is analytically prior to the notion of a maximally great being. The RF video fails to mention that Craig in his writings defines a maximally great being in terms of a maximally excellent being (i.e., that a maximally great being is a maximally excellent being that exists in all possible worlds). Finally, AP3 conforms to the definitions and basic rules pertaining to possible worlds semantics (as expounded by Plantinga and Craig), as the reader of my essay ("A Critique of the Plantinga Version of the Modal Ontological Argument" [available at http://infidels.org/library/modern/arnold_guminski/]).
Posted by: ParaclitosLogos
« on: November 23, 2016, 09:00:55 PM »AP3 begs the question against necessary truths, or/and it is a non sequitur, since it is true that possible worlds can be formed by the negation of different conjuncts in a maximal description, but this does not imply that it must be the negation of each and every conjunct, some conjuncts staty the same, while others are negated.
There is a possible world where 2+2=4 , but, possible worlds can be formed by the negation of different conjuncts in a maximal description, so it is possible that it is not the case that 2+2=4 .
What reasons are there to accept that it is possible that it is not the case that 2+2=4?
Posted by: Arnold T. Guminski
« on: November 03, 2016, 07:12:56 PM »1. I promised in my May 23, 2016 post to provide a summary of my critique of the Plantinga Modal Ontological Argument (PMOA) (as further expounded and advocated by William Lane Craig) in the near future; but have thus far failed to do so. Alas! How fast time flies. However, I am now prodded to provide the promised summary after having viewed and studied the reasonablefaith video “The Ontological Argument.”
2. The video’s argument begins with the declaration that If it is logically possible that God exists, then it follows logically that God exists. The video proceeds to define “God” as the “maximally great being” (hereafter. MGB). MGB is a being that is maximally powerful, maximally knowing, and morally perfect in all possible worlds. Possible worlds are ways in which the world could have been. Thus, for example, a world in which unicorns exist is logically possible even though this world is not actual. And, on the other hand, this our actual world is but one of many logically possible worlds.
3. The video sets forth the ontological argument as follows:
(1) it is possible that a MGB exists.
(2) A MGB exists in some possible world.
(3) If a MGB exists in some possible world, then it exists in every possible world.
(4) If a MGB exists in every possible world, then it exists in the actual world.
(5) A MGB exists in the actual world.
(6) Therefore, a MGB exists.
It is important to keep in mind that what the video means by the term possible world is a logically possible world.
4. The video declares that the idea of a MGB, unlike that of an unmarried bachelor, is logically coherent. However, it acknowledges that if the idea of a MGB is logically incoherent then the argument fails. The video shows why parodies of the ontological argument such as the maximally great pizza are logically incoherent in that no such or similar hypothesized maximally great being exists in all possible worlds.
5. Interestingly, the video does not follow Craig’s general practice followed in his writings apropos the PMOA to first define a maximally excellent being (hereafter MEB) as a being that is maximally powerful and knowing, and morally perfect; and then to define a MGB as a MEB that exists in all possible worlds. To define, as the video does, “God” as the MGB is not analytically or even, in the long view, polemically useful. This practice is annoying and distracting because there are many theologically conservative Christians and other Theists who deny or question that a MGB exists because the notion of MGB is logically incoherent. And, furthermore, there are some those who deny or question that “God” defined as a MEB actually exists but who do not deny that the notion of a MEB is logically coherent in the sense that this being exists in some possible world.
6. The denial of the existence of a MGB does not entail the denial of the existence of a MEB in some logically possible worlds. To affirm that “God,” defined as the MEB, exists in the actual world but not in all possible worlds is consistent with the notion that this being is factually necessary (i.e., given that God (i.e., the MEB) exists, it is impossible that this being ever came into or will go out of existence because he is uncaused, eternal, incorruptible, and indestructible. (See, e.g.,Craig, “Doctrine of God (part 3) 1. Attributes of God” --http://www.reasonablefaith.org/defenders-2-podcast/transcript/s3-3);
7. The video concludes with the declaration that since it is logically possible that God (i. e., the MGB) exists then God actually exists. But is the notion of a MGB logically incoherent? Needless to say, there is much disagreement about whether the proposition (1) above (i.e., it is possible that a MGB exists) is true. The PMOA, as expounded by Plantinga and Craig, as a stand-alone argument or otherwise, is plausible (if not persuasive) if and only if the notion of a MGB is logically coherent.
8. In my essay, “A Critique of the Plantinga Version of the Modal Ontological Argument” (2016) (accessible at http://infidels.org/library/modern/arnold_guminski/plantinga.html), I present the following argument designed to show that the PMOA is fatally flawed. My anti-PMOA argument is as follows:
AD1. A possible world is a maximal description of reality or a way reality might conceivably but not factually be. [Citation omitted.]
AD2. Only one of these descriptions will be composed of conjuncts all of which are true and so will be the way reality actually is, that is to say, the actual world. [Citation omitted.]
AD3. The possible conjuncts which a possible world W comprises must be capable of being true in W both individually and together. [Citation omitted.]
AD4. A possible world is a conjunction which comprises every proposition or its contradictory, so that it yields a maximal description of reality such that nothing is left out of such a description. [Citation omitted.]
AD5. Different possible worlds are formed by negating different conjuncts in a maximal description. [Citation omitted.] (This proposition is to be understood as meaning that any candidate maximum description is composed are conjuncts capable of being true both individually and together since there will be cases in which a negation of a proposition in W entails the negation of other propositions in W.)
AD6. A maximally excellent being is a being with such excellent-making properties as omnipotence, omniscience, and moral perfection. [Citation omitted.]
AD7. A maximally great being is a maximally excellent being that exists in every possible world. ([Citation omitted.] (This proposition should be understood as meaning that if a particular entity is a maximally excellent being in any one possible world then it is also maximally excellent in all possible worlds In which it exists.)
AP1. A maximally excellent being exists in some possible world.
AP2. A possible world can be formed by the negation of different conjuncts in maximal description.
AP3. If a maximally excellent being exists in some possible world and since possible worlds can be formed by the negation of different conjuncts in a maximal description, then a maximally excellent being does not exist in some (other) possible world.
AP4. A maximally excellent being does not exist in some possible world. (AP1, AD5.)
AP5. If a maximally excellent being does not exist in some possible world, then a maximally excellent being does not exist in all possible worlds. (AD5, AP1, AP2)
AP6. A maximally excellent being does not exist in all possible worlds.
AP7. If a maximally excellent being does not exist in all possible worlds, then a maximally great being does not exist in the actual world.
AP8. A maximally great being does not exist in the actual world. (This proposition contradicts [proposition 5 of the Video version of the ontological argument which that states that a MGB exists in the actual world].)
9. As I explain in my essay (note omitted):
“The critical steps in the argument are AP2-AP4 since AP2 involves a negation of the relevant conjunct of the possible world mentioned in AP1. The proposition in the PMOA that it is possible that a maximally great being exists … presupposes the proposition that a maximally excellent being exists in some possible world. Indeed, the notion of a maximally great being is defined in terms pertaining to the notion of a maximally excellent being. Thus the negation in AP2 of the conjunct of the possible world mentioned in AP1 is analytically prior to determining whether the notion of a maximally great being is admissible based on PWS [Possilbe World Semantics] conditions. The anti-PMOA-argument confirms the widely held view that there is something rather piscatorial about the PMOA in that it fails to explicitly include in the argument relevant equivalents of AD1-AD5. My conclusion is that [the proposition that a MGB exists in some possible world, although perhaps prima facie coherent, turns out nevertheless to be radically defective because it is not a well-formed statement in terms of PWS. Despite appearances, a maximally great being is not really possible after all—it is not really coherent after all.”
Otherwise and more briefly stated, the intuition that a MEB does not exist in some possible world has analytic and epistemic priority over any intuition that a MGB exists in some possible world. For this reason, we must conclude that the notion of a MGB is logically incoherent.
10. I insert here one compelling argument which can be viewed as independently showing why the PMOA is fatally flawed. The argument goes as follows:
“Other rival candidate premises would be those in which the relevant differences pertain to constitutive matters with respect to G-CMEB i.e., God conceived as a MEB]. Thus, for example, one such candidate would be a G-CMEB described as one unipersonal spiritual being within the context of historical Unitarianism and Arianism. The complementary, or rather competing, candidate would be a G-CMEB described as tripersonal, unisubstantial spiritual being. The standard Christian doctrine of the Trinity is that officially professed by the Roman Catholic, Eastern Orthodox, and historical and mainline Protestant Churches. According to this doctrine, there are three persons in Godhead, i.e., the Father, the Son, and the Holy Spirit. Each person is really distinct from the other two yet consubstantial (i.e., the three persons having the numerically one divine essence, substance, or nature. Thus the Father is God; the Son is God; and the Holy Spirit is God; but there are not three God's but one God.[n.8] Thus we have two additional analogs to [the proposition that it is possible that a maximally great being exists].: (1) It is possible that the unipersonal G-CMGB [i.e., God conceived as a MGB] exists and (2) It is possible that the tripersonal G-CMGB exists. In which case, it ultimately follows that both the unipersonal G-CMGB and the tripersonal G-CMGB actually exist—which conjunction involves a manifest contradiction in excelsis (in the highest degree).
[note 8. Here I assume that a tripersonal, unisubstantial maximally excellent being is broadly logically possible. Recall that the standard opinion among theologically conservative, Trinitarian Christians is that we can only know, or reasonably believe, that God is unisubstantial and tripersonal by virtue of the deliverances of supernatural (i.e., special) revelation.]”
11. I invite the reader to read my essay in its entirety for other matters which I present as supporting my principal argument why the PMOA implodes. The prospect is quite tantalizing. Showing that the notion of a maximally great being is logically incoherent is but a skip and a hop from showing that the Stephen T. Davis—William Lane Craig version of the Leibnizian cosmological argument from contingency also implodes.
2. The video’s argument begins with the declaration that If it is logically possible that God exists, then it follows logically that God exists. The video proceeds to define “God” as the “maximally great being” (hereafter. MGB). MGB is a being that is maximally powerful, maximally knowing, and morally perfect in all possible worlds. Possible worlds are ways in which the world could have been. Thus, for example, a world in which unicorns exist is logically possible even though this world is not actual. And, on the other hand, this our actual world is but one of many logically possible worlds.
3. The video sets forth the ontological argument as follows:
(1) it is possible that a MGB exists.
(2) A MGB exists in some possible world.
(3) If a MGB exists in some possible world, then it exists in every possible world.
(4) If a MGB exists in every possible world, then it exists in the actual world.
(5) A MGB exists in the actual world.
(6) Therefore, a MGB exists.
It is important to keep in mind that what the video means by the term possible world is a logically possible world.
4. The video declares that the idea of a MGB, unlike that of an unmarried bachelor, is logically coherent. However, it acknowledges that if the idea of a MGB is logically incoherent then the argument fails. The video shows why parodies of the ontological argument such as the maximally great pizza are logically incoherent in that no such or similar hypothesized maximally great being exists in all possible worlds.
5. Interestingly, the video does not follow Craig’s general practice followed in his writings apropos the PMOA to first define a maximally excellent being (hereafter MEB) as a being that is maximally powerful and knowing, and morally perfect; and then to define a MGB as a MEB that exists in all possible worlds. To define, as the video does, “God” as the MGB is not analytically or even, in the long view, polemically useful. This practice is annoying and distracting because there are many theologically conservative Christians and other Theists who deny or question that a MGB exists because the notion of MGB is logically incoherent. And, furthermore, there are some those who deny or question that “God” defined as a MEB actually exists but who do not deny that the notion of a MEB is logically coherent in the sense that this being exists in some possible world.
6. The denial of the existence of a MGB does not entail the denial of the existence of a MEB in some logically possible worlds. To affirm that “God,” defined as the MEB, exists in the actual world but not in all possible worlds is consistent with the notion that this being is factually necessary (i.e., given that God (i.e., the MEB) exists, it is impossible that this being ever came into or will go out of existence because he is uncaused, eternal, incorruptible, and indestructible. (See, e.g.,Craig, “Doctrine of God (part 3) 1. Attributes of God” --http://www.reasonablefaith.org/defenders-2-podcast/transcript/s3-3);
7. The video concludes with the declaration that since it is logically possible that God (i. e., the MGB) exists then God actually exists. But is the notion of a MGB logically incoherent? Needless to say, there is much disagreement about whether the proposition (1) above (i.e., it is possible that a MGB exists) is true. The PMOA, as expounded by Plantinga and Craig, as a stand-alone argument or otherwise, is plausible (if not persuasive) if and only if the notion of a MGB is logically coherent.
8. In my essay, “A Critique of the Plantinga Version of the Modal Ontological Argument” (2016) (accessible at http://infidels.org/library/modern/arnold_guminski/plantinga.html), I present the following argument designed to show that the PMOA is fatally flawed. My anti-PMOA argument is as follows:
AD1. A possible world is a maximal description of reality or a way reality might conceivably but not factually be. [Citation omitted.]
AD2. Only one of these descriptions will be composed of conjuncts all of which are true and so will be the way reality actually is, that is to say, the actual world. [Citation omitted.]
AD3. The possible conjuncts which a possible world W comprises must be capable of being true in W both individually and together. [Citation omitted.]
AD4. A possible world is a conjunction which comprises every proposition or its contradictory, so that it yields a maximal description of reality such that nothing is left out of such a description. [Citation omitted.]
AD5. Different possible worlds are formed by negating different conjuncts in a maximal description. [Citation omitted.] (This proposition is to be understood as meaning that any candidate maximum description is composed are conjuncts capable of being true both individually and together since there will be cases in which a negation of a proposition in W entails the negation of other propositions in W.)
AD6. A maximally excellent being is a being with such excellent-making properties as omnipotence, omniscience, and moral perfection. [Citation omitted.]
AD7. A maximally great being is a maximally excellent being that exists in every possible world. ([Citation omitted.] (This proposition should be understood as meaning that if a particular entity is a maximally excellent being in any one possible world then it is also maximally excellent in all possible worlds In which it exists.)
AP1. A maximally excellent being exists in some possible world.
AP2. A possible world can be formed by the negation of different conjuncts in maximal description.
AP3. If a maximally excellent being exists in some possible world and since possible worlds can be formed by the negation of different conjuncts in a maximal description, then a maximally excellent being does not exist in some (other) possible world.
AP4. A maximally excellent being does not exist in some possible world. (AP1, AD5.)
AP5. If a maximally excellent being does not exist in some possible world, then a maximally excellent being does not exist in all possible worlds. (AD5, AP1, AP2)
AP6. A maximally excellent being does not exist in all possible worlds.
AP7. If a maximally excellent being does not exist in all possible worlds, then a maximally great being does not exist in the actual world.
AP8. A maximally great being does not exist in the actual world. (This proposition contradicts [proposition 5 of the Video version of the ontological argument which that states that a MGB exists in the actual world].)
9. As I explain in my essay (note omitted):
“The critical steps in the argument are AP2-AP4 since AP2 involves a negation of the relevant conjunct of the possible world mentioned in AP1. The proposition in the PMOA that it is possible that a maximally great being exists … presupposes the proposition that a maximally excellent being exists in some possible world. Indeed, the notion of a maximally great being is defined in terms pertaining to the notion of a maximally excellent being. Thus the negation in AP2 of the conjunct of the possible world mentioned in AP1 is analytically prior to determining whether the notion of a maximally great being is admissible based on PWS [Possilbe World Semantics] conditions. The anti-PMOA-argument confirms the widely held view that there is something rather piscatorial about the PMOA in that it fails to explicitly include in the argument relevant equivalents of AD1-AD5. My conclusion is that [the proposition that a MGB exists in some possible world, although perhaps prima facie coherent, turns out nevertheless to be radically defective because it is not a well-formed statement in terms of PWS. Despite appearances, a maximally great being is not really possible after all—it is not really coherent after all.”
Otherwise and more briefly stated, the intuition that a MEB does not exist in some possible world has analytic and epistemic priority over any intuition that a MGB exists in some possible world. For this reason, we must conclude that the notion of a MGB is logically incoherent.
10. I insert here one compelling argument which can be viewed as independently showing why the PMOA is fatally flawed. The argument goes as follows:
“Other rival candidate premises would be those in which the relevant differences pertain to constitutive matters with respect to G-CMEB i.e., God conceived as a MEB]. Thus, for example, one such candidate would be a G-CMEB described as one unipersonal spiritual being within the context of historical Unitarianism and Arianism. The complementary, or rather competing, candidate would be a G-CMEB described as tripersonal, unisubstantial spiritual being. The standard Christian doctrine of the Trinity is that officially professed by the Roman Catholic, Eastern Orthodox, and historical and mainline Protestant Churches. According to this doctrine, there are three persons in Godhead, i.e., the Father, the Son, and the Holy Spirit. Each person is really distinct from the other two yet consubstantial (i.e., the three persons having the numerically one divine essence, substance, or nature. Thus the Father is God; the Son is God; and the Holy Spirit is God; but there are not three God's but one God.[n.8] Thus we have two additional analogs to [the proposition that it is possible that a maximally great being exists].: (1) It is possible that the unipersonal G-CMGB [i.e., God conceived as a MGB] exists and (2) It is possible that the tripersonal G-CMGB exists. In which case, it ultimately follows that both the unipersonal G-CMGB and the tripersonal G-CMGB actually exist—which conjunction involves a manifest contradiction in excelsis (in the highest degree).
[note 8. Here I assume that a tripersonal, unisubstantial maximally excellent being is broadly logically possible. Recall that the standard opinion among theologically conservative, Trinitarian Christians is that we can only know, or reasonably believe, that God is unisubstantial and tripersonal by virtue of the deliverances of supernatural (i.e., special) revelation.]”
11. I invite the reader to read my essay in its entirety for other matters which I present as supporting my principal argument why the PMOA implodes. The prospect is quite tantalizing. Showing that the notion of a maximally great being is logically incoherent is but a skip and a hop from showing that the Stephen T. Davis—William Lane Craig version of the Leibnizian cosmological argument from contingency also implodes.