A Modal Aporetic Tetrad

Here is a four-limbed aporetic polyad:

1. The merely possible is not actual.

2. To be actual is to exist.

3. To exist is to be.

4. The merely possible is not nothing.

Each limb is plausible, but they cannot all be true.  The first three limbs, taken together, entail the negation of the fourth.  Indeed, any three, taken together, entail the negation of the remaining limb, as you may verify for yourself. 

Now which limb ought we reject in order to avoid logical inconsistency?  (1) is non-negotiable because purely definitional.  Everything actual is possible, but not everything possible is actual.  'Merely possible,' by definition, refers to that which is possible but not actual.  This leaves us three options.

(2)-Rejection.  One might reject the equivalence of the actual and the existent analogously as one might reject the equivalence of the temporally present and the existent.  Just as one might maintain that past events exist just as robustly as present events despite their pastness, one might maintain that merely possible items exist just as robustly as actual items.  David Lewis' extreme ('mad dog') modal realism is an example of (2)-rejection.  On his modally egalitarian scheme there is a plurality of possible worlds all on an ontological par.  Each is a maximal mereological sum of concreta.  Each of these worlds is actual at itself, but no one of these worlds is actual simpliciter.  For each world w, w is actual-at-w, but no world is actual, period.  Thus there is no such property as absolute actuality.  It is not the case that one of the worlds is privileged over all the others in point of being actual simpliciter.  What is true of a world is true of its occupants:  I enjoy no ontological privilege over that counterpart of me who is bald now and living in Boston.  Actuality is world-relative and 'actual' is accordingly an indexical term like 'now.' When I utter a token of 'now' I refer to the time of my utterance; likewise, on Lewis' theory, when I utter a token of 'actual,' I refer to the world I am in.

Having rejected (2), a Lewis-type philosopher could gloss the other limbs of the tetrad as follows.  To say that the merely possible is not actual is to say that merely possible objects (e.g. bald Bill the Bostonian) are denizens of worlds other than this one.  To say that to exist is to be is to say that there is no distinction between the existence of an object and its being in some world or other.  To say that the merely possible is not nothing is to say that objects which are not denizens of this world are denizens of some other world or worlds.

I am tempted to say that this solution, via rejection of (2), is worse than the problem.  For one has to swallow an infinity of equally real possible worlds.  Further, my possibly being bald is not some counterpart of mine's being bald in another possible world.  (This critique of course needs to be spelled out in detail.)

(3)-Rejection.  A second theoretical option is to reject the equivalence of being and existence, of that which is and that which exists.  Accordingly, there are things that are but do not exist.  They have Being but not Existence.  Everything is, but only some things exist.  The early Russell, in the Principles of Mathematics from 1903, toyed with this view although he rejected it later in his career.  If existents are a proper subset of beings, then one could locate merely possible items in among the beings that do not exist.  The merely possible would then have Being but  not Existence or Actuality.

This solution leads to an ontological population explosion much as the Lewis theory does. 

(4)-Rejection.  A third option is to deny (4) by affirming that the merely possible is nothing in reality, that it has no ontological status.   One might construe the merely possible as merely epistemic, as being merely parasitic on our ignorance, or as having no status outside our thought.   A view along these lines can be found in Spinoza. 

Intuitively, though, it seems mistaken to say that there are no genuine, mind-independent possibilities.  My writing desk, for example, is one inch from the wall, but it could have been two inches from the wall.  It is not just that I can imagine or conceive it being two inches from the wall; it really could be two inches from the wall even though this possible state of affairs was never actual and never will be actual. (Moreover, what I CAN imagine or conceive refers to real but unactual possibilities of imagination and conception; or will you say that these possibilities are themselves derivative from acts of imagining or conceiving?  If you do, then a vicious infinite regress is in the offing.))

Now suppose I had provided more rigorous and more convicing rejections of each of the three theoretical options.  Suppose that a strong case can be made that all four propositions must be accepted.  Then we would have four propositions each of which has a very strong claim on our acceptance, but which are collectively inconsistent.  (Assume that the inconsistency is demonstrable.) What might one conclude from that?  (A) One possibility is that we ought to abandon the Law of Non-Contradiction.  (B) A second is that one of the solutions must be right even though we have good reason to think that every solution is mistaken.  (C) A third is that the aporetic tetrad is an insoluble problem, a genuine intellectual knot that cannot be untied.

Note that (A), (B), and (C) form a meta-aporia.  Each of them has a claim on our acceptance, but they cannot all be true.

Suppose there are genuine but absolutely insoluble philosophical problems.  What would that show, if anything?

Comments

[Steven]

Dr Vallicella,

Can we say that those things which are not actual are nonetheless "real" in the sense that they are ideas in the mind of God? There is no object in the world which is "bald Bill the Bostonian", yet God has an idea of a person so named. Is there a solution somewhere along these lines?

[Pete Wolfendale]

I think there are three points I can add here:-

1. There is an alternative way of rejecting 3. Instead of agreeing with Meinong that there are beings that do not exist, taking existence to be the stronger concept, one could take being to be the stronger concept and hold that there are existents that are not beings. Another way of putting this would be to hold that there are existents that are not real, and that being involves reality/realness. A view like this is held by Kit Fine in his paper 'The Question of Ontology'.

So, for instance, we might take that it in some sense it is in some sense *actually* true that 'Harry Potter has a best friend', but that it could feasibly not have been the case. Here there would be some thin notion of existence that could be understood in terms quantification over an actual domain. There could thus be fictional objects that are in some sense actual without being real (e.g., Harry Potter and his best friend), simply in virtue of our ability to coherently enumerate them. Of course, this approach has its own problems. The notion of actuality here is quite weak, and would need to be coherently explained, and the notion of reality/realness is very strong, and ultimately doing most of the heavy lifting, and really needs to be explained. I don't buy Fine's own proposal for how the latter notion should be explained, although I do think it points in the direction of some interesting conceptual connections.

The one other problem with this approach is that it might fall foul of your own and other's objections against Quinean accounts of existence in terms of quantification, even if the notion of 'real' is playing the role of so called 'thick' existence. I'm particularly thinking of the instantiation objection, wherein instantiation can't be understood without some notion of existence, which would seemingly preclude even a 'thin' notion of existence understood in terms of quantification. My own response to this would be to claim that this objection doesn't hold against substitutional accounts of quantification, and to follow Brandom in providing a substitutional account of the pragmatics of quantification, which underpins an objectual semantics. I think this gets around most of the ordinary problems people have with substitutional accounts (e.g., quantifying over infinite sets of various cardinalities), while also helping to explain why the 'thin' notion of existence is so thin (i.e., insofar as we have a set of coherent substitutional practices, we've got some existents).

The final point under this heading is that the notion of realness would need to be such that it didn't apply to whatever one counts under the heading of 'merely possible', be it possible entities, possible worlds, or possibilities simpliciter. This leads on to the second point.

2. There are various ways of understanding what the 'merely possible' consists in. Most decisions on this matter tend to be settled by modal semantics. It suffices here to point out that there are ways of construing modal semantics in terms other than that of fully determinate possible worlds. There have recently been attempts to take possibilities, which are not fully determinate, as the primary semantic interpretant, though I can't remember any names off of the top of my head. My own preference (unsurprisingly) is Brandom's incompatibility semantics for modal operators. This takes incompatibility relations between propositions to be the semantic primitive, and because these are implicitly modal (if P and Q are incompatible, then it is impossible that P&Q), he can use them to build up something like an S5 semantics for possibility and necessity. I won't go into the various ways that choices of modal semantics could affect the debate here, but I think it is important to recognise that they do so affect it, because they present different options for what one is denying being or reality to.

3. There is an alternate Spinozan metaphysical view that one can adopt (and which I endorse). This is to say that the real metaphysical features of the world that underlie our modal talk about it are not possibilities, but capacities. One can then say that whichever capacities are actualised are in some sense necessarily actualised, but that there are nonetheless unactualised capacities. Put differently, there is more potential than is realised, even if whatever potential that is realised is necessarily so realised.

The idea here would be that our counterfactual talk about various alternate possibilities serves to help individuate more or less general capacities that could be actualised in different ways, thus facilitating prediction of future events. This can include both individuating the specific capacities of individuals beyond the way they are actualised in a given situation, and abstracting the capacities of types of entities from these individuals. One can then think of claims about possible counterfactual states of affairs being true just insofar as predictive generalisations of them are true, and being true precisely insofar as they ignore the additional features of the fully determinate actual world which necessitated that the counterfactual did not actually obtain.

One would have to tell a novel story about the semantics-metaphysics interface here, given that we can't talk about these capacities without talking about concrete counterfactual situations in which they would be actualised, which is prima facie a reason to take such possible situations as the primitive metaphysical category. Nonetheless, I think such a story could be told, and that it makes sense to think of capacities as what underlie the *production* of actual situations, even if our understanding necessarily runs in the opposite direction (via the counterfactual). A good reason to think that this kind of story is a good one is that it can also apply to the case of probability, whereof there have been plenty of debates about how to reconcile its objectivity with determinism. Here we could talk about tendencies as opposed to capacities, and say that our talk of probability really tries to individuate tendencies, which similarly underlie the production of actual states of affairs, for predictive purposes. This provides a sketch of the reality of the modal as something which is not determined by the semantics of modal discourse, without thereby being at odds with it.

[George R.]

I don't know if there are any absolutely insoluble philosophical problems. But if there are, I don't think this is one of them.

If you change 4 to read, "The merely possible is nothing,except insofar as its principles inhere in the actual," the apparent contradiction disappears.

[Bill Vallicella]

Steven,

Which of the four propositions are you denying? You appear to be denying (3): to exist is to be. You are suggesting that a merely possible being does not exist but has being as a mere object of divine thinking. This may be the beginning of a solution. But how do you respond to someone who calls it a deus ex machina?

[Bill Vallicella]

Peter W,

Thank you for your rich and detailed comments. In #3 you write, >>There is an alternate Spinozan metaphysical view that one can adopt (and which I endorse). This is to say that the real metaphysical features of the world that underlie our modal talk about it are not possibilities, but capacities. One can then say that whichever capacities are actualised are in some sense necessarily actualised, but that there are nonetheless unactualised capacities. Put differently, there is more potential than is realised, even if whatever potential that is realised is necessarily so realised.<<

Capacities, powers, dispositions and such would seem to take us straight back to the notion of the possible. If x has the power to do A, then it is possible that x do A. In what sense are actualized capacities necessarily actualized? That strikes me as false, but it depends on what exactly is meant. I have actualized my capacity to play chess but not my capacity to play Go. But the respective actualization and non-actualization are surely contingent.

I don't understand why you say that a potentiality that is realized is necessarily realized. Roger Bannister had the potential to run a 4 minute mile before he did so. His realization of that potential was a contingent event, one that might not have occurred.

[Bill Vallicella]

George,

The scholastic term 'principles' is obscure. It would be nice to have an example of a merely possible individual or state of affairs whose 'principles' inhere in the actual.

[Steven]

"Which of the four propositions are you denying? You appear to be denying (3): to exist is to be."

I'm not sure I'm denying any of the propositions; I'm just suggesting we be a bit more explicit about we mean by "actual", "exist", etc.

"You are suggesting that a merely possible being does not exist but has being as a mere object of divine thinking."

Maybe. I'm saying that there are perhaps modes of existence--what it is for me to exist is something different than what it is for me in a different possible world (where I never read your blog before) to exist.

If possibility-existing is a different mode than actual-existing, then we can say that possible objects exist, and actual objects exist, but in different modes.

"This may be the beginning of a solution. But how do you respond to someone who calls it a deus ex machina?"

I'd say this. If we don't bring God into the picture, then perhaps we have a genuine insoluble problem. But if we see that it is easily resolved (though I'm not saying *in fact* it is easily resolved, just it *seems to be*) when we bring into the picture something like God, then that may be evidence to think that God does exist, and the move is legitimate. Maybe if God existed, we should expect him to be playing a central role in much of the way we think about philosophical issues such as these. He'd be the ultimate reality; we should expect him to play a big part in the way the universe is structured. Of course, this assumes that other methods of resolving the problem are failures or something close enough.

[Pete Wolfendale]

Thanks Bill,

As I noted in my comment the difficulty for Spinozan picture I painted is that we can't talk about capacities without talking about possibilities, which tends to suggest that we should take possibilities to be metaphysically primary. However, I was suggesting that this needn't be the case. To see this, it's first important to get clear about the distinction between possibilities and capacities.

Possibilities are always particular situations that might or might not be actualised. We can either talk about future possibilities or counterfactual possibilities, but in each case we are talking about *states of affairs*, that either could become, or could have been actual. This means that we can talk about the counterfactual situation in which I got up 3 hours late today, or the future possibility in which I get up 3 hours late tomorrow. Possibilities don't need to be completely determinate (as possible worlds are supposed to be), so we don't need to specify the movements of distant galaxies in either the counterfactual or projected situations we're discussing, but we must specify a particular time at which they occur. If we just say something like 'Pete could get up 3 hours late (on any day)', then we're saying something about my capacities, and the way these capacities contribute to the production of various actual states of affairs. Now, that particular statement is very lax, but conditional statements like 'Pete could write a book if he had sufficient time and resources' are far more normal, and more proper. It is by further qualifying such conditionals, adding further defeasors and counter-defeasors that we individuate the capacities of a given thing. We can also abstract from given entities to talk about the general capacities of types of entities (e.g., 'Trained philosopher's are able to write books given sufficient time and resources'). All of this can be seen as part and parcel of trying to understand the causal laws governing the interactions of various different types of entities within the world.

Now these kinds of conditionals can be applied to particular states of affairs, to show that, if we *stipulate* that this particular aspect of the situation had been different, then other aspects would have been different in a systematic way. This is entirely compatible with some kind of Spinozan determinism in which we hold that those aspects that we stipulated as being different could nonetheless not have been otherwise. The important point here is that the only way we are able to argue about these conditionals (and thus properly individuate individual and general capacities) is via positing specific counterfactual situations through this kind of stipulation. This is the reason why it seems that possibilities should be metaphysically primary.

Normally, on a possible worlds view, we either have to deny determinism, or accept that all variation between worlds is a result of either a) variation in initial conditions or b) variation in laws. Given that the major point of modal talk is to individuate laws, we end up getting pushed back to (a). The problem with (a) is that it is not obvious that there could be a change in initial conditions corresponding to each counterfactual possibility we would like to discuss. We can talk about the counterfactual scenario in which your desk is precisely 3 inches away from your wall, but what reason do we have there to suppose that there is some minute variation of the initial conditions of the universe that results in this - and only this - variation, other than the fact that it makes the possible worlds interpretation of counterfactual reasoning work. I think this is very implausable. The Spinozan alternative is to ignore such variation in initial conditions, accept that there is only one way the world could have turned out, but to hold that the way the world turns out at each point is a direct result of the way that the real modal features of entities within the world constrain eachother's actualisation.

We can thus legitimately claim that Roger Bannister had the potential to run a 4 minute mile before he did so, it's just that everything else in the world constrained the way his capacities were actualised such that he only did it when he actually did so. If the world had been different, then his capacity could have been actualised differently, but it couldn't have been so it wasn't.

To phrase the metaphysical idea a bit differently, each thing has genuine modal features (capacities and tendencies), and these constrain (and even partially determine) which actual states the thing will find itself in, but they do not *fully* determine it. Only the contribution of the rest of the world is sufficient to select which capacities are actualised, and in what way.

Does this help clarify my position a bit?

[George R.]

"It would be nice to have an example of a merely possible individual or state of affairs whose 'principles' inhere in the actual.”

Bill,

By principles I mainly mean causes. A statue, for example, is possible because blocks of marble (material cause), sculptors (formal and efficient causes), and commissioners of artwork (final cause) are actual. Thus, the extra-mental reality of possible things is found only in actual things.

But there is another Aristotelian principle that determines what is possible that is not a cause; and that is privation. For example, one of the reasons your desk is potentially two inches from the wall is because it is not two inches from the wall. Privation is the actual state from which something is moved in order for the possible to be made actual.

In my opinion, Aristotle completely solved actual/possible dilemma, which is why I’m simply regurgitating his teaching here.

[Bill Vallicella]

Steven,

Well, you have to be denying one of the propositions, because they cannot all be true. Any three of them, taken together, entails the negation of the remaining one. That's why there is a problem. You have four plausible propositions, but they cannot all be true. So which one do you reject?

In effect, you are denying (3) by introducing modes of being.

I like the rest of what you say.

[Steven]

I think I see now how I am rejecting (3). I wasn't not paying enough attention to how you used "exist" in your original post.

Do you think that my "Divine Ideas" suggestion is subject to the "ontological population explosion" objection like you say in your original post?

[Steven]

Ugh... that was terrible:

"I wasn't not paying enough..."

should be

"I wasn't paying enough..."

[Bill Vallicella]

Steven writes, "Do you think that my "Divine Ideas" suggestion is subject to the "ontological population explosion" objection like you say in your original post?"

No, because mere possibles on your shceme would not be independent beings but only accusatives of divine thoughts.

[David Brightly]

Bill, as one of your modally-challenged readers I'd like to suggest we reject (1). The picture of modality this gives is one in which, at every moment, we can partition all states of affairs into three sets: the actual, the merely possible, and the impossible. As time passes no doubt these sets change. But this is an absolute sense of the possible when we need a relative one. For consider the proposition 'it is possible for me to be in New York at noon tomorrow'. This is true now (subject to provisos with regard to volcanic ash clouds) but once I have missed the last flight from London (a century ago, the last ship) it becomes false and remains false from then on. So in general we should speak of the possibility of state s2 obtaining at time t2 relative to a state s1 obtaining at time t1. My suspicion is that your intuition concerning your desk arises from the correct judgement that at any time since the desk came to the house it would have been (relatively) possible to move it to two inches distance---there being nothing to prevent such a transition. I'm assuming intuitions derive from experience, and that experience is always of local phenomena, so a true intuition of a modal property of an absolute and far-reaching nature is an impossibility. So I accept the reality of possibility as you urge in your justification for (4) but reject its absolute conceptualisation implicit in (1).

[Bill Vallicella]

David,

Here is 1. The merely possible is not actual. There is no way this can be rejected since it is a matter of definition. Suppose you thought that everything is actual. Then nothing would be merely possible. But it would still be the case that the merely possible is not actual. It's just that the extension of 'merely possible' would be the null set.

[David Brightly]

I take your point, Bill. Let me try again. I see your tetrad as a reductio ad absurdum. Suppose the actual, the possible, etc, are sets of states of affairs. Let the merely possible be the possible less the actual. But to have any reality the merely possible must be a subset of the actual. Contradiction. Therefore the possible, etc, cannot be sets of states of affairs. In other words, possibility cannot be captured in a one-place predicate. I try to suggest reasons for thinking that a four-place relation, with explicit reference to time, might be more fruitful.

[Bill Vallicella]

David,

I see what you saying. But consider *Your being in New York one minute from now.* Since you are now in London, there is a clear sense in which that is not possible. But surely it is logically possible in that the supposition involves no logical contradiction. So we need to distinguish various senses of 'possible': logical, broadly logical, nomological, technologically possible, doable given constraints of time, money, energy, etc. For example, in 1950 it was narrowly logically, broadly logically, and nomologically possible to put a man on the moon. After all, neither the laws of logic nor the laws of nature ruled out such a trip. But it was technologically impossible. In 1969 it was technologically possible for the Americans and presumably also tech. possible for the Soviets, but not doable by the Soviets for economic reasons.

I am not saying that 'is possible' is always a 1-place predicate, but I think there are cases in which it is. Let n = the number of active volcanos on earth right now. Now consider the state of affairs *There being n + 1 active volcanos on earth right now.* Why can't I attach the one-place predicate 'is broadly logically possible' to a name of that state of affairs?

[David Brightly]

I do agree that it's useful to distinguish different senses of 'possible', such as the nomological, the technical, the economic, the political, etc. I feel we all understand these constraints quite readily. After all, our success as actors in the world is not unrelated to our judgement of possibility. But on reaching 'broadly logical possibility' (BLP) my intuition fails me. I would want to understand BLP in terms of freedom from contradiction. What would prevent p from being BL-possible is the presence of q and ~q amongst the logical consequences of p taken together with some set G of 'background' propositions which explicate the terms in p. But I doubt we could agree on what to put in G. Let's start with G empty, and suppose, for sake of definiteness, that there are 5 active volcanos on earth right now. I have no problem with 'it is BL-possible that there be 6 active volcanos on earth right now'. Concepts don't in general place constraints on how many times they are instantiated (although 'side of Trafalgar Square' and like concepts are perhaps exceptions). But suppose that we include in G propositions to the effect that volcanos are physical structures of a certain size, that the earth has a limited surface area, etc. A proposition like 'there are 1,000,006 active volcanos on earth right now' begins to look rather less free of contradictory consequences. In fact, we seem to have found our way back to physical impossibility, but described in logical terms. This is my problem with BLP---how do we demarcate its boundaries so that it is non-trivial and interesting but also so that it doesn't slide into one of the other categories of possibility we have indentified?

[Bill Vallicella]

Good comments, David. I'm working on a response.