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Can every single event in the universe, be metaphysically necessary? In other words, could it be that the whole notion of possibility is wrong and that there is only one possible world?

One might argue that this makes no sense without a deterministic law, atleast on the subatomic scale. But if a subatomic event like the decay point of a radioactive atom can occur for no known cause, why can’t the entire universe’s fundamental history occur for none?

It is not as if we have any evidence that the universe could have been otherwise anyways. And it is not as if we can ever test this as well. We make that inference because we think we can’t predict certain events in the universe. But indeterminism does not imply contingency or alternative possibility.

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  • Of course, it can, as you well know. Universe could be necessitated by fate or God without determinism, even determinism does not guarantee necessity if the initial state is contingent, and we do not need "evidence" that it could have been otherwise (assuming that makes any sense, which is doubtful), we have practical uses for modeling alternative possibilities regardless. Please reformulate the question and specify your sense of "necessity". It is unclear what you are asking beyond a triviality.
    – Conifold
    Nov 17, 2023 at 22:00
  • @Conifold I edited it to mean metaphysically necessary. Could there be only one possible universe without fate, God, or laws? Fate or God seems to imply some sort of “book” of every event that all events adhere to. This still seems to be a “law” of some sorts, the law being that events are in some magical way adhering to that book. This also seems to imply an indirect form of causation if this book or god exists before the universe or outside of it. What if there simply is no cause or no reason behind the events in the universe playing out in only one possible way?
    – user62907
    Nov 17, 2023 at 22:08
  • After thinking about this further, actually, the answer to what I just asked might be yes. If there is some God or Book or some other Law that decides this fate, that itself would have to be metaphysically necessary. But if those things can exist uncaused, then the entire history of the events of the universe may be uncaused but also be metaphysically necessary without fate or God being involved (unless by fate you simply mean metaphysically necessary but then the notion of fate isn’t useful).
    – user62907
    Nov 17, 2023 at 22:20
  • Consider what substance there is to "metaphysically necessary" with the expansive use you want to make of it. Kripke coined the modern notion explicitly to match folk counterfactuals where more than physical but less than logical necessity seems to be assumed. The centerpiece of it are rigid designators, and its intended application is philosophy of language. The way it works is that some objects and maybe relations are posited as "necessary" and possible world talk is built around them. It makes little sense on this conception to pick free floating objects and ask if they are "necessary".
    – Conifold
    Nov 18, 2023 at 6:06
  • "Metaphysically necessary"? Does that mean that your metaphysics cannot accept contingency? Because metaphysics are not about what is necessary, except in this psychological sense. It's about how we chose to look at the world and what we expect from it. If you expect necessity and order, that's what you will focus on at the expense of the 'noise'. If you expect disorder, you will find some.
    – Olivier5
    Nov 18, 2023 at 8:11

3 Answers 3

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The words used here, "neccesary" and "determinism," are complicated. They have very precise meanings in several contexts, but those meanings do not always align. When answering here, I will try to be explicit about the meanings that I believe you intended, which will hopefully give an opportunity to correct me.

"Neccesary" is a word indicating that things can only go one way. In mathematics, "neccesary" is typically used with respect to an expression or statement: "For X to be true, it is necessary that Y is also true." The best formalization I am aware of for this term is its treatment in modal logic, represented by the ◻ operator. The above sentence might be rendered as "X⊨◻Y". X being true entails that it is necessary that Y is also true.

I move towards this modal logic notation because the semantics of modal logic (particularly Kripke semantics) does a good job of capturing what you have said in words with phrases such as "could have been otherwise" and "contingency or alternative possibility." It provides a mathematical grounding for those words which gives us the ability to either pinpoint the meaning of those words, or at the very least identify which words are not perfectly captured by those semantics.

I believe the most applicable aspect of these semantics to your question is the definition of a relational model, <W, R, V>. In this, W is a set of possible worlds, R is an "accessibility" relationship between worlds, and V is the value of each of those relationships. Mathematically R and V are separate entities for formal reasons -- informally we can combine them to say that R(u, v) is true if "v" is accessible from "u", and false if it is not. This "accessibility" term is used to define the subset of W that one uses when determining if something is necessary(◻) or possible(◊). The nature of this access relationship defines the logic one is using -- there's no one correct relationship for modal logic.

I spent a whole paragraph on accessibility because it is important for disambiguation. If one makes two statements, one about necessity and one about determinism, they may use different accessibility criteria. One very common (potentially the most common) definition of determinism uses an arrow-of-time accessibility relationship. The potential worlds are snapshots in time, and the accessibility is typically built up from causal chains of events between these snapshots. A world has access to all worlds that follow from such a chain. This leads to the intuitive definitions of necessary and possible which align with their English usage. But in the end, determinism results in a clear second order claim. For every modal expression 𝜑, there exists some function f(w) such that f(w)↔𝜑. In words, any statement of necessity or possibility about accessible worlds can be mapped into a function that only considers the current world. The current world determines all of its accessible worlds.

Necessity, on the other hand, could potentially use other accessibility relationships. They don't have to be cause and effect. They could be goal related, or arbitrary. This is important for one particular question you ask: "Why can't the entire universe’s fundamental history occur for [no cause]." One potential answer would be to say you're right, it absolutely can exist for no cause, because one chooses to view the concept of necessity from a non-causal relationship. (and indeed, if one looks at modal logics, there are many properties accessibility relationships which generate different kinds of relationship, such as reflexive, symmetric, and transitive properties).

If one is using one of these non-causal relationships for necessity, I can help no further without pinning down which relationships are meaningful to you. So, for the sake of discussion, let us assume that you are using causal relationships to define accessibility. Where does that lead us?

If there is only one possible world in the set W, then we can at least answer your question with the answer Kripke semantics provides (satisfying or not). If there is one possible world, call it w, then the accessibility relationship has only two possibilities. Either w accesses itself (reflexive), or it does not (irreflexive). The irreflexive case provides little insight: the behavior of ◻ and ◊ will be dictated by our semantics, as there are no accessible worlds to reach. ◻X will be vacuously true (because it is true for all 0 elements) and ◊X will be vacuously false (because there are no elements to choose from). The more useful case is the reflexive case. ◻X and ◊X will both be entailed iff X is true.

Up to this point we have not defined what property we wish to speak about. I've just called it X. To fill in the X in ◻X, we have to ask "what are we claiming is necessary." To approach your question, the closest X you might be interested in is ⊤ - the tautological true statement. ◻⊤ is necessary. But rather than exploring such strange edge-cases, I'll note that we can make a lot of statements about necessity and causality which are true for all X. And, in the particular case with 1 world, reflexively accessed, it is trivial to see that this accessor relationship is causal, and thus must qualify as "determinism."

So in the end, with the most natural application of modal logic, one finds that if there is only one possible world, necessity and determinism coincide. You can't have necessity without determinism in the |W| = 1 case.

Or can you? I quickly walked away from the irreflexive case. With your necessity captured using an irreflexive accessability relationship, the world is clearly not deterministic - there are no cause effect chains to be had. But in this case, "necessity" is not so much a property of the universe but rather a property of the language used to describe it. The fact that ◻X is entailed for all X (if |W| = 1 and irreflexive acccessor) is a language detail of how we have chosen to write mathematics. The properties of the world itself do not apply, only our conventions.

So in the end, the question can be answered with more questions. Is the access relationship you are thinking of reflexive? Are you comfortable with the definition of an edge case of determism, where |W| = 1? Typically determinism is phrased in terms of past and future, with a different possible world at each moment. |W| = 1 may not qualify as determinism at all, in your book. It may only apply for |W| > 1. And finally, does Kripke semantics for modal logic actually capture the nuanced meanings of "necessary" and "determinism" that you seek? If not, then the math that result from applying those semantics won't be satisfactory. But hopefully, at the very least, it provides a framework with which to refine.

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  • Suppose there is only one metaphysically possible world but no practically predictable way (such as a mathematical law) to determine the evolution of the universe starting from any initial state. Then, even though there is only one way for the universe to play out, there would be no way to predict anything. Does this classify as a necessary universe without determinism?
    – user62907
    Nov 17, 2023 at 21:29
  • @thinkingman If there is no way to predict the world's possible or neccesary states based on the state of the current world, and there was only one possible world, then mathematically that would fall into the case where the world does not "access" itself. I spoke to that case in the second to last paragraph. One can speak of its necessity, tautologically., and it is indeed not deterministic by the definition I used, but has quite a few quirks of its own. I find those quirks more interesting than the original answer sought.
    – Cort Ammon
    Nov 20, 2023 at 0:02
  • That’s too much jargon for me. @Cort Ammon Honestly, the whole notion of metaphysically possible worlds makes no sense to me. If a particular world didn’t occur, in what sense could it have occurred? If it didn’t occur, it doesn’t exist. There’s only one actual world we see. It would be more beneficial to talk about caused/determined events vs. not determined
    – user62907
    Nov 20, 2023 at 0:12
  • @thinkingman I'm a fan of the jargon because its intellectually honest. If one disagrees with the outcome, one must disagree with the initial axioms, or disagree with logic itself. But that's the nature of corner cases. I think that if one talks of events, as you say, the logic gets much simpler, and the terms start to make more sense. Also, the logic gets more natural if one talks about specific necessities, such as "it is necessary that little Johnny go to college." But when talking about worlds as a whole, and talking about necessity in the global sense, it can get odd.
    – Cort Ammon
    Nov 20, 2023 at 0:24
  • As a straight up example, it is very typical when talking about determinism to define the world as snapshots that can "access" all future worlds that might be. But to construct a definition of determinism that way, one must necessarily have multiple worlds... at least one for each event that can occur. Without that, the language degenerates quickly.
    – Cort Ammon
    Nov 20, 2023 at 0:27
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Philosophy has shown that the efforts to derive our universe from necessary propositional logic have to date all failed. Applying inferential reasoning, we conclude that our universe is contingent. And this contingency seems to extend to what math applies to it, and what logic.

BUT -- all inferential logic is by definition not certain. Quine-Duhem applies to every conclusion we reach based on it. There are always multiple possible alternate theories that could fit all our observations to date. All apparently falsified theories are patchable. There is therefore potentially a way to patch "necessity" as well, and we could be wrong about our universe being contingent.

However, our best method of characterizing our world is by inferential empiricism, and acceptance of our reasonable inferences as true, even if there is a remote possibility of their being wrong. This is how we do all science, and all empiricism, and actually all reasoning too -- as we can always be mistaken about reasoning and have not yet realized it.

I encounter multiple ideologues who like to seize upon Quine-Duhem to argue that their preferred worldview is not definitively refuted. And this argument is true -- NO wild theory, crackpot ideology, religious theology, or bizarre philosophy can EVER be DEFINTIVELY refuted, per Quine-Duhem. But that is not sufficient justification for anyone to ACCEPT the claim the ideologist is advocating for!!

A key first step before one can try to understand ontology, or basically anything about our world, is to understand how to do epistemology. And the inference from useful working model to inferring that model to be true/valid, is the central principle behind the useful ontology that has led to our developing tremendously successful understandings of our world. The pragmatic success of empiricism is the effective refutation of your "what if" wish it were so for necessity.

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  • But how does empiricism even suggest contingency in the first place? How does pure indeterminism, if true, even inductively give support to the idea of contingency? We only observe one actual world. Science is about testing and we cannot test things by replaying the universe. Note that by contingency I don’t mean dependency. I mean the idea of alternative possibilities of events playing out.
    – user62907
    Nov 17, 2023 at 17:20
  • @thinkingman but we don't observe only one possible world, we observe myriads of them, even if only one observed world is also actual. At least, that is one option to consider in the epistemology of modality. There are also arguments to similar effect in deontic logic ("ought implies can" reasoning, for example). Nov 17, 2023 at 23:17
  • How do we observe a myriad of worlds? By observe, I of course mean one and only one actual world.
    – user62907
    Nov 17, 2023 at 23:20
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Work in a propositional-quantification modal logic and consider expressions like ∀AMA, for propositions A and modal operators M. For example, one might speak of everything being possible, or necessary, or obligated, or in the future, etc. But this kind of circumstance would be a modal explosion, on an analogy with a pure logical explosion from contradiction.

Explosions are taken for failures of the system in which they appear, as at least contraindicating the usefulness of the distinctions otherwise drawn. For if everything is forbidden, say, or necessary, or possible, or exists, etc., then what is the point of differentiating between the permitted and the forbidden, the contingent and the necessary, the possible and the actual, the existent and the nonexistent, etc.? Saying that everything whatsoever has some property, and in such a way as makes the having of this property superfluous, seems to defeat the purpose of going out of one's conceptual way to specifically attribute something to some object.

In the alethic modal context, we will say: either there are multiple possible worlds or there is no reason to talk about possible worlds as such anyway. So either this world is not absolutely necessary in every possible way, or talk of necessary worlds is no more to be countenanced than talk of merely possible ones. (That is, imagine taking the definition of possibility from necessity, respecting the box and diamond operators; and then of reformulating all the modal characterizations in terms of quantification over necessary worlds: something is necessary if true in some necessary world, is contingent if true in no necessary worlds, is possible if true in all necessary worlds(?). But now if there is only one necessary world, again, why go through the trouble of bringing in necessary-worlds talk anyway? How illuminating would it be, then, if not even fictionalistically granted?)


A positive caveat: imagination

When I know that I have imagined some X, I more or less also know that I could have imagined something else X', or X'', etc. So in the causal history of my imagination, I know it was possible a priori to imagine things that I haven't yet imagined; that I can imagine a unicorn and then a dragon, or a dragon and then a unicorn, etc. This is not to say that imaginability is evidence of alternative possibilities with respect to the external content of the imagination: this is not to say that unicorns and dragons themselves are alternate biological possibilities that are disclosed to us via our imagining them. No: I mean to say that possible states of imagination are themselves intuitively recognized multiple alternative possibilities. So it is possible, for example, that I could have imagined a phoenix at time 1, then a hybrid of a unicorn and a dragon; and there is some possible world where I did that at time 1, another where I did so at time 2, etc.

Essentially, the reasoning is this: second-order imagination is strong enough to discern alternative first-order imaginings; imagination by itself is not evidence for outward possibilities, but imagination-of-imagination is evidence for imaginary possibilities. But these need not be full-blooded other, "parallel" realities, need not enter into Lewisian counterpart relations (but note that the counterpart relation is rendered superfluous in a possible-worlds theory with only one possible world at all), but can be "abstracted over" one truly actual world. But this is because all these possibilities are actual possibilities, so are true in the actual world. Thus the actual world can be taken to contain the other possible worlds on a different level of representation more in general/the abstract, so the question of the isolation or plenum of all possible worlds must be answered in multiple ways itself.

Note that our modal theorizing might be taken to be epistemically contingent, in terms of epistemic possible-worlds semantics no less, or then it is possible that some or another stronger or weaker, more concrete or more abstract, etc. theory of modality will "win the day," one day. It is hard to insist that the world is substantively necessary when one has not enough of a difference between actuality and mere possibility at the start of the whole system (to say nothing of the actuality/necessity distinction itself!).


Now that I think of it...

There is something perhaps incoherent about the presupposition of the title question: if everything is necessary for a natural reason, then everything is naturally determined (including modally), so how would we talk about such an everything as necessary but not determined? For being naturally determined is being naturally necessitated, and vice versa, here.

Also, again, the point of possible-worlds talk is to cash out our assertions of alternative possibilities in the first place. One might as well forego using the words "necessary" and "possible" rather than think to use only the word "necessary." If it is possible that there is only one metaphysically necessary world, but possible for there to be multiple such worlds, then it will already be that there are other possible worlds in some sense, will it not? Even if these other worlds are just abstract rearrangements of actual, but not instantiated, haecceities (say).

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