What is a possible world?
I started a rather vague and inconclusive thread a while ago when I was worrying about what a 'world' might be.
One reason I was fretting was that I find the parameters of 'possible worlds' very hard to get a grip on, and I wondered if I could first define 'world' for myself, so the concept didn't slide out of control.
Well, that didn't work. So how about diving in and considering what a 'world' is when it's a 'possible world'? I am taking it for granted that modal logic is a grand idea, such that it makes sense to say things like 'X is necessarily true' or 'Y is possible if it is true in some possible world', and to express these things in the familiar symbolic logic. If you don't think it's such a grand idea, fine, but please, the thread is for those who do so think.
(I wrote a lot of fiction in my time. I am secondarily interested in whether possible worlds are at all useful in talking about fiction)
Taking my lead from the Stanford entry by Christopher Menzel, which is bang up to date, there are three broad options. If anyone would just like to say which option they go for and why, I'm sure that would set a discussion going.
1. Concretism. David Lewis is the arch-proponent. Other possibilities are concrete in other actual worlds, where there are 'counterparts' to the objects there are here in the actual. There are as many possible worlds as are needed to explain our talk.
2. Abstractionism. Other possibilities are a manner of speaking. Williamson and Plantinga are the names I know advocating the two strands of this: 'new actualism' and 'hacceity'.
3. Combinatorialism. Other possibilities are a different arrangement of things, e.g. of sets of triples within certain spatial coordinates. This is claimed sometimes to be a Wittgensteinian approach derived from a Tractatus view, the world being the totality of facts.
Logically one handles (2) and (3) differently from (1), or so I understand it, but I'm trying to understand the notions in bare words, although I'm open to the possibility (sic) that bare words may not be up to the job, e.g. that necessity and possibility are in a sense logical concepts whose semantics aren't easily expressed in a non-formal language like this chit-chat. Views welcome.
One reason I was fretting was that I find the parameters of 'possible worlds' very hard to get a grip on, and I wondered if I could first define 'world' for myself, so the concept didn't slide out of control.
Well, that didn't work. So how about diving in and considering what a 'world' is when it's a 'possible world'? I am taking it for granted that modal logic is a grand idea, such that it makes sense to say things like 'X is necessarily true' or 'Y is possible if it is true in some possible world', and to express these things in the familiar symbolic logic. If you don't think it's such a grand idea, fine, but please, the thread is for those who do so think.
(I wrote a lot of fiction in my time. I am secondarily interested in whether possible worlds are at all useful in talking about fiction)
Taking my lead from the Stanford entry by Christopher Menzel, which is bang up to date, there are three broad options. If anyone would just like to say which option they go for and why, I'm sure that would set a discussion going.
1. Concretism. David Lewis is the arch-proponent. Other possibilities are concrete in other actual worlds, where there are 'counterparts' to the objects there are here in the actual. There are as many possible worlds as are needed to explain our talk.
2. Abstractionism. Other possibilities are a manner of speaking. Williamson and Plantinga are the names I know advocating the two strands of this: 'new actualism' and 'hacceity'.
3. Combinatorialism. Other possibilities are a different arrangement of things, e.g. of sets of triples within certain spatial coordinates. This is claimed sometimes to be a Wittgensteinian approach derived from a Tractatus view, the world being the totality of facts.
Logically one handles (2) and (3) differently from (1), or so I understand it, but I'm trying to understand the notions in bare words, although I'm open to the possibility (sic) that bare words may not be up to the job, e.g. that necessity and possibility are in a sense logical concepts whose semantics aren't easily expressed in a non-formal language like this chit-chat. Views welcome.
Comments (76)
It must be noted that this is all going off a nominalist, reductionist, predicate logic, view of "the world".
So sure one can define a world in these mechanical terms and find its a useful computational tool for argument.
But if your concern is ontology - of what worlds really are - then this logicist's view leaves out the very things that physics might think definitional - like generalised coherence (that is emergent organisation via the interaction of globalised constraint).
If worlds - as arrangements - are dynamical balances, then modal logic only applies as the useful approximation after a generally persisting balance, or lawful state of affairs, has been achieved.
So sure. One can look for the ontic implications of taking predicate logic seriously as actuality. But any answer is going to be wrong if real worlds - like our Universe - just don't work like that.
Quoting Metaphysician Undercover
Yep. But again, there is a big difference between local counterfactuality - whether or not some particular statement is true or false of our observably factual existence - and the kind of global logical consistency which matters for "a world".
So at the level of the existence of "a world", anything might be possible, yet then in that being so, a ton of those possibilities are going to be self-cancelling and thus unable to in fact manifest. Each is the contradiction of the other, so their own being ensures their mutual non-being. As reals, they can only be virtually real - mutually annihilating as fast as they present.
So modal reasoning concerns itself only with independent and unentangled possibilities. That is the kind of world it imagines.
But process philosophy, based on good old fashioned dialectics, deals in interactions, relations and histories. So that is where global consistency takes over to shape things. The demand is for generalised coherence. And it then becomes the incoherent that is the "not even possible" counterfactual for such a "worldly" state of affairs.
On my view, "possible world" isn't saying anything different than talking about possibilities, period, and possibilities obtain simply by virtue of the fact that things will and can turn out to be (a) particular way(s) given (i) relevant facts (states of affairs) at present and (ii) how present existents can and/or will "behave."
Unless you're quite certain of what a world is, why shouldn't you feel like the thing which you call a world is really a possible world? This is what you say in the op:
Quoting mcdoodle
If you do not know what a world is, how could you ever know whether or not you live in a world? So if it feels like you live in a world, why would you think that this is anything other than a possible world?
I basically agree with that, although I wouldn't say that it depends on facts, as I don't see facts as basic. Also, a lot of the Armstrong metaphysics explained in the section I took that from just seems silly to me.
I wonder what he'll say about the Quantum Cheshire Cat.
My first question with that is "what, exactly, are we measuring--what are our instruments directed towards, when we measure the magnetic moment, and why aren't we taking that to be what's exhibiting the property?" (That is, if we don't take the instruments themselves to be exhibiting the property.)
Then consider the Kipling/Twain issue. Twain tells Kipling he's going to rewrite Tom Sawyer. Kipling says that isn't possible. Twain says he can because it's his story. Who's right?
The story is public domain at the time the conversation takes place.
Correcting someone re Hamlet's nationality would have to be with respect to what's written in the Shakespeare play, for example.
Re Kipling/Twain, it's the same issue I've been talking about with Metaphysician Undercover re a particular chair being that particular chair. You can't rewrite the story from the perspective of logical identity--the original story is the original story regardless of what we do subsequently, but per what an individual counts as "that story," it could be rewritten. For this latter concern, there aren't right or wrong answers.
There aren't right or wrong answers, in general, about Hamlet's nationality, either. There are only right or wrong answers with respect to particular instantiations of Hamlet, or particular thoughts about/imaginings of Hamlet.
"Abstract" and "mental" are different. Numbers, math in general, sets... these are abstract objects, not mental objects.
For me it's better to look at the concepts without ontological considerations. If you subsequently want to say there is no such thing as an abstract object.. fine. Ontology does not provide leverage for redefining terms.
Yeah, they're not synonyms. But the "abstractions" circle is wholly in the "mentality" circle in a Venn diagram in my view. Obviously, I don't buy that mathematics/mathematical objects exist extramentally. I'm an antirealist on all abstracts.
Still, it is tempting to think that, when a team of mathematicians have finished programming a computer to perform a proof, and finally, after months of toil, run the program, that there is indeed a mathematical proof being performed by the computer.
If no mathematical proof was performed by the computer, if abstract entities were not instantiated and operated upon, then it is quite difficult to explain just what is going on.
Electrical signals are being directed around silicon chips, mechanically influencing the pixels on the display. Presumably nothing's going on that can't in principle be seen with a sufficiently powerful magnifying glass (the uncertainty principle notwithstanding).
Talk of the computer performing a mathematical proof is simply a useful narrative for our benefit, and doesn't entail realism about the abstract.
You mean like the electrical signals in your brain, mechanically influencing your fingers?
Sure. So how does that help the idea that computers somehow have real abstracts in them?
I'm not sure how the set of all non-elephants might be instantiated. And its membership doesn't come and go depending on whether anybody's thinking about it. But this is all for a different thread called "What is an abstract object?"
What else could it be?
An unreal abstraction?
That idea does not even make sense.
At least not to me.
What does it mean to say abstractions are not real?
Either abstractions are a possible reality or abstractions are not a possible reality.
If abstractions are not a possible reality then abstractions do not, by definition, actually exist.
If abstractions are a possible reality, then when abstractions exist, they are real.
A real, concrete particular.
What is an example of an abstraction you'd say that's in a computer?
Quoting m-theory
They do not occur in the extramental world.
Of course, my answer that you'd only have concrete particulars in computers is a bit disingenuous, because mental abstractions are concrete particulars on my view--namely, they're concepts that we formulate as individuals. But it doesn't seem that anything other than minds can formuate concepts--that seems to be a unique property available to some brain stuff, so to speak.
Before the invention of computers computation was only an abstraction.
If that abstraction did not actually apply to reality then computers would not exist and would not even be possible.
Again either abstractions are a real possibility and thus exist, or abstractions are not a real possibility and do not exist.
If you agree that abstractions exist then in some sense you are acknowledging that abstractions are real.
It is really that simple.
.
I agree with this insight, and it's not just 'physics' that might make us other factors matter. Perhaps the idea of possible worlds is indeed the locus for a sort of clash between the formal and mechanistic, on the one hand, and the formal and chaotic (in the best sense) on the other.
I think my philosophical journey, starting as it does late in life, partly involves trying to marry the language I'm accustomed to and the language(s) philosophers use. I find this gulf clarified in Wittgenstein which is why I've become hooked on much of his approach. So in ordinary life - which includes in my case writing and enjoying fictions, so I don't mean that an ordinary life is a simple one - I'm confident of what 'a world' is. But I'm not confident that all my ordinary human experience has prepared me for what the analytic philosopher types call 'a world', and that's where I become uncertain of my own judgment.
(TS, I appreciate this is a quote from Stanford not from you.)
It's interesting, if one starts from this point, to decide how 'abstractions' invented by human beings fit in. And here abstractions might include the economy, or the Potterverse, or the mathematics of an imaginary computer. It's the human imagination that conjures up possibility. Then we devise different rules depending on what sort of imaginary objects are involved.
One part of all such rules will then define what apo called the 'not even possible'. I think that's one zone I'm puzzled by. I certainly have been to philosophical talks for instance where people bandy about phrases like 'logically impossible' rather readily and I'm always running to catch up. Perhaps I was a fiction writer for too long, there's something about 'logically impossible' that gives me the urge to respond with 'Ah, but what if...?'
Such fiction might not need to be constrained by physical coherence - time travel or use telepathy if you like - but generalised emotional and social coherence would surely be a must?
If the characters are imagined clearly, they should write the story themselves pretty much. There's a logic to what they would and wouldn't do.
First, do you understand that "real" in the sense I'm using refers to whether something is extramental or mental-only?
Sorry I am confused about what is your point.
How does this mental-only and external distinction you have made apply to possible worlds?
That's the first problem we're having then--you're not simply reading the question and answering. You're trying to contextualize it into the "point" I'm making.
With the question I'm asking, I'm not making any point. I'm simply asking if you understand that I'm using "real" to make a distinction between whether something is extramental or whether it's instead mental-only. I'm asking you that because it wasn't clear to me that you understood that I was using the term "real" that way.
When I asked you what is the point I am asking rather that you should not derail the topic of the thread.
You should clearly indicate how your distinction between mental-only and external is related to the topic of *possible worlds.
I'd rather have a conversation with you, so that when you write this:
Quoting m-theory
In response to me saying that I don't buy that there are real abstractions, we can clear up whether you're understanding what I mean by the term "real" contra how you may be using it differently.
Perhaps it makes sense to understand that the ambition of classical logic is to establish a rigorous syntax in which to speak about the world. The world, in the end, is irreducibly semantic, so logic can in fact only approach this ideal. And yet still, logical laws can be framed which reduce the scope of semantics to pretty much binary, yes or no, answers.
The formal theory says existence reduces logically to these two options. Then it becomes a matter of observation - the informal act of measurement - as to what reality replies.
So logic is all about a syntax that - by application of rules, the modelling of constraints - can reduce our questions about existence to their most telling form. Slipping now into the subtleties of the Peircean view, logic forces us into the realm of pure sign. Instead of looking about the world and taking it in any old way, we get shifted into the mode of seeking the signs that logic says are indexical of the noumenal.
It's the number on dials story. The real world is irreducible semantic - vague, entangled, messy, continuous. But logic gives us the grounds to ignore the real world and focus on the numbers or other "truth values" we can attach to it. We can convert reality back into a series of symbols, a collection of counterfactually definite measurements, that allows us to get on with a computational level of thought.
So we construct the two world relationship described by triadic semiosis. We have the logical world of a clean syntactic play of symbols and the real world of messy entangled dynamics. Measurement - the act of transcribing one reality into the other - is then made as constrained as possible. As fast and simply as we can, we read off the numbers that we can accept as indicative of reality.
The less we are actually caught up in the world during this tricky act, the better. Smash and grab. Get in and get out. And that is why good logical syntax wants to reduce our observations of nature to simple binary ticks. Hanging around in the realm of the thing in itself means getting energetically entangled and losing the modeller's detachment from the modelled. You don't want to start merging with the world you measure. So logic gives you the rules to form the fastest binary dial reading. That way you can return to the realm of thought and get back to the security of its syntactical rigour.
Anyway, the point is to show that the practice of logic has this inherent problem. It cannot afford to tarry in the world of the real,too long. It's goal is to maximise syntactical order, and so even measurement or observation must be made as syntactically constrained as possible.
And - as your reference describes - the problem for the acceptance of modal logic was that it didn't seem sufficiently distant from messy real world semantics. That is what necessitated work on constructing a suitably syntactical notion of possible worlds. Logic needed its Procrustean rack to ignore the reality of reality and trim it to fit as the kind of reality with which it could compute.
The result is too simple for doing actual metaphysics. But hey, the technological success of computers and digital thinking means that syntactic mechanism has become the dominant Metaphysical paradigm over the past 50 years. It has become irresistible to project the manifest image of modal worlds back on the reality from whence it was derived. The map becomes what we believe the territory to actually be.
Would you say it's a triadic system of constraints?
And you earlier proved my case in seeking the choice among the interpretative options given in the OP that could function as the sign, the big tick, your nominalistic ontology demands.
You could point to 2 - abstraction - tell us all it was close enough, get in, get out fast, and say once again the world is exactly as you expect it to be. Prejudice confirmed by unassailable logic.
I wonder if you talk like that when you're just hanging out with friends and drinking beer or whatever.
I didn't have many professors who gave bonus points for poetic bullshit. Did you go to UT Austin or New School or something? Who is giving you bonus points here, anyway? It's a message board.
Terripin is pretty much right here.
The possible world is not an manifestation of constraint, but rather freedom or radical contingency-- the possible world defies the constraint of actuality, to remain true no matter what's happening in the world. Logic does not constrain the world (that would be what exists, not the logical rule or semantic sign), but rather is expressed in the constraint of existing states.
Sometimes states of existence express on logical rule, at other times it's another; one possible world expressed here, a different possible world expressed there.
For example, to speak of a possible world in which Donald Trump lost the 2016 presidential election to Hillary Clinton is to consider the potential outcome of a future scientific experiment in which the state of planet earth immediately prior to the conclusion of the election is approximately reproduced either here on earth or elsewhere on another planet such that the counterfactual result follows. The required precision and accuracy of this experimentally reconstructed copy of the past state that produces the counterfactual result depends on what information is demanded by the modal argument.
Obviously such a formulation of possible worlds means that neither "Trump" nor "Hillary" are designated rigidly, with "trump" and "Hillary" in the "possible world" referring to mere stand-ins for their original counterparts that are judged to be playing their respective roles "well enough" for the modal argument under consideration.
You are jumping ahead to the claimed result and not thinking about how the framework is developed. The OP article in fact is a very good one. It makes the issues explicit.
So the informal picture is that worlds are constructed by going from the particular to the general - recognising the increasingly generic constraints that can still bind a set of parts as a whole.
This is just the reverse view of how particularity develops - by the world becoming increasing crisply formed as it gathers ever more localised or specific states of constraint.
And then to keep the game going, Lewis had to argue for the notion of counterpart likeness.
So the argument is that what constraints don't care about can be treated modally as accidental rather than universal properties. If a difference doesn't make a difference, then what it "actually is" becomes logically a matter of indifference.
If you are applying this to individuation - the prime target of predicate logic - then it says we know Algol well enough not to mistake her for any other dog even if we were to encounter her in some entirely different world. There is something essential about her that defines her.
Or at least - reductionism being desperate to cash out nominalism - there is so little different about her (our "mental" idea of her, heh, heh) that we are content to take this counterpart Algol as a token of a type. I mean, a sign of a thing.
Oh dear. I seem to have slipped again into the semiotic account that reveals the full extent of the semantic games being played. :-O
??
Maybe you should read the OP.
What conflicts can't exist?
Yeah, the reason your writing is incomprehensible is because you're using words I don't know. Haha.
That's just the same way the random pomo essay generator works. It triadically employs a systematic constraint of semiotic ninethness.
A combination of projection, arrogance and assumptions rooted in stance and disposition biases.
Yes, and not only can a Turing machine be instantiated in Reality, but that Turing machine can instantiate another Turing machine abstractly. But then that's what Turing machines do - they abstract!
And, as you point out, if Reality did not have this ability to instantiate abstractions, computers could not exist. But taking your argument a little further, computation (as performed by humans) would not be possible, the same goes for language and thought.
Quoting m-theory
Some entities are purely abstract, and I see no reason to describe them as "possibilities". Take the set of non-computable numbers. How could they be described as "possible" when they are explicitly not.
Quoting m-theory
It may be that simple, but it does get interesting.
As you don't point out, but I keep asking you, what's an example of something that a computer does or has that's an abstraction?
Here's a rather striking example of the literally trillions of possible examples that could be chosen:
http://www.nature.com/news/two-hundred-terabyte-maths-proof-is-largest-ever-1.19990
Now I've got a couple of questions for you:
1. What is the special physics that exists only in the human brain that makes it the only place abstractions can be instantiated?
2. How do computers work - perform proofs, play games, simulate reality, if they don't instantiate the abstractions upon which they are operating?
Are you saying that the computer formulated a concept? (And so you believe that we've already created artificial consciousness?) Or are you meaning something else by "abstract"?
Quoting tom
It's rather the exact matter and dynamic structures that make the difference.
Before I answer your second question, I just want to clear up (as I asked above) how you define abstractions. Do you agree that they're just concepts that we formulate?
I see your point though and it is interesting.
I still doubt that you have ever taught philosophy professionally.
Did not mean to cause any discomfort, but we know the non-computable numbers and the non-computable functions exist because they are indispensable in our explanation of why certain numbers and functions are computable.
Our connection with concrete reality is via our theories and tests. Our connection with abstract reality is via proof.
I meant to type uncomputable
Sure, and I'm not at all surprised that you doubt that. My response to your comment earlier wasn't at all facetious. It was serious.
But you don't actually teach philosophy professionally do you, and never have.
Right.
Your belief about this would hinge on what I say about it?
I have not actually seen you make this claim.
I only have seen some one else make this claim about you.
Are you saying that you have or do teach philosophy professionally?
I would be surprised because you do not seem to be that educated in logic, and one would think credits in a logic course would be a requirement before you were qualified to teach any philosophy.
Of course that may not be so.
LOL given your comments on logical matters.
lol
you still avoiding the question?
why?
I'll answer as soon as you answer my question (in a way that I consider an answer)
People often call worlds like Hamlet's 'fictional' worlds, though I prefer 'imaginative'. In that sense, they can then be instantiated, as theatrical worlds (where Hamlet may well be Argentinian, the child of the Perons, perhaps). Indeed, then there's often argument among aficionados and between authors (as you cite Twain/Kipling) about the allowable parameters of the world.
I am also interested in worlds not yet invented and how they relate to the possible world schema. I mean both fictionally imaginative - did the world before J K Rowling had a Lightbulb Moment have a Potterverse as a possible world? - and scientifically imaginative - was graphene a possible substance before it was invented?
Quoting Mongrel
This tale also reminds me of the issue about whether to redo Huck Finn with the word 'nigger' removed or replaced, which it seems to me would take the story away from being Twain's, as the world of Huck Finn is related to the author and his place and times. I think, for instance, that every production of a Euripides play however modernised pays a certain respect to Euripides' vision.
It always makes a difference. Algol of another possible world is in fact an entirely different dog. In discussion of modal logic, many people fail to understand individuation. They errounosuly take semiotic similarity to mean two entirely different states are the same. It's particularly common in the context of counterfactuals and time-travel. People are imagined as a universal, a semiotic rule which individuates in same in all circumstances, supposedly making Willow in any possible world the same person. It's a failure to understand time and possible world make a difference to individuation. The Willow who not make this post is not me, no matter how similar or different we might be.
Indeed, there is something "essential" that defines each state, but it's a worldly feature. The Algol of one possible world is, by definition, not the Algol of another possible world. Each is a particular state of a world with its own semiotic expression. Semiotics doesn't create any state. Such expression is embedded in within it from the moment of its emergence. The Algol of each possible world is never anything other than the Algol of that world.
"Contraints" cannot do anything because there is never any state on which they might act. Since any state of the world has its semiotic expression for the moment it emerge, there is no "formless foam" to be "constrained." Semotic expression is given with every state and means that it is individuated: there are only discrete states with express various "universals." Signs are not what makes the world, but rather what any existing state expresses.
Any "universal" is not a constraint on the world, but an expression of freedom. The law of gravity, for example, is only expressed in particular possible world where existing states of interest behave in a particular way. Outside that possible world (i.e. one where states don't or cease working to the law of gravity), there is no such law.
Quoting apokrisis
So this picture is a contradiction. It argues a a whole is formed out of the particular, but it actually claims that the whole (generic) constraint forms the particular (the parts expressing the whole), such that particulars are defined by the generic constraint rather than themselves (e.g. "Algol" supposedly the sign which defines the existence of the particular dog Algol in any world).
But of the three options I outlined from Stanford at the outset, they each take a separate view of the issue of individuation, surely? You seem to be arguing the Lewis concretist view here, where the 'others' are counterparts. In abstractionist or combinatorial versions, I had presumed that the exact variation from world to world might adjust appropriately - Algol being historically the same dog, for instance, until a possibility forked one of him away from 'the actual'?
In the historical fork, there is only the Algol of one possible world. The Algol which follows after the present in particular causal links (e.g. this particular body, with its history of location and interactions).
I'm not arguing the concretism view. There is no need for a possible world to be actual. I can coherently speak of a possible world where I am the king of England (two possible worlds, but the Willow of one possible world) or a possible world where another Willow is king of England, without it ever being actual. Indeed, what defines a possible world is it's an abstraction of logic, a necessary truth of what might have happened, so actuality is exactly what a possible world does't need.
Individuation is not only present in actuality, but also in logic. We might say all states are, themselves, their own logical object, expressing their own respective possible world.
So you didn't read the article or failed to understand the point?
The counterpart argument is that even under the concrete reductionist interpretation, Algol is near enough the same dog as makes no possible difference. So to talk about an entirely different dog would be one that is no longer even a counterpart version.
My point is counterparts are incohrent: it makes no sense to speak of them. Modal logic shouldn't entertain them at all. The sign (e.g. Algol) is not a universal "constraint" which creates the particular of Algol in any world. Each Algol is entirely their own state, belonging to its own possible world.
Any world is, in fact, a collection of specific objects, only they are logical (or semotic) objects too. The reductionist's mistake is not claiming the world is only a collection objects, it's suggesting that their presence is the only significance. The colour red doesn't just exist, it has a logical meaning expessed nowhere else. As does any state or object we might encounter or imagine.
So the general ontic issue here is that the choice (following holism) is either to accept the actuality of vague objects, or (insisting on reductionism) having to suffer the ill fate of having to swallow many worlds in some guise.
If you insist on the absoluteness of the law of identity - no even counterpart fuzziness when it comes to being - then you have to multiply worlds to fit in the infinity of infinitesimally different versions of any object that is the logical result.
This is exactly the problem of quantum physicss. Every fork in the pathway has to bifurcate a new pair of worlds. You can't in fact tell which is the real Algol or Willow whose future had two possibilities to choose from. So both paths were taken and the dog and its master continue in their two worlds.
Yes, it doesn't make any sense at all to duplicate entire world histories at the drop of a hat. So if you want to talk ontology, vague objects dig you out of that hole. You only need an Algol or Willow that fits their description to the degree any differences don't matter.
Willow puts his eye out with a stick. Algol is now a stray not a pet. Yet being objects still of the same world - individuated by its particular history, its particular steady accumulation of constraints - that history alone can still determine whether Willow is still near enough Willow, or Algol is Algol.
On the microscale, they both are certainly vague objects. Most of their molecules are turned over each day, breaking down and getting remade. Functionally (that is, teleologically) it makes no real difference to anything if microtubule a is replaced by microtubule c rather than microtubule b deep in some cell of Willow in the next five minutes. And yet that is a haphazard possibility.
So a "functional actuality" has no logical problem at all with vague objects. Near enough is good enough for a making call on identity. Because that call is made from a higher level of organisation. And semiotically, it is founded on a principle of bounding indifference.