A standard objection to traditional arguments for God is that even if the arguments were successful, they fail to prove that there is just ONE god, leaving open the possibility that polytheism is true, and that monotheism is false.  In Phase 5 of his case for God in When Skeptics Ask (hereafter: WSA), Dr. Norman Geisler presents an argument that is intended to deal with this standard objection:

We have said that God is all-powerful, all-knowing, all-good, inifinite, uncreated, unchanging, eternal, and omnipresent.  But how many beings like that can there be?  He is a class of one by definition.  If there were two unlimited beings, how could you tell them apart?…There can only be one infinite Being and no other.  (WSA, p.28)

The question Geisler poses is clearly a rhetorical one.  It is just a way of asserting this claim:

If there were two unlimited beings, then we could not tell them apart.

There is also an unstated assumption that connects this idea to the conclusion that Geisler seeks to establish.  I have made that assumption explicit in my statement of this argument, as premise (104):

Argument of Phase 5

100.  There is at least one being that is eternal, omnipotent, omniscient, and perfectly morally good.

101.  A being X is an unlimited being IF and ONLY IF being X is eternal, omnipotent, omniscient, and perfectly morally good.

THEREFORE:

102. There is at least one unlimited being.

103.  If being A is an unlimited being and being B is an unlimited being, then we cannot tell being A apart from being B.

104. If we cannot tell being A apart from being B, then being A is the very same being as being B.

THEREFORE:

105. If being A is an unlimited being and being B is an unlimited being, then being A is the very same being as being B.

THEREFORE:

106.  There is at most just one unlimited being.

102. There is at least one unlimited being.

THEREFORE:

107.  There is exactly one unlimited being.

Premise (100) is dubious for many reasons, so this argument rests on a very shaky foundation.  Premise (100) is based on many of the preceding unsound arguments put forward by Geisler, and it has at least these problems: Geisler has failed to show that there is any eternal being, any omnipotent being, any omniscient being, and any perfectly morally good being, and Geisler has also failed to show that there is any eternal omnipotent being, any eternal omniscient being, and any eternal perfectly morally good being, and Geisler has failed to show that there is any being that is both omnipotent and omniscient, and any being that is both omnipotent and perfectly morally good, and any being that is both omniscient and perfectly morally good, etc.  Geisler has failed to establish each and every element of this claim.  His failure could not be any more complete or absolute.

The Phase 5 argument ought to be rejected simply because it rests on premise (100), but there are other problems as well.

The two other key premises of this argument are (103) and (104):

103.  If being A is an unlimited being and being B is an unlimited being, then we cannot tell being A apart from being B.

104. If we cannot tell being A apart from being B, then being A is the very same being as being B.

If these two premises were true, the rest of the argument would be solid, because the logic is correct (assuming that the phrase “we cannot tell being A apart from being B” means the same thing in both of these premises,  so that this argument does not involve the fallacy of equivocation).

Premise (103) appears to be FALSE.  The fact that two being have the same degree of duration, power, knowledge, and moral goodness does NOT make it impossible to tell the two beings apart from each other.  For example, if one being was green all over, and the other being was red all over, then we could tell the beings apart by their color.  Duration, power, knowledge, and moral goodness are NOT the only attributes or characteristics that can be used to identify a being, or to distinguish one being from another.

It might be objected that physical attributes like color, shape, size, and weight do not apply to a being that is omnipotent and omniscient, since such a being would also be omnipresent, and thus would NOT have a specific location in space.

But other attributes or characteristics could be used to distinguish two unlimited beings.  For example, if being A was an unlimited being who created the universe and being B was an unlimited being who did NOT create the universe, then we could distinguish between being A and being B by the fact that one created the universe and the other did not.  Therefore, premise (103) is false, and we ought to reject the Phase 5 argument for this reason too, in addition to the highly dubious foundational premise (100).

Furthermore, premise (103) appears to be analogous to a claim which most Christians are bound to reject:

103A.  If person A is an unlimited being and person B is an unlimited being, then we cannot tell person A apart from person B.

This assertion implies that we cannot tell Jesus (the Son of God) apart from God the Father.  The Christian doctrine of the Trinity includes the claim that Jesus and God the Father are two distinct persons, that they are persons that we can tell apart.  But the doctrine of the Trinity also teaches that Jesus the Son of God is an unlimited being, and that God the Father is an unlimited being.  The assertion (103A) contradicts the doctrine of the Trinity, and thus most Christians would have to reject (103A), in order to accept the doctrine of the Trinity and to avoid this logical contradiction in their beliefs.  Since most Christians are bound to reject (103A), and since (103A) appears to be analogous to premise (103), this casts significant doubt on (103), from a Christian point of view.

Premise (104) also appears to be FALSE.  If we understand the phrase “we cannot tell being A apart from being B” in a straightforward and literal way, then this premise makes the nature of reality dependent upon our limited and finite human cognitive abilities.  But this makes no sense.  An ant cannot understand algebra or calculus or  the laws of chemistry and physics, but that does not mean that there are no such things as the laws of chemistry and the laws of physics; it only means that there are aspects of reality that humans can understand and perceive that ants cannot understand or perceive.  So, if a human being can distinguish one substance A from another substance B by analyzing the chemical structure of both substances, and if an ant is unable to tell substance A apart from substance B, it does not follow that substance A is there very same substance as substance B.

Similarly, if limited finite human minds cannot tell unlimited being A apart from unlimited being B, that might simply be the result of our human inability to understand and perceive some real difference that exists between being A and being B.  So, the fact that humans are unable to tell apart being A and being B does NOT prove that there are no actual differences between these beings.  There could be real differences that human beings are unable to detect or discern.  The limitations of our human minds do not constrain the nature of reality; they only constrain what we humans are able to understand and perceive about reality.

Furthermore, this common-sense assumption is one that every Christian must accept, because Christian theology teaches that God is real but that the God’s nature transcends limited finite human minds: human beings cannot completely understand and perceive God’s nature.  Thus, Christian theology assumes the view that our human minds are limited and finite and that the limitations of our minds do NOT constrain the nature of reality; they only constrain what we humans are able to understand and pereceive about reality.

Premise (104) could be modified, in order to eliminate the subjectivist view that it presupposes:

104A. If there is no attribute of being A (including the lack of an attribute) that differs from the attributes of being B, then being A is the very same being as being B.

This is basically Leibniz’s principle of “the idenity of indiscernibles”:

The Identity of Indiscernibles is a principle of analytic ontology first explicitly formulated by Wilhelm Gottfried Leibniz in his Discourse on Metaphysics, Section 9 (Loemker 1969: 308). It states that no two distinct things exactly resemble each other. This is often referred to as ‘Leibniz’s Law’ and is typically understood to mean that no two objects have exactly the same properties. (from the opening paragraph of “The Identity of Indiscernibles” in Stanford Encyclopedia of Philosophy)

On this interpretation, this second premise is much more plausible, but then premise (103) would need to be modified in a similar manner:

103B. If being A is an unlimited being and being B is an unlimited being, then no attribute of being A (including the lack of an attribute) differs from the attributes of being B. 

Given this modification of premise (103) it is even more clear that this premise is FALSE, because “unlimited being” implies only attributes related to duration, power, knowledge, and moral goodness, and it is clearly the case that there are many other attributes that a being can have besides those (e.g.  a being could be the creator of the universe).  So, if we modify premise (104) to eliminate the subjectivist presupposition (which constrains the nature of reality based upon the limitations of human cognition), that does make (104) more plausibly true, but it also makes premise (103) more certainly false (because of the necessary analogous modification to that premise).

In conclusion, the Phase 5 argument FAILS.  Premise (100) is based on several dubious claims, none of which Geisler has shown to be true, premise (103) appears to be false, and premise (104) is dubious because it is based on a subjectivist presupposition. If we modify (104) to eliminate the subjectivist presupposition, then premise (103) must be similarly modified, making it even more certain that premise (103) is FALSE.  This argument is based on a highly dubious premise (100) and a false premise (103), so this argument FAILS, like every other argument in Geisler’s case for God.

===============

UPDATED 5/21/17

In the above post, I clarified and simplified Geisler’s somewhat unclear concept of an “unlimited being”.  There are, however, other possible interpretations of this concept that are suggested by specific comments that Geisler makes in WSA.  So, to be fair to Geisler we should briefly consider these alternative interpretations of this concept, to see whether that helps to strengthen his Phase 5 argument.

The “whatever He has” Definition

In Phase 4 when Geisler is arguing that “God” (i.e. the cause of the beginning of the universe) has unlimited power, unlimited knowledge, and unlimited moral goodness, he hints at a specific meaning of the concept of an “unlimited being”:

Because of His necessity, He can only have whatever He has in a necessary way.  That means, as we have seen, without beginning, without change, and without limitation.  (WSA, p.28)

Geisler is here assuming that there is a cause of the beginning of the universe, and that this cause is a “necessary being”, and from these assumptions he infers that this being (which he mistakenly and confusingly refers to as “God”, once again demonstrating the great unclarity of his thinking) “has whatever He has” in a way that is “without limitation”.  Here is a definition of “unlimited being” based on the above quote:

101A.  A being X is an unlimited being IF and ONLY IF all of the attributes that being X has are had by X in an unlimited way.

Would this interpretation of premise (101) help the argument of Phase 5?  The inference from (100) combined with (101) would no longer work, so this change damages the initial inference in his argument.  However, an alternative premise to (100) would fix that inference:

100A. There is at least one being that is such that all of the attributes that being has are had by that being in an unlimited way.

Geisler thinks that he has shown that there is a “necessary being” (though he has not shown this) and he thinks that a necessary being has all of its attributes in an unlimited way (though he has not shown this either), so Geisler would agree to (100A) and think that he has shown (100A) to be true.  Since Geisler has NOT shown the assumptions that (100A) is based on to be true, (100A) remains dubious, just like (100), so this does not improve his initial inference/argument that is part of the Phase 5 argument, but it also does not damage that initial inference/argument either, at least not in an obvious way.

There are some reasons, however, to doubt that a being that has unlimited power, unlimited knowledge, and unlimited moral goodness can exist.  The problem is that these “attributes” can step on each other’s toes.  In other words, when some attribute is thought of as being unlimited, it tends to constrain and restrict other attributes of the being in question.

If we think of unlimited power, this implies the power to do evil.  But the God of Christianity is supposed to be perfectly morally good, so God cannot do evil.  In other words, the perfect or unlimited moral goodness of God creates a constraint or limitation on what God can do; it creates a limitation on God’s power.

If a being has unlimited knowledge, then the being knows infallibly every detail of every event that is going to happen in the future, but in that case the being in question does NOT have free will, because it knows infallibly in advance every detail about every choice and every action it will ever perform prior to making those choices and performing those actions.  This is possible only if those choices and actions are pre-determined, only if those choices and actions are NOT free.  But such a being cannot be a perfectly morally good being, cannot be a being of unlimited moral goodness, because a being that lacks free will cannot be a morally good being at all, let alone have unlimited moral goodness.  Thus, unlimited knowledge does not merely constrain a being’s moral goodness, it eliminates the very possiblity of moral goodness.

So, one serious problem with (100A) is that it can be used as the basis for showing that Geisler’s concept of “God” (i.e.  an “unlimited being” that has the attributes of power, knowledge, and moral goodness) is incoherent and contains logical contradictions, and thus does not and cannot exist.

This alternative definition leaves my previous objections to (103) untouched, and also creates the opening for at least one additional objection to (103).  On the definition of “unlimited being” in (101A), we can have the following two examples of an “unlimited being”:

• Unlimited being A has unlimited size but no weight.
• Unlimited being B has unlimited weight but no size.

These two beings have the attributes they have in an unlimited way, but they have different attributes, so we can tell them apart.  The really big being is A, and the really heavy being is B.  So, the definition in (101A) provides an additional reason to doubt premise (103).

Premise (104) does not mention the concept of an “unlimited being” so the alternative definition does not change the meaning of premise (104), and I don’t see any impact on my objections and comments about premise (104), so the definition given in (101A) does not help or damage Geisler’s argument in relation to (104).

I conclude that the alternative definition in (101A) does NOT help strenghen the argument of Phase 5, and it does appear to create the potential for some additional objections.

The “unlimited in His perfections” Definition

After Geisler presents his case for God, he considers various objections that might be raised.  One of the objections relates to the concept of an “unlimited being”, and Geisler’s response indicates another possible interpretation of the term:

When we say that God is unlimited, we mean that He is unlimited in His perfections.  Now evil is not a perfection; it is an imperfection.  The same is true of nonexistence, weakness, ignorance…and any other characteristic that implies limitation or imperfection.  (WSA, p.31)

If we take Geisler to be explaining what he means by an “unlimited being”, then this quote can be used as the basis for an alternative definition of that phrase:

101B.  A being X is an unlimited being IF and ONLY IF all of the perfections that being X has are had by X in an unlimited way.

Since power, knowledge, and moral goodness are considered to be “perfections”, an unlimited being that has those attributes would have them in an unlimited way, according to the definition in (101B).

Once again, this modification of premise (101) makes it so the inference from (100) and (101B) is logically invalid.  However, we can modify premise (100) to fix the inference:

100B. There is at least one being that is such that all of the perfections that being has are had by that being in an unlimited way.

This premise may be more difficult to establish than the original premise (100), because showing that there is a being that has unlimited power, unlimited knowledge, and unlimited moral goodness would NOT be sufficent to establish that there is a being such that ALL of the perfections of that being were unlimited.  One would have to either show that the being in question had no other perfections besides power, knowledge, and moral goodness (which is NOT the case with God, according to Geisler and Christian theology) or one would need to somehow show that all of the other perfections possessed by the being in question were also possessed by that being in an unlimited way.

On the other hand, it may be easier to establish (100B) than the original premise (100), because one does not have to prove the existence of a being that has unlimited power, unlimited knowledge, and unlimited moral goodness, in order to establish (100B).  One only needs to show that a being with one or two perfections of some sort or other had that perfection or those two perfections to an unlimited degree.  I cannot think of any examples of such a being off the top of my head, but with some effort someone might well be able to come up with an example of such a being.

In any case (100B) currently remains as dubious and as unproven as premise (100).

How would the alternative definition in (101B) impact premise (103)?  Premise (103) would clearly be FALSE given the definition of an “unlimited being” in (101B), because this definition only requires that a being’s perfections are all unlimited; it does not require that a being have many perfections or any particular perfections.  So, this creates the potential for the existence of a wide variety of unlimited beings, each having a different perfection or different set of perfections.  We could tell such beings apart on the basis of the specific perfection or set of perfections possessed by that being.  Thus, the definition in (101B) does not help strengthen Geisler’s argument in relation to premise (103).

Since premise (104) does not use the phrase “unlimited being”, changing the definition of that phrase does not change the meaning of premise (104). My objection to premise (104) is not affected by this change in the definition of “unlimited being”.

If we use the modified premise (104B), which avoids the subjectivist presupposition, then premise (103) would need to be modified in a similar way to logically connect with (104B):

103B. If being A is an unlimited being and being B is an unlimited being, then no attribute of being A (including the lack of an attribute) differs from the attributes of being B. 

Given the alternative definition of “unlimited being” in (101B), it seems fairly clear that (103B) is FALSE.  The alternative definition does not require a being to have more than one perfection, or to have any particular perfection, so we can consider all kinds of possible examples of unlimited beings with just one or two perfections of various different perfections in various combinations, so it seems highly unlikely that we would be unable to come up with two examples of beings with different perfections, and where “all” of those perfections were possessed in an unlimited way.  If the two unlimited beings had either different perfections or a different combination of perfections, the at least one attribute of the first being would differ from the attributes of the second being, making (103B) false.

I conclude that modifying premise (101) to (101B) would not strengthen Geisler’s argument for Phase 5.

Neither of these two alternative definitions of an “unlimited being” helps to strengthen the argument for Phase 5, so my previous conclusion still stands: the Phase 5 argument FAILS, just like every other argument in Geisler’s case for God.