It seems that the caravan has moved on while I was away. But thank you both for making me think through what I was saying.

Nuh. I reject your arguments because they are muddled. — Banno

You are still looking for epistemic truth in a semantic system. — Banno

Your ability to amuse me with your ridiculous straw manning never ceases to amaze me. Again, you take your own error "muddled" arguments (here represented as "epistemic truth in a semantic system"), and you pretend that your error is mine. For example, defining an infinite set as "complete" only creates a muddled mess of contradiction.

These sets are not "incomplete" - you trade on an ambiguity here. M is not the actual world, as you think, but an interpretation of a modal system. — Banno

You still completely ignore, and disrespect the second truth condition stated by the SEP. The one I've quoted three or four times now. The actual world of the modal system must "in fact" be the actual world. Here is the complete package of conditions:

Say that M is the “intended” interpretation of ℒ if (i) its set W of “possible worlds” is in fact the set of all possible worlds, (ii) its designated “actual world” is in fact the actual world, (iii) its set D of “possible individuals” is in fact the set of all possible individuals, and (iv) the referents assigned to the names of ℒ and the intensions assigned to the predicates of ℒ are the ones they in fact have. — SEP

@Banno, until you accept the real necessity of "(ii) its designated “actual world” is in fact the actual world", you will never understand the real epistemological problems of modal logic, and why there is so many distinct interpretations. Look:

For abstractionists, however, actuality is a special property that distinguishes exactly one possible world from all others — the actual world is the only world that happens to obtain; it is the one and only way things could be that is the way things as a whole, in fact, are. However, for most abstractionists, the distinctiveness of the actual world does not lie simply in its actuality but in its ontological comprehensiveness: the actual world encompasses all that there is. In a word: most abstractionists are actualists. — SEP 2.2.3

The reason for so many different interpretations, is because it is impossible to make "possibility" as we understand it, consistent with "the truth about the actual world of empirical observation", as we understand that. These two are fundamentally incompatible as Aristotle decisively, and irrefutably demonstrated thousands of years ago. In modern times this incompatibility is known as the uncertainty principle. A fundamental particle cannot have a true, actual location (this implies not moving), and also have the possibility of moving, at the same time.

The multitude of interpretations arise from the attempt to establish compatibility between two incompatible ideas. Human beings are very creative, and industrious, so they will keep trying more and more different ways, never succeeding. They will not succeed because the two are incompatible, and the only way to understand the both of them properly is to model them separately, in a dualist way, with a form of mediation between them.

You haven't followed what is going on in the SEP articles. — Banno

I think I've followed very well. I see section 2 as proposing three distinct interpretations of possible worlds semantics, each of these being insufficient, due to the problem described above. You seem to want to focus on one, the abstractionist interpretation, as if it is the only acceptable interpretation, not allowing for the possibility that it is just as faulty as the other two.

Again, it seems to me that what you are doing is attempting to critique modal theory, which is based on semantic theories of truth, by replacing that basis with a correspondence theory. It's no surprise that this doesn't work. — Banno

Sure, replace correspondence with some other theory of truth. That is just a move of ignorance, denial of the problem, which is the fact that the mode of "possibility" is inconsistent with "the truth about the actual world of empirical observation". Remove yourself from the relevance of the truth about the actual world of empirical observation if you like, but then what good will your logic serve? I mean, you might argue that predictive capacity is far more useful than truth about the physical world, but then why not go to a probabilistic semantics of modal logic. That makes far more sense. Instead, you want "possible worlds", which pretend to assume some sort actual world of fact, yet not respecting that as the basis for "truth". What kind of muddled nonsense is this?

Tarski's semantic theory of truth provides a rigorous, mathematical framework for understanding what makes sentences true. His famous T-schema—"Snow is white" is true if and only if snow is white—captures a correspondence intuition: a sentence is true when it corresponds to how things actually are.
However, there are some important nuances: — Relativist

The problem, as I indicate above, is that it is a pretense to correspondence. That is the problem I mentioned earlier, of replacing intension with extension. Correspondence becomes simply a stipulation, instead of criteria for judgement. The actual world of the modal model "is" the actual world of fact, because this is stipulated as a necessity for truth.

So, "snow is white " is true if and only if snow is white. Yes, now we stipulate "snow is white" (or in the case of possible worlds, the actual world of the modal model is stipulated as in fact the true actual world), and voila, "snow is white" is true by stipulated correspondence, and the actual world of the modal model is true, by stipulated correspondence. But of course, we can all see that this is just a pretense of correspondence.

Banno seems to be trying to deny the pretense of correspondence, to claim some other basis for "truth" in possible worlds semantics. Clearly this is just denial, as reference to "in fact the actual world", in the truth conditions, indicates that truth is based in correspondence. Correspondence by stipulation ("snow is white" is true because snow is white) becomes very problematic, so Banno wants to deny that it's even a part of the modal semantics of possible worlds.

As was noted in §2.1.2, for the concretist, there is no special property of the actual world — actuality — that distinguishes it, in any absolute sense, from all of the others; it is simply the world that we inhabit. For abstractionists, however, actuality is a special property that distinguishes exactly one possible world from all others — the actual world is the only world that happens to obtain; it is the one and only way things could be that is the way things as a whole, in fact, are. However, for most abstractionists, the distinctiveness of the actual world does not lie simply in its actuality but in its ontological comprehensiveness: the actual world encompasses all that there is. In a word: most abstractionists are actualists. — 2.2.3 Actuality and Actualism

Several ideas are introduced here, one being to obtain.

Obtaining is something a state of affairs does. In other words, I can conjure a state of affairs that does not obtain. The distinction between an obtaining state of affairs and a true proposition is kind of fuzzy. The early Bertrand Russell said they're the same thing:

Russell took over from Moore the conception of propositions as mind-independent complexes; a true proposition was then simply identified by Russell with a fact (cf. MTCA, 75-76). — SEP

But we generally draw a distinction between them with a proposition being the content of an expression (or hypothetical expression), and a fact, or state of affairs, being a complex of things and concepts.

So when we say abstractionists are actualists, this means they hold that any state of affairs that obtains, is a resident of the actual world. The actual world itself is a set.

It's not significantly different because Truthmaker theory is a correspondence theory. There are other correspondence theories, and the differences are subtle. Congruence theory differs in terms of the nature of the correspondence:

"A congruence theorist holds that a truthbearer and what it corresponds to are both structured complexes, and that when one corresponds to the other, there is likeness of structure, and correspondence of components to components."

Truthmaker theory allows for truthmaking to simply be logically entailed by simple existents.

As I said, it's subtle.

:up:

Several ideas are introduced here, one being to obtain. — frank

My understanding of 2.2.3

There are Concretists such as Lewis and Abstractionists such as Plantinga.

For the Abstractionsists:
There is the actual world, an actual world, a State of Affairs that exists and obtains.
There are possible worlds, non-actual worlds, States of Affairs that exist but fail to obtain.

Most Abstractionalists are Actualists.

There are two types of Actualists, Trace Actualists and No-trace Actualists.

The problem with No-trace Actualists is that they cannot explain standard modal semantics, in that it is possible that for some x, x is an Exotic. But for the No-trace Actualists, there is no x.

There are two types of Trace Actualists, New Actualists and Haecceitists.

Trace Actualists can explain standard modal semantics, in that things, whether objects or properties, do exist in possible worlds. It is possible that for some x, x is an Exotic (so different to an actual object that no actual object could be an Exotic)

It is possible that on the table is an apple. There is a possible world where the apple is on the table.

For the New Actualists, the apple necessarily exists, but is not necessarily concrete. The apple is only contingently concrete.

For the Haecceitists, such as Plantinga, even though in a possible world the apple does not exist, the property “being an apple” does exist.

For Trace Actualists, things in possible worlds can exist. This allows the modal semantics of (23) ◇∃xEx is true if there is a world in which ∃xEx

The problem, as I indicate above, is that it is a pretense to correspondence. That is the problem I mentioned earlier, of replacing intension with extension. Correspondence becomes simply a stipulation, instead of criteria for judgement. The actual world of the modal model "is" the actual world of fact, because this is stipulated as a necessity for truth. — Metaphysician Undercover

Any truth theory could be considered stipulation, although one is free to examine various theories and choose the best, or least offensive. It seems untenable to just abandon any concept of truth.

Correspondence isn't intended to be a criteria for judgement. Judgement is epistemological. Rather, correspondence is the conceptual basis for what truth is. Truthmaker theory is a specific form of correspondence theory that more specifically stipulates that the correspondence is between a proposition and an element of of the actual world, called the truthmaker.

So, "snow is white " is true if and only if snow is white. Yes, now we stipulate "snow is white" (or in the case of possible worlds, the actual world of the modal model is stipulated as in fact the true actual world), and voila, "snow is white" is true by stipulated correspondence, and the actual world of the modal model is true, by stipulated correspondence. But of course, we can all see that this is just a pretense of correspondence. — Metaphysician Undercover

There's more to the analysis:

It is true THAT snow is white IFF snow is white

The italics phrase reflects a proposition; the bold phrase represents an element of actual reality. It is assumed these meanings are clear, and that there is a distinction between a proposition and actual reality, and that truth entails that the proposition (its meaning) mirrors the element of reality.

If you don't like this view, then what view do you think better captures the concept of truth?
.

See how the sentence you keep quoting begins with "Say that...".

Why?

Here's the whole paragraph:

On the assumption that there is a (nonempty) set of all possible worlds and a set of all possible individuals, we can define “objective” notions of truth at a world and of truth simpliciter, that is, notions that are not simply relative to formal, mathematical interpretations but, rather, correspond to objective reality in all its modal glory. Let ℒ be a modal language whose names and predicates represent those in some fragment of ordinary language (as in our examples (5) and (6) above). Say that M is the “intended” interpretation of ℒ if (i) its set W of “possible worlds” is in fact the set of all possible worlds, (ii) its designated “actual world” is in fact the actual world, (iii) its set D of “possible individuals” is in fact the set of all possible individuals, and (iv) the referents assigned to the names of ℒ and the intensions assigned to the predicates of ℒ are the ones they in fact have. Then, where M is the intended interpretation of ℒ, we can say that a sentence φ of ℒ is true at a possible world w just in case φ is trueM at w, and that φ is true just in case it is trueM at the actual world. (Falsity at w and falsity, simpliciter, are defined accordingly.) Under the assumption in question, then, the modal clause above takes on pretty much the exact form of our informal principle Nec. — SEP

See how the single line you quote is part two of four of the antecedent of a mooted definition of true-in-M that is being true in any arbitrarily selected world. The conclusion is the opposite of what you suggest: any world might have been chosen to take on the place of the actual world, with the same result.

For those reading on, Meta isolates (ii) (“its designated ‘actual world’ is in fact the actual world”) and treats it as if it were doing independent semantic work. That is a mistake.

Again, there Might be a point Meta could be making, but his utter inability to understand and use the formal logic here incapacitates his expressing his view. Meta might be gesturing at a familiar philosophical concern, namely that the appeal to an “intended model” smuggles metaphysics into what is advertised as a purely semantic account. To make that objection, Meta would have to distinguish object-language truth conditions from metasemantic stipulations, recognise the difference between fixing a model and evaluating formulas within it, and understand how conditional definitions work in formal semantics. There may be a point Meta could be making, but his inability to understand and use the formal logic prevents him from expressing it.

You seem to want to focus on one, the abstractionist interpretation, as if it is the only acceptable interpretation — Metaphysician Undercover

No, Meta. I haven't moved past it because i keep answering your silly quibbles. My bad, yes, i should go back to ignoring you.

Yep.

Yep. We might be clearer about Plantinga’s view. It's not primarily about properties like “being an apple”. It is about individual essences (haecceities). For Plantinga very individual has a haecceity (e.g. being that very apple), and haecceities exist necessarily, and oddly it seems worlds contain haecceities whether or not they are exemplified. So in a world where the apple does not exist, the haecceity "being that apple" exists, and is unexemplified. That haecceity is what does the semantic work for quantification.

All of which looks quite contrived to my eye. Not keen on Plantiga's approach.

For Trace Actualists, things in possible worlds can exist. This allows the modal semantics of (23) ◇∃xEx is true if there is a world in which ∃xEx — RussellA

Isn't it more that ◇∃xEx is true if there is an accessible world in which ∃xEx can be represented? Roughly, if we can posit, or perhaps talk abuot some world in which ∃xEx?

I'll have a bit of a bitch about Plantinge awhile we are here.

It seems to me that Plantiga takes a way of talking and turns it into a thing. Suppose I say that I might have had an apple for breakfast. Plantinga would say that the apple I might have had necessarily has a thing that makes it what it is, and that this thing is what I might have had for breakfast. It would be ridiculous to say that there is an apple that I might have had for breakfast, and Plantinga tries to avoid the ridicule by replacing that apple with a haecceity-of-apple, as if that were any better.

Perhaps something like this sits behind @Metaphysician Undercover's confusion, or @Relativist's disquiet. Something like it seems to underpin the essentialism that the forum Thomists misuse.

How do you address the ontology of the hypothetical apple? Is it a mental state?

Plantinga would say that the apple I might have had necessarily has a thing that makes it what it is, and that this thing is what I might have had for breakfast. — Banno

I don't think Plantinga would say that. He's an essentialist, so he believes that apples are an essential kind, and an individual apple has a unique essence that makes it the particular apple that it is. He would say there's a possible world in which you ate this particular apple (transworld identity is associated with individual essence), and also there's a possible world identical to this one except the apple you ate was a different one (a different essence).

I take issue with essentialism. Transworld identity requires it.

Is it a mental state? — frank

No. The apple can't be a mere mental state because we are now each talking about the very same apple, and your mental states are not my mental states.

It has to be something shared, or at least public.

My view isn't all that firm yet, but I've mentioned to @Ludwig V that I think all three views suffer from the same error in that they presume maximally complete worlds. I don't see that as needed, and what follows might be a more ad hoc and constructive approach.

We talk as if there were an apple. That's just one of the many games we play with words. And that's related to the counts as... stuff from Searle; we just do talk about apples in this way, like we talk about property and credit, none of which are things in the way the apple in the fruit bowl is.

For Plantinga, individuals are identified across worlds by their haecceities, not by their kind membership, a “different apple” in another world isn’t just a different instance of the same kind; it is a different haecceity. The semantic machinery that lets us say “I could have eaten this apple” relies on the haecceity of the apple, even if it is unexemplified in that world.

Your reading of Plantinga is through a kind-essentialist lens: i.e., the identity of transworld apples is determined primarily by kind. Plantinga’s haecceity-essentialism is individual-specific, not kind-specific. It’s not “an apple of kind K in another world,” it’s “the very same apple’s haecceity in another world,” which may or may not be instantiated.

So do you conflate kind-essentialism with individual (haecceity) essentialism? Plantinga’s machinery is much more fine-grained, tracking this very apple, not “an apple of the same kind.”

Basically his use of haecceities looks to me to be reworking the problem rather than solving it.

We talk as if there were an apple. That's just one of the many games we play with words. And that's related to the counts as... stuff from Searle; we just do talk about apples in this way, like we talk about property and credit, none of which are things in the way the apple in the fruit bowl is. — Banno

My own view is kin to this, except I think we each treat the world around us as an interlocutor. The set of all things I might have had for breakfast is an aspect of expectations I have about the way the world is. I don't fall into a private language problem because the world is there to test me.

I don't think there's really enough talk between us humans to cover all the sets I have at my mental fingertips.

A haeecity is an essence, or at least an essential property (a component of an essence).

I'm probably wrong about Plantinga being a kind-essentialist, I don't recall him making those claims. Nevertheless, it seems to me a possible world in which you eat a different apple depends on kind-essentialism - the essence of what an apple is.

So do you conflate kind-essentialism with individual (haecceity) essentialism? — Banno

No.

A haeecity is an essence, or at least an essential property (a component of an essence). — Relativist

We need to take care here.

Here is a way in to talk about essences that make sense: the essence of some individual is those properties that it has in every possible world in which it exists.

Here's a way to talk about essences that is somewhat obtuse: the essence of something is that which makes it what it is and not another thing.

Here's a complication on the latter: we can call the thing that makes something what it is, its haecceity... And the italics are there to mark the hypostatization, the presumption that what makes a thing what it is, is yet another thing...

Muddle on muddle, compounded mud.

Nevertheless, it seems to me a possible world in which you eat a different apple depends on kind-essentialism - the essence of what an apple is. — Relativist

How to make sense of this? A possible world in which I didn't eat a different apple to the one I didn't eat for breakfast? :chin:

I didn't eat an apple for breakfast, and yet it's not the case that this is the apple that I didn't eat for breakfast. Plantinga wants this to be the apple I didn't eat - he wants there to be a particular uneaten apple in some possible world.

Plantinga would respond that haecceities are primitive - they don't reduce to qualitative properties (including kind-properties). But this makes transworld identity mysterious; he inevitably smuggles in kind-essences when reasoning about counterfactuals.


The apple is an apple, with no need for essence or haecceity or other bloody philosophical obfuscation. And there is no particular apple that I didn't eat for breakfast, despite my not having eaten an apple for breakfast.

A haeecity is an essence, or at least an essential property (a component of an essence). — Relativist


We need to take care here.

Here is a way in to talk about essences that make sense: the essence of some individual is those properties that it has in every possible world in which it exists. — Banno

That's coherent, but it doesn't say much.
Suppose the properties that comprise an individual essence is comprised of this maximal set: 100% of the individual's intrinsic and relational properties at every point it time that it exists. There is a relation to everything that exists in this world, and therefore the set of possible worlds in which the individual exists is just the one: the actual world. I suggest this is the base case - because it does clearly identify an individual.

Going beyond the base case: if we wish to make the case that the the individual exists in non-actual possible worlds then we would need to identify a subset of this maximal set of properties that are necessary and sufficient If there is haeecity, that could be it. But why even think there is haeecity? And that seems to be your point here:

Here's a way to talk about essences that is somewhat obtuse: the essence of something is that which makes it what it is and not another thing.

Here's a complication on the latter: we can call the thing that makes something what it is, its haecceity... And the italics are there to mark the hypostatization, the presumption that what makes a thing what it is, is yet another thing... — Banno

Agreed. The theory that there is haecceity is logically posterior to the assumption that there is something that makes each thing what it is. A set of necessary and sufficient properties would also do the trick, but my sense is that there's no consistent means of culling down the maximal set I mentioned. This relates to the problematic quote of Kripke's I gave earlier:

"Really, adequate necessary and sufficient conditions for identity which do not beg the question are very rare in any case. Mathematics is the only case I really know of where they are given even within a possible world, to tell the truth. I don't know of such conditions for identity of material objects over time, or for people. Everyone knows what a problem this is. But let's forget about that." N&N p43

I don't think we should forget about it.

So in a world where the apple does not exist, the haecceity "being that apple" exists, and is unexemplified. — Banno

To my present understanding:

If I say “the apple might be on the table”, then there is a possible world where the apple is on the table.

Following (23) ◇∃xTx is true if there is an accessible world in which ∃xTx, it is possible that for some apple, the apple is on the table is true if there is an accessible world in which for some apple, the apple is on the table.

As you say, we need to specify what kind of worlds we are talking about, and may decide to limit possible worlds to those worlds that have the same natural laws as ours. The SOA, the apple is on the table, may exist even though it does not obtain. One advantage of the Trace Actualists is that a State of Affairs (SOA) may exist even though it does not obtain.

Here, “exist” is being used in a particular way. This has a different meaning to ordinary language, where exists means obtains.

For Wittgenstein in The Tractatus, if a SOA obtains then it is a fact in our actual world. Then it is a fact that the apple is on the table.

However, if in our actual world the proposition “the apple is on the table” is false because there is no apple on the table, the proposition “the apple might be on the table” is true because there might be an apple on the table, prescribing accessible worlds as having the same laws of nature as ours.

Therefore, in order to accommodate modal semantics, even though the SOA the apple is on the table does not obtain, the possibility of there being an apple on the table requires some kind of existence.

The New Actualists solution is that the apple exists in a concrete sense. Even if not necessarily concrete in an actual world, contingently concrete in a possible world.

The Haecceitists' solution, as for Plantinga, the apple exists in its haecceity, both in the actual world and all possible worlds. This haecceity is not Platonic Realism, where the property of appleness exists even if never instantiated by an apple. This haecceity is not that of mental abstract concepts independent of any physical manifestation.

Heicceity is an historic term, going back to John Duns Scotus in the 13th C, who proposed that although an object is no more than its set of properties, haecceity makes the object unique and different to any other object.

The idea was continued by Leibniz in his Principle of the Identity of Indiscernables, where even though two objects sharing the same properties must be identical, they remain unique and different to all other objects because of their haecceity.

For Plantinga, every entity exists and has a unique haecceity, a primitive “thisness” that cannot be reduced to anything else, and has this haecceity even in those worlds where the entity does not obtain.

Then how to explain Plantinga’s haecceity as something that exists in a mind-independent world, especially as he is neither proposing Platonic Realism nor suggesting that haecceity exists as a mental concept.

How can the haecceity of an apple exist in the world even though no apples exist in the world?

Perhaps the answer to this may be given by those who believe that numbers are discovered and not invented. I personally believe that numbers are invented in the mind. However, there are those who believe that numbers are discovered in the world, such that the number 9 exists in the world even though never instantiated in the world. In this sense, numbers may also have an haecceity.

If there were, problems would arise. Suppose an haecceity of Theseus’s ship existed in the world even though Theseus’s ship did not obtain in the world. We know that parts of Theseus’s ship can be removed. Then for every possible configuration of Theseus’s ship there world be a different haecceity in the world, becoming infinite in number.

Even if Platonic Realism is dismissed, haecceity as a mental concept can be understood, but Plantinga is suggesting the haecceity of an individual exists in a mind-independent world even in the absence of that individual.

The fact that Alvin Plantinga is a Christian philosopher, and a defender of theism, may take the nature of his haecceity into the spiritual realm and away from the material realm. But that is another story.

How do you address the ontology of the hypothetical apple? .... — frank

"I might have had an apple for breakfast" (a) is puzzling when we ask which apple I might have had for breakfast, and then we wonder about the ontology of the hypothertical apple as if it were a kind of apple. We understand "I might have had that apple in the bowl" (b) for breakfast without positing an hypotherical apple; we even understand "I might have had one of the apples in the bowl for breakfast" (c) without positing hypothetical apples. The puzzle lies entirely in the difference between (a) and (b) or (c). (a) is perfectly comprehensible until you ask the follow-up question which apple you might have had. The question doesn't have the context that would enable an answer. Brutally, there's no such thing as a hypothetical apple; there are only hypotheses about apples.

Heicceity is an historic term, going back to John Duns Scotus in the 13th C, who proposed that although an object is no more than its set of properties, haecceity makes the object unique and different to any other object. — RussellA

We can ask whether this object is red or heavy or... We then notice that there is nothing to prevent something else having just the same properties. After all, a property is inherently something that can occur more than once. There is no guarantee that the same bundle will not occur again. But it is no help to posit yet another property and attributing to that property the magical capacity to be uniquely found in that object. It just makes another puzzle. In specific cases and contexts, we distinguish objects from each other in specific cases and contexts.

The italics phrase reflects a proposition; the bold phrase represents an element of actual reality. — Relativist

But there is nothing which you are calling "actual reality" in the modal model, that's the problem. "Actual" reality is simply stipulated, even Banno accepts this, as indicated below. So in the case of "It is true THAT snow is white IFF snow is white", the latter "snow is white" is simply stipulated. So the meaning of "It is true THAT snow is white IFF snow is white", is that "snow is white is true" if we stipulate that snow is white. "True" is already used, so it would be meaningless to say "It is true THAT snow is white IFF it is true that snow is white". So the latter "snow is white" is stipulated based on arbitrary or subjective principles according to whether you want "snow is white" to be true or not.

See how the single line you quote is part two of four of the antecedent of a mooted definition of true-in-M that is being true in any arbitrarily selected world. The conclusion is the opposite of what you suggest: any world might have been chosen to take on the place of the actual world, with the same result. — Banno

That's exactly the point I am making. The truth condition stated as " its designated 'actual world' is in fact the actual world" is never met, because "any world might have been chosen to take on the place of the actual world,". So the modal "actual world" is never "in fact the actual world", and the conditions for truth are never met.

Again, there Might be a point Meta could be making, but his utter inability to understand and use the formal logic here incapacitates his expressing his view. Meta might be gesturing at a familiar philosophical concern, namely that the appeal to an “intended model” smuggles metaphysics into what is advertised as a purely semantic account. To make that objection, Meta would have to distinguish object-language truth conditions from metasemantic stipulations, recognise the difference between fixing a model and evaluating formulas within it, and understand how conditional definitions work in formal semantics. There may be a point Meta could be making, but his inability to understand and use the formal logic prevents him from expressing it. — Banno

Obviously the problem cannot be expressed in formal logic, because the nature of the problem is that it renders the formal logic as fundamentally unsound. To try and express it as formal logic would be a self-defeating exercise, because accepting it's rules is implied by using it. Instead, to demonstrate the problems of formal logic, we must show that the absurd conclusions it produces are because the logic is faulty.

But if you know about the problems of possible worlds semantics, as you claim here, then accept it, and reject possible worlds semantics for what it is, misleading sophistry.

For the Abstractionsists:
There is the actual world, an actual world, a State of Affairs that exists and obtains.
There are possible worlds, non-actual worlds, States of Affairs that exist but fail to obtain. — RussellA

The glaring problem I see with abstractionism is that the entirety of the observed, empirical world, cannot be captured by "states of affairs". This is due to the reality of change, activity, and motion. If we assume that the world could be captured as states of affairs, we end up with Zeno paradoxes. So, as Aristotle demonstrated, "being" (states of affairs) is fundamentally incompatible with "becoming" (change and activity). The changes, motion and activity which we observe in the world, cannot be described by states of affairs.

The demonstration is like this. If the world is describable as state A, and then it becomes state B, we can conclude that change occurred between A and B, We could then assume a state C as the intermediary between A and B and describe the change as state C, but this would imply that change occurred between A and C, and also between C and B. We could posit state D between A and C, and state E between C and B, but we would still have the same problem again. As you can see, this indicates an infinite regress, and we never get to the point of understanding what change, activity, or motion, really is. Activity, change, motion, is what occurs between states of affairs, when one becomes the other.

Because of this, Aristotle determined that we must allow that the nature of "possibility" is such that the fundamental laws of logic are violated by it. If at one moment, t1, an object has property X, and at the next moment, t2, it does not have property X, indicating change or motion, then to accurately understand what change or motion is, we must allow that either the law of non-contradiction, or the law of excluded middle is violated in the meantime, between t1 and t2. Either the object both has and does not have the property during this activity, or it neither has nor does not have the property during this change. Aristotle stipulated that we must not violate the law of noncontradiction, and opted for a violation of the law of excluded middle. This forms the basis for our current, common understanding of "possibility". The thing which is said to be "possible" is understood to to have a status of being neither what is the case nor what is not the case. As such, "possibility" cannot be understood through the application of states of affairs.

But there is nothing which you are calling "actual reality" in the modal model, that's the problem. — Metaphysician Undercover

It is the reality that we perceive with our senses. You could say that we are stipulating this reality exists (=solipsism is false), but I suggest that we innately believe we are perceiving an external world. So this "stipulation" just reflects an abstraction of our innate world-view.

the meaning of "It is true THAT snow is white IFF snow is white", is that "snow is white is true" if we stipulate that snow is white. — Metaphysician Undercover

Same "stipulation": we are perceiving aspects of reality apart from oneself. We have perceptions of color, and of that cold, powdery stuff. We perceive these even without naming them, but by naming them we can reflect on them abstractly.

It is true THAT snow is white IFF snow is white", is that "snow is white is true" if we stipulate that snow is white. — Metaphysician Undercover

We have named the perceived color of the cold powdery stuff, "snow" a stipulation in English, but the reference is the same for Germans, who have similar perceptions, but stipulate it to be "schnee". Again, this is grounded in our innate trust in the mental image of the world that our minds present to us.

Straightforwardly, we apply words to perceived objects, but by extension - we also apply them to abatract concepts- like "true". A plausible hypothesis: in our evolutionary history, we developed language - enabling cooperative behaviors. We could communicate perceived aspects of the world to one another. This also meant that we could recognize a discrepancy between what another person tells us, and what we perceive- a grounding for the twin concepts of true/false.

You said this to Banno:

That's exactly the point I am making. The truth condition stated as " its designated 'actual world' is in fact the actual world" is never met, because "any world might have been chosen to take on the place of the actual world,". So the modal "actual world" is never "in fact the actual world", and the conditions for truth are never met. — Metaphysician Undercover

I have given you a grounding for "actual world" that no fictional world can have: our direct interaction with it.

The world we interact with is represented abstractly in our minds, and this enables us to entertain variances to this abstract world image: the fictional worlds that get the (questionable*) label "possible worlds".

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*I can rationalize use of "possible"in terms of different modality, but I'll defer for now. "Fiction" seems like something we could agree on.

There is no guarantee that the same bundle will not occur again. But it is no help to posit yet another property and attributing to that property the magical capacity to be uniquely found in that object. It just makes another puzzle. — Ludwig V

Perhaps this is the case:

Ordinary language
In ordinary language, “it is possible that the apple is on the table”.

Possibility 3 - the apple is not on the table
Possibility 6 - the apple is not on the table
Possibility 9 - the apple is on the table
Possibility 12 - the apple is on the table

In 3 and 6, we are referring to something that does not exist as if it existed, which is a puzzle.

Therefore, the apple referred to in 3 cannot be the same thing as the apple referred to in 6, as non-existent things cannot be identical to each other.

Modal logic
(23) ◇∃xTx is true if there is an accessible world in which ∃xTx

Possible world W3 = ¬ ∃xTx
Possible world W6 = ¬ ∃xTx
Possible world W9 = ∃xTx
Possible world W12 = ∃xTx

In modal logic, rather than as in ordinary language referring to something that does not exist as if it existed, we can say x exists even if x does not obtain.

As with ordinary language, the x in W3 cannot be the same thing as the x in W6, as non-obtaining things cannot be identical to each other. Therefore, they must be uniquely different.

Plantanga proposed “haecceity” to account for this uniqueness of entities.

The glaring problem I see with abstractionism is that the entirety of the observed, empirical world, cannot be captured by "states of affairs". This is due to the reality of change, activity, and motion. — Metaphysician Undercover

However, the world only exists at one moment in time, which is the present. The world cannot exist at two moments in time. Even our memories of the past exist in this present moment in time.

I agree that a State of Affairs can only capture one moment in time, but as the world can only exist at one moment in time, a State of Affairs is able to describe the world.
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As such, "possibility" cannot be understood through the application of states of affairs. — Metaphysician Undercover

The world can only exist at one moment in time. At this present moment in time, the object does not have property X, and we have the memory that in the past the object had the property X. However, this memory of the past also exists in the present.

The Law of Contradiction would be violated if an object has the property X and does not have the property X at the same time. However, this is not the case. There is only one moment in time, and that is the present. In this present, the object does not have the property X.

The Law of Excluded Middle has not been violated, as the proposition “the object as it is in the present does not have the property X” is true.

At this present moment in time is my thought that it is possible that the apple is on the table. Possibility exists in this present moment in time, in the present State of Affairs. Possibility can be understood within the State of Affairs that presently obtains.

It is the reality that we perceive with our senses. You could say that we are stipulating this reality exists (=solipsism is false), but I suggest that we innately believe we are perceiving an external world. So this "stipulation" just reflects an abstraction of our innate world-view. — Relativist

In the modal model there is a world stipulated as the actual world. It is obviously not the external world which we perceive. The reasons for the stipulation are fundamentally subjective. It may be intended that the stipulated actual world is a representation of the external world we perceive, but even so, that representation may be false in the sense of correspondence, because of mistake.

Same "stipulation": we are perceiving aspects of reality apart from oneself. We have perceptions of color, and of that cold, powdery stuff. We perceive these even without naming them, but by naming them we can reflect on them abstractly. — Relativist

When someone says "It is true THAT snow is white IFF snow is white", perceptions are completely irrelevant. Notice, it does not say "iff snow is perceived as white", and there is nothing to indicate that "white" refers to a perception.

We have named the perceived color of the cold powdery stuff, "snow" a stipulation in English, but the reference is the same for Germans, who have similar perceptions, but stipulate it to be "schnee". Again, this is grounded in our innate trust in the mental image of the world that our minds present to us. — Relativist

That would require a further definition. "White" would need to be defined as a specific type of perception. But that is not what is intended, as the intention is to avoid intension. So "white" is simply a predicate, and the predication "snow is white" is true if it is a fact that snow is white. We can thereby stipulate that snow is white (this is a feature of the actual world), then "snow is white" is made to be true, by the means of that stipulation.

I have given you a grounding for "actual world" that no fictional world can have: our direct interaction with it. — Relativist

But that's not the grounding of possible worlds semantics, it is your personal choice, your grounding for "actual world". Other people could use other groundings because the stipulation of "actual world" is subjective.

However, the world only exists at one moment in time, which is the present. — RussellA

That is not consistent with empirical observations. We see activities, things moving. Therefore what we perceive as "the existing world", is a world in which time is passing, things are changing, and this is inconsistent with your statement "the world only exists at one moment in time".

I agree that a State of Affairs can only capture one moment in time, but as the world can only exist at one moment in time, a State of Affairs is able to describe the world. — RussellA

That the world exists at a moment in time, as a State of Affairs, is a faulty assumption. It is faulty because it is inconsistent with empirical observations, which indicate to us that time is always passing, and change is always occurring. That is why there is an uncertainty principle in physics.

Possibility 3 - the apple is not on the table
Possibility 6 - the apple is not on the table
Possibility 9 - the apple is on the table
Possibility 12 - the apple is on the table — RussellA

I don't quite understand this. 3 and 6 appear to be identical; so do 9 and 12. So we are considering two possibilities.
"It is possible that the apple is not on the table" and "It is possible that the apple is on the table".
Both these sentences presuppose that there is some specific apple in question. Normally, one would work out which one from the context. But here, there is no context, so no clear interpretation of the sentences is available.
As they stand, the first sentence means "There is no apple on the table" which doesn't refer to anything non-existent and "There is an apple on the table", which refers to the apple on the table, which does exist.
So I don't see your problem.

The possible worlds could supply an appropriate context. But whether the apple in W3 is the same apple as the apple in W6 or the apple in W9 is the same as the apple in W12, - or perhaps the same apple is in question in all four worlds - is a question of trans-world identity. That's an awkward question, but at least we have a context that supplies an apple to be referred to. But I wouldn't be dogmatic about how all that works.

The general problem of non-existent objects has two facets. The only such objects that we can talk about are objects like "the present king of France" or "Pegasus" or "Clark Kent a.k.a. Superman". These are all defined in a context which gives the terms some meaning, while at the same time stipulating that their existence is confined to those specific contexts and excluded from what we are pleased to call the real world. It requires a certain mental gymnastics, but people seem to manage it, on the whole. Without some such conceptual device, I don't see how one can say anything at all about non-existent objects. They have to exist in some sense if we are to talk about them at all.

Plantanga proposed “haecceity” to account for this uniqueness of entities. — RussellA

So far as I can see, "haecceity" has no meaning beyond "the property that accounts for the uniqueness of entities". It is just a label for the problem.
Since non-existent objects don't exist, they can't possess haeccity". So it is doesn't help with non-existent objects. .

Suppose the properties that comprise an individual essence is comprised of this maximal set: 100% of the individual's intrinsic and relational properties at every point it time that it exists. There is a relation to everything that exists in this world, and therefore the set of possible worlds in which the individual exists is just the one: the actual world. I suggest this is the base case - because it does clearly identify an individual. — Relativist

Nice.

Such an individual immediately brings about modal collapse, since p→☐p. What we have is further reason of rejection the notion of essence as resulting in incoherence.

Ok. We need to keep the quantification in line - again, there is a difference between any apple and a particular apple and the apple I didn't eat need not be any particular apple. So is

...the proposition “the apple might be on the table” is true because there might be an apple on the table, — RussellA

About a particular apple or not? Is it that there might be an apple - any apple - on the table, or that some particular apple is on the table? And then how, if it is possible that the apple is on the table, do we understand the haecceity of the apple being on the table but not the apple?

All this by way of mostly agreeing with you. Including the suspicion that Plantinga is misled by his faith.

"Actual" reality is simply stipulated, even Banno accepts this, as indicated below. — Metaphysician Undercover

What twaddle.