Given their acceptance of NEC, REF advocates are committed toNEC’s right-to-left reading:
-
EN

And, assuming the factivity of necessity, EN entails:
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EF

The first puzzle is that complementary entities—possible entities that, due to conflicting essential properties, are not compossible—serve as counter-examples to both of the above principles and, consequently, to NEC.
The first example of complementary entities concerns events. Suppose we flip a coin c, at time t in location l. There are two possible outcomes—two events that might subsequently occur. One is the event Tails, which consists of flipping c at time t in location l and its landing tails. The other is the complement event, Heads, which involves c being flipped and landing heads at t in l.Footnote 11
Clearly, both Tails and Heads are possible—i.e., possibly, c lands heads at time t and in location l, and, possibly, c lands tails at t in l. However, they are mutually exclusive—Heads and Tails cannot both obtain. Further, if we take events to be fine-grained (either because, following Kim (1973, 1976), we take them to be structured, or because, following Lewis (1986), we think fine-grained events are necessary for an adequate account of causation), then part of what makes the event Tails the very event that it is, is that it involves c’s landing tails at this time and in this location. Consequently, it is plausible to say that c’s landing tails is partially constitutive of the very identity of Tails—it is part of what the event is, in the metaphysical sense of the term. Similarly, it is part of what makes Heads the very event that it is, that it involves c landing heads at this time, in this location. So, ‘c lands tails at time t and location l’ is true in virtue of the essence of Tails, and ‘c lands heads at time t and location l’ is true in virtue of the essence of Heads.
This leads to a problem. Given EF, it follows that both ‘c lands tails at t in l’ and ‘c lands heads at t in l’ are true. But it isn’t possible for both to be true—that would be a contradiction. Similarly, given EN, both are necessary. But this is false—after all, both Heads and Tails are possible outcomes of our flipping the coin! And note that, like with NEC, the quantification in EN and EF ranges over all possible entities. So the fact that (e.g.,) Heads doesn’t actually obtain (because Tails actually did) is irrelevant—all that is necessary to generate the problem is the fact that both complementary events are possible.Footnote 12
A second case involves tropes. Take this ball b’s redness-all-over-at-time-t trope r, and the distinct, mutually exclusive, albeit equally possible, trope of b’s greenness-all-over-at-time-t g. Part of what makes the former the thing that it is, is that it involves b’s being red all over at t. Similarly, part of what makes the latter the thing that it is, is that it involves b’s being green all over at t. So, if anything is true in virtue of the essence of r, it is that b is red all over at t. And if anything is true in virtue of the essence of g, it is that b is green all over at t.
By EF, these entail that the ball is red all over and green all over at t. But this is impossible. Further, by EN, it follows that necessarily, the ball is red all over at t and necessarily, the ball is green all over at t. But both of these necessity claims are false, because, given the possible existence of r and g, possibly the ball is green, and not red, all over at t, and possibly the ball is red, and not green, at t.
Consequently, complementary entities generate counter-examples to EF, EN and, by extension, NEC.
REF advocates might try to circumvent this puzzle by denying that there are any complementary entities. This, however, seems implausible. For one, it is clear that, if we understand events as fine-grained, then certain possible events will be mutually exclusive. Similarly, the identity conditions for tropes naturally deliver complementary cases.
Of course, some might not include events and tropes in their ontologies. But even this won’t block the puzzle, since there are complementary objects. For example, Fine himself (1995a: p. 244) suggests that certain conceptions of God and Satan are plausibly understood as complementary—e.g., if it is part of God’s essence that She is more powerful than every other entity, and part of Satan’s essence that he is more powerful than every other entity, then the two cannot co-exist. And the broader essence literature offers other cases. Following Salmon (1981: p. 210), by virtue of their being radically different table-types, Richard, a folding card table, and Judy, a dining table with a removable spacer, both of which could have been made from some specific collection of planks, are distinct. Assuming origin essentialism, Richard and Judy are complementary: if we make Judy, we ‘use up’ the planks, thereby preventing ‘further table productions from those [planks]’ (Rohrbaugh and deRossett 2006: p. 382). In particular, we are prevented from producing Richard.Footnote 13 So there definitely seem to be complementary entities, including complementary events, tropes, and objects.
A second, more plausible response involves conditionalizing. As the problem cases all involve non-necessary entities, mimicking moves used in the debate about so-called ‘weak’ necessities,Footnote 14 a REF-er might modify EN and EF by conditionalizing upon the existence of the relevant entities:
These alternative principles avoid the problematic results described above: the truth of both ‘if Tails obtains, then c lands tails’ and ‘if Heads obtains, then c lands tails’ is not contradictory, nor is there a problem with both conditionals being necessary. And whenever the relevant entity exists, the associated proposition will be true. Thus, if it is the case that Heads obtains, then c lands heads.
Unfortunately, this brings more trouble than it is worth.Footnote 15 Adopting EN* and EF* requires modifying NEC to something like:
However, NEC* only delivers conditionalized necessities, and many of the necessities we want to derive are non-conditional. For example, NEC* only guarantees that necessarily, if Socrates and the Eiffel Tower exist, then they are distinct. Yet the non-conditional necessity is the case too—i.e., necessarily, Socrates is distinct from the Tower.
REF advocates might try to dodge this problem by treating Socrates and the Tower as essential existents—i.e., entities whose essences include their own existence. As essential existents, their essences could then guarantee the necessity of the conditional’s antecedent, and hence, by distribution, the necessity of the consequent. In this way, we seem to be able to derive the non-conditional necessity from the conditional. However, it is implausible that Socrates and the Tower are essential existents; indeed, Fine himself says that ‘we do not want to say that [Socrates] essentially exists’ (1994a: p. 6). Further, this kind of solution is going to generate new problems: for example, necessarily, Heads is distinct from Tails, but we can’t stipulate that these complementary entities are both essential existents without reviving the problems discussed above.
The biggest problem is that it is unclear how to derive an analogue of POSS from NEC*. Following the previous method, we might try via a universal plurality U and the inter-definability of necessity and possibility: Suppose
. Given NEC*, this entails
(U exists
). Via inter-definability, we then get
(U exists
). This is equivalent to
(U exists & P). Distribution then gives us
.
However, it is not possible that U exists: U is the universal plurality, meaning it includes all the entities, including numerous non-compossible entities (namely, all the complementary ones). Consequently, there is no world where U, the vast, contradictory collection of every possible entity, exists. So, the step before distribution fails, and we can’t get an account of possibilities from NEC*.
One might try to avoid this problem by using the collective essences of maximally consistent sub-collections of U, but this leads to new difficulties. Suppose that MC1 and MC2 are distinct maximally consistent sub-collections of possible entities, such that the former includes trope g and the latter trope r. There will be much that MC1 is silent about. In particular, MC1 will say nothing about whether, if r exists, it is not distinct from {r}.Footnote 16 But
(r exists \(\rightarrow \) {r}) in turn entails that
(r exists \(\rightarrow \) r is not distinct from {r}), which is flatly false: necessarily, if r exists, then r is distinct from {r}! And what goes for MC1 will also go, mutatis mutandis, for MC2, or any other maximally consistent sub-collection: each of them will deliver false possibilities concerning the entities they do not include. Thus shifting to EN* and EF* does not help resolve the puzzle.
A third and final response REF advocates might pursue is to directly contest the essentialist statements used to generate the counter-examples. Consider the Tails/Heads case again. What led to the problem was the idea that part of what makes Tails the very event that it is, is its involving c’s landing tails. Similarly for Heads—part of what makes it the event it is, is that it involves c’s landing heads. Consequently, ‘c lands tails’ looks to be true in virtue of the nature of the former, and ‘c lands heads’ true in virtue of the latter.
However, one might contend that these are not true in virtue of the relevant natures. Rather, what is true are certain identity statements. For (according to this response) what it is to be Tails is to be the event of c’s landing tails at time t in location l, and what it is to be Heads is to be the event of c’s landing heads at time t in location l. So what is true in virtue of Tails’ nature is that Tails is the event of coin c’s landing tails at t in l. And what is true in virtue of the nature of Heads is that Heads is the event of c’s landing heads at t in l. These identity statements do not contradict—meaning no problem for EF—and both of their necessitations seem true—meaning no problem for EN.
Similar reasoning applies in the trope case: what is true according to r’s nature is that r is the trope of ball b’s being red all over at time t, and what is true according to g’s nature is that g is the trope of ball b’s being green all over at time t. Again, these do not contradict, nor are their necessitations false.
An initial counter is that the embedded definite descriptions are existence entailing—i.e., if ‘Tails is the event of c’s landing tails at t in l’ is true, then there exists an event that is such that c lands tails at t in l. And, of course, the existence of an event that is such that c lands tails entails that c lands tails. Consequently, by EF, it being true in virtue of the nature of Tails that Tails is the event of c landing tails at t in l entails that c lands tails at t in l. And its’ being true in virtue of the nature of Heads that Heads is the event of c landing heads at t in l entails that c lands heads at t in l. So, we hit the contradiction. Further, the existence entailing nature of the definite description means that necessity of ‘Tails is the event of c’s landing tails at t in l’—as guaranteed by EN—entails the necessity of ‘c lands tails at t in l’. And as the same will hold for Heads’ essentially being the event of c’s landing heads at t in l’, the original problem for EN will also emerge.
Of course, not everyone agrees that definite descriptions are existence entailing. With that in mind, a second issue is that this response leads to a kind of ‘revenge’ version of the problem. Consider the fact that Tails occurs and the complementary fact that Heads occurs—i.e., [Tails occurs] and [Heads occurs]. Plausibly, it is true in virtue of the nature of [Tails occurs] that c lands tails—after all, c’s landing tails is a vital part of what makes this fact the very fact that it is, serving to individuate and characterize it. For similar reasons, it is true in virtue of the nature of [Heads occurs] that c lands heads. As both facts are possible, they generate counter-examples to EF, EN, and NEC, even in light of the above response.
REF advocates might try to block this revenge problem by making some distinctions at the level of essence statements.Footnote 17 Following Correia (2006, 2013), let us distinguish between objectual, generic, andalethic essence statements.Footnote 18 The key difference between these is that the first describes the natures of things, the second the natures of ways of being, and the third of things being a certain way. For example, consider:
-
(1)
It is essential to Socrates to be human
-
(2)
It is essential to being a human to be a rational animal
-
(3)
It is essential to Socrates’ being a human that he be a rational animal
Here, (1) expresses objectual essence—it tells us something about Socrates’ nature—while (2) expresses generic essence—it tells us something about the nature of being a human—and (3) expresses alethic essence, as it says something about the nature of Socrates’ being a certain way (namely, his being a human).
Importantly, according to Correia (2013: p. 277),Footnote 19 alethic essence statements cannot be reduced to objectual essence statements. Plausibly, part of what [Tails obtains] is, is that [Tails obtains] is a fact. However, it does not seem part of what it is for Tails’ obtaining to be the case is that [Tails’ obtains] is a fact, nor that there are facts at all. So there is a difference between the former, objectual essence claim, and the latter, alethic essence claim.
Using this distinction, the REF advocate can reject the key claim in the ‘revenge’ argument. In other words, according to this reply, while it is part of nature of Tails’ obtaining that c lands tails, it is not part of the (objectual) nature of [Tails obtains] that c lands tails at t in l. So ‘c lands tails at t in l’ is not true in virtue of the nature of [Tails obtains], and the counter-example does not get going. Instead, the closest thing that is true in virtue of the nature of [Tails obtains] is another identity claim: namely, that [Tails obtains] is the fact that c lands tails at t in l. But, as before, this does not generate a problem (assuming we set-aside the matter of whether the embedded definite description is existence entailing).
I must confess that I find denying that it is true in virtue of the (objectual) essence of [Tails obtains] that c lands tails at t in l counter-intuitive. And, obviously, if this is true, then the above attempt to circumvent the puzzle fails. That said, even if we grant that it is not part of the essence of [Tails obtains] that c lands tails at t in l, we can still get the puzzle going.
Recall again that there are complementary objects: Fine’s example of God and Satan, and the two tables, Richard and Judy, both of which essentially originate from some specific collection of planks. The counter-examples to EF and EN feature objectual essentialist claims. For example, ‘it is essential to God to be more powerful than any other being’ is a statement of objectual essence, as is ‘it is essential to Satan to be more powerful than any other being’. Plugging these objectual essence claims into EF gives us a contradiction: God is more powerful than Satan, but Satan is more powerful than God. Similarly, plugging them into EN gives us conflicting (and false!) necessities: necessarily, God is more powerful and necessarily, Satan is more powerful. The alethic/objectual distinction does not seem to help in these cases. Consequently, the problem remains.
The general upshot is that complementary entities pose a problem for the REF, in that they entail the falsity of NEC. And until a proposal is put forward that handles these cases, the REF is in trouble.