Actual Alternate Possibilities… don’t exist.

Or “On the Non-​​Existence of Actual Alter­nate Possibilities”.

On my view there are three major cat­e­gories of pos­si­bil­ity: log­i­cal, meta­phys­i­cal, and actual. Log­i­cal pos­si­bil­i­ties are those per­mit­ted by logic, meta­phys­i­cal pos­si­bil­i­ties are those per­mit­ted by logic and [the laws of meta­physics, of which the best way we have come up with to dis­cern is through con­ceiv­abil­ity exper­i­ments], and actual pos­si­bil­i­ties are those per­mit­ted by logic, [the laws of meta­physics], and actuality.

There are alter­nate log­i­cal pos­si­bil­i­ties all over the place. For exam­ple, there is no log­i­cal rea­son why there couldn’t be an object which is opaquely red all over and opaquely green all over in the same way at the same time. While such an object is incon­ceiv­able and so it is not meta­phys­i­cally pos­si­ble, there is noth­ing log­i­cally con­tra­dic­tory about it and so it is log­i­cally pos­si­ble. But in addi­tion to log­i­cal pos­si­bil­i­ties that are not meta­phys­i­cally pos­si­ble, all meta­phys­i­cal pos­si­bil­i­ties are also log­i­cal possibilities.

There are also man­i­fold alter­nate meta­phys­i­cal pos­si­bil­i­ties. For exam­ple, there is no meta­phys­i­cal rea­son why there couldn’t have been a larger or smaller quan­tity of mat­ter in the uni­verse. While the actual uni­verse has exactly as much mat­ter in it as it does and so there is no actual pos­si­bil­ity that the uni­verse has a larger or smaller quan­tity of mat­ter, there is noth­ing incon­ceiv­able about it and so it is meta­phys­i­cally pos­si­ble. But in addi­tion to meta­phys­i­cal pos­si­bil­i­ties that are not actu­ally pos­si­ble, all actual pos­si­bil­i­ties are also meta­phys­i­cal possibilities.

How­ever, there are not any alter­nate actual pos­si­bil­i­ties. This is not to deny that there are any actual pos­si­bil­i­ties, but only that there are any alter­nate actual pos­si­bil­i­ties. This can best be under­stood by exam­in­ing actual pos­si­bil­i­ties in three phases.

Firstly, there are actual pos­si­bil­i­ties con­cern­ing the past. Obvi­ously it was actu­ally pos­si­ble for Barack Obama to get elected, because he did. But because he got elected, there is no longer any chance that in the actual world, Obama does not get elected. And this is true for all propo­si­tions con­cern­ing the past: there are no alter­nate actual possibilities.

Sec­ondly, there are actual pos­si­bil­i­ties con­cern­ing the present. Obvi­ously it is actu­ally pos­si­ble for it to be gloomy in Coeur d’Alene, because it is. But because it is cur­rently gloomy, there is no chance it can actu­ally be sunny. There­fore, there are not any actual alter­nate pos­si­bil­i­ties con­cern­ing the present.

Finally, there are actual pos­si­bil­i­ties con­cern­ing the future. Obvi­ously what ever ends up hap­pen­ing in the future, such will have been actu­ally pos­si­ble. But because the future will unfold one way as a mat­ter of fact and not another, there are not any actual alter­nate pos­si­bil­i­ties. Another way of putting this is that future con­tin­gents, those propo­si­tions con­cern­ing the future which are not true out of meta­phys­i­cally neces­sity, each have a truth value. It is cur­rently either true or false that Jesus will actu­ally return at some­time in the future. And the fact that such is cur­rently either true or false means that whichever one is the case is true of the actual world. And if it is true of the actual world, then no actual alter­nate pos­si­bil­ity exists. The fact that it is con­ceiv­able that Jesus not return makes such sce­nario a meta­phys­i­cal pos­si­bil­ity, but not [nec­es­sar­ily] an actual one.

13 thoughts on “Actual Alternate Possibilities… don’t exist.

  1. Derek

    Good stuff, Louis. 

    If I’m read­ing you right, it seems no actual pos­si­bil­ity has its alter­na­tive com­pli­ment. I.e. if p is actu­ally pos­si­ble, then ~p is not actu­ally pos­si­ble (for simplicity’s sake, just assume p is time indexed to the past, though you seem to make all true time indexed propo­si­tions, includ­ing future ones, actual pos­si­bil­i­ties, which seems to rule out gen­uine alter­na­tives for the future). 

    Thus, if p is actu­ally pos­si­ble, then ~p is actu­ally impos­si­ble. But despite ~p being actu­ally impos­si­ble, could it still be meta­phys­i­cally pos­si­ble that ~p be actu­ally possible? 

    So let’s p say ‘I went to idaho’ and let p be true. On your view, p is actu­ally pos­si­ble, and it seems that ~p, which says ‘I want to idaho’ is false, is actu­ally impos­si­ble. My ques­tion: is it meta­phys­i­cally pos­si­ble that ~p is actu­ally possible?

    Think about it.

  2. Louis

    You’re read­ing me cor­rectly. Actual pos­si­bil­i­ties have no com­ple­ments. All actual pos­si­bil­i­ties are actual necessities.

    is it meta­phys­i­cally pos­si­ble that ~p is actu­ally possible?”

    No, because p con­cerns the actual world, and is true. So ~p is meta­phys­i­cally pos­si­ble, but not actu­ally possible.

  3. Derek

    So ~p is meta­phys­i­cally pos­si­ble, but not actu­ally possible.” 

    And hence, it’s not meta­phys­i­cally pos­si­ble that ‘~p is actu­ally possible’.

    Sup­pose that p is both L and M pos­si­ble, but that p is nei­ther L nor M nec­es­sary. Such a p might be “Derek is Louis’ friend”. Sup­pose that p is true, and hence, p is actu­ally pos­si­ble. You agree that if p is actu­ally pos­si­ble, it is both L and M pos­si­ble. Since p is M pos­si­ble, and nei­ther L nor M nec­es­sary, it seems that ~p and p are both L and M pos­si­ble. But in order for ~p to be L and M pos­si­ble, it must (it seems) be the case that it could have been the case that ~p is actu­ally pos­si­ble. Sup­pose the fol­low­ing sub­junc­tive con­di­tional is true:

    © Had David not known Derek, then Derek would have never know Louis. 

    The truth of © entails ~p, since you can­not be friends with some­one you don’t know. 

    Sup­pose that © is actu­ally true. It fol­lows that © is actu­ally pos­si­ble. And if © is actu­ally pos­si­ble, it seems that its con­se­quence, ~p, is pos­si­ble. For the fol­low­ing is an axiom of modal logic: 

    (AS) {[Vp & (p–>q)] –> Vq}

    Where V = “it is pos­si­ble that”

    (AS) reads: If “it is pos­si­ble that p, and it is true that ‘p entails q’,” then ‘it is pos­si­ble that q’.”

    Applied to our orig­i­nal case,
    (1) if © is actu­ally pos­si­ble, then so is any of its con­se­quences, which includes our orig­i­nal ~p.
    (2) © is actu­ally pos­si­ble.
    (3) ~p is actu­ally pos­si­ble.
    There­fore, it is actu­ally pos­si­ble that “Derek is Louis’ friend” is false.

  4. Derek

    I sup­pose you could get out of this by say­ing that though whole con­di­tional, ©, is true, it’s antecedent, ‘David does not know Derek’, is false, and there­fore actu­ally impos­si­ble, and there­fore its con­se­quent, ‘Derek does not know Louis” is false, and thereby actu­ally impos­si­ble, and hence, ©‘s con­se­quent, that ~p, is not thereby actu­ally possible. 

    Fine.

  5. Derek

    Good. Thanks for help­ing me through this. As long as we (oddly) have the power to make it the case that p is actu­ally pos­si­ble (and thereby actu­ally nec­es­sary) , where p describes what we have done or will do with our (lib­er­tar­ian) free­dom, I’m okay with every­thing so far.

  6. Louis

    And hence, it’s not meta­phys­i­cally pos­si­ble that ‘~p is actu­ally possible’.”

    That’s right, as p is world-​​indexed to the actual world, and p is true.

    Let’s rename your new “p” to “p”” for the sake of dis­tin­guish­ing it from our pre­vi­ous p or p’s.

    Sup­pose that [p”] is both L and M pos­si­ble, but that [p”] is nei­ther L nor M nec­es­sary. [Let p”] …be “Derek is Louis’ friend”. Sup­pose that [p”] is true, and hence, [p”] is actu­ally pos­si­ble. You agree that if [p”] is actu­ally pos­si­ble, it is both L and M pos­si­ble. Since [p”] is M pos­si­ble, and nei­ther L nor M nec­es­sary, it seems that ~p and p are both L and M possible. ”

    That’s all correct.

    But in order for ~p to be L and M pos­si­ble, it must (it seems) be the case that it could have been the case that ~p is actu­ally possible.”

    Here’s where we diverge. On my view, all actu­al­i­ties (actual pos­si­bil­i­ties and actual neces­si­ties, which on my view hap­pen to be the same de facto) are true in the actual world, and ipso facto, all propo­si­tions which are not true in the actual world are there­fore not actualities.

    In other words, if a propo­si­tion does not describe the actual world, it is not actual. Thus, meta­phys­i­cal pos­si­bil­i­ties that do not obtain in alpha are not actual possibilities.

    There­fore p”, since it does not describe the actual world, is not an actual pos­si­bil­ity. So, p” could have been the case. This is what meta­phys­i­cal pos­si­bil­ity is designed to express. But p” could not have actu­ally been the case.

    I admit that this is a non-​​intuitive use of the Eng­lish word “actual”, but such is the price we pay for using vul­gar terms in tech­ni­cal senses.

    I sup­pose… though [the] whole con­di­tional, ©, is true, it’s antecedent, ‘David does not know Derek’, is false, and there­fore actu­ally impos­si­ble, and there­fore its con­se­quent, ‘Derek does not know Louis’, is false, and thereby actu­ally impos­si­ble, and hence, ©‘s con­se­quent, that ~p, is not thereby actu­ally possible.”

    That’s cor­rect.

  7. Jonathan Charles Wright

    Response to main post:

    So, there’s the stuff that happened/​happens/​will hap­pen, and the stuff that could have hap­pened, or could be hap­pen­ing, or could hap­pen in the future. The stuff that hap­pens in time con­sti­tutes the actual world. The coulda-​​stuff is the stuff of pos­si­ble worlds. The for­mer actu­al­ity; the lat­ter pos­si­bil­ity. I think I get all that.

    But am I to read “actual alter­nate pos­si­bil­i­ties” as ‘stuff that could hap­pen past/​present/​future, given stuff that hap­pens past/​present/​future’? Your idea is to fix the course of his­tory com­pletely, and then to ask what pos­si­bly could hap­pen given this com­plete history.

    If this is what you intend, then it seems fishy. I won­der about what “pos­si­bil­ity” as a basic notion even comes to when what has, is, and will hap­pen is ‘fixed’ in this way. It seems that when­ever we ask whether some­thing is pos­si­ble, just in reg­u­lar speech, we are ask­ing what at some later time could occur given what has hap­pened before, keep­ing in mind rel­e­vant logical/​metaphysical/​physical laws.
    Even when we talk about stuff that ‘could have hap­pened’ in the past, like in the Obama case, we imag­i­na­tively ret­ro­spect to some time before the event in ques­tion and then say, given what had hap­pened up to that point and given the rules of the uni­verse we want to take into account, what could hap­pen next? But when you pro­vide a full descrip­tion of what is the case in the entire world at time T, we don’t ask what could pos­si­bly hap­pen at time T, since that’s pro­vided. Even the actual world’s his­tory is called a ‘pos­si­ble’ way things could play out by virtue of its stand­ing amongst a host of other ways things could have gone.

    So, your ‘actual alter­nate pos­si­bil­ity’ doesn’t seem like pos­si­bil­ity, or at least not like any inter­est­ing kind. Surely not the kind of pos­si­bil­ity we intu­itively mean when we say that A “could have done otherwise”.

    Do I mis­un­der­stand you? Am I clear? I feel like that was rambly.

  8. Jonathan Charles Wright

    Response to comments:

    My only thought in read­ing the com­ments was that the way you use “actual pos­si­bil­ity” is how I would use “actu­al­ity”. I don’t see how it’s a kind of pos­si­bil­ity at all. You might reply, ‘but the actual world is one pos­si­ble way things are’, and I’ll say sure, but what­ever sense of pos­si­bil­ity you invoke in say­ing so of the actual world is some inde­pen­dent sense of pos­si­bil­ity by which we eval­u­ate the actual world and pos­si­ble worlds alike: other worlds are that kind of pos­si­ble too. So when you say, ‘okay, but now that i have you admit­ting that the actual world is a pos­si­ble world, i want to talk about the spe­cific kind of pos­si­bil­ity that only the actual world boasts’ you fail to pick out some spe­cific kind of pos­si­bil­ity. There is not unique kind of pos­si­bil­ity that the actual world picks out: the actual world is indis­tinct from a mul­ti­tude of non-​​actual worlds, in terms of their mere pos­si­bil­ity. The thing that makes the actual world unique is its actu­al­ity, not its man­i­fest­ing some spe­cial ‘possibility’.

    I hope this is clear. I only harp on it because I think you mean to make the lan­guage of ‘pos­si­bil­ity’ do some work for you as things progress, and I think it will have been by a kind of trick. Again, I hope I’m clear.

  9. Louis

    Your idea is to fix the course of his­tory com­pletely, and then to ask what pos­si­bly could hap­pen given this com­plete history.”

    Yes, I believe his­tory is fixed. How­ever, con­sider the following.

    …’actual alter­nate pos­si­bil­ity’ doesn’t seem like pos­si­bil­ity, or at least not like any inter­est­ing kind. Surely not the kind of pos­si­bil­ity we intu­itively mean when we say that A “could have done otherwise”.”

    By that insight we can see that his­tory is not fixed in any inter­est­ing sense. There will be a lot more on this in a future post.

    As for your remarks about my use of “actual pos­si­bil­ity”, I want to say I agree that the lan­guage is uncon­ven­tional and there­fore mis­lead­ing. I thought about what else I could call the “actual” in “actual pos­si­bil­ity”, but noth­ing accept­able came to mind. I will con­sider “fac­tual”, but think I will run into sim­i­lar seman­tic prob­lems as I am with “actual”.

    As for the “pos­si­bil­ity” word choice in “actual pos­si­bil­ity”, I con­cede that it too is uncon­ven­tional and there­fore mis­lead­ing. But this time it is much more inten­tional, for it will become rel­e­vant in future posts.

  10. Louis

    though you seem to make all true time indexed propo­si­tions, includ­ing future ones, actual pos­si­bil­i­ties, which seems to rule out gen­uine alter­na­tives for the future”

    Just to be extra clear, I rule out ‘actual’ alter­na­tives, not ‘gen­uine’ alternatives.

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