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If something happened, was it necessary for it to happen?

  
 
Good Intentions
08:50 / 25.04.08
So, in modal logic class yesterday we were going over a claim Aristotle made (2500 years old and still relevent, too bad he couldn't count women's teeth), where he says that future-tense sentences aren't true or false. Now, lots of people have had a go at giving their own explanation of why this is right or wrong, but we spent most of our time on one of the premises of his argument, which is a pretty interesting argument in itself. Aristotle says that what is true is necessarily true, a claim he cashes out as follows:

if a thing is white now, it was true before to say that it would be white, so that of
anything that has taken place it was always true to say that a thing is or will be,
it is not possible that it should not be or not be about to be, and when a thing
cannot not come to be, it is impossible that it should not come to be, and when
it is impossible that it should not come to be, it must come to be. All, then, that
is about to be must of necessity take place.

So, breaking it down, it becomes something like this:

For some event 'e':
(i) If ‘e is happening’ is true, then ‘e will happen’ was always true.
(ii) If ‘e will happen’ was always true, e cannot not happen.
(iii) If e cannot not happen, then it is necessary for e to happen.
Conclusion: If ‘e will happen’ was always true, it was necessary that e e would happen.

I think this is a very smart thing to say. It takes a fact about how we use words, comes to an informative conclusion, and each step of the way teaches us something about how we actually use modal terms in our vocabulary, terms like 'possible', 'necessary', etc. Since modal logic is the project of trying to make clear how truth and falsity works, this argument seems to be modal logic from the top shelf.

Let's look at the premises in order:

(i) is the one which does all the work, I think. It captures something non-obvious about the way we track the truth of statements made at some time throughout the timeline, ie, if I say tonight that 'Auckland will wring the rugby tomorrow', meaning that on Sat 26 April 2008 Auckland will win the rugby, and it turns out that they do, I would have been right now to say what I did. If I said it yesterday it would have been true as well, in fact, if I had made that claim at any time throughout history, it would be true (let's not be confused by the indexical 'tomorrow', I'm not saying that, whatever day we might consider, Auckland will win the rugby the day after, but pointing to tomorrow, 26 April 2008). For instance: people often wail on Marx for predicting that it is inevitable that the workers of the world would bring about communism through revolution, because in the absence of such a revolution it seems like his claim turned out to be false, but if this revolution were indeed to happen, then Marx would have been right all along. So, if some event occurs, saying that that event would occur would always have been true.

(ii) might be a tautology, but attached to (i) it becomes an informative claim. The tautology is: if something were always true, then it could never have been false. (ii) is: if it were always true that some event would happen, then that event never could not happen.

(iii) brings about the conclusion, and is another tautology: if something cannot not happen, it was necessary for it to happen. This seems to be what 'necessary' means. And attached to (i) and (ii) we have come to the conclusion: if something happened, it was necessary for it happen. We started off with an observation of what we typically think is true, added the meanings of words at work, and have ended up supporting a substantive claim. Great stuff.

So, is everything that has happened actually inevitable? The above argument certainly gives you reasons to think that it is. There are points where you can put pressure on it, of course: the most important point would be whether we should accept that the way we use modal terms in our vocabulary actually accurately represents possibility and necessity in the world as it is. If you are going to reject the conclusion about the inevitability of events, then you're going to have to say that we simply have possibility and necessity wrong, and our use of modal terms need to be revised. That, or poke a hole in the argument.

[The following is probably only of interest to those who care about modal logic. You've been warned. I searched for good sources to look at if you quickly want to know what 'model K tau-rho' and things like that means, but trust me, those I found were all pretty technical and you're better off not reading any of them. If you start losing interest in what follows, jump to after the next set of square brackets for more open-to-anyone chin-scratching.]

People normally try the latter route, and they have had 2500 years to go about it. Recently, after some formal logical systrems for modal logic have been developed (only since the 1950s, since formal logic is a very recent field), some have shown that, in the best of these models, either (ii) or (iii) isn't a tautology, and thus, that the argument doesn't follow. This is true in the modal logic system most people consider the best candidate for actually reflecting the way we use modal terms, model K tau-rho, also called S4 (all of that means something, but formal logic is as opaque to non-logicians as any formal field is to outsiders). Accordingly, Aristotle is often said to have been guilty of a 'modal fallacy'. I could do the formal logic work on this point if anybody is interested (I don't think anybody would be - those folk who are really into this stuff already know it, and most people simply aren't that interested), since it would just be me doing my homework. A point worth making: there are dozens, if not hundreds, of different modal logics in circulation, each of which with slightly different rules and preconditions, etc, eachl of them trying to show some feature of our modal vocabulary, all of which is in service of determining what modal logic is the correct one for making sense of what we mean with truth and falsity. Model K tau-rho is merely the current favourite for being the 'correct' modal logic.

The long and short of all this is that my reply is: so much for model K tau-rho. It is the job of modal logics to give an explanation of how these modal terms work. It's an open question whether model K tau-rho actually accomplished this, while Aristotle's arguments make no use of any formal system but only rely on the meanings of words in our natural language - significantly, meanings that persist in the modal vocabulary of any language, as far as I know. So, Aristotle has clearly latched onto how modal terms work in our natural language, and if model K tau-rho, or any other formal model, disagrees, then it is probably the one that is wrong, not Aristotle. Since Aristotle is not making a point about modal logics in general, but about the modal logic we actually use, his non-adherence to formal systems developed 2500 years after the fact is simply irrelevent. (If I had done all the formal logic work here, I could have showed how, while it tells a plausible story of how we use 'possible' and 'necessary', model K tau-rho doesn't have anything like what is implied by premise (i), a way of tracking the truth of some proposition from time to time, and that that is probably where model K tau-rho goes wrong).

[Here ends the more opaque modal logic stuff]

So, what now? One way we can square the conclusion of 'what has happened was necessary to happen' with how we that multiple realities are possible is as follows: while it might seem that there are a lot of possible futures which could be played out, it is a matter of fact that we have only one actual past. While it might seem to me now that there are a lot of ways tomorrow will work out, by this time tomorrow I would also have only one actual past. I can continue this worm forwards, until it is clear that there is in actuality only one time line, and that other possibilities have turned out to be phantoms born out of my ignorance of how the world actually will turn out. Perhaps you want to resist this, because this is too strong a conclusion to be drawn out of something as simple as saying 'the weatherman was right that it wouldn't rain today'. I'd disagree with you, listing the reaosns I've given above, but we'd be busy with an interesting discussion.

In the spiel above there's a lot of places someone might go 'no, now wait a moment, that's not right' and argue against what I've been arguing. Anyone interested?

Anyway, like I said, I was very impressed by this little argument. It's all smart and stuff.
 
 
All Acting Regiment
09:23 / 25.04.08
Very good post (although I'm no-one to judge, needing to read a lot more of this sort of thing).

So what about the idea of infinite pathways of possibility branching off from every single point? Is that still possible in this model?
 
 
Closed for Business Time
10:28 / 25.04.08
I _think_ that in an Everett-type multi-verse cosmology model, the branching off of universes means that they become informationally closed to each other, still leaving us with one linear past, and no way to check on alternate histories for what might have been - thus leaving Aristotles conclusion as is: What has been must of necessity have been so. I could be missing something here tho. I also have a niggling feeling that certain anthropic principle ideas might impact on the truth-status of modal terms, but I'm too damn busy and tired to work that out.
 
 
Good Intentions
10:52 / 25.04.08
So what about the idea of infinite pathways of possibility branching off from every single point? Is that still possible in this model?

Well, we'd have to give that up, won't we? That's one of the consequences of this argument, and people often argue against this argument because they are asked to give up that type of view. I think the common opinion among modal logicians is that Aristotle was simply wrong, because of some modal fallacy, but I'm not convinced of that in the slightest, and it's still an open question.

After an event has occurred, that event has only one actual past. When I say 'Auckland won the rugby, but it was possible for them to lose the game' I am saying, according to this view, 'in the past it seemed uncertain whether Auckland would win the rugby, but now I know that in actuality they did win', and that's merely a claim of what you knew at the time, not one about the actual facts of the matter. To say anything stronger would be to be confused: if you insisted that it was possible for Auckland to lose, then the response is that Auckland did in fact not lose, that someone who said Auckland would win the rugby on 26 April 2008 would have always been right, no matter when they said it or whether they were justified in making that claim, so at no time could they be wrong, so all the other possibilities in fact turned out to be false and only the actual result could have happened. All the other possibilities evaporated, they collapsed into what actually happened, and it turns out that only one result was possible, the necessitated one. And if we can say this of past events, it's simple to show that can say the same of future events, not whether they are true or false, but that whatever turns out to be the truth of the matter was the only possible truth. When in the future the question is resolved, ie when the game is played and Auckland win or not, then we will see which of the possibilities actually turned out to be true in virtue of the event's actual past (what actually happened at the Auckland game), and since all the possibilities save one are false, the actual event will be the necessitated one. If a possibility is false, like 'Auckland lost on 26 April 2008' is false, and similarly as is 'Auckland will lose tomorrow', it means that to entertain the possibility is to imagine that the world is other than how it actually is, but what Aristotle is trying to track isn't the truth and falsity of hypotheticals, but of statements pertaining to the actual world.
 
 
Albert Most
15:21 / 25.04.08
I don't know from modal logic, but i like this. It links back to what i was saying in my Normativity thread (hint, hint) about the temporal contingency of reasons for behavior and therefore of rational judgement itself.

Anyway, just now talking off the top of my head: Language has to allow for time, because it exists within that dimension, but "truth" in a pure sense (or at least in the sense of ancient Greek usage of the word) can exist outside of time - so the statement "X will happen" is always true right up to the moment of X - regardless of how uncertain the prospect of X is at the time of the utterance. This however, doesn't mean that, prior to the moment of X, it would be in any way untrue to say that "X's happening is uncertain" because X, no matter how necessarry it is, retains the temporally-contingent property of being uncertain until (and unless) the moment of X. At which moment (or *point in time*), the atemporal necessity of X penetrates the dimension of time and makes X temporally AS WELL AS atemporally necessarry.

So the possibility of X and its attendent uncertainty are still always (i.e. throughout time) metaphysically truthful properties, even if X never occurs, but they are *temporally contingent* metaphysical properties, meaning they are true only by virtue of the fact that the dimension of time opens up space for them. The statement "X is possible" is true *within time* only prior to the moment of X. However, insofar as it makes sense to talk about the POSSIBILTY of a given event existing outside of time (which isn't very far) i suppose there's also an extraneous and temporally irrelevant sense in which the statement "X is possible" is Atemporally truthful apart from and alongside the atemporal truth of X's being necessary. So, while the atemporal truth of X's necessity is temporally infinite and therefore always temporally relevant, the atemporal truth of X's possibility is temporally finite and therefore temporally relevant only irregardless of its atemporality (whaaa?). This makes me think now that perhaps it's better to talk about it in terms of the "INFINITE truth of X's necessity" and the "FINITE truth of X's possibility" rather than relying SOLELY on the "atemporal" and "temporal" qualifiers . . .

The upshot however, as has already been pointed out, is that *necessity* - perhaps, among other things, by definition - has NO relevant regard for time; the statement "X is necessarry" being equally true before, during, and after the moment of X.

Interestingly though, the statement "X is possible", despite the temporal contingency of its truth, remains true EVEN IF X NEVER occurs, in time or otherwise, because the "possibility" of X is contingent not upon X happening in time, but rather upon X NOT HAVING happened in time (notice, however, the temporally descriptive quality of the phrase "not having happenED"). So, X can truthfully be BOTH metaphysically possible and necessarry at the same time in the *finite* sense, but can only be both metaphysically possible and necessary in the *infinite* sense OUTSIDE of time.

okay, enough jabber for now . . .
 
 
Albert Most
18:15 / 25.04.08
"What has been must of necessity have been so."

perhaps with the caveat that "what has been might also of necessity have been otherwise"? . . . or something?

because if we place necessity in time, it can only be guaged post-facto. this is the tautological nature of determinism, wherein the proof that things had to happen the way they happened is that they, in fact, happened that way. Or, along the same line, the ubiquitous phrase (at least on this side of the pond)of "It is what it is", usually in reference to something which has *already happened*. For purposes of time (and perhaps sanity) the PAST "is what it is" of necessity, but "was what it was" only by its contingency upon a linear timeframe. Similarly, *of necessity*, the future (a term who's use automatically places us within linear time) only is what it is not yet, and only will be what it later shall have been. On the other hand, the present, insofar as it exists (it tends to be rather elusive, after all) will always of necessity be what it is BOTH *within* and *outside* of time.

or, uh, something . . .
 
 
Good Intentions
01:47 / 26.04.08

"What has been must of necessity have been so."

perhaps with the caveat that "what has been might also of necessity have been otherwise"? . . . or something?

No, this is ruled out by the second premise of Aristotle's argument, the one I marked as (ii). If saying 'Auckland will win the rugby on 26 April 2008' is right, it has always been right, and it has always been wrong to say 'Auckland will lose the rugby on 26 April 2008'. Because it was false to say so in every possible instance, there was no opportunity for it the be true, which means there was no possibility for it to true. All you have done is to deny the second premise, but have given no reasons for doing so.

Most of your posts seem tautologous and uninformative - could you spell out your claims for me? All the talk about the temporality of necessity - that's all meaningless. Sometimes some modal terms, like necessity, is used temporally, like in this argument, and sometimes it isn't. The modal behaviour of these terms make no reference to whether they are temporal or not. All you have accomplished, uncertainly, is that sometimes use modal terms in reference to temporal events. Yes, that's part of what modality means, I've known that all along just from being a competent user of such terms.
 
 
Albert Most
13:38 / 26.04.08
The entire argument is a tautology: to say that because something happens it had to happen. That's very basic - like saying that because you can feel, see, and smell the bullsh*t in the road, it exists. You can make it satisfyingly pretty with logic or dizzily obfuscate it lots of text, but either way what you end up with is just an artifact of the ways in which we percieve and discuss the world. In the end, it's still a description of how we are accustomed to arranging reality, and not a discovery of how things are. The conclusion of the argument as your modal logic frames it, that of the atemporal necessity of everything that happens, cannot be proven except using terms which are artifacts of a temporally-conceived world. Unfortunately, if we step OUT of time (insofar as that's possible which, again, is not very far) and view the stuff of our sequentially experienced reality as a contiguous, non-sequential block or landscape, then nothing ever "happens", it just *is*. And the conclusion to be drawn then becomes "what IS is necsarry". Well, duh.

If youre watching a rerun of some show on TV, and you already "know" what's going to happen (you've already, in one sense, traversed that particular linear portion of time depicted by the show) you can listen to the predictions of your sibling sitting next to you who hasn't yet seen the show and determine the accuracy or, if you prefer, "truth"fullness of his or her forecast of the events to take place. When s/he says "I bet he divorces her when he finds out about this", YOU can say whether or not that is *necessarily* the case, but s/he cannot. So hir statement is a truthful determination of the possibility of those events taking place based on the event s/he is witnessing and has already witnessed on the screen, BUT if you (who have already seen the show) were to say, "youre wrong, he decides not to divorce her because he doesn't want to forgo the inheritance" youre making a truthful, post-facto (assuming that's what actually happens) determination of the *necessity* of the reality of the show conceived (by you) as a whole, rather than in time.

So, for those who haven't seen the show, to say what happens before it happens isn't a description of the necessity of the events, it's a prediction of possibilities, still subject to accuracy OR inaccuracy - if the words they use "he will not divorce her" happen to accurately describe in advance what has not yet happened, then they are true, but not in a necessary sense, because they are uttered in time and necessity (in the deterministic sense outlined in your logic exercise) is an atemporal characteristic. There still exists for those who have not seen the show but are making the prediction, in one sense (i'd say the more IMPORTANT sense, preactically speaking), the possibility that what will happen might not conform to what they are positing might happen, even if someone who has seen the show (and therefore can, in the same sense, stand OUTSIDE of time) "knows" better.

So the statement "Auckland will win the match tomorrow" may or may not be a truthful description of the *necessity* of Auckland's victory, but only veiwed either in retrospect, or from outside of time, by, say, God, or the ghost of Aristotle, or whoever we are imagining might exist outside of time. For those making the statement TODAY, prior to the match, it is not an expression of necessity, but of possibility - the tuthfulness of the utterance is still contingent upon events which do not yet exist in time, and so any post-facto accuracy we later attribute to those statements (over pints at the pub after the game) doesn't yet qualify that statement.

The problem with the argument you present is not that it's wrong, but that it's just a description of itself, like all logic as applied beyond the spatio-temporal reality from which that logic originated.

So yeah, these are all elaborate tautologies (even the sequence of words we use to demonstrate them as tautologies turns out to be a tautology) - i guess i had supposed that was a given. I didn't imagine that anyone was operating under the perception that they were anything but. "Truth" in the metaphysical, metatemporal sense will always be a tautology to those who exist, perceive, and function within the realm of the physical and temporal. Like the old "proofs" of God's existence (perfectly logical, yet still inconclusive).
 
 
Good Intentions
23:36 / 26.04.08
The entire argument is a tautology: to say that because something happens it had to happen. That's very basic - like saying that because you can feel, see, and smell the bullsh*t in the road, it exists.

This is false.

The argument hinges on premise (i), which is not tautological, but a non-obvious observation about how we track the truth of statements thorughout time, something unrelated to modal terms. Modal terms, you'll remember, are words like: must, will, can, etc., which seem to be reducable to being forms of 'possible' and 'necessary'. Nothing about the use of these terms implies what is claimed in (i). It is when (i) is joined to tautological claims about modal terms, (ii) and (iii), when the interesting conclusion is reached. You don't seem to have understood the argument, and I think you're simply trying to be too smart.
 
 
Albert Most
15:14 / 27.04.08
You fail to understand my argument, i think youre simply trying too hard to be right.

start here:

" For instance: people often wail on Marx for predicting that it is inevitable that the workers of the world would bring about communism through revolution, because in the absence of such a revolution it seems like his claim turned out to be false, but if this revolution were indeed to happen, then Marx would have been right all along."

Now consider:

"So, if some event occurs, saying that that event would occur would always have been true."

This is the conclusion of your argument, correct?

How is any of the truth of that statement NOT an artifact of language? *Saying* X would occur may have been hypothetically true up to the moment of X, but only IF X occurs, and then only in retrospect, because in either case the statement (which is uttered at a certain point in time) CANNOT be correct until/unless it acurately corresponds to some event in time, UNLESS you are speaking from outside of temporality in which case everything that is going to happen in time already IS, and is therefore atemporally necessary.

However, when you say that:

(i) If ‘e is happening’ is true, then ‘e will happen’ was always true.

This statement is loaded with temporal qualifiers "was always true" means it was always true in retrospect, NOT that it was true *before* it was true (by definition it cannot be true in time *until* it is true in time, which requires that it accurately describe some fact about a temporal event, in other words, it's not true until it happens, it's merely a temporal *possibility*, regardless of it's *atemporal* necessity). Until it becomes true in time it's still only a prediction - the more open ended, the more likely it *will* be true and therefore you *will* be able to say that it *was* true, but in that case the truth *was* only a possibility *until* it *became* a necessity (which requires it either to be happening or to already have happened). "Was" implies retrospect. Youre taking temporally qualified words and trying to make them true ouside of time. Unless you can rephrase (i) without using any temporally qualified words then either your argument is a tautology OR the "necessity" which you are trying to attribute to the event (something that can be done ((by us mortals)) only at a certain point in time upon or after the event's occurence) is trivial because it is *temporally contingent*, which means that all youre really saying is that what is already true about the past is necessarily true about the past.
 
 
Albert Most
15:48 / 27.04.08
The fact that things have to happen the way they happen is proven by the fact that they happen that way.

This is true, and it's a fun linguistic circle to traverse - but it doesn't tell us anything new about the world, and when you apply it outside of time all you get is:

X is X, and that is necesarrily true.

Which means all youve done is decribed logic using logic.
 
 
astrojax69
02:27 / 28.04.08
bergson argues that nothing is possible until it happens, and then after that is was inevitable. well, more or less.

he discussed the historical necessity for a history of the actor requiring it to be as it was for the thing (production of work, invention, ascending to a position, etc) such that without that exact history the thing was never possible; in fact impossible. so even more so, albert, on the 'was possibly true' theme of your reply above...

an interesting position, not one i've put a huge deal of thought into as it seems to rely somewhat on a certain notion of what 'time' is and what properties it therefore holds. i'll come back to this thread.
 
 
Good Intentions
10:12 / 01.05.08
bergson argues that nothing is possible until it happens, and then after that is was inevitable. well, more or less.


"Nothing is possible until it happens" could be interesting. It draws out quite nicely what is meant by determinism, and if joined to Aristotle's argument leads to the following: it is when something becomes possible that it happens and becomes necessary, that is, in the actual world possibility entails necessity, and since there's only one actual world, there's only one possible way for things to happen, the necessary way - and now we're determinists. Now, the question is, can we show that this claim, that something is impossible up until it happens, follows from Aristotle's argument, or can we formulate an argument for it in its own right?

It doesn't seem obvious that Bergson's claim follows, as similar as it appears to Aristotle's argument. It could turn out to be purely rethorical, or rely on an intuitive correctness, which is not nearly good enough for a modal logic. Hmm. Let me think about it.

Actually, no, it doesn't follow from Aristotle's argument, because otherwise there would be an equivocation of 'be true at some time'. In Aristotle's argument at no time predicting some actual event can be false, whereas in Bergson's claim it is that if some event does happen, it could happen at no other time. Aristotle's argument does not commit you to saying in advance that if an event is going to happen, it will happen at a particular time. If the event you are predicting is 'Auckland will score in the last minute of the rugby tomorrow', then of course the prediction is only true if Auckland score at the time specified - the prediction specifies a particular time. If the prediction doesn't, say, 'Auckland will never win the Super 14 again', then how does Bergson's claim make sense of it? 'Auckland can't possibly lose, until they do, as they will every year'? Compared to 'if Auckland never win again, it was necessarily so'? No, these claims are very different, one does not follow from the other, and Bergson's claim needs justifying, if it isn't just going to be a statement of some idea of determinism (which Aristotle's argument isn't committed to), or be some rethorical flourish.

There are temporal modal terms - 'sometimes' and 'always', which are more or less 'possibility in time' and 'necessity in time', respectively. Aristotle's argument makes the move from 'always' to 'necessarily' in a valid way (well, it looks valid to me, though it isn't in the most favoured formal modal logics, which is why Aristotle's argument is commonly considered unconvincing). Talk of 'temporal possibility' and the like is in serious danger of simply being nonsense.
 
 
astrojax69
06:16 / 04.05.08
i don't think bergson's idea does neatly outline the precepts of determinism. determinism is the doctrine that whatever happens was destined - predetermined - to happen all along. bergson's point is that until the moment of an event, or the creation of a work (which was his arena of discussion), that event/work was literally im-possible, so certainly not pre-determined.

his idea, i think, is that the work was created by that artist (for want of any other term here) through the confluence of the history of that person and the history of their environment such that until the work was created there was no antecedent way for it to have been created, in any other way or by anybody else. after the creation of the work it becomes impossible for it not to have been created, which seems, if not paradoxical, then a bit begging the question for mine.

only had a superficial reading of bergson recently, must get into it more and tease out his ideas - but they do sit within what it is the point of this thread was, i think.

personally, i have always been an adherent of free will and make some ambit claims about how this is possible through appeals to what our brains do to make decisions, to choose possible choices, etc. not very convincing as i have no real way to counter claims by determinists that the choices were illusory and that i was pre-destined to choose as i did, but i think bergson's work gives some weight to my side...

i don't think bergson would have been much of a rugby man, by his arguments! well, he wouldn't have had anything to say about the claim that 'aukland will never win a super 14s trophy' apart from saying that until they do, it will be impossible for them to do so - but that claim will be true of all 14 teams and victory will only be possible for the winners (sadly, prob'ly not the brumbies this year - though the 'tahs look almost likely) when they win bergson is not very predictive - indeed, anti-predictive, i'd guess. can't imagine how he would have reared children?! [dad, can we go to the pool tomorrow? sorry kids, it is impossible...]
 
 
Anna de Logardiere
13:44 / 22.05.08
is everything that has happened actually inevitable? The above argument certainly gives you reasons to think that it is.

The argument you've relayed hasn't done that, I think that I understand what Albert Most is saying...

(i) If ‘e is happening’ is true, then ‘e will happen’ was always true.
(ii) If ‘e will happen’ was always true, e cannot not happen.
(iii) If e cannot not happen, then it is necessary for e to happen.
Conclusion: If ‘e will happen’ was always true, it was necessary that e e would happen.

'e will happen' was not always true, the argument does not distinguish 'a when e had not happened' from 'c when e had happened'. 'b when e is happening' is the moment between a and c so while 'e will happen' was always true it was not necessary that e would happen at a. 'e will happen' is true only at b and c. At a it is a statement that is true or false.
 
 
Albert Most
19:14 / 03.06.08
Let:

"x will happen" = (W)

and

"x may happen" = (M)

and

"the point in time at which 'x' happens" = (P)


Now, my favored way of thinking about it at this point is that the statement represented by (W) is never NECESSARILY true prior to (P) - any certainty or necessity expressed by (W) is purely an artifact of the language being used. Prior to (P),(M) and (W) have the the same truth value - they are both predictions and can never be anything more unless and until (P). I think part of the confusion comes from the fact that we use the terms "will" and "may" differently to make such predictions based on what we induce to be the *likelihood* of 'x' - but NIETHER term expresses an absolute certainty prior to (P), only varying degrees of likelihood, and since the intrinsic point of view expressed in both (M) and (W) is temporally forward looking, neither statement can be necessary without x having happened, at which point they become only *trivially* necessary - like saying "it will rain yesterday" the day after a monsoon. On the other hand, "It MAY rain tomorrow" generally means it might or it might not rain, more of an uncertain proposition than "It WILL rain tomorrow", which generally implies that, at the very least, rain is in the FOREcast, but NEITHER statement expresses a necessary truth at any point prior to tomorrow, because (as per Hume) there are no *necessary* truths to be gleaned from induction.

(W) can only be *necessarily* true if the dimension of time is removed. However, by removing the dimension of time, we negate the predictive aspect of the statement, so that the temporally qualified, forward-looking 'will' becomes an 'is', reducing the statement to "x is happened", which is essentially the statement "x is x", which is necessarily true, but only in a trivial sense.

Hence, a statement of the form (W) can never be *necessary* except in retrospect (that is, REviewed from outside of the timeline intrisic in the meaning of the statement) - a point of view from which it is also always trivial.

The problem with Aristotle's argument was that he was talking from within what he conceived to be a 3 rather than a 4 dimensional universe. Finitude plays havoc with semantics in ways with which humans had yet to become familiar at the time the argument was proffered - Ultimately, these kinds of questions are both the limits and the origins of formal logic.
 
  
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