What is a possible world?

mcdoodle

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.

Michael

I'd go for Abstractionism. Seems the simplest to me. Although I admit I don't really understand Combinatorialism.

Metaphysician Undercover

My opinion is that you should start by nullifying the presupposition that there is an actual world. From this perspective anything spoken is taken as a possibility. Statements which are consistent with each other, not logically exclusive, may co-exist as "truths" within a given possible world. Statements which are logically exclusive (contradictory for example) are exiled to separate possible worlds. If one desires to produce "the actual world", then conditions, criteria, are stipulated upon which a given possible world is said to be the actual world. Therefore I think your question would be better stated as "what is the actual world", as any logically consistent description is a possible world, but what is unknown is what makes a given possible world the actual world.

mcdoodle

↪Metaphysician Undercover

Thanks MU. My first worry with your proposal is that it's multiplying my problems not simplifying them. It certainly works against my intuitions, which are (a) there just is an actual world, where I live and move, and (b) in that world I talk about possibility and necessity, but struggle to relate those concepts to other 'worlds'. I don't feel as if I live in a possible world, should I? Hope I'm not missing your point.

apokrisis

there are three broad options. — mcdoodle

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.

Therefore I think your question would be better stated as "what is the actual world", as any logically consistent description is a possible world, but what is unknown is what makes a given possible world the actual world. — 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.

Terrapin Station

Re your choices, abstractionism would be closest to my view. However, I also do not understand combinatorialism very well.

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."

Metaphysician Undercover

I don't feel as if I live in a possible world, should I? — mcdoodle

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:

...I wondered if I could first define 'world' for myself, so the concept didn't slide out of control.

Well, that didn't work... — 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?

Terrapin Station

According to Christopher Menzel via the Stanford Encyclopedia, combinatorialists hold that "an object exemplifying no properties, and . . . an unexemplified property are considered incoherent; insofar as they exist at all, the existence of both particulars and universals depends on their 'occurring' in some fact or other. Whatever their exact ontological status, it is an important combinatorialist thesis that exactly what objects and universals exist is ultimately a matter for natural science, not metaphysics, to decide."

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.

Michael

According to Christopher Menzel via the Stanford Encyclopedia, combinatorialists hold that "an object exemplifying no properties, and . . . an unexemplified property are considered incoherent; insofar as they exist at all, the existence of both particulars and universals depends on their 'occurring' in some fact or other. — Terrapin Station

I wonder what he'll say about the Quantum Cheshire Cat.

Terrapin Station

↪Michael

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.)

Mongrel

↪mcdoodle

Frequently a world is an abstract object. Hamlet's world is abstract to some extent. That means that if I said Hamlet was Argentinian, you could correct me.

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.

Terrapin Station

Abstractions being strictly mental, of course.

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.

Mongrel

Abstractions being strictly mental, of course. — Terrapin Station

"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.

Terrapin Station

"Abstract" and "mental" are different. — Mongrel

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.

Mongrel

↪Terrapin Station

OK.

tom

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. — Mongrel

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.

Michael

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. — tom

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.

tom

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. — Michael

You mean like the electrical signals in your brain, mechanically influencing your fingers?

Terrapin Station

You mean like the electrical signals in your brain, mechanically influencing your fingers? — tom

Sure. So how does that help the idea that computers somehow have real abstracts in them?

Mongrel

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. — tom

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?"

m-theory

Sure. So how does that help the idea that computers somehow have real abstracts in them? — Terrapin Station

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.

Terrapin Station

What else could it be? — m-theory

A real, concrete particular.

What is an example of an abstraction you'd say that's in a computer?

What does it mean to say abstractions are not real? — 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.

m-theory

↪Terrapin Station

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.

.

mcdoodle

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 — apokrisis

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.

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? — Metaphysician Undercover

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.

mcdoodle

...exactly what objects and universals exist is ultimately a matter for natural science, not metaphysics, to decide... — Terrapin Station

(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...?'

apokrisis

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...?' — mcdoodle

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.

Terrapin Station

If you agree that abstractions exist then in some sense you are acknowledging that abstractions are real.
It is really that simple. — m-theory

First, do you understand that "real" in the sense I'm using refers to whether something is extramental or mental-only?

m-theory

↪Terrapin Station

Sorry I am confused about what is your point.
How does this mental-only and external distinction you have made apply to possible worlds?

Terrapin Station

Sorry I am confused about what is your point. — m-theory

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.

m-theory

↪Terrapin Station

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.

What is a possible world?

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