:grin: IE, it is wrong to say that there are actual possible worlds. — RussellA

Or, any possible world might have been actual, but only the actual world is actually actual... :wink:

I agree, as this seems to follow what Banno wrote: — RussellA

Yep.

For Kripke, that an object, an individual such as Aristotle, is the same object in all possible worlds, is a Rigid Designator, is a consequence of his Theory of Naming. — RussellA

Yours is a good account. That's why I have come back to it - it's close enough to what I understand that I can use it in these explanations.

However I think the quote is around the wrong way.

We have a formal account that talks of things in possible worlds. We want to take that back to our natural language. We have so far two ways of doing this. the first is Lewis' idea that the possible worlds are all concrete, and we look for and match the most similar individuals in each. The second is Kripke's idea that we simply refer to the same individuals with the same name in any possible world in which they exist.

What Kripke expresses that view in natural languages, the result is that proper names are used to refer to the very same individual in every world in which they exist.

So, it's not that rigid designation is a consequence of his theory of meaning, but that his account of modal logic has as a consequence that proper names rigidly designate, and his theory of naming tries to account for that.

That is, the "a"'s and "b"'s in formal logic are most simply understood as cognates of proper name sin English. So since those "a"'s and "b"'s refer to the same thing in different possible worlds, then it seems we might do well to presume that the proper names of English do likewise.

You are right that what Kripke calls an "essence" are those properties that belong to an individual in every possible world.

He uses the example of Queen Elizabeth; we might think the following is an innocent question: "What if Queen Elizabeth had different parents?" It might have been that the babes were swapped at birth, for instance, or some such muck up. But then the person who, in the actual world, is Queen Elizabeth, would, in that other possible world in which the babies were swapped, not have gone on to become queen - perhaps she ran a fish and chip shop in Bristol instead - and the baby for whom she was swapped went on to become the Queen.

Now look carefully at what just happened. We asked the innocent question, "What if Queen Elizabeth had different parents?", and it turned out that this could not have happened! The person who, in the actual world, became Queen Elizabeth, could not have had different parents.

What might have happened is that some other baby, with different parents, could have become the queen.

That's a very different situation.

In parsing the English sentence "What if Queen Elizabeth had different parents?" into our modal logic, we find that what looks to be a question about Queen Elizabeth is better considered as a question about two different people.

So being the child of King George VI and Elizabeth Bowes-Lyon is true of Queen Elizabeth in every possible world, and in those worlds in which the apparent Queen of England is not the daughter of King George VI and Elizabeth Bowes-Lyon, we are talking about some other individual becoming the Queen...

Think on it a bit. Certain characteristics belong with an individual in every possible world in which it exists. This account of essence is quite different to scholastic notions, but has many advantages, not the least being a clear definition.

but in most modern discussions of logic) to have got to a situation where what logic one uses is just a function of what project one is pursuing. — Ludwig V

Logical pluralism rather than pragmatism. The challenge is to use formal grammar to exhibit the incoherences and inconsistencies in our philosophical meanderings. It's not picking a logic that gives the answer we want, but looking at what we have to say using formal tools that set out clearly the problems.

See, for a small example how

What this shows is that Meta's way of talking is incompatible with the formal account. Meta is helping himself to the expressive resources of possible-worlds semantics (modal operators, actuality, evaluation) while rejecting the background grammar that makes those resources coherent. He's not offering an alternative theory. He is attempting to take something he expresses in informal talk, and express it in our best formal language. And in doing so we find that it becomes incoherent. This is precisely where formalisation earns its keep; not by settling metaphysical conundrums, but in exhibiting ways of speaking that cannot be regimented without contradiction. Once that’s shown, the choice is stark: revise the talk, or abandon the framework. You don’t get to keep both - unless you are Meta, and simply double down on your errors.

Looks right.

In standard modal logic there is exactly one actual world. Meta's supposing otherwise is another misunderstanding. We've a set of possible worlds, W, and we can label any one of these the actual world, w₀.

In terms of modality, w₀ is not treated any differently to any other world within the formal semantics. It's a convention of the interpretation, an indexical, like "here" or "now"; a thing of convenience. It usually marks the place who's access relations we are considering

What we haven't looked at much is how accessibility works. It's not mentioned much in the article. Accessibility is the relation that sets out which worlds we can "get to" from a given possible world.

So if I am about to flip a coin, I am in a world that can access a world in which the coin comes up "heads", or a world in which the coin can come up "tails". Both are available. But if I just flipped a coin, and it came up "tails", the possible world in which it came up "heads" is no longer accessible.

Importantly, accessibility is not causal, temporal, or epistemic unless specified. And it can be so specified. It constrains what worlds we have access to.

Let's look at temporal logic. A simple temporal logic sets the accessibility relation between possible worlds so that one possible world is the past and other possible worlds are the future. From the past world, many future possible worlds are accessible. But from those future worlds, only one past world is accessible.

We might specify w₀ as now, and various other worlds as possible futures and pasts. In our world it is true that Caesar crossed the Rubicon, and if we want to model history, we stipulate that we cannot access those worlds in which he disbanded the 8th and returned to Rome. But if we want to write an historical fiction, we would thereby access a world in which he did just that. The access relations depend on what it is we wish to model.

To be clear, there are a range of temporal logics, and which you make use of depends on what it is you wish to model. This is just one example.

And there are similarly logics that model causation in terms of accessibility. Lewis constructed such a logic. The coin flip mentioned earlier is a simple example of one possible approach, but there are many others.

The take-away: the structure of possible world semantics that Kripke set up has been used to formalise a wide variety of situations by amongst other things constructing suitable accessibility relations. Since these are dependent on the core possible world semantics, it might be good practice to make sure we understand what that is before we go off talking about these applications of that logic.

Folk hereabouts who jump to causation and temporality quickly become quite muddled.

Puzzling.

RIghto. Carry on.

it ignores the controversies... — Relativist

Clarifies, would be a better word.

Your

You're conflating possibility with potential. There is no potential for a different past, but we can consider whether a past event was necessary or contingent. — Relativist

is pretty much right. Contingency is modal, potential is causal, such that if we mix the two, then we ought keep close track of which is which.

Unfortunately your definition of contingency mixes causality and and modality. If it were a definition of determinacy, it would work.

The past event E was contingent if the causal factors (C) that produced E had the potential (at the time) to produce E or ~E. IOW, both E and ~E were possible. — Relativist

For those reading along, the standard definition of contingency is roughly just that an event is contingent if it is true in some but not all possible worlds.

This has the great advantage of not involving any notion of causality or temporality.

One of the things happening in this side conversation is that modality, temporality and causality are being mixed together with little clear idea of how they interact - that is, without a suitable logic.

One of the great advantages of possible world semantics is that it can be used to provide such logics.

Makes sense.

No, not with that, I think. I'm just picking on "includes a's existence". So it's "possible world" that the Abstractionist sets out to define, and uses "maximally consistent states of affairs" for his definition. And what asked what it is for an individual to exist in a world, what more could there be than being an item in the domain? Then we can use

a exists =def ∃(x)(x=a)

Doing this avoids treating existence as a property, avoids reifying “existence” as a state of affairs, and matches first-order semantics.

This thread is now somewhat superfluous...

But here's a question for you @Jamal, nevertheless.

Top left, under my profile picture, says I've made 29.7k comments. But on the members page it says I've 29,847 Posts.

So some posts are not comments?


What's not counted?

AE2 Individual a exists in possible world w =def w includes a's existing.

Wouldn't this be better expressed as "Individual a exists in possible world w =def w includes a in its domain"? Point being much the same as my aside:

This differs somewhat from the article, which talks of a state of affairs being possible, risking the appearance of circularity; what is meant is consistency, as is clear from "they are consistent — i.e., possible" It would have been preferable had Menzel not used "possible" in the definition of "possible world", but it is clear that what is meant is that a possible world must be consistent.

We have worlds as sets of propositions / states of affairs, and individuals as elements of a domain relative to a world. So it's pretty straight forward to say that to exist is to be in the domain, much as we do with first-order logic. It also keeps actuality away from existence.

I fail to see the solution even more. — Copernicus

That;s what happens when you ask questions without answers.

More parochial stuff. Yes, your education system is a bit fucked. As are your health and social security systems. Other nations are progressing, if slowly.

The objection here is to the "we" in the title.

So I'll move on to Abstractionism. We might take it as granted that we say things such as "Anne Might be in her office", and that in doing so we are talking about how things might have been other than they are. If we grant that, then we might look to how we can talk in a coherent and consistent fashion about such possibilities. We saw how Lewis would have us talking not about the Anne in our world, but about another Anne, a counterpart Anne', in an alternate world, who was very, very similar to our Anne, except that unlike our Anne, Anne' was in her office. What are the consequences if instead we say that the Anne who is in her office simply is our Anne, the very same individual?

We end up with something not too dissimilar to Lewis' counterpart world, a world in which the moon circles the Earth, Anne's neighbour is mowing the lawn, Anne has an office with a desk, filled out maximally so that every possibility is settled. And the difference is that Anne is in her office.

What is the nature of this world, if it is not of the sort set out by Lewis?

We might have it that the possible world w is (described by) a set of propositions such that each is either true, or it is false. We can call such an arrangement, a State of Affairs. So Anne's being in her office is a state of affairs, and in some worlds it will be true, in others, false. Notice that it can only be true in those worlds in which Anne exists; and "exists" here means that Anne is one of the individuals in the domain of that world. It is not to say that Anne is "actual". To be sure, one of those mooted worlds happens to have the states of affairs that are the same as the state of affairs in the actual world, and in that world, presumably Anne both exists and is actual.

It should be apparent that if certain things are true in some world, other things will also be true. So if "Algol is a pet" is true, then "there are pets" is also true. It seems odd to need to point this out, but given some of the side conversations here, it might be useful. There are logical implications for many of the propositions we are considering; they have implications that follow not from the metaphysics but from the way in which our talk is structured. We can phrase this as some truths either including or precluding others. Importantly, this is about the implications of how we set things out, not about how things in the world are structured.

This brings us to the definition of a possible world for Abstractionism - AW2. A possible world is a set of states of affairs that is consistent and total - a set of propositions that is self-consistent and to which we cannot add any further propositions.

(This differs somewhat from the article, which talks of a state of affairs being possible, risking the appearance of circularity; what is meant is consistency, as is clear from "they are consistent — i.e., possible" It would have been preferable had Menzel not used "possible" in the definition of "possible world", but it is clear that what is meant is that a possible world must be consistent)

Possible worlds then, are maximally consistent sets of propositions. One of those maximally consistent sets of propositions happens to set out how things are in the world we inhabit, and we call this the actual world.

Might stop there for a bit.

Cheers, . Glad to hear that this has been of use to some. Possible World Semantics provides a coherent structure to our modal considerations, a structure that was absent through classical and medieval thinking, as well as from Quine and middle analytic thinking.

I'd point back to the summary on the last page. The logic of possible worlds is agreed on by Kripke and Lewis. Indeed, it is a logic, a way of setting out our discussion consistently, and as such it's not so much a question of its being true of false as it is of its being applicable or agreed.

Then, separately, there is the issue of how we apply the logic. And this is were Lewis and Kripke differ.

Disagreeing with the logic is akin to disagreeing that four and two is six. One might coherently doubt that there are four sheep in one paddock and two in the other, but not that if there are four in one and two in the other then there are six altogether.

Meta, Relativist and Leon disagree as to the number of sheep, but think they can disagree as to the sum of four and two.

Again, there are ontological implications in the logic. It treats of individuals and predicates and possibilities, and so presumes their existence. It is however silent as to the nature of those individuals and predicates and possible worlds.

...there's s logical dependency on essentialism — Relativist

Again, that is the cart before the horse. For Kripke Essence is a consequence, not a beginning.

Logic learned to free itself from ontology. Not entirely; the domain, and the notion of "something", remain. That's no bad thing. Those who cannot see the advances since the logic of Aristotle suffer a sort of intellectual myopia.

This means that the actual world (and this is the factual "actual world") must be a possible world. — Metaphysician Undercover

The alternative, as has been pointed out, is that for Meta the actual world is impossible.

The rest, again, mischaracterises and misunderstands modal logic.

Kripke was an essentialist: he believed individual identity was associated with its essence - a subset of an individual's properties... So his theory of possible worlds is contingent upon essentialism being true. — Relativist

Yes, although in a way very different to others hereabouts. An individual's essence, for Kripke, consists in those properties that the individual has in every possible world in which it exists. Kripke does not start with a prior metaphysical theory of essences and then build modality on top of it. He starts with modal semantics (possible worlds, necessity, rigidity) and then derives essentialist claims as consequences of that framework. So the claim that “Kripke’s theory of possible worlds is contingent on essentialism being true” gets the explanatory order wrong. Essence is explained in terms of necessity, not necessity in terms of essence.

You simply assume it's the same. — Relativist

Not me, Kripke. Again, that it is the same individual in some way is inherent in the definition of possibility and necessity: fa is necessarily true if a is f in every possible world in which it occurs.

If a is going to be f in every possible world, then we have to be able to talk about a in every possible world. How do we do that?

Simple answer: "a" refers to a in every possible world that includes a. More devious answer: "a" refers to a different but corresponding individual in each world.

I'm not sure how popular Lewis' view is. It's kind of nutty. — frank

Yeah, but technically very clever. It explains the modal operators, rather than taking them as fundamental. They are just a broader quantification across the worlds. It's very neat. But yes, quite mad.

Under my view of individual identity, that is logically impossible. — Relativist

Then I'm afraid you have misunderstood something.

Which do you think is closer to approximating the way we really think about modality? — frank

The second is closer to my way of thinking, for the reasons I gave - "Banno might not have answered your post" is a sentence about me, not a sentence about some other bloke in some other world who just happens to be similar to me in certain ways.

I find that argument pretty convincing. So Kripke, not Lewis.

Others find it less convincing.

— Relativist

A rigid designator refers to a specific individual in this world[/quote] A rigid designator refers to the very same individual in every world in which it exists. This, pretty much regardless of the properties of that individual. That's the point. Here's the logic common to rigid designators and counterparts. We have in possible world semantics the definition that ☐f(a) if true will be true in all possible worlds. That's the logic. ☐f(a) is true at a world w iff f(a) is true at all worlds accessible from w. Now what, exactly, does "a" represent? The interpretation must supply a rule that tells us how the denotation of “a” at w₀ figures in the evaluation of f(a) at w₁. So we have two interpretations. For Kripke, "a" is a name that refers to the very same individual in every world in which it exists. It rigidly designates that individual, regardless of whatever predicates it might have - regardless of if it satisfies "f" or not. For Lewis, in any possible world w₁ there may be an individual which is maximally similar to "a" is w. That's the individual to which "a" refers in w₁.[code]
A rigid designator refers to a specific individual in this world
A rigid designator refers to the very same individual in every world in which it exists.

This, pretty much regardless of the properties of that individual. That's the point.

Here's the logic common to rigid designators and counterparts. We have in possible world semantics the definition that ☐f(a) if true will be true in all possible worlds. That's the logic. ☐f(a) is true at a world w iff f(a) is true at all worlds accessible from w.

Now what, exactly, does "a" represent? The interpretation must supply a rule that tells us how the denotation of “a” at w₀ figures in the evaluation of f(a) at w₁.

So we have two interpretations. For Kripke, "a" is a name that refers to the very same individual in every world in which it exists. It rigidly designates that individual, regardless of whatever predicates it might have - regardless of if it satisfies "f" or not.

For Lewis, in any possible world w₁ there may be an individual which is maximally similar to "a" is w. That's the individual to which "a" refers in w₁.

Filling out that last point, Kripke and Lewis give different ontological readings of the same formal machinery. Their logic is the same, but the metaphysical story differs.

Kripke (Naming and Necessity):

• Proper names refer rigidly to the same individual across worlds.
• Necessity is primitive and tied to rigid designation.
• Modality is not reduced to something non-modal; it is taken as metaphysically basic.

Lewis (Modal Realism / counterpart theory):

• Worlds are concrete; individuals do not literally exist in more than one world.
• Identity across worlds is determined via counterpart relations.
• Modality is reduced to quantification over concrete worlds.

Shared Logic / Semantics

• Possible worlds semantics: Both use worlds as the basis for evaluating modal statements.
• Quantified modal logic: Both accept first-order quantification over individuals.
• Transworld reference: Both presuppose a way to interpret identity or counterparts across worlds.
• Truth-at-a-world: Both define modal truth in terms of what holds at particular worlds.
• Accessibility relations: Both can accommodate structured relations between worlds (for temporal or metaphysical distinctions).
• Formal rigour: Both agree that modal claims can be modelled systematically, independent of metaphysical interpretation.

Summarised by ChatGPT

...but entertaining it does not entail that it was truly possible. — Relativist

I wonder if you follow this thread from the start.

The word "truly" should fill a philosopher with dread. The whole of the logic set out here is exactly about what is in truth possible. What we are doing here is using Tarski's approach to truth in order to set out a coherent consistent way of talking about modality. "Truth" is built in to the very structure by it's reliance on Tarski's system.

Temporal logic takes possible world semantics and applies it in a temporal context. It uses the very same basis that we have here. The usual order of operation is to work out what we're doing in the modal logic and then to treat temporal logic as a subclass. There is SEP articles on this topic that will explain this, but essentially what they do is set up rules of access between past present and future.

....what is it that makes any object the SAME object — Relativist

In Kripke's system, and in the example we just gave, Prince Charles is imposed, fixed by the act of rigidly designation, and it's this very supposition that sets out that the Prince Charles in the alternative possible world is exactly the same Prince Charles as is in the actual world.

In Lewis' system, there is an algorithm to decide which person in some other possible world is the counterpart of Prince Charles.

Transworld identity or counterpart theory is not discovered by the model, it is presupposed by the interpretation function. This is a central feature of the logic we have been studying, and accepted by both Kripke and Lewis. Both Kripke and Lewis agree on this point; they diverge only in how identity should be metaphysically understood. The difference is in whether that identity is set by rigid designation or by counterpart theory.

Just to be clear, there is a difference between Kripke's semantics on the one hand, and which is accepted by both Kripke and Lewis, and pretty much everyone else except Meta; and the further, metaphysical approach taken differently in Naming and Necessity and in Lewis' work. The logic is shared. The metaphysics differs.

Do we both agree that natural and normal are two different things? — L'éléphant

I hope so.

Yep. See the thread on disability.

But someone committed to transworld identity say that haecceity is what's left. — Relativist

I don't see that haecceity is needed at all to explain transworld identity. Indeed, i have trouble seeing that there is an issue here. We ask "What if Prince Philip had passed before his mother?" and understand that this is about sentences about Prince Philip and Queen Elisabeth, and we do that without the need for the philosophical baggage of haecceity.

~~

Very good. But of course, rejecting one proposal does not resolve the problem of transworld identity. — Metaphysician Undercover

"The problem of transworld identity" is a result of your misunderstanding. Try to follow this.

Kripke and I would say that "What if Nixon didn't win the 1972 election?" is a question about Nixon. Those who accept haecceity might say that it was not a question about Nixon, but about Nixon's haecceity, which makes Nixon, Nixon, and not some other thing. Do we have one thing or two here?

So

just because something is not concrete, does it follow that it cannot be real? — Questioner

Do we have one thing, Nixon, or two things, Nixon and that-which-makes-Nixon-what-he-is-and-not-another-thing?

I'll opt for one thing, not two.

And that's the issue with reification - it multiplies entities beyond necessity.

Now to be sure, Occam's principle is more an aesthetic than a logical principle, but I think it applies here. I can't see what explanatory value there is in invoking haecceity. Rather, it shifts whatever issue there might be along one step, giving the mere illusion of an answer.

Furthermore, because worlds are (plausibly) defined entirely in nonmodal terms, the truth conditions provided by Lewis's translation scheme themselves appear to be free of any implicit modality. Hence, unlike many other popular accounts of possible worlds (notably, the abstractionist accounts discussed in the following section), Lewis's promises to provide a genuine analysis of the modal operators. — ibid

That bit has me intrigued. A world is a unit such that none of its parts are not "spatiotemporally related to anything that is not also one of its parts". No modality is involved in that definition... at least explicitly. Something is necessary if it is true in all possible worlds. That quantification, for Lewis, is just over ordinary objects inhabiting other worlds. Modality is for Lewis just quantification. It means “true everywhere” rather than “could not have been otherwise”. So Modality is reduced to quantification.

In other systems, modality remains primitive, unreduced.

When was the restraint removed? — Athena

Well, for England, over a long and sometimes bloody history, from Magna Carta (1215) through the Civil War (1642–51) and the Glorious Revolution (1688), to the Bill of Rights (1689). For Japan, on January 1, 1946, at the request of the Supreme Commander for the Allied Powers (SCAP), Emperor Hirohito issued an Imperial Rescript in which he publicly denied the concept of his divinity. Sweden limited the power of it's King in 1809 after a heavy defeat by Russia. The Danish Grundloven was established on 5 June 1849. Norway limited it's monarch with a new constitution in in 1814, by the Constitution of Eidsvoll.

When did the US do likewise?

The US constitution rejects monarchy but centralises executive power in a single office with weaker structural restraints than modern constitutional monarchies. From the mid-20th century onward, especially after 1945 and 2001, restraints on the president ceased to function effectively in practice.

we'll need to now define what they are — Copernicus

And presumably then you will requirer definitions for the terms used to define "Local" and "true"; and then for those terms, in turn.

Do you not see the problem?

When did the US remove the restraint of the president's power and authority? This is not an argument. I intend to open this discussion. — Athena

Hu?

"Thisness", usually.

Seems to me the epitome of philosophical reification.

So three basic approaches.

Concretism, or modal realism, looks at the logic and wants to say that all possible worlds are metaphysically on the same footing. That possible worlds are metaphysically the same as the actual world. So there is a world in which Algol is not one of John's pets. And that world is as real as the actual world in which Algol is John's pet. To maintain consistency it invokes counterpart theory and discounts rigid designation.

Abstractism looks at the logic and says that individuals can be in other possible worlds, and so invokes rigid designation - proper names refer to the very same thing in multiple possible worlds. These worlds are not physically real, but are abstacta of on sort or another.

Combinatorialism looks at the logic and sees the various possible worlds as constructed by arranging the various individuals in different ways.

Of course, there are details to be considered in each.

So, what's Haecceity?

It's what a thing has that makes it what it is.

So, what is it that a thing has that makes it what it is?

Well, Haecceity, obviously.

And... what's Haecceity...?

And so on.

Off topic, but in S5 "it is possible that there exists a necessarily existing God. Therefore God exists" leads to modal collapse. And if one wants to move from a possible necessity to a necessity, then one needs S5.