I think uncomfortable numbers can still be said to exist in the sense that there is a formal abstraction that defines them.
I see your point though and it is interesting. — m-theory

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.

lol that was auto correct.
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.

I would be surprised because you do not seem to be that educated in logic, — m-theory

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)

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. — Mongrel

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?

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? — 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.

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. — apokrisis

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.

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. — 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).

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. — TheWillowOfDarkness

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.

Algol of another possible world is in fact an entirely different dog. — TheWillowOfDarkness

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.

You are just assuming the extensibility that for modal logic - in wanting to include the dichotomy of possibly vs necessary - is what it must establish.

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.