Axiom S5 states that if something is possible then necessarily it is possible1. If Socrates is a possible being then this fact could not be otherwise; it is always and forever true that Socrates is a possible being. Possibilities do not change or pass away—they are a necessary part of the ‘deep’ ontological structure of reality and thus are set throughout all possible worlds.
S5 is the standard modal system. Although some have suggested problems with this axiom most philosophers accept its claims about possibility and accessibility and appeal to it in their modal reasoning. In philosophy of religion it is most commonly associated with Plantinga’s modal ontological argument2, where it is appealed to in the premise that a necessary being’s existence in any possible world entails its existence in the actual world, though is in fact vital to others arguments such as the Gale-Pruss cosmological argument and the argument from the Powers theory of modality.
S5 however is open to some intriguing potential counter-examples3. Now, if the axiom is shown to hold in some contexts that does not a priori invalidate its use in our arguments but it would leave use all, theist and non-theist, with the duty of providing some criterion of where it does apply. At present were all of the different counter-examples bona fide then we should have to restrict its application to truths about kinds, and not possible individuals, and maybe to only some classes of temporal truth.
This entry will discuss a specific counter-example I have not seen elsewhere. Throughout I will use ‘possibility’ and its associated modal terms in the widest sense, that of metaphysical possibility, and not in the temporal or nomological sense. It may be the case that problem outlined in fact pertains only to temporal modality in which case I would be grateful for my readers to call me out. The counter-example arises as a result of a conflict between S5 and another well-respected Kripkean modal claim, that of origins essentialism (for a quick overview of the position see here).
Origins Essentialism, or as it is sometimes known, the necessity of origin, states that every particular being has its material and causal origins i.e. the material out of which it was made and the casual process which brought it about, essentially4. (To give the textbook example it would be impossible for Socrates to have been born to parents other than those Socrates was actually born to.) Philosophers find origins essentialism appealing both because it seems to present a clear-cut intuitive case of a posteriori necessity and because in the absence of individual essences it provides a unique, identifying property for each individual being.
Axiom S5 and origins essentialism are in conflict, I believe, because of the contingent nature of origins conditions. In under to see why let us look at a potential conflict between claims about posteriori entailed by these two positions.
First of all we have the standard S5 claim applied to beings:
1. If a being X is possible then necessarily it is possible.
From this however it might be argued that we can entail the following:
2. If a being X is possible then it is possible at any given time (if a temporal being).
Why accept 2? Because if it were not the case then it would mean the truth of the proposition X’s being possible was subject to change dependent on time and thus contingent and not necessary. ‘Possible’ here is used in the sense of alethic modality and not temporal modality. Of course how one reads 2 will depend on what positions one takes on the nature of temporal change5. For the purposes of this essay we are assuming an endurantist account of temporal objects. Those who are temporal parts theorists will presumably grant that it is possible for a being to have different temporal parts than it does in the actual world.
If one accepts realism about natural kinds one might claim origins essentialism commits one to a thesis that spells trouble for 2. Call this the thesis of natural origin:
TNO: All [species name] are necessarily born either of [species name] parents or parents of an evolutionary precursor species.
This tension is most clearly highlighted if we look at cases where the natural kind in question is that of an extinct species—for the purposes of this essay let us take dodos as our example.
TNOD: All dodos are necessarily born either of dodo parents or parents of an evolutionary precursor species.
Which conflict with an applied version of 2:
2D. Dodos are possible at 16:30 on the 24th of March 2017.
Presumably this world is dodo-free, there are no secret dodo republics on undiscovered islands, but at one point dodos certainly did exist and thus were possible. Likewise the evolutionary precursor to dodos is long dead too. According to S5 then dodos are still possible (the proposition ‘dodos exist’ is still possibly true), as possibilities are themselves necessary, hence claim 2D holds. TNOD, our applied version of the thesis of natural origin, however rules this out—if there are no dodo parents nor parents of an evolutionary precursor species at 16:30 on the 24th of March then dodos themselves are not possible at that time, for according to origins essentialism it is necessary that dodos are caused to exist only by either of those two types of parents. If this is the case then it is no longer necessarily true that dodos are possible (in fact it is necessarily false). But then axiom S5 is false since it just is the claim that all possibilities are necessary.
At this point the theistic proponent of S5 might leap up and accuse of the critic of begging the question against his position. They might say: Divine Omnipotence gives us reason to hold that God could create dodos ex nihilo and given that we are already willing to accept a disjunctive account of necessary origins (born to dodo parents OR born to parents of an evolutionary precursor species) then we should be perfectly happy to allow another disjunct, created directly by God, particularly if it is in the interest of protecting such a well-respected claim as S5. Our applied origins thesis would then be amended to:
TNO2: All [species name] are necessarily born either of [species name] parents or parents of an evolutionary precursor species or created ex nihilo by God.
Whilst dodos and their evolutionary precursors, each contingent beings, might go out of existence, God, a necessary being, is certainly not going to, thus the possibility of dodos has a permanent grounding allowing us to preserve S5.
This revision would save the axiom but would leave one wondering about its roll in theistic proofs; consider, if theism is required to justify S5 then it is epistemically precarious—to say the least—to appeal to S5 in order to justify theism. On the other hand the fact that theism entails such a widely held and plausible modal system could be taken as point in its favour in terms of explanatory value.
The more analytically inclined will have noticed there is something distantly suspicious about TNO and its dodo-specific application. To see what it is consider a parallel claim:
All presidents of the United States of America are necessarily born of human parents
This claim is true on a de re reading, as every individual who was president of the United States of America in the actual world was born of human parents (and has this property necessarily given origins essentialism), but false on a de dicto reading as there are worlds in which beings without human parents become president (legal difficulties aside). That latter sense is better articulated with the addition of another modal operator:
Necessarily, all American Presidents are necessarily born of human parents
Our claim contains a similar de re/de dicto ambiguity. Taken in a de re sense it means:
TNOD1: All dodos (where ‘dodos’ mean actual individuals that are dodos) are necessarily born either of dodo parents or parents of an evolutionary precursor species.
The critic of S5 however takes it in a de dicto sense with a concealed modal operator, in which case it means:
TNOD2: Necessarily, all dodos are necessarily born either of dodo parents or parents of an evolutionary precursor species.
Critics of evolutionary theories aside, the former claim appears to be true. All individual dodos in the actual world were either the progeny of other dodos or whatever creature dodos evolved from and, given that, have their respective origins properties necessarily6. It is a contingent matter however that these individual dodos happened to be actual, and so perfectly possible for there to different individual dodos that have different origins. This allows us to accommodate dodos de dicto coming to be in different ways e.g. through direct divine creation, Davidsonian swamp man scenarios, cloning and other genetic modifications. As at least some of these alternative origins are not temporally specific and so compatible with 2D; the thesis of natural origin is shown to be unmotivated thus origins essentialism in this context does not present a genuine problem for S5.
So far the first problem, stemming from the thesis of natural origin, was found to be toothless, as said thesis derived most of its force from linguistic sloppiness including a de re/de dicto shirt and a concealed modal operator. Origins essentialism only entails that individuals of a certain kind have whatever origins they in fact have necessarily and not what origins all possible instances of that kind must have.
However there are still problems lurking on the horizon for those committed to strong variants of origins essentialism. Perhaps there is something disturbing about certain individuals having their origins of necessity.
Let us consider an individual dodo, Horacio Dodo, progeny of Winston and Celica Dodo. Horacio is a possible being, a possible individual instance of a possible kind, and thus according to the conjunction of 1 (the S5 claim) and 2 is possible at 16:30 on the 24th of March 2017. Yet if the origins conditions e.g. the fertilised egg from Winston and Celica or those redoubtable dodos themselves, do not exist at that time (or in the relevant time window) then Horacio is not possible. If this is the case then Horacio’s existing is only possibly possibly true and not necessarily possibly true (◇◇p instead of □◇p), a blatant counter-example to S5 which holds that all possibilities themselves necessary.
This objection works on the same principle as the former version: origins conditions for seemingly possible beings are in some cases temporally specific and thus contingent, a consequence being that the possibility of said beings themselves turns out to be contingent as well. It is unsurprising the problem should occur in the case of possible individuals; one if not the major threat to the universal application of S5 comes from the claim that there are no truths about non-existent possible individuals, a position Alvin Plantinga termed ‘Existentialism’. Such a position is motivated by a number of concerns including existential predication, certain Millian accounts of reference and difficulties with singular foreknowledge7. Note also that the other major objection: Hugh Chandler’s animadversion about identity and part variation between worlds, also focuses on individuals (Chandler’s argument is designed to show that the identity of an individual object is not always transitive and thus some worlds are not accessible from others). Whereas the conflict might lie with the notion of possible individuals themselves we shall briefly raise some of the specific issues relating to the objection discussed in this article.
Possible Worlds and Temporally Indexed Propositions
Let us take the classical definition of a possible world as a maximally inclusive conjunct of all true positions. Presumably this conjunct includes temporally indexed propositions e.g. ‘Caesar crossed the Rubicon on January the 10th 49BC’; indeed aside from (some) propositions about abstract objects and perhaps God any existential or property-attributive position can be further assayed as a temporally indexed propositions e.g. ‘the Great Pyramid exists and the Hanging Gardens of Babylon do not exist’ becomes ‘the Great Pyramid exists in the year 2018 and the Hanging Gardens of Babylon do not exist in the year 2018’. But do all temporal propositions have a truth value? Some would argue propositions about the future are neither true nor false, and thus cannot be part of the maximally inclusive world conjunct.
Although such an account would have widespread repercussions for our understanding of worlds it does not seem to directly affect the sort of modal propositions under discussion. Even if one admits that at any time preceding the present year (2018) the proposition ‘the Great Pyramid exists in the year 2018’ lacks a truth value that in itself does not entail that ‘possibly, the Great Pyramid exists in the year 2018’ lacks such a value or is false. Propositions that defy bivalence are about what actually happens in the future and not what could possibly happen. So this position does not directly generate the modal problems we are discussing.
The theist can object that it is possible for Horacio at said time. Recall that although origins essentialism prevents God creating Horacio ex nihilo God still possess the power to create Horacio by instigating a causal chain which leads to his coming to be. If however the prior link in said causal chain e.g. Winston and Celica do not exist at the time immediately prior to Horacio’s coming to be then Horacio is not possible. Baring dubiously coherent scenarios in which God can alter the passage of local time or change the past it appears that even God cannot cause Horacio to exist at the stipulated time.
Classical theists can claim that this presents a false picture of God’s causal activity. God does not decide at a certain time to create something and then act on that intention at another time or even instantaneously, for this would imply that God is temporal, something many theists, classical or otherwise deny. Instead—they say—divine creation is from eternity, meaning that God is not obliged to bring about the causal chain leading to the existence of X at Y time within a certain time frame following His decision. God has the whole of temporal history prior to X’s coming to be for the relevant causal chain to unfold, as the decision to create X was logically prior to temporal existence. As of this in any world in which God chose to create Horacio Winston and Celica and all of his other necessary antecedents right back to the first dodo, whether coming to be through creation ex nihilo or abiogenic process, also existed.
Even on such an account there still appear situations where origins essentialism and temporal constraints affect possibility. Let us stipulate that Horacio is the result of a very long causal chain, each member of which requires a certain period time prior to carrying out their causal activity; if so then presumably not even God can cause Horacio to exist at some point in time earlier that would permit such elapsed causal time periods, say, a few seconds after the Big Bang. So reverting to our old point if Horacio cannot exist at time X then Horacio is not possible at time X, ergo Horacio’s being possible is only contingently true.
Is it really a counter-example?
The problems we have been discussing in this essay all derive from claim 2, that if a being is metaphysically possible then it is metaphysically possible at all times. They key notion here is metaphysical possibility though; proponents of S5 are happy to admit that in weaker senses pertaining to other forms of modality i.e. temporal or ‘accidental’ modality, a being might be possible in some times and not in others. We believe truths about the past are now unalterable and thus in a sense necessary e.g. now that the proposition [Caesar crossed the Rubicon on January the 10th 49BC] has been made true it cannot be otherwise. The necessity of the past though is not the metaphysical necessity philosophers deal with when they make use of possible worlds however. Following William of Ockham we shall term the necessity attached to propositions dealing with past events accidental necessity8.
We might try to explain the aforementioned impossibility of Horacio at a certain time in a similar way, as an instance of this temporal accidental necessity. Unfortunately I do not immediately see how this can be done. There are temporal elements in our problem but the modality pertaining to origins essentialism is fully fledged metaphysical modality. The worlds that are accessible from the actual world change over time and in a stronger sense than being temporally possible.
What to do?
To round things up: if S5 is the correct modal system, something most philosophers are keen to affirm regardless of Plantinga’s ontological argument, partly because of the perceived obscurity of relative possibility, then one of the premises in the above arguments must be false. The natural candidate is 2, the claim that if an existential proposition about an individual being is possibly true then it is possibly true at all times. As has been alluded to this claim is subject to parody and might arouse our suspicion by the admixture of temporal concerns. Yet the exact problem with it proves hard to detect. Alternatively, and this is the approach I would tentatively suggest, we might discard such a strong variant on origins essentialism and prefer a weaker thesis e.g. that every materially constituted organic being has its genetic structure necessarily9. Philosophers might be unwilling to give up origins essentialism but that position does have its own problems and I suspect the usefulness of S5 would carry the day against it.
If one rejects these proposed amendments one might well have to bite the bullet and accept that axiom S5 does not apply in all contexts. If one cares to pursue possible world metaphysics as opposed to just formal semantics ascertaining what these contexts might be will be the next task. Even Nathan Salman, a critic not only of S5 but also of its weaker antecedents B and S4, recognises that there are some substantive modal claims that are invariant across all possible worlds regardless of accessibility relations. What I propose this suggests is that the concept of metaphysical modality is too broad; instead of lumping all kinds of less than narrowly logical necessity we need a more fine grained analysis which distinguishes between different varieties of ontological necessity, some of which may be best captured by S5 whilst others might warrant weaker systems such as Brouwer or even T10.
1. More formally it states that if p is possibly true then p is necessarily possibly true. When applied to beings as it will be in the course of this essay read p as ‘X exists’.
2. In a fascinating but frustratingly brief section in his book on the argument Graham Oppy suggests that the modal ontological argument can in fact be reformulated in a variety of modal systems as weak as T (pp. 71-72, Ontological Arguments and Belief in God, 1994). If this is the case then attacking the axiom solely on the basis of the role it plays in Plantinga’s formulation of the argument is foolish to say the least.
3. The locus classicus of anti-S5 argumentation is Hugh Chandler’s short essay ‘Plantinga and the Contingently Possible’, in which it is argued that tolerance for part-replacement leads to cases where identity is no longer transitive. These problems are taken up by Nathan Salmon in Reference and Essence and the article ‘The Logic of What Might Have Been’ and further developed to proffer objections to S4 and the Brouwer axiom. A major position which entails the falsity of S5, ‘Existentialism’, is discussed later.
4. To use a well-known example it might be necessary both that the Mona Lisa was composed out of the individual materials i.e. pigments and canvas, and that it was caused to exist by Leonardo. There is no prima facie reason why a philosopher could not hold to only one of these theses however. As we shall see later on many objections to modal systems S5, S4 and Brouwer appeal to necessity of material origin whereas the problem of this essay depends on causal origin.
5. A critic of 2 might attack that position by claiming it is not relevantly different from:
2*. If a being X is possible then it is possible at any given location (if a spatially extended being)
Most of us would be willing to accept 2* as false without thinking it has any bearing on metaphysical modality. A mammoth’s status as a possible being should not be compromised by the impossibility of fitting said furry pachyderm into a tea cup. A more reductionist B-theoretical reading of ‘time’ in our original 2 as ‘space-time region’ only makes this comparison more pointed.
6. The strong thesis of natural origins, the claim that every possible dodo has to originate from dodo parents of those of an evolutionary precursor species has counterintuitive consequences. For one it would follow that a dodo clone, even one qualitatively identical to the being from which it was cloned, would not count as a genuine dodo.
7. An overview of arguments in support of the positions can be found in Plantinga’s ‘On Existentialism’. More modern variants are discussed in Christopher Menzel’s ‘Temporal Actualism and Singular Foreknowledge’ and throughout the works of Barry Miller.
8. There is a possible risk of confusion here. Although accidental necessity is a modality pertaining to time philosophers often reserve the term ‘temporal necessity’ for ‘existence at all times, a hangover from diachronic accounts of modality. We introduce the additional term to satisfy the sharp-eyed (or the pedantic).
9. One notes a haunting resemblance between the recycling problem for origins essentialism and Chandler’s bicycle animadversion against S5. The fundamentally dubious Ship of Theseus problem lurks at the hearts of both.
10. One might, for instance, distinguish mereological necessity from mathematical necessity and the plain ol’ ontological necessity involved in property entailment and incompossibility.
Freddoso, Alfred (1983). ‘Accidental Necessity and Logical Determinism’ Journal of Philosophy vol. 80. Accessible here.
Chandler, Hugh (1976). ‘Plantinga and the Contingently Possible’ Analysis
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Kremer Elmar J (2014). Analysis of Existing: Barry Miller's Approach to God, Bloomsbury
Menzel, Christopher (1991). ‘Temporal Actualism and Singular Foreknowledge’ Philosophical Perspectives Vol. 5, Philosophy of Religion.
Salmon, Nathan (1989). ‘The Logic of What Might Have Been’ The Philosophical Review Vol. 98, No. 1.
Graham Oppy (1995). Ontological Arguments and Belief in God, Cambridge University Press.
Plantinga, Alvin (1983). ‘On Existentialism’ Philosophical Studies vol. 44, No 1. Accessible here.
Plantinga, Alvin (1974). The Nature of Necessity, Clarendon Press Oxford.
Kripke, Saul (1981). Naming and Necessity, Blackwell Publishing.
Vance, Chad (2014). ‘Origins Essentialism’ 1000-WordPhilosophy: An introductory Anthology. Available here.