The Incoherence of a Metaphysically Necessary Being

Abstract

In this paper I argue that the existence of an essentially necessary being is impossible because the concept is incoherent. By essentially necessary being, I mean a simple entity whose essence is identical to its existence and exists in every possible world. Traditionally, theologians have wished to say that God has this kind of necessity. Kant (1781) and Russell (1900) denied that existence was a property and for this reason they denied the coherence of an essentially necessary being. Swinburne (2012) claims that God has existed from eternity and is indestructible, but does not exist in every possible world. Craig (2016), Feser (2017), Pruss and Rasmussen (2018) defend the coherence of such a being, but Feser denies the efficacy of ontological arguments. 

I. Introduction

Although it may be tempting to believe that it is possible for an essentially necessary being (henceforth, N) to exist, because the concept of is coherent, instead, in this paper, I will argue that it is possible for N to exist because it is conceivable that N does not exist and to deny its existence is not self-contradictory. I begin by giving background on relevant concepts, then I present an argument for my view, then I explain the premises and address four objections before a final conclusion. 

II. Necessary Existence

Plantinga (1976, p. 105) treats existence as a property rather than a quantifier and says that “every object has the property of existence essentially,” but “only some things,” have necessary existence—“perhaps God.” Some propositions are self-contradictory and hence could not be true in any possible world, but other propositions are true by definition and hence are true in every possible world. (Ibid., p. 108) Non-existence is a property that nothing has because “there are no non-existent objects.” (Ibid., p. 105) On such an account, metaphysically speaking, an entity must have the property of existence before it can have any further properties. I will consider three types of necessary existence under this account:

[A] Firstly, traditional sort of necessity which God is supposed to have. An entity whose essence is to exist. For every other entity, their essence and identity are distinct. For this reason, God must exist and cannot fail to exist. [B] Secondly, what Plantinga (1976, p. 105-6) calls ‘necessary existence’ is a kind of modal status, the property of existing in every possible world, and it need not require that the entity’s essence is identical to its existence. An entity might have this kind of necessity without any further explanation for why it does besides its own ‘maximal greatness.’ (Plantinga 1974, p. 209-211) [C] Thirdly, the sort of necessity that analytic propositions, and mathematical theorems have. They are true in every possible world because they are true by definition and hence are self-contradictory to deny. (Plantinga 1976, p. 108.) Their modal status is inferred from the structure of the proposition expressed by sentences that spell them out.

In my estimation, the type of necessity denoted by [C] is meaningful enough, because there is an intelligible reason for it. When one understands a sentence expressing an analytic proposition (e.g. ‘there are no married bachelors’), she can see that the proposition must be true, and it is inconceivable that it is false. For these reasons, she can validly conclude that the entity in question is necessary. However, N would be an entity that has the kind of necessity denoted by [A] or [B] and this kind of necessity is incoherent or impossible because the concept is not realizable. 

III. An Argument 

The argument then, is this: 

1. If N existed, then its nonexistence would be inconceivable and a sentence denying the existence of N would be self-contradictory. 

2. The nonexistence of N is conceivable. 

3. A sentence denying the existence of N is not self-contradictory. 

4. Hence, N does not exist. 

Premise 1. This first part of this premise assumes the conceivability thesis, that if a state of affairs, S, is conceivable, then it is logically possible because it is not possible to conceive of a self-contradictory S. Something is logically possible if it does not entail any contradiction. (Ney 2014, p. 191.) This thesis requires, however, that one understands what S is under consideration. If the reasoner does not have a sufficient comprehension of the S in question, then the thesis is not of use, even if some S is self contradictory it may be apparently conceivable until some further facts are learned that reveal the contradiction. Hume (2007, p. 64.) defends something like the first part of this premise in his ‘Empty Worlds’ argument, “there is an evident absurdity in pretending to demonstrate a matter of fact, or to prove it by any arguments a priori. Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction.” Which is to say that the concept of necessity is not meaningfully applied to things other than propositions, sets, or theorems which are definitionally true. 

By a sentence I mean some set of words or symbols arranged in a meaningful pattern but by a proposition I refer to the meaning expressed by that sentence. N’s existence is either impossible or necessary. If some S is logically possible, then there is some possible world where that S obtains. The only things which do not obtain in any possible world (henceforth W) are things which are self-contradictory. Hence, if there is an N, there could not possibly be any S incompatible with its existence. Therefore, N either exists in every W, or in none of them and any sentence which denies the existence of an N must express a self-contradictory proposition—or there is no such thing as N. 

Premise 2. There are many conceivable W in which a N does not exist, e.g. if the ‘photon world’ is coherent, it is one such world. Many philosophers think that the actual world does not have a N in it. 

Premise 3. It is not possible that any sentence which merely affirms or denies the existence of some entity could be self-contradictory, e.g. to say “there is no God,” “there are no fairies,” and “there is no reigning Tzar of Russia” could not be self-contradictory statements. 

IV. Addressing Objections

Objection 1. An objection to Premise 1 is that the conceivability thesis is false because conceivability is not a guide for possibility. 

In rebuttal, I would say that the thesis is at least true when one understands sufficiently the state-of-affairs (henceforth S) in question. Tidman (1994, p. 298.) defines the conceivability thesis this way: “If S is conceivable, then S is possible.” It is possible to verify that the conceivable thesis is true by considering a modest version of the inconceivability thesis which claims: If S is self-contradictory, then S is inconceivable. (Tidman, 1994, p. 297) If this modest version of the inconceivability thesis is true, then a modest version of its converse is true, namely, if S is not self-contradictory, then S is conceivable. 

Various examples can prove this to be the case. It is not possible to mentally picture a square without any edges because this S is self-contradictory but it first requires knowing the basic definition of a square. If someone did not know that a square has four edges, then they may think it possible for there to be a square without any edges. Such examples show that if someone first comprehends the sentence that describes the S in question then the conceivability thesis is of use. This principle is also applicable to mathematical theorems. In the case of newly discovered theorems, it was conceivable that they might be false until they were understood and demonstrated to be true definitionally. Once mathematicians understand some theorem, then they see that it is necessarily true and it is inconceivable that it is false. 

Objection 2. The non-existence of N is apparently conceivable but it is not ideally conceivable because it is not possible to comprehend the essence of N. If a philosopher fully comprehended the nature of N then she would see that N must exist. This is traditionally what theologians have taught concerning the necessary reality, Pseudo-Dionysius the Areopagite says that N is ineffable, “Never, then, is it true to say, that we know God; not from His own nature (for that is unknown, and surpasses all reason and mind), but, from the ordering of all existing things.” (Parker 1897, p. 91.) John of Damascus, “it is clear that God exists, but what He is in essence and nature is unknown and beyond all understanding.” (Chase 1958, p. 170.) Gregory Palamas claimed “this essence transcends all affirmation and all negation." (Meyendorff 1983, p. 97.)

In rebuttal, I say that if someone makes the claim that N exists or does not exist, this claim is only meaningful if the variable can be defined and understood. The very theologians who teach divine ineffability, go on to write lengthy treatises making all sorts of claims about the nature of N. Defenders of ontological arguments who expect their audience to assess the truth of their arguments thereby assume that the concept of N is comprehensible enough to be analyzed in this manner. Therefore, it is possible to understand enough about the essence of N to assess whether it exists and whether its nonexistence is ideally conceivable, otherwise it would make no sense to do theology proper, or to philosophize about these issues at all and we are left with agnosticism about the question of whether N exists. 

Objection 3. A further objection to premise 2 would be to claim that there is a hidden contradiction in supposing that N does not exist. Though theologians have been unable to spell out this contradiction for the past few thousand years, it may still lay undiscovered. 

In rebuttal, I say that sometimes it is not possible to comprehend some S, and in such cases it is not possible to know whether it is truly conceivable or not. Some problems are too complex for human minds to comprehend. It is not possible for any human being to have an exhaustive knowledge of every entailment of all propositions. Due to our lack of omniscience, it is almost always possible there is some hidden contradiction in a particular proposition when one applies the conceivability thesis but as Swinburne (1993) comments: 

“Of course, there  just might be contradictions buried in the statements which we have been considering, but in the absence of argument to the contrary, we ought to assume what clearly appears to be the case that there are no such buried contradictions… Atheism is a coherent supposition.” (1993, p. 275)

To claim ‘N does not exist’ is asserting there is nothing which fits the description of such a being. It does not seem that a statement of this sort could ever be self-contradictory. Perhaps it is the case that “a negative existential sentence cannot entail a contradiction.”  (Swinburne 2012, p. 1, 13-14) 

Objection 4. An objection to premise 3 would be to claim that the atomic sentence ~ N is self-contradictory, it expresses that “the being which must exist does not exist.” 

In rebuttal, I say the intended meaning of the proposition ~ N is not ““the being which must exist does not exist.” It is rather that “there is no such being as ‘the being which must exist and does not exist.’” It is claiming that there could not be anything which fits the description of N or if one must use Plantinga’s terminology, it is to say that it lacks the property of necessary existence, and so it does not have any further properties either. (1976, p. 105-16) These are both coherent and intelligible claims that do not involve contradictions. 

V. Conclusion

In conclusion, I have argued that the traditional sort of necessity that theologians have wished to ascribe to God is impossible because of what it would imply. If there were an entity which had the kind of necessity denoted by [A] or [B] then its existence would be self-contradictory to deny, and its non-existence would be inconceivable. But negative existential statements of the sort ‘there is no such thing as N’ could never be self-contradictory. Further, it is conceivable that no such entity exists. 

Bibliography

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Craig, William Lane. 2016. God Over All: Divine Aseity and the Challenge of Platonism. New York: Oxford University Press.

Chase, Frederic H. Jr. 1958. The Fathers of the Church: A New Translation. Vol. 37, St. John of Damascus: Writings. Reprint, 1999 (The Catholic University of America Press).

Feser, Edward. 2017. Five Proofs of the Existence of God. San Francisco: Ignatius Press.

Hume, David. 1965. A Treatise of Human Nature. Edited by L. A. Selby-Bigge. London: Oxford University Press.

Hume, David. 2007. Dialogues Concerning Natural Religion and Other Writings. Ed. Dorothy Coleman. New York: Cambridge University Press.

Meyendorff, John. 1983. Gregory Palamas: The Triads. New Jersey: Paulist Press. 

Ney, Alyssa. 2014. Metaphysics: An Introduction. New York: Routledge.

Parker, John. 1897. Dionysius the Areopagite: Works. London: James Parker and Company. 

Plantinga, Alvin. 1974. The Nature of Necessity. New York: Oxford University Press.

Plantinga, Alvin. 1976. "Necessary and Essential Existence." Canadian Journal of Philosophy 6 (1): 105–111.

Pruss, Alexander, and Joshua Rasmussen. 2018. Necessary Existence. New York: Oxford University Press.

Pruss, Alexander R. 2006. The Principle of Sufficient Reason: A Reassessment. Cambridge: Cambridge University Press. 

Russell, Bertrand. 1900. A Critical Exposition of the Philosophy of Leibniz. London: Cambridge University press. 

Kant, Immanuel. 1781. Critique of Pure Reason. Translated by Paul Guyer and Allen Wood. Cambridge: Cambridge University Press, 1998.

Swinburne, Richard. 2012. "What Kind of Necessary Being Could God Be?" European Journal for Philosophy of Religion 4 (2): 1–18.

Swinburne, Richard. 1993. The Coherence of Theism. Oxford: Clarendon Press. 

Tidman, Paul. 1994. "Conceivability as a Test for Possibility." American Philosophical Quarterly 31 (4): 297-309.

An Excess of Negatives

0. Introduction

Some correspondence theorists such as Armstrong (2004) and Jago (2018) have argued that every truth has a truthmaker; this view is typically called “truthmaker maximalism” (henceforth “TM”). To account for negative propositions (e.g. ‘there are no wizards’) some defenders of TM treat absences or negative states of affairs as spatiotemporal entities. In this paper, I will argue that Barker and Jago’s (2012) model of TM is false because there is no good reason to think that negative states of affairs actually exist.

In the first section, I describe precisely what negative facts are supposed to be, then I defend an argument against their existence and consider objections to my own account of negative facts before a final conclusion.

1. Negative Facts

Negative facts are supposed to be real entities located in space and time in Jago’s version of TM. Maximalists today typically claim: “Every sentence is such that it is true if and only if it has a truthmaker.” (Rodriguez-Pereyra 2006, p. 2) To say that every truth has a truthmaker is a strong metaphysical claim because it means there always exists some state of affairs in the world which gives sentences their truth value, contingently or necessarily. In other words, some sentences are true because the meanings they express somehow correspond to states of affairs in the world. Existence seems to be a positive property so is tempting to say all facts are somehow positive, as Russell observed:

“You have a feeling that there are only positive facts, and that negative propositions have somehow or other got to be expressions of positive facts.” (2009, p. 41-42)

But there are negative facts and they must be explained, such as the sentence, “Ern Malley does not exist.” The non-maximalist usually explains negative truths such as these by saying that there are some truths with no truthmakers. The sentence is true because of what does not exist, not because of what does; "the absence of Ern Malley" does not refer to anything with properties but to the lack of the existence of a particular thing. In contrast, the maximalist must say that there exists truthmakers even for negative propositions, “there are specific entities such as the absence of Ern Malley.” (Jago 2018, p. 132) The sentence is true because there exists an entity ‘the absence of Ern Malley’ to which it corresponds. These absences are variously called “negative states of affairs” and “negative facts.” (Jago 2018, p. 132) Jago (2018) admits that the non-maximalist explanation should be preferred if it can account for negative truths because TM does carry many metaphysical obligations. Mumford (2007, p. 48) says that TM seems to treat non-existence as though it were existence, and suggests that treating absences as though they were entities is a misuse of language:

“[C]an it really be a fact that in the world that there is no hippopotamus in the room? This sounds like an absence of a fact, and an absence is nothing at all. Alternatively, could the fact in question be the non-hippopotamus that is in the room?”

Jago and Barker (2012, p. 2) present a model upon which ‘the absence of the hippopotamus in the room would be an entity spatiotemporally located in the room, “we want our negative facts to exist just as much as our positive facts.” This negative fact is supposed to be a fundamental kind of entity, from which properties are abstracted. Negative facts have a kind of non-mereological composition. Jago and Barker (2012, p. 6): 

“As a consequence, we accept negative properties and relations into our ontology, as abstractions from negative facts. If [Fa] — is a negative fact, then λx[Fx]—, the property of non-Fness which is abstracted from it, is a negative one. We then have a corresponding positive fact, [(λx[Fx]−)a]+, the fact that a possesses non-Fness.”

If a is not F and we abstract from this the property of non-Fness, but we must ask whether this is truly a property. Is lacking a property, itself a property? This seems an unnecessary claim. For Jago and Barker (2012, p. 4), absences are also located in time and space—so what about those which are universally true? If there are no fairies, and never will be any fairies, then the entity which is ‘the absence of fairies’ is really omnipresent. It is not located in any particular place, it is at all places and it is true at all times (even timelessly). The fact that there are no fairies would be located in every region there is.

Consider properties like non-Fness again. I would say that this is just the negation of a property, and non-Fness is nothing more than an idea, a way of thinking about our perception of an absence of F. But if it were a property, and nothing possessed Fness, it would then follow that everything has the property of non-Fness. There would be no way to localize non-Fness to any particular space or time.

2. An Argument

Non-Fness is not a property unless lacking a property is itself a property. But the lack of property ought not to be considered a property because this would result in a very bloated ontology. It is also difficult to see what distinguishes one negative property from another aside from appeals to a kind of thisness. The argument might be summarized this way:

1. If absences (or negative states of affairs) are entities, then there are an infinite number of them. (Premise)

2. For there to be an infinite number of absences, they must be distinguished by individuating properties. (Premise)

3. But absences could not have such individuating properties. (Premise)

4. Hence, there are not an infinite number of absences. (From 2 and 3)

5. Hence, absences are not entities. (From 1 and 4)

The truth of the first premise is shown by the fact that there are an infinite number of properties which nothing has. If negative properties exist, TM would commit us to saying that every object has an infinite number of negative properties which are just as existent as their positive properties, e.g. an apple has the negative properties of ‘not-humanness,’ ‘not-numberness,’ ‘not-planetness,’ and so on. An apple would have an infinite number of such negative properties because there are innumerable properties which the apple does not have and will never have.

With regard to the second premise, the sentence “Ern Malley does not exist” would be true according to TM because of an entity which is ‘the absence of Ern Malley.’ But the defining property of this entity is that it is not something. But what other properties does this absence have, other than it is not Ern Malley? Consider also the entity, ‘the absence of fairies’; any other properties it might have are abstracted only from its being an ‘absence of fairies.’ Both absences are universally located and true at all times. Why not say there is a single entity which is both the absence of fairies and the absence of Ern Malley? There must be some individuating properties which distinguish the two entities.

“We’ve presented our theory of facts. However, let’s admit it: our clarification of negative facts is achieved through the notion of anti-instantiation. And what kind of clarification can that be, given that anti-instantiation is opaque? We admit the opacity.” (Jago and Barker, 2012, p. 9)

The third premise states that there are no such individuating properties because there does not seem to be any way to determine whether ‘the absence of Ern Malley’ is a distinct entity from ‘the absence of fairies’; or whether there is actually a single entity which is ‘the absence of Ern Malley and the absence of fairies.’ The defender of TM might make an appeal to a kind of thisness, and argue it is a brute fact that ‘the absence of Ern Malley’ is not ‘the absence of fairies.’ But it is a dubious thing to say that there is nothing that does the metaphysical work of distinguishing these two entities. For TM to be true, there must be an infinite number of such entities which are likewise distinguished by brute facts of identity. At this stage TM becomes more opaque and difficult than any problems it seeks to solve.

In short, I have argued that there does not seem to be any good way to distinguish one negative fact from another and this is especially the case with universal negatives. This problem can be avoided entirely by simply denying the privilege of existence to negative facts.

3. Conceptual Existence and Negative Facts

It is better to regard negative facts as having only a conceptual existence which avoids the costly metaphysical commitments of TM. I shall give my own non-maximalist account of true negative propositions of the sort “Ern Malley does not exist,” and then see if it survives the objections Jago (2018) levies. If it is even possible that my account is true, then it should be preferred because it is simple and does not require postulating an infinite number of entities. In my view, negative facts have only a conceptual existence. When I say “Ern Malley does not exist” I mean only that I have a concept of what it would mean for Ern Malley to exist, but there is no state of affairs in the world which corresponds to this concept. The sentence is true precisely because the opposite sentence “Ern Malley exists” does not have a truthmaker, there is not an entity (e.g. the absence of Ern Malley) that exists which ensures the truth of the sentence because it is not the kind of sentence that would require one. There is no such person as Ern Malley in the furniture of the world, and this is what makes the sentence true.

Jago (2015) responds to this kind of view firstly by saying that it implies that there are three differing types of true propositions, positive (e.g. ‘the sun exists’), negative (e.g. ‘Ern Malley does not exist’) and derivative (either ‘Mark is pacing or Ern Malley does not exist’). I think this threefold distinction is correct. Only the first sort of propositions always require truthmakers. The second sort, as we have seen, do not, and the third sort does if one of the disjuncts is a positive proposition. Jago argues that this categorization fails because of certain true epistemic propositions that do not fall into any of the three categories just spelled out. Hence, the non-maximalist position is implicitly committed to TM or has more fundamental problems, Jago (2015):

“I still think this theory won't work. Here's why: take this proposition—”Max knows there are no daleks.” We've got to work out what kind of proposition that is, according to the non-maximalist lines… it better not be the positive kind; if it is, then it has a truth-maker… Knowledge is factive, so the truth-making must be some entity in the world that guarantees that there are no daleks. And that's just the kind of entity the non-maximalist wanted to avoid—some weirdo absence that somehow guarantees that such and such won't exist.”

So then, the proposition “Max knows there are no daleks” isn’t negative because it involves a claim about what Max knows. It is not positive because it would require a truthmaker ensuring what Max knows. The third option is that the proposition is a derivative proposition. But Jago (2015) objects that this would require a reductive theory of knowledge to which he says, “people have been trying to work out what knowledge is trying to give a reductive definition of knowledge for absolutely honest that hasn't worked out good.” But if a reductive theory of knowledge is at least possible, then this is problematic for TM. The existence of any negative facts or absences is already controversial and is at least as controversial as reductive theories of knowledge, Jago and Barker (2012, p. 1) describe an "enmity to negative facts” among their peers.

Further I would say that modern physics has had much benefit in describing the world in terms of laws and initial conditions, but has had no use for positing negative states of affairs or negative initial conditions. Our scientific theories are useful because they describe reality accurately to some extent. Godfrey-Smith (2003, p. 91-92) gives the example of building a bridge which people will use to cross. If the principles of physics and engineering underlying this project were faulty we ought not to expect success in our project. But physics has been very successful without positing these negative entities. This objection of mine assumes a modest scientific realism, that our theories, to some extent actually describe “what the world is like” and that this issue does not involve metaphysical truths that do not hide beyond the edges of physics. (Godfrey-Smith, 2003, p. 347) But this is a reasonable assumption, if something is metaphysically necessary then it should reflect in our physics in some way. In the case of negative facts or absences, Jago and Barker (2012, p. 1) address concerns they are “causally inert" by suggesting that they might be regarded as having causal powers. If absences are really existent entities which have causal powers, then they should be detectable in physics or at least useful to the physicist in her theorizing.

If their existence would make no difference to physics, then I would say that TM is guilty of causal overdetermination. In contrast, it is better to treat positive states of affairs as synonymous to an extent with initial conditions and negative facts as the lack of any such conditions. The non-maximalist explanation fits in well with modern physics. Our physics should inform our metaphysics whenever possible to avoid unfalsifiable theory crafting when we can.

It seems to me that the central problem which might be faced by the non-maximalist solution which I have given is how well it fits with the English language. When we talk about absences or negative facts, it is common to talk about them as though one is referring to entities that exist. But I would say that most people do not believe negative facts are real entities and so even when they use language that seems to imply that they are the sentences or unintended to express that proposition. Negative facts should be regarded as statements about properties that nothing has or things that do not exist in the world. Such statements could only be false if those things or properties actually did exist in the world.

4. Conclusion

Non-maximalist explanations are less problematic than TM because they require less ontological commitments. There are also significant challenges to distinguishing one universal negative fact from another on TM, and solving this problem (if possible) would require further costly metaphysical commitments. The primary objection to non-maximalism raised by Jago regarding reductive theories of knowledge, even if true, is less costly than what TM requires.

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Armstrong, D. (2004). Truth and Truthmakers. Cambridge University Press, Cambridge. 

Godfrey-Smith, Peter (2003). Theory and reality: an introduction to the philosophy of science. Chicago: University of Chicago Press.

Jago, Mark (2018). What Truth Is. Oxford: Oxford University Press.

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Jago, Mark, (Jan 30, 2015). Lecture: “What Truth is” at the University of Edinburgh https://www.youtube.com/watch?v=jyOGlrIiWR

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