Existential Quantification and Counterfactuals

To expand, we can say that certain counterfactuals occupy a type of logical space (modal logic).

Then to assert a different type of logic (predicate logic) of assigning an existential quantifier to a counterfactual would be to assert that logical space as real wrt. to the logical space of modal logic AND predicate logic.

Hence, can we do that or is it incoherent to assign one logical space of predicate logic to another, of say a counterfactual (modal logic)?

Thus, to say under a unitary logic that encompasses all types of logic under one conceptual schema, that a counterfactual "obtains" or is "instantiated" is redundant.

Thoughts?

I'm not sure you can quantify a counterfactual statement existentially. The nature of EQ is to assert that there is at least one object being quantified that exists. A priori, then, EQ should necessarily exclude counterfactuals.

Was there some particular counterfactual proposition and its formulation you were thinking about?

Reply to Mentalusion

So, the logic of modally dependent counterfactuals does not reconcile with predicate logic?

Is, so then why?

Well, it's not that it doesn't reconcile, it's just that PL isn't sophisticated enough to capture the logic of counterfactuals. That's why you have separate modal logics which include PL + the modal operators.

Quoting Mentalusion

That's why you have separate modal logics which include PL + the modal operators.

Could you or someone else expand on this? What type of logic is that?

Or to phrase the question differently, why don't existential quantifiers apply to counterfactuals?

Reply to Wallows

I mean, I can give a 30k ft. view, but there are whole text books that deal with developing the semantics for different modal systems.

The basic idea is that you introduce the concept of an order triple which includes a (set of) possible world(s), an accessibility relation and a value assignment to propositions in the possible world. The semantics of possibility and necessity are given in terms of the accessibility, "r", of different possible worlds to each other. A proposition, p, is possible w/respect to some possible world W, just in case W is accessible to some other possible world, W', such that WrW' and p is either true or possibly true in W'. Necessity is defined as the truth of some prop, p, in every world accessible to W.

Ok, so let's start.

What is a set of possible world(s)?

What is an accessibility relation?

What is a value assignment?

If you can recommend a good book available online I'd greatly appreciate that.

Waiting with great anticipation @Mentalusion!

This is relevant. Quine was opposed to quantification of modal relations.

https://plato.stanford.edu/entries/logic-modal/#QuaModLog

Sorry friend. I tend to be here when I have downtime at work...which there has not been much of the last couple days.

I see you got another thread going on accessibility. I assumed that would be the biggest question.

Reply to Mentalusion

Yes, I'm really into quantified modal logic as of late, thanks to you.

What's your interpretation of the Barcan Formula? Actualist or possibilist?

I guess I don't share the intuition that it's accurate. It doesn't seem to me to be the case that if something possibly exists with property X, that therefore something like that does exist. I'm not sure what the argument for it's plausibility is though. I think the converse for necessity is intuitive though, so if it's necessary that all things are X, then for all things, it is necessary they are X.

Reply to Mentalusion

What are your thoughts about quantification across possible world's if I may also ask.

"The nature of EQ is to assert that there is at least one object being quantified that exists"

In that case, is 'empty set' factual, counterfactual, both, neither?

Quoting id-entity

"The nature of EQ is to assert that there is at least one object being quantified that exists"

In that case, is 'empty set' factual, counterfactual, both, neither?

I would simplify the concept and ask the pertinent question as to whether empty names are representative of an empty set in natural language. If so, then what's the idea behind quantification of empty names?

Quoting Wallows

Does existential quantification apply to counterfactual statements?

Lower predicate logic, including existential quantification, is included in Kripke's semantics. The Barcan formula is not a thesis of his system.

Quoting Banno

The Barcan formula is not a thesis of his system.

Why not?

Reply to Wallows That's a modbot question, isn't it.

Because it isn't.

Now I think this one of the advantages of his system.

Reply to Banno

But, doesn't the Barcan Formula eliminate the appeal of "discovering" instead of "stipulating" possible worlds. That whole distinction sort of gets dissolved with the Barcan Formula. It also holds great import for the issue of trans-world identification.

Reply to Wallows You will have to explain this to me.

Quoting Banno

You will have to explain this to me.

You are aware of the actualist and possibilist interpretations of modal logic?

Under the Barcan Formula, individuals across the domain of possible worlds remain the same and can't magically grow from one world to the other. This seems to appeal to the actualist account of modal logic.

Or in other words, there's nothing to be discovered from one possible world to the next, since there are no new individuals populating said possible world.

If we assume that individuals can magically come about in another possible world, then we are indeed appealing to "discovering" some new entity or individual in another possible world.

Quoting Wallows

If we assume that individuals can magically come about in another possible world, then we are indeed appealing to "discovering" some new entity or individual in another possible world.

I don't see that this counts against stipulation as a way of avoiding the multitudinous issues of transworld identity.

I can posit new individuals: Suppose I had a footrest; then I could uncross my legs. If an actualist account cannot parse this, then so much the worse for it.

If I posit a world in such a way that some novel individual is needed, then so be it. In some possible world, I can put my feet up; therefore in that possible world there is a footrest.

I don't see any magic.

Quoting Banno

I don't see any magic.

So, Santa Claus isn't a magical being? Because we might as well refer to empty names when we "discover" through creating (or is it stipulating?) these new individuals in other possible worlds.

Reply to Wallows Think that through for me. What sort of stipulation would allow us to bring Santa Clause into existence?

Quoting Banno

Think that through for me. What sort of stipulation would allow us to bring Santa Clause into existence?

Through adhering to the only thing that the proper name "Santa Claus" refers to, his descriptive content of being a fat plump man living at the North Pole, who know's whether you've been naughty or nice, and rewards accordingly with coal or presents.

Reply to Wallows A fictional fat plump man living at the North Pole, who knows whether you've been a good or bad, and rewards accordingly with coal or presents.

The best you could do would be to posit a world in which there was a different individual, who is called Santa Claus, because he differs from Santa Claus by not being fictional; who is fat plump man living at the North Pole, who knows whether you've been a good or bad, and rewards accordingly with coal or presents, and who even happens to have the same name as Santa Claus.

Reply to Banno

But, it's the same individual due to his (its) descriptive content. Therefore we can assume that we're talking about the same individual.

Quoting Wallows

But, it's the same individual due to his descriptive content.

No, it isn't. The description is not a rigid designator.

In some possible world, Wallows is a a fat plump man living at the North Pole, who knows whether you've been a good or bad, and rewards accordingly with coal or presents.

See?

Quoting Banno

The description is not a rigid designator.

Going back to the example of the meter-stick, the length of the meter stick is the definite description, not the meter stick itself.

Anyway, what I've seen going on in the other thread is the matter of placing the horse behind the cart. Namely, if we are to talk about rigid designators, then it seems to me that the description of it is what guarantees its rigidity in possible worlds where they obtain.

@Wallows

Let's go over the Barcan formula.

(x) ??(x) ? ?(x)?(x)

If: everything necessarily has a particular property.

Then: necessarily, everything has that particular property.

Accepting this means that we cannot stipulate things that are not already in this world, because that would allow us to stipulate things that did not have the property ?.

But we can stipulate things that are not already in this world.

So there are things we can do in English that are ruled out by the Barcan formula. Hence, logics which include the Barcan formula cannot parse some sentences of English.

This does not bring unstipulated beings into existence, though... Does it?

Compare this thread: All A is B and all A is C, therefore some B is C, where things are said to appear in a puff of logic.

Quoting Wallows

Going back to the example of the meter-stick, the length of the meter stick is the definite description, not the meter stick itself.

Hm. The length of the metre is rigidly designated by the name "metre". "The length of this stick" is a definite description. Keep the quotes in, to show we are talking about the words, and not the length of the stick.

Quoting Banno

So there are things we can do in English that are ruled out by the Barcan formula. Hence, logics which include the Barcan formula cannot parse some sentences of English.

If you want to take a hard reading of the Barcan Formula, then the stuff that is beyond the scope of the Barcan Formula, are known unknowns or metaphysics if you will. Did I mention that the Barcan Formula applies to The Simplest Quantified Modal Logic?

Quoting Banno

Compare this thread: All A is B and all A is C, therefore some B is C, where things are said to appear in a puff of logic.

Yeah, and the Barcan Formula eliminates such confusions with asserting properties that exist and can be stipulated, not properties belonging to the realm of stuff existing in Meinong's Jungle or Plato's Beard.

The Barcan Formula is what Occam's Razer is to quantified modal logic.

Reply to Wallows :grin:

Quoting Banno

Hm. The length of the metre is rigidly designated by the name "metre". "The length of this stick" is a definite description. Keep the quotes in, to show we are talking about the words, and not the length of the stick.

I propose that "the length of this stick" attains its meaning from the fact that a meter is defined as the length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of a second. A second is the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

So, a "meter" is the same as the definite description that is empirically true in any possible world where the above relations are the same or "actualized" as in the actual world where they obtain.