At any rate, anyone who chooses to take possible world analysis seriously ought to understand the dependency on coherence theory of truth. — Relativist

Yes, there are many different definitions of truth (SEP - Truth). The question of what establishes the truth of a statement then depends on which definition of truth is being used.

The question of what establishes the truth of a statement then depends on which definition of truth is being used. — RussellA

And the one being used in the article is Tarski’s Truth Definition.

And the one being used in the article is Tarski’s Truth Definition. — Banno

:up:

For example, if you plan on a holiday to somewhere you have never been before, you presuppose that where you are going is an actual and concrete place. — RussellA

The place signified "Chicago" is not an imaginary thing, it is understood as real, actual. In the case of possible worlds, they are imaginary things, not real or actual, but possible. The analogy is incorrect.

No, we don't have to assign existence to it. All we have to do is to imagine or suppose that it exists. — Ludwig V

That would be very interesting if you could explain a reasonable difference between these two. The former would be an actual predication, the latter would be an imaginary predication. Is that what you're saying?

If Aristotle, and perhaps Homer, never actually existed, yet Aristotle and Homer are rigid designators, then what is Aristotle and Homer actually designating. — RussellA

Well, Homer is the author of the Iliad and the Odyssey. So presumable "Homer" designates that person whoever he may be. The difficulty is not just that someone else wrote those epics, but that they were a) not written down (until long after they were created) and b) not created by a single author. The poems were part of an oral tradition in which each poet created their own version(s), so b) our ideas of authorship and texts do not apply in that culture. I wouldn't press this as any kind on knock-down argument here. It's just an interesting conundrum.
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That would be very interesting if you could explain a reasonable difference between these two. The former would be an actual predication, the latter would be an imaginary predication. Is that what you're saying? — Metaphysician Undercover

It's easier than that. Existence is not a predicate. I'm not quite sure whether being imaginary counts as a predicate, but there's no doubt that "imaginary" excludes "exists". What does exist (in our world) is the account that people give of what they have imagined. Whatever has been imagined would then count as a possible object, and so existent in another world, not this one. Yes?

The place signified "Chicago" is not an imaginary thing, it is understood as real, actual. — Metaphysician Undercover

This statement needs unpacking.

The first part of the statement, “The place signified "Chicago" is not an imaginary thing” is from a mind-independent viewpoint.

The second part of the statement, “it is understood as real, actual” is from the viewpoint of a mind.

The first part of the statement linguistically clashes with the second part of the statement, making it difficult to answer.
==============================================================

In the case of possible worlds, they are imaginary things, not real or actual, but possible. — Metaphysician Undercover

Again, this statement needs expanding. “For whom”?

For Lewis’ Concretism, the statement is true from our viewpoint, in that from our viewpoint, these worlds are imaginary worlds, not real or actual.

But the statement is not true from the viewpoint of those people living on these worlds, in that from their viewpoint, these worlds are not imaginary worlds, are real and actual.

Well, Homer is the author of the Iliad and the Odyssey. So presumable "Homer" designates that person whoever he may be. — Ludwig V

Continuing:

1) Suppose a single person originated the Iliad, which was either written down or passed down as part of an oral tradition.
2) Whoever originated the Iliad has been given the name “Homer”.
3) Suppose, in fact, that the Iliad was originated by Hesiod.
4) Hesiod had a friend, Homer, who was in fact a baker.

Does the name “Homer” designate Hesiod, as for Kripke’s Rigid Designation, or does “Homer” refer to “the person who originated the Iliad”, as for Russell's Theory of Descriptions?

What, exactly, is not possible? — Banno

Frodo existing in (or interacting with) the real world, because he's fictional.

Doing what you suggest is inconsistent with correspondence theory of truth - the Frodo statement is not "true" under this theory.
— Relativist
Have you an argument to go along with that? — Banno

Here's my statement that began this line of discussion: "The book establishes a fiction. We could examine this fictional world for coherence, and draw valid inferences if (and only if) it is, but the inferences are all qualified by, "within Tolkien's fictional world...". But no unqualified objective truths can be inferred.""
You objected to my reference to "unqualified" objective truths. I was referring to a correspondence theory of truth. So my argument is simply that there is nothing in the actual world corresponds to Frodo, or hobbits in general.

My broader issue is that there's no obvious means of distinguishing between a fictional world (like Tolkein's) and a non-actual possible world (a non-actual world in which a contingent event actualized differently than it actually did).

And what of it - we are using Tarski's semantics, not correspondence.And what of it - we are using Tarski's semantics, not correspondence.

First of all, you've been referring to indexicality, which is beyond Tarski (as far as I can tell, from both the the article you linked and my book on Truth theories) but I get it that this makes sense in terms of the article. But we're discussing any and all aspects and issues with the two articles referenced in the Op.

Strictly speaking, Tarski's approach is mathematical - and it works well with mathematical systems. However:

"To extend Tarski's definition to any large fragment of extra-mathematical language is...not easy."
- Truth: Princeton Foundations of Contemporary Philosophy, Burgess & Burgess, p 88

The difficulty is a consequence of the fact that Tarski's theory deals with language/semantics. Tarski defines "formally correct" this way:

For all x, True(x) if and only if ϕ(x), where True never occurs in ϕ

This actually does apply to correspondence theory, which is deflationary. Deflationary theories are based on the equivalence principle:

It is true that snow is white iff snow is white

The italicized words are a proposition. The bold words describes a state of affairs in the world. It fits Tarski because "true" is not an aspect of the world; it is strictly an aspect of propositions.

But that's incidental.

Most importantly, I'm raising issues entailed by the thesis discussed in the article, not debating what the article says. By contrast, it appears you think the discussion should be limited to trying to understand the articles - is that correct? I think this also fits your disagreement with Metaphysician Undercover.

,

You pretend your already repudiated arguments were adequate. — Banno

As usual. you reject my arguments because they are inconsistent with what you believe, without even addressing the the truth or falsity of the premises, or the validity of the argument. Look:

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, — SEP

Possibilities are infinite, so we cannot have "the set of all possible worlds", as required for the truth conditions. That is impossible because any proposed set will be incomplete. We will never have the true actual world (M), therefore the stated truth conditions for possible worlds semantics are necessarily violated, truth cannot be obtained.

It's easier than that. Existence is not a predicate. — Ludwig V

But you used it as a predicate, when you said that one could imagine that something exists. otherwise its a verb, but that becomes even more difficult, to explain the activity which is referred to as "exists".

Whatever has been imagined would then count as a possible object, and so existent in another world, not this one. Yes? — Ludwig V

Yes, but concretism would have the other world exist as well. That's when it becomes problematic. The only place the other (possible) world exists is in the mind, because it is a fabrication, a mentally produced possibility. But now we have to say that this mental fabrication has actual concrete existence.

This statement needs unpacking.

The first part of the statement, “The place signified "Chicago" is not an imaginary thing” is from a mind-independent viewpoint.

The second part of the statement, “it is understood as real, actual” is from the viewpoint of a mind.

The first part of the statement linguistically clashes with the second part of the statement, making it difficult to answer. — RussellA

I don't see you complaint. Both parts are "from the viewpoint of a mind". In the first part the mind is using the word "Chicago" to refer to something believed to be independent from that mind. The second part describes that independence as "real, actual".

For Lewis’ Concretism, the statement is true from our viewpoint, in that from our viewpoint, these worlds are imaginary worlds, not real or actual.

But the statement is not true from the viewpoint of those people living on these worlds, in that from their viewpoint, these worlds are not imaginary worlds, are real and actual. — RussellA

I really don't see the problem you are alluding to. A statement is made from the perspective of the one who makes it, unless the person signifies that this is supposed to represent a different perspective. Then it would be an imaginary perspective. We could make a statement about the perspective of a person in a different imaginary world, but that would still be a statement made from the perspective of the person making the statement, and that person would be stating an imaginary perspective.

So it's still an imaginary perspective. We can't get to the point of having a real perspective from an imaginary world. If a person in the imaginary world could talk to you, and describe the perspective, that would just be your imagination describing the perspective. And if a person in the actual world describes a different perspective to you, that is a perspective from the actual world, not the imaginary world. So there is no way that we can get to the conclusion that the people in an imaginary world have a real and actual perspective.

, , keep in mind that a rigid designator only refers to an individual in those possible worlds in which that individual exists.

If Homer didn't exist, then "Homer" doesn't refer to anyone.

I was referring to a correspondence theory of truth. — Relativist

Indeed, but very clearly what is being used in modal logic is a semantic theory of truth.

...you've been referring to indexicality, which is beyond Tarski. — Relativist

Well, we can use Kaplan's account, if you like. It's an extension of the semantic theory of truth that does deal with indexicals.

This actually does apply to correspondence theory, which is deflationary. Deflationary theories are based on the equivalence principle: — Relativist

Nuh. It's not deflationary. It's very much one of the substantive theories of truth.

The core problem with what you are saying seems to be that you are trying to use the correspondence theory in the place of the semantic theory, and bumping up against the problems this causes.

As usual. you reject my arguments because they are inconsistent with what you believe, without even addressing the the truth or falsity of the premises, or the validity of the argument. — Metaphysician Undercover

Nuh. I reject your arguments because they are muddled.

Take:

Possibilities are infinite, so we cannot have "the set of all possible worlds", as required for the truth conditions. That is impossible because any proposed set will be incomplete. We will never have the true actual world (M), therefore the stated truth conditions for possible worlds semantics are necessarily violated, truth cannot be obtained. — Metaphysician Undercover

It contains at least a half-dozen compounding errors. There are infinite sets, and indeed uncountably infinite sets; and we can give truth conditions for those sets. Consider ℕ and ℝ. 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. A model M is an ordered structure ⟨W, R, V⟩, and the actual world is a distinguished element w∈W. Kripke prooved that K, T, S4, and S5 are both complete and consistent, so truth can be "obtained" (your term) for those systems.

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

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

The core problem with what you are saying seems to be that you are trying to use the correspondence theory in the place of the semantic theory, and bumping up against the problems this causes. — Banno

No, I identified the core problem in my prior post, but you didn't read my entire post:

Most importantly, I'm raising issues entailed by the thesis discussed in the article, not debating what the article says. By contrast, it appears you think the discussion should be limited to trying to understand the articles - is that correct? I think this also fits your disagreement with Metaphysician Undercover. — Relativist

I'll add that you never stipulated that you were limiting the discussion. I'm also surprised you didn't pick up on the context of our statements. If this broader context wasn't of interest to you, there was no need to comment on what I said.

This thread was set up specifically to work through the two articles. Look:

This thread is for a read through of two SEP articles on possibility and actuality. — frank

I've said previously that before we embark on a critique of the implications of possible world semantics, we need both a strong grasp of modal logic and an understanding of the main theories concerning its application. That's what I have been doing. I don't think what you have said demonstrates such a grasp on your part.

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.

I'm more than happy to consider the consequences of possible world semantics. Indeed, with others here, we have been doing just that. But not by first misunderstanding it.

This actually does apply to correspondence theory, which is deflationary. Deflationary theories are based on the equivalence principle:
— Relativist
Nuh. It's not deflationary. It's very much one of the substantive theories of truth. — Banno

Here's what Burgess and Burgess have to say:

“What do the different views called ‘deflationist' all have in common, to make them all deflationist?” itself admits no easy answer. Deflationists are, however, typically committed to three theses about the phrase “is true,” usually called the natural language truth predicate....First, applying the truth predicate to something is equivalent to just saying it. One version of this equivalence principle is embodied in Tarski's T-scheme"

This is essentially what I was passing along.

Tarski's theory is incomplete because it doesn't directly deal with the world, or we could say it leaves it open. Correspondence theory does exactly that.

I'm no expert on Tarski, so I asked Claude, "Is correspondence theory of truth consistent with Tarski's theory? Here's the response:

"Yes, they're quite compatible. Tarski actually saw his work as a formal vindication of the correspondence theory.

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:

Where they align:

. Both involve a relationship between language and reality

[*] Tarski's biconditionals seem to express correspondence: the sentence on the left corresponds to the fact on the right
[*]Tarski himself described his work as capturing the "classical Aristotelian conception" of truth
[*]Tarski himself described his work as capturing the "classical Aristotelian conception" of truth


Where things get complicated:

[*]Tarski was deliberately austere—he avoided metaphysical commitments about what "facts" or "correspondence" really means
[*]His theory works entirely through formal semantic machinery (satisfaction, reference), not by invoking a substantial relation of "correspondence"
[*]Some philosophers argue Tarski's theory is actually deflationary rather than correspondence-based, since it doesn't explain why or how language hooks onto reality—it just systematically pairs sentences with their truth conditions


So you could say: Tarski's theory is consistent with correspondence theories and often seen as their formal implementation, but it's neutral enough that deflationists also claim him. The key question is whether you think giving truth conditions via the T-schema constitutes explaining correspondence, or whether it merely describes truth without explaining the metaphysical relation that makes correspondence hold.
What's your sense—does the T-schema capture what correspondence theorists care about?"

Me: "I think that you are overlooking truthmaker theory, which is both deflationary and is a correspondence theory"
Claude:
"You're right to call that out—I was being too binary. Truthmaker theory is a great example of how these categories can overlap in more sophisticated ways than I suggested.

Truthmaker theory can indeed be both deflationary (in accepting something like Tarski's T-schema without adding metaphysical bloat) and a correspondence theory (in insisting that truths require grounding in reality—that there must be something in the world that makes true sentences true).

The key insight is that truthmaker theorists accept the T-schema while adding a substantive constraint: for every truth, there must exist some entity (a truthmaker) whose existence necessitates that truth. This gives you correspondence—truth depends on how reality is structured—without the traditional correspondence theory's commitment to facts as special ontological items or to a mysterious "correspondence relation.

So I was wrong to suggest correspondence theories must reject deflationary elements or that deflationary approaches can't involve real metaphysical commitments about truth's dependence on reality. Truthmaker theory shows you can be minimalist about truth's definition while robust about truth's metaphysics."

For the read-through, I think we are up to 2.2.3 Actuality and Actualism.

Correspondence theory is not a deflationary account. The t-schema is trivially true. It's not a definition of truth in the way correspondence is.

For the read-through, I think we are up to 2.2.3 Actuality and Actualism. — Banno

:up:

I don't know how to reply to that. It's not clear to me where you want to go with what you have said.

Correspondence is not a deflationary theory of truth. Tarksi is compatible with any theory of truth worthy of consideration. Whether it counts as a deflationary theory is a subject of some considerable discussion, but Tarksi thought not.

I don't see how introducing yet another theory - truth makers - is illuminating.

Can we move on?

Correspondence theory is not a deflationary account — frank

You're right. I'll stick with the specific theory I embrace: truthmaker theory. Truthmaker theory is a correspondence theory, but it includes some deflationary truths (specifically: truths about mere possibilities). But overall, it's not deflationary.


Note the correction. I was trying to be too general. Truthmaker theory is my theory of choice. It is correspondence, but in general it is not deflationary.

Note the correction. I was trying to be too general. Truthmaker theory is my theory of choice. It is correspondence, but in general it is not deflationary. — Relativist

Why, when the article we are reading clearly uses the semantic theory, and with good reason, is this even worth mentioning? I prefer pistachio nougat - but it's not relevant to this thread.

You're right. I'll stick with the specific theory I embrace: truthmaker theory. Truthmaker theory is a correspondence theory, but it includes some deflationary truths (specifically: truths about mere possibilities). But overall, it's not deflationary. — Relativist

Truthmaker theories aren't theories of truth. They're theories about truthmakers.

Why, when the article we are reading clearly uses the semantic theory, and with good reason, is this even worth mentioning?. — Banno

This confirms that you did feel the only correct topic of discussion was the correct interpretation of the article. I considered my points worth mentioning because they are issues that arise from this theory. The Op did not set boundaries on what should be discussed (not that many of us actually honor the supposed topic of the Op for the life of a thread). You decided what the boundaries are, and that you would respond to everyone on that basis.

I've said previously that before we embark on a critique of the implications of possible world semantics, we need both a strong grasp of modal logic and an understanding of the main theories concerning its application. That's what I have been doing. I don't think what you have said demonstrates such a grasp on your part.

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

I'm identifying issues with SOME OF THE WAYS possible world semantics is applied. That's not at all a critique of modal theory. Modal theory is not equivalent to possible world semantics. It's a convenient paradigm for analyzing counterfactuals. Modal theory concerns modal truths (what is necessary, possible, impossible) under various modalities (epistemic, conceptual, physical, metaphysical, and others). When I've brought up these issues, you had the choice of replying to the issue I raised, or not. What you did was to simply tell me I was wrong, because what I said was inconsistent with the article.

Admittedly, I've made some mistakes along the way. When shown my mistakes, I acknowledge them. Breaking your boundaries is not one of them.

I can't imagine why you say truthmaker theory of truth is not a theory of truth. It's classified as such in the literature.

I can't imagine why you say truthmaker theory of truth is not a theory of truth. It's classified as such in the literature. — Relativist

Can you give an example?

I'll give 3 examples:

Here's a quote from the SEP article on The Correspondence Theory of Truth:
"The correspondence theory of truth is often associated with metaphysical realism. Its traditional competitors, pragmatist, as well as coherentist, verificationist, and other epistemic theories of truth, are often associated with idealism, anti-realism, or relativism. In recent years, these traditional competitors have been virtually replaced (at least in terms of publication space) by deflationary theories of truth and, to a lesser extent, by the identity theory (note that these new competitors are typically not associated with anti-realism). Still more recently, two further approaches have received considerable attention. One is truthmaker theory: it is sometimes viewed as a competitor to, sometimes as a more liberal version of, the correspondence theory.

------------------
Truth- PRINCETON FOUNDATIONS OF CONTEMPORARY PHILOSOPHY, by Alexis and John Burgess is a book that surveys a wide variety of Truth Theories. The book covers Tarski, vaieties of Deflationism, Realism, and Anti-Realsm. Truthmaker theory is classified under Realism.

Chapter 5: Realism, section 3 is titled "Truthmaker Theories" (plural).

______________

Stephen Mumford's book, "David Armstrong" summarizes Armstrong's comprehensive metaphysical system, and refers to Armstrong's truthmaker theory as a "theory of truth".

I've never heard of such a thing. What is the theory?

To put it simply, correspondence theory defines Truth as a correspondence to an element of reality. Truthmaker just adds to this by naming that particular element of reality "the truthmaker". Other correspondence theories may simply refer to it more vaguely as a "fact," - which can be interpreted as something platonic. Truthmaker theory is consistent with physicalism.

It's more nuanced than I've indicated. A more rigorous description is here: Truthmaker Theory

Correspondence theory says truthbearers correspond to truthmakers. Truthmakers are central to correspondence theory.

As that article you just linked says, it's not clear how what's being called truthmaker theory is significantly different from traditional correspondence.

Both parts are "from the viewpoint of a mind". — Metaphysician Undercover

You say “The place signified "Chicago" is not an imaginary thing, it is understood as real, actual.”

The fact that I imagine the city of Chicago to be a real and actual place, means that the city of Chicago is in addition also an imaginary thing in my mind.
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So there is no way that we can get to the conclusion that the people in an imaginary world have a real and actual perspective. — Metaphysician Undercover

I cannot know that people in other possible worlds are real, but I can theorise that they are.

I can never know for certain that the person I am talking to is as conscious as I am, but I can theorise that they are.