Attempted Refutation of the possibility of the god described in traditional monotheism using several reductiones ad absurdum

Comments welcomed as to whether this works or not.

Introduction

The monotheisms of Christianity, Judaism and Islam all claim that there is a being that is eternal, immaterial, infinite in presence, omniscient, omnipotent, perfect and (as a bonus) benevolent and who is the greatest being possible such that it is "that than which nothing greater can be thought" [1]. This being is given the name God, a word that is almost universally accepted as perfectly synonymous with the above mentioned attributes.

This definition of "God" will be adopted here for purposes of analysis of some of the claims of theism. When the word God is written it will be understood to refer to the boundless, perfect and benevolent being described by monotheisms, and not to the idea of a divinity in general (for example a Greek or Egyptian God), which in many cases is little better than a mortal.

The several reductiones ad absurdum to follow will show that such a god - that is, a necessary (eternal) , non-physical (immaterial), plenistic (everywhere & infinite in presence), almighty (omniscient & omnipotent) [2], perfect (symmetrical) and good (benevolent) being - is impossible both metaphysically and physically, and that only finite contingent beings are possible (such beings being readily observable and well known facts about the world).

The subsequent argumentation is offered in the spirit of that which Guanillo once offered his refutation St Anselm's Ontological Argument for the Existence of God, by replying to him under the guise of a fool. St Anselm (1033-1109) as everyone will recall, was "the outstanding Christian philosopher and theologian of the eleventh century", where as Guanillo was the outstanding Fool of the same period. For more on this fascinating exchange visit the Stanford Encyclopedia of Philosophy article on St Anselm and his Ontological Argument.

Negation 1

Proposition N1: There is a being, God, who is an almighty, necessary being "that than which nothing greater can be thought" (St Anselm, Proslogion).

Reductio 1:

1. There is an almighty necessary being who is the greatest being possible
2. An almighty being can do absolutely anything [definition of almightiness]
3. An almighty being can cause itself to cease existing [an example of almightiness]
4. Necessary beings are uncaused and exist eternally without beginning or end [definition of necessary being]
5. Therefore, there are no almighty, necessary beings [contradiction of premise 3 by premise 4]

Reductio 1 shows that God cannot be both an almighty and a necessary being since these attributes cannot coherently co-exist because, as seen, they lead to a contradiction. The existential condition (or "existential nature”) necessary existence and the predicate almighty are mutually exclusive. An object that embodies an existential nature of necessary existence is prohibited a priori from ever possessing the attribute of almightiness[3].

Reductio 1 shows that Proposition N1 is false. That is to say that a being that is both almighty and necessary is metaphysically (logically) impossible, from which it follows that such a being is also physically impossible. But this is all that N1 confirms explicitly and it does not deny the possibility of either a necessary non-almighty being, or a contingent almighty being.

Reductio 1 in fact apparently allows that the greatest being possible, "that than which no greater can be thought" (which , a posteriori, must necessarily exist, since beings are observable facts and therefore there is logically a "greatest" among them), could in fact be a necessary being or an almighty being but not both.

However, on closer inspection Reductio 1 implicitly shows that almighty beings per se are absolutely impossible, irrespective of their existential nature (which in this case is "necessarily existent"), since, irrespective of whether or not the being is necessary or contingent, it can do nothing about its existential condition, since doing so is a priori prohibited. That is, it is a priori true that a necessary being must for eternity be a necessary being and can never be at any time contingent -since to be contingent means that it will have to have begun to exist at sometime or other, which is in contradistinction to existing necessarily, always, without beginning or end. And also the converse is true; that is, it is a priori true that a contingent being can never become a necessary being, since having the existential nature "contingently existent" it at one time began to exist and therefore has not existed always.

Nonetheless, the impossibility of almighty beings is only implicit in Reductio 1, since the reductio only explicitly shows, the impossibility of both necessary existence and almightiness simultaneously pertaining to, and predicating, a being, respectively. It says nothing about the possibility of necessary beings lacking almightiness existing, in which case it is initially conceivable that necessary beings are possible. And it says nothing, apparently, about almighty beings being possible, provided that they also do not embody necessary existence.

To show incontrovertibly that almighty beings are impossible requires showing that either necessary beings are the only beings possible, in which case Reductio 1 would show that almighty beings are impossible (because necessary beings cannot be almighty); or that, if necessary being is impossible, then the converse of necessary being – that is, contingent being – can (incorrectly it will turn out) be predicated by almightiness.

Some analysis of the possibility of necessary being is helpful.

Affirmation 1

Logical possibility of necessary being

Proposition A1: Necessary existence is logically possible

1. Necessary existence is logically possible
2. A necessary being is uncaused and exists eternally without beginning or end [definition of necessary being]
3. Premise 2 is a priori logically coherent [no internal contradictions]
4. Therefore necessary existence is logically possible

Affirmation 2

Physical possibility of necessary existence

Proposition A 2: Necessary existence is physically possible

1. Necessary existence is physically possible
2. Something beginning to exist where before there was nothing cannot be explained [contingent existence] [4]
3. Anything existing always cannot be explained [necessary existence]
4. There is no reason to assert that either premise 2 or premise 3 are true or false, or that one is more probable than the other, since both must, in the absence of evidence, be considered to be a priori equally likely states of reality and further, both must be considered to be equally a priori inexplicable. [That is, no good reason can be given as to why anything should begin to exist (premise 2) except that it is impossible for something to exist always; and equally, no good reason can be given as to why anything should exist always without beginning or end (premise 3) except that no-thing can begin to exist and that therefore, given that things exists, these things have existed always. This "symmetry of inexplicability" and mutual exclusivity suggests that neither of these possible states of reality can be ruled out as descriptions of reality, and that therefore both must be held to be physically possible.]
5. Therefore both necessary existence and contingent existence are physically possible states of reality.

Summary 1

Affirmations 1 & 2, though they do not explicitly demonstrate the physical reality of necessary existence, do show the logical and physical possibility of it. That is, neither necessary existence nor contingent existence can be shown to be logically and physically true descriptions of current reality, but equally, neither can they be shown to be logically and physically impossible descriptions.

Therefore, as there is no inherent logical or physical inconsistency in assuming the possibility of necessary being, it is therefore coherent to hold that necessary being is logically and physically possible.

Synthesis 1

Affirmation 1 shows that necessary existence is logically possible. Combining affirmation 1 with negation 1 it follows that if necessary beings are the only beings possible, then almighty beings are impossible.

However, Affirmation 1 also shows that contingent existence is possible (which is also an observable fact) which opens up the (absurd) possibility that such beings can be predicated by almightiness.

To formally rule out the absurdity of almighty contingent beings it is perhaps only sufficient to note the contradiction in the term “almighty contingent being”. Nevertheless, Negation 2 will demonstrate this intuitively obvious fact rigorously.

Negation 2 will explicitly show what is already implicit in Negation 1: that almighty contingent beings are impossible.

Negation 2

Proposition N2: there are beings that are both almighty and contingent.

(Note: Negation 1 precludes the simultaneous realisation of both almightiness and necessary existence in the same being, leaving only one logical existential alternative nature to accompany the predicate "almighty, and that is contingency).

Reductio 2:

1. There are almighty contingent beings
2. An almighty being can do absolutely anything [definition of almightiness]
3. A contingent being will have begun to exist and may cease to exist at sometime [definition of contingency]
4. A necessary being is uncaused and exists eternally without beginning or end  [definition of necessary being]
5. An almighty being that is contingent can, on premise 2, cause itself to become necessary
6. It follows that there are no almighty contingent beings [contradiction of premise 5 using premises 3 and 4, rendering premise 1 absurd]

Clearly, a being that is contingent can never become necessary.

Therefore proposition N2 is false. There are no almighty, contingent beings.

Notes:

The conclusion (6) in Reductio 2 is true irrespective of whether there are necessary beings, as might be well be the case.

Premise 5 is clearly false, but there is even some doubt as to whether the proposition it represents is in fact meaningful and sufficiently internally consistent as to serve as a premise in a reductio. It seems meaningless not to mention absurd to say that something that is contingent can become necessary. Indeed, "Reductio 2" is trivial and cannot even command respect as a well formed argument.

Now that almightiness as a predicate of any being, whether of necessary or contingent nature, has been shown to be impossible it can, without concern, be removed from the illustrious list of attributes supposedly possessed by God.

On the above arguments using reductio ad absurdum, it is true that almighty beings of any existential description, whether necessary or contingent, are impossible.

Nonetheless it would be interesting to continue further and to explore other possible existential and predicate conditions of being. Doing so will expose why theologians have claimed that God is an infinite, almighty necessary being.

Negation 3

Proposition N3: There are necessary, finite beings

Finite is used to convey limited power, or non-almightiness, as well as spatial and, especially, temporal limitedness and is a convenient antonym of almighty. Feeble will be used to convey limited power but not limited extension or duration; that is, a feeble being (on this definition) can exist everywhere and eternally but is not almighty .

It should be immediately apparent, even without embarking on what will prove to be another trivial as well as questionable reductio, that the proposition "there are necessary finite beings" is internally inconsistent. However:

Reductio 3:

1. There are finite necessary beings
2. A finite being cannot do all and any thing, or exist everywhere or exist eternally [definition of finite being]
3. A necessary being is uncaused and exists eternally without beginning or end [definition of necessary being]
4. Existing eternally is non-finite
5. Therefore there are no finite necessary beings. [Premise 4 shows that necessary being (premise 3) involves infinitude, which conflicts with premise 2, rendering premise 1 incoherent; that is, absurd]

To be finite and necessary is inconsistent since one contradicts the other.

Therefore proposition N3 is false. There are no necessary, finite beings.

To see if there are any feeble necessary beings:

Proposition N3a: There are necessary, finite beings

Reductio 3a

1. There are feeble necessary beings
2. A feeble being cannot do all and any thing, but can, as part of its existential nature, exist everywhere and/or exist eternally [definition of feeble being]
3. A necessary being is uncaused and exists eternally without beginning or end [definition of necessary being]
4. Therefore, feeble necessary beings are possible [there is no inconsistency between premises 2 and 3 and moreover premise 3 is implicit in premise 2, rendering premise 1 coherent].

These negations seem somewhat unnecessary and needlessly harsh on theism, since N3 denies the possibility of a necessary being that is in every way finite (which is intuitively obvious); and N3a allows only the possibility of a necessary being that is simply feeble - that is, it is limited in power and can only exist eternally if it already happens to exist eternally (it has no choice in the matter and in that sense it is truly a sorry and feeble being).

Together with Negation 1, which denies the simultaneous realisation of the predicate almightiness (infinitude in all respects) and the existential nature necessary being , there is no possible accommodation for God to be a necessary being of any sort other than a feeble necessary being (that is, limited in power but not in duration or extension). The possibility of a necessary being that is either infinite or finite is utterly denied.

Finally, some trivial exercises in showing that finite contingent beings are possible. First the logical argument

Affirmation 3 (using deduction)

Proposition A3: Finite contingent beings are logically possible

1. Finite, contingent beings are logically possible
2. A finite being cannot do all and any thing, or exist everywhere or exist eternally but it can do some things [definition of finite being]
3. A contingent being will have begun to exist and will cease to exist at sometime [definition of contingency]
4. Therefore, finite contingent beings are logically possible. [no contradiction among any of the premises]

Affirmation 4 (using induction)

Proposition A4: Finite contingent beings are physically possible

1. Finite contingent beings are physically possible
2. Finite beings exist [fact 1, observational]
3. Contingency is evident in the beings and things that exist [fact 2, observational][5]
4. Therefore, finite contingent beings are physically possible.

This last affirmation, together with Reductio 3a demonstrate the obvious, observationally verifiable fact that apart from the as yet undetermined question of the spatial, temporal and causal finitude or infinitude of the universe itself, the only kinds of beings that are both logically and physically possible and which may possess causal powers, are either finite and contingent or necessary but feeble.

Summary and conclusions

It turns out that, contrary to the claims of theism, the being identified as God, cannot exist and could not possibly possess all the attributes and natures outlined in the introduction. Specifically the above arguments show that:

"God" can be necessary but not almighty (Reductio 1, Affirmations 1 & 2), which from Reductio 3a turns out to be in fact "necessary and feeble".

"God" can be contingent, but not almighty (which as it turns out is also Richard Swinburne's thesis)

And that under no circumstance (i.e. not for any existential nature) can there be almighty beings.

It is clear from this that God in the sense intended by the Anselmian perfect being theology adopted by monotheistic religions is an impossible being. This accounts for the quotation marks around the word God above, since the beings so mentioned can no longer be identified with the god of monotheism.

Negation 1 clearly shows the impossibility of both almightiness and necessary being inhering in the same being. And Reductio 3 shows the impossibility of finiteness and necessary being. The only possible necessary beings are demonstrated by Reductio 3a, and those are the feeble beings that are causally limited though they may not be spatially or temporally limited (Not withstanding the Universe itself which may be either spatially or temporally infinite or both, but which strictly speaking is not a being in the sense of possessing willful causal powers unless we consider the thesis that our consciousness and hat of any other possible being counts as the universe become conscious).

Notes

The negations and affirmations have taken into account the physical aspects to the arguments though, in fact, they needn't have. This follows from the fact of the claim of the monotheism’s that God is an immaterial entity, and therefore it would have been sufficient to have simply considered logical possibilities of necessary being. However, since the Universe itself is a “being” or in fact the being (a verb, as in something existing, being, persisting and so on and not a being, or this or that being) physical possibility of necessary being was considered.

There is a tendency even among scientists to conflate the concept of God as set out by the monotheisms with the idea of a "deity" that can be identified as being the laws of nature, a kind of folkish Hegelianism. This idea can and should be rejected on two grounds. First, it is just one more preposterous hypothesis that explains nothing, and is in fact preposterous because it explains nothing. And second because it strips away the essential attributes of God that form the pillars of monotheisms' conceptualisation of him - intelligence, personhood, will and benevolence. Though there are good grounds for rejecting all of these anyway, not to mention the fundamental idea of God to which they relate in any way, any discussion of monotheism’s  conceptualisation of god, or even that of theism's in general, must deal with the genuine article so to speak, and not some relativistic substitute such as the Laws of Nature or the fact of "human progress" as in Hegel's dialectical system.