Modal Logic Puns

Hi! I'm a Maths undergraduate. Amongst the various fields in Mathematical Logic, I feel like some like Set Theory and Model Theory are more Mathematical (that is, its practice can be as "devoid of epistemic meaning" as any branch of Algebra, limited to proving theorems), and others like Modal Logic might have more room for relationships with Philosophy, Epistemology, Philosophy of Mind or Artificial Intelligence. Is this so?

Don't get me wrong, I figure much purely Mathematical work is done in Modal Logic, which limits itself to proving theorems. But given the treatment of necessity and possibility, and the construction of Modal Logic as a kind of analogue to our reasoning (contrasting Set Theory and Model Theory, which deal with Mathematical objects more akin to other structures like fields or groups), it might be a discipline more prone to theoretical or foundational analysis of a range of issues.

I'd like to study a textbook in quantified modal logic to supplement a seminar I'll be taking soon on Ruth Barcan Marcus' work. I have studied propositional modal logic out of the Open Logic Project Boxes and Diamonds text, so I have some background.

So far as I can see, the main options are Fitting and Mendelsohn, First Order Modal Logic, and Garson, Modal Logic for Philosophers. F&M seems more attractive to me after reading a bit and doing some exercises - but I'm not far in yet, and could switch if Garson seems the better option. Anyone have a preference between these texts or another recommendation?

This is a long shot but my girlfriend is studying a philosophy degree and is looking for resources to help her understand how to answer the question:

“Explain how Modal Logic can be used to clarify certain philosophical questions”.

After she asked on the newly renamed social and got shut down I was hoping Reddit would be kinder. Any explanation or places to look would be much appreciated for both our sanity. Let me know if this post breaks any rules and i’ll remove.

Edit: Thank you for the responses they’ve been immensely useful and i’m in the good books

Can you suggest any good playlists/videos on Computability theory or Modal logic?
Thanks in advance!

When I say Modal Logic, I mean specifically, "Modal Logic", not the whole category of different modal logics. Temporal logic sounds like it should be useful for some application, though I don't know enough about it.

What is modal logic for?

In propositional logic, I have:

A

So, in modal logic, I have:

□A

And what can I learn from □A?

A

So far as I'm aware ◊ just doesn't do anything. I understand that ◊A means ~□~A, but what's the point in ever having ◊A?

I can use propositional logic to solve NP-complete or easier problems. I can use first-order logic for knowledge bases. Second order logic is for proving theorems. Fuzzy logic is being investigated for use in artificial intelligence, but that area of research isn't clear to me.

I get the idea behind having, say, a three-valued logic system. Modal logic seems like it's trying to do something similar, but in a more complicated way.

Does modal logic have any practical application?

Dear logicians of Reddit! I am about to dive into proof theory for modal logics: to be more precise, I want to research labelled sequent calculi for PDL and other multi-agent logics. But I feel a lack of knowledge of the basics to understand articles. Maybe you could recommend some handbooks including topics such as sequent calculus for normal modal logic, labelled sequent calulus and covering some classical results with proofs like cut elimination, Herbrand theorem, Harrop theorem, Craig interpolation theorem, etc.? I have tried "An Introduction to Proof Theory" by Sam Buss. I don't like that theorems mentioned above are presented with a proof sketches or lacking proofs at all.

Have there been any practical applications in science or the philosophy of science with modal logic? I’m aware of modal logics being used in computer science, but I’m more talking about modal logic being used to formulate scientific theories.

As an example, Lewis’s account of dispositions attempts to lay out the framework for talking about objects with certain properties that obtain only in certain conditions. Has someone taken Lewis’s work (or work similar to his) and used it in formulating scientific theories?

What are some other applications of modal logics in philosophy?

I understand that Quine took logical truth to be a product of syntactic structure, and truth. I also understand that he was not a big fan of modal logic.

My question is this: how does his view hold up for theories of modal logic that no longer seem to be dealing with mere grammatical structures?

For one thing, modern modal logics seem to rely heavily on possible world semantics, which doesn’t really seem to be syntax anymore. But even if you could reduce alethic (and maybe deontic) modal logics to truth preservation across syntactic structures, it seems to be incorrect to consider things like dynamic or epistemic logic to be merely grammatical. Does this cause troubled for this view of logic?

Where are other places to read up on this?

context: I've done Stanford's symbolic logic courses(I believe there're two, one on Coursera, the other from Stanford Online), and completed all the exercises and practice papers. I'm a Sophomore, interested in theoretical CS research, and think that PHIL 4424 Modal Logic is a good preparation for me to self-learn temporal logic and formal specification language like TLA+.

For those who took the course before:

1. what textbook were you using? the point of asking is to see whether the course takes on from an algebraic perspective.
2. what were the courses that you took before Modal Logic that you found useful?

Thanks a lot!!

So I stumbled across a problem yesterday when trying to create my own Modal. Whenever I tried to use tab while the modal was opened, it would still have the ability to focus on buttons or stuff that were underneath the modal overlay, even though it shouldn't.

I looked up how to solve this issue and read up on "modal focus trapping" where the idea is you take the element itself that can have child nodes/elements that can be focusable, and only allow focus on those inner elements?

So lets say if I only want focus to work for the Modal Container (the modal container is a child node inside the overlay itself). I'd essentially use `querySelectorAll` to get all possible elements that can be focused that are INSIDE of the Modal Container, e.g: Buttons, Form Inputs, Links, etc.

So I'd end up with a list of nodes that can be focused, that are all inside the Modal Container. And then every time tab is pressed, I can just only allow those nodes to be focused?

Not 'modal metaphysics' (modal realism v anti-realism, for example), but modal logic itself with all the axioms and stuff.

Hello! I just finished a course on the philosophy of logic and couldn’t help but think that Lewis’ modal logic frameworks seems to have potential applications to a wide range of scientific inquiry. Does anyone know what sorts of applications these have had?

Just some thoughts I had after reading the comments on my previous post on ontological arguments. I've been looking for a solid philosophical argument for the immortality of the soul and I think I may've found one (this is my own idea as far as I know):

1. It is possibly necessary that the soul is naturally immortal.
2. Whatever is possible occurs in some possible world
3. Therefore the soul is necessarily naturally immortal in some possible worlds
4. But since the soul's natural immortality is necessary it would apply in all possible worlds
5. Whatever is the case in all possible worlds exists in the actual world
6. Whatever exists in the actual world exists in reality
7. Therefore, the soul is naturally immortal in reality.

What's being discussed is metacontextual, and double-quote delimited strings are evaluated in a context-free semantic regarding the proposed logic.

In plain English: What's being discussed is "Context matters". The answer by Kethryvis can be filed ontologically under "Context matters". The Content Policy's official language says "We understand there are sometimes reasons to post violent content (e.g., educational, newsworthy, artistic, satire, documentary, etc.) so if you’re going to post something violent in nature that does not violate these terms, ensure you provide context to the viewer so the reason for posting is clear." -- i.e. "Context Matters".

In short: That is what's being discussed - Context.

Hello, I am grateful to have found this subreddt. Logic really impresses me, my eyes glow when I read about it.

My background is as following: I read two introductions to logic with one of them being really bad. I am a native German speaker, so I read them in German. 'Zoglauer, Thomas, Einführung in die formale Logik für Philosophen' and 'Detel, Wolfgang, Grundkurs Philosophie Band 1'

I want to read an English introduction now which uses natural deduction and explains it briefly. I got the concept of it, but I am not very confident in using it. Also, I would like to come in contact with truth trees. It shouldn't only focuses on first order logic, I want to become more familiar with model logics. One of the books I read so far, explained modal logics very superficially.

Furthermore, I search for a book about modal logics alone. Rod Girle's book on this subject looked interesting to me, but what would you recommend? And what are you thoughts about Peter Smith's books dealing with Gödel's theorem? Are they good? Do you recommend a different one?

I saw some online resources here in this subreddit, but I really like physical books.

Thanks in advance

I want to learn modal logic and then linear temporal logic. Since I will be learning by my own I need to have some exercises with answers or full solutions if possible. Could you recommend me some book or internet course on that topics.

Is it just because modal logic accounts for things like necessity, possibility, impossibility, essence, and accident and therefore, since things like temporality, conditionality and relevance can be somewhat related, the logics that account for them (temporal logics, conditional logics, and relevance logics) get jumbled up with "modal logic" broadly defined?

I hope alex will read this comment. It is about this video, timestamp 37:27

I thought about this argument and tried to prove it with modal logic, but then I realized that there is a problem, and here is why:

1. (◻P & P→Q) → ◻Q (if p is necessary and p implies q, then q is necessary. The square is the symbol for necessity in modal logic)
2. ~(◻P & P→Q) v ◻Q IMPL (implication)
3. ~◻P v ~(P→Q) v ◻Q DM (morgan's law)
4. (◻P → ◻Q) v ~(P→Q) IMPL
5. ◻(P→Q) v ~(P→Q) CMQ (change of modal qualifier, aka distribution rule)
6. (P → Q) → ◻(P→Q) IMPL

So 1 is equivalent to 6. It says that if any implication is true in one possible world, it is true in all possible world. But that is a fallacy of necessity. An implication that is true in one world might be false in another one.

The argument would need to be modified to either

• a) to (◻P & P→Q) → Q; or (assuming axiom M that says that ◻A → A. It would then reduce to Modus Ponens)
• b) (◻P & ◻(P→Q)) → ◻Q. (Notice that with that change, by step 5 we would have a tautology.)

Either you change the premise to say that the implication is necessary or change the conclusion to say that it is true in that world, but not necessarily true in every world.

I don't know if Hajib had that in mind or if he just got lucky. Who knows.

EDIT: speaking of mistakes, I just noticed a grammatical error in the title =P. English is not my first language.

There are some interesting types of modal logic, such as S5, where there are modal operators, additional axioms, rules of inference.

Using this logic it's clear and pleasant to express various inferences and get to some theses.

The question is: can each thesis of a modal logic be expressed in propositional logic? And a related question: can each proof/inference also be expressed in propositional logic?

We can perform a simple translation of modal operators into words, such as:

◻ = "is necessary" and ◊ = "is possible". Then we can have formulas translated, for example:

◻p -> p becomes "if it's necessary that p, therefore p".

So can I easily translate a simple argument expressed in modal logic into an argument expressed in propositional logic without losing anything of value? And, can I express a modal logic proof into a corresponding proof of propositional logic?

Maybe another way of asking would be: is there anything in modal logic that cannot be in any way expressed as an inference/argument in propositional logic?

Of course we would lose some clarity and such, but could we at least retain power and meaning?

I'm in a modal logic class right now and it is... kicking my ass, to say the least. I didn't expect it to be this hard, but on every homework assignment there are questions that I just stare at, and I can't even figure out what the question is asking. I keep up with lecture notes, and I feel like I'm understanding things, but then I just can't implement anything. Does anyone have any particular tips that helped their understanding of modal logic mature? Or know of any resources like textbooks or YouTube channels that help explain Modal Logic in a clear way?

Editing my post to add more context: I'm familiar with Carneades on YouTube, and I've tried reading through textbooks by Girle, Priest, and Garson, but they rarely use the same definitions as those used in my class (at the very least, they call the same things by a different name), and so I have been left in the dark up until now. Is there a general problem with lack of standardization across modal logic curriculums?

I am particularly having trouble with the phrase, “Necessary in any possible world.” I’ve had it explained to me that “possible” means “true in at least one world,” and “necessary” means “true in all possible worlds.”

I keep encountering the claim:
>”X is necessary in some possible world,”

Using the definitions above, this would appear to translate to:
>”X is true in every world in some world.”

This sounds like nonsense, oxymoronic: “in every world in some world.” Necessity is a trait of all worlds, so how can the necessity of x be evaluated by looking at “some world”?

What exactly does it mean to be necessary in some possible world?

 
Edit:
The context is an argument that goes something like:
1)X is necessary in some possible world.
2)If x is necessary in some possible world, then x is necessary in all worlds.
3)X is necessary in all worlds.

Or
1)Possibly necessarily x.
2)If possibly necessarily x, necessarily x.
3)Necessarily x.

Hi all, thanks for your time!

FWIW this isn't a homework problem. I'm trying to understand a particular argument which uses modal logic, and I'm hoping to find out whether I've made any math errors. I'm very new to modal logic (and formal logic in general), so I may have committed some very basic errors...

Here are the assumptions:

A1: P

A2: ~◊(P & ~Q)

1: ☐~(P & ~Q)

Apply de Morgan's law:

2: ☐(~P | Q)

I think I can drop the ☐ here, since necessity implies truth in all related worlds

3: (~P | Q)

And for all worlds in which P has been asserted, we have:

C1: Q

EDIT: After u/ron_pro's response I've re-done the first proof and dropped the second (both are still included below, as a record of just how wrong I was :) ). Hopefully I haven't introduced new errors...

--------------------------------------------------------------------------------

Here's the long story, if you're interested...

I came across this problem when reading about the "modal fallacy", and the source material only discusses the fallacy (a single non-sequitur) rather than giving the proper conclusions that follow from the problem's assumptions -- so I decided to find out what conclusions do follow from those assumptions when the fallacy is avoided. If my math is right, then whether or not you use or avoid the fallacy it leads to the same conclusion! Of course this is completely consistent with the concept of validity in deductive arguments: in the article's example, the fallacy just happens to lead to the same conclusion as a valid argument does (if my math is right).

However, if you care to look at the 2nd paragraph of the "Concluding Remarks" section (section 8) of that article you will probably understand why I find this explanation very dissatisfying. One purpose of this article is to demonstrate that the conclusion "foreknowledge of an event implies free will is not possible" is arrived at via a "modal fallacy". But if my math is right, then the article has simply built and refuted a straw-man of the argument which leads to that conclusion, by framing it with a non-sequitur instead of the valid logic which leads to that exact same conclusion.

Please help me find errors in my math! I want to know whether the argument presented in this article holds water.

--------------------------------------------------------------------------------

For transparency, here's my original (flawed) work that I've

Hi there, I'm looking for a multimodal logic that deals with knowledge and intention (knowing that one has an intention, believing that one has tried to do something, and these kind of statements).

I could work it out by myself but I just want to be sure there has been no attempt to develop one before. A preliminary search turn up unsuccessful, know of any such logic?

Cheers.

So recently I came across Gödel and his theorems, and found them really really interesting.

I'm curious as to what, if anything is required to read and understand his works. I don't have great mathematical knowledge, don't understand modal logic notation and haven't read too much about analytic philosophy/philosophers and their related ideas.

All help greatly appreciated.

This is an etymological question, really.

Also, does the term "modal" here have any common reference with "mood" as it applies to syllogisms?

Hey there!

I've long been interested in learning about modal logic, but I'm not entirely sure where and how to start. To be clear, I am not taking courses on philosophy, or math, or logic; I'm a software dev that finds logic fascinating.

Currently, my plan was:

• refresh myself on basic propositional logic (using A Logic Book)
• refresh myself on the metatheory and whatnot (using The Logic Book)
• jump in to modal logic (using Modal Logic)

All of these books were recommended to me by an old teacher, a long time ago.

Is there any prereq that I've missed? I've gone through the Logic Book before, and paged through some of Modal Logic, and noticed quite a lot of talk of sets. Is set theory necessary for this venture? Is there anything I'm missing that might benefit me?

I've also noticed that most treatments of modal logic tend to be establishing systems and whatnot, and that's it. Not much in the way of discussing its use. Why is that? Are there any resources that take an approach like that? I remember when I took my first course on logic, and we did things like learn how to symbolize, how to apply rules of inference, etc.

Thanks for you help!

I've been learning about modal logic as a hobby for about a month now, and I'm working on an interesting problem for practice. This post focuses on metaphysical and physical (nomic?) modalities, though general advice (and even interesting off-topic advice, lol) is always welcome :) Thanks in advance!

Anyway, I think the problem I'm working on is best expressed using a combination of metaphysical, physical, and epistemic modal operators, and I've reached what seems to be a dead end -- unless I'm able to derive and exploit relations between the various types of modalities. Here's the first one I've come up with, between metaphysical and physical modalities:

Definitions:

P == any proposition

☐ == metaphysical necessity; ◊ == metaphysical possibility. Other worlds are metaphysically accessible as long as ??? (I don't really know how to describe this relation...)

🄿 == physical (nomic?) necessity; p == physical possibility. Other worlds are physically accessible as long as they share the same physics laws and constants.

For both types, I think the usual relation between necessity and possibility operators holds: ~◊~P <--> ☐P , and ~p~P <--> 🄿P

Proof:

1. pP <--> "in at least one physically accessible world, P" --> "in at least one metaphysically accessible world, P" <--> ◊P [I think this is OK, since all worlds which are physically accessible are also metaphysically accessible (?). Also, sorry about the English verbiage -- I wasn't sure how to say this with notation alone.]

2. Therefore, pP --> ◊P [Restatement of 1, for ease of reading. 3 starts from this implication.]

3. ~🄿~P --> ◊P [LHS operator replaced by the relation: ~🄿~P <--> pP]

4. 🄿~P <-- ~◊P [Negated both sides]

5. Define some Q <--> ~P

6. 🄿Q <-- ~◊~Q [~P has been substituted by Q everywhere]

7. 🄿Q <-- ☐Q [RHS operator replaced by the relation: ~◊~Q <--> ☐Q]

I agree with (1), since the physical is a subset of the metaphysical -- it seems contradictory to say something is physically possible but not metaphysically possible. Yet I question (7), because if the physical is a strict subset of the metaphysical, then metaphysical necessity should imply some type of necessity, but not necessarily physical necessity.

So maybe I'm missing at least one conjunction on the LHS of (1) and (2), which would put (2) in the form "pP V �P --> ◊P", where "�" represents the possibility op

Hi guys,

I'm new here, I'd like to see some examples of implementing modal operators in prolog, if possible.

I've seen some academic papers online, but it's hard to understand them. I'd like to see code.

E.g., imagine the facts:

A. peter is a cat : cat(peter).

B. peter is black: black(peter).

C. every cat is an animal. animal(X) :- cat(X).

Question: Is it permissible for an animal to be black? (yes).

Question: Is it permissible for a cat to be black? (yes).

Question: Is it mandatory for a cat to be black? (undetermined from the above).

Thank you. (I hope I got the example right.)

Hi guys,

Recently, I got especially interested in Modal logic and I've been considering it for a future dissertation topic. I have done Formal Logic before but I don't have any maths education (which concerns me because it appears to me that Modal Logic is heavily reliant on maths). I was wondering if you could give me some advice on how to approach the topic, what papers to read (currently I'm reading Kripke's Semantical Analysis on Modal Logic), or maybe whether I should get involved with maths more... that kind of things.

Thank you to whoever takes off their time to answer my questions!

Hello,

I have a question about a point made in Priest's intro text that i'm having some trouble wrapping my head around.

In his discussion of modal logic, priest says that:

a → ◻ b

does not follow from

◻ (a→b)

As I understand it, ◻ (a→b) means that the conditional a→b is true in every possible world. However, I'm having a little trouble getting completely clear on what a → ◻ b means.

Is it correct to interpret this proposition as saying that, for a given situation s, if a is true in the actual world s0, b is true in every possible world s0 - sn, or have I completely missed the mark?

If this is the correct interpretation, are there any true conditional statements that have this form? I'm having trouble thinking of examples.

This has been gnawing at me for days, so any help is greatly appreciated!

I know modal logic includes a few different ideas, so I'm asking in a general sense.

If one really wanted to, they could symbolize ordinary arguments and evaluate them, bearing in mind prop logic's limitations. Can the same be done with modal logic?

I've found modal logic to be very interesting, but considering I'm not well-versed in philosophy (or other areas that might use it), I'd really hate for it to be something that I learned and promptly forgot.

Three Questions;

1. Is the only alternative to adopting a modal interpretation of logic (i.e. Tarsky Models) proof-theoretic-semantics (i.e. inferentialism)?
2. Am I correct in thinking that proof-theoretic-semantics doesn't given you a notion of truth but rather correctness?
3. Are Tarsky Models only considered modal because they define validity in terms of all possible interpretations?

Please go easy on me in terms of the logic, I am very much first and foremost a (undergraduate) philosopher who has some knowledge of logic (taken undergraduate courses in intermediate logic and set theory). Writing a paper in metaphysics on modality and Genuine Modal realists get very angsty about anti-realists falling back on logic as a resource since it's obviously under standard interpretations modal itself. Been having a hard time understanding why they don't just fall back on a proof-theoretic-semantics (I know about the Tonk thing but I've seen good arguments via Brandom against it) I'm guessing it's because of proof-theoretic-semantics not giving you a notion of truth? Thus makes trying to justify logic giving you underlying metaphysical truths a bit harder???

Hi there, I am looking for introduction and elimination rules for 􀀀. I have found the following online for S4 and S5:

(􀀀I for S4): If Γ ⊢ A, then Γ ⊢ 􀀀A, provided that, for some set Δ, Γ = 􀀀Δ

(􀀀I for S5): If Γ ⊢ A, then Γ ⊢ 􀀀A, provided that, for some sets Δ0 and Δ1, Γ = 􀀀Δ0 U ¬􀀀Δ1

(Common 􀀀E): If Γ ⊢ 􀀀A, then Γ ⊢ A

What would be a corresponding 􀀀I rule for the system K? Comparing to modal logic possible worlds semantics, the 'provided that' conditions for the introduction rules would seem to relate to the frame conditions for S4 and S5, but of course K has no frame conditions. But then removing the condition altogether would trivialize the introduction/elimination of 􀀀.

Any help appreciated!

I have been using Garson's Modal Logic for Philosophers, 2nd edition, to learn how to use natural deduction with modal logic. (BTW, does anyone know where there's an answer key for chapters 1 and 2 of Garson?)

For some of the exercises, it seems to me that the obvious approach is to use indirect proof (IP), which Garson includes (of course) among the rules for PL, and therefore for K and other modal logics. Unfortunately, Garson does not give an example of a proof of a modal sentence involving IP.

The problem I'm running into is that I am able to establish a contradiction in a modal subproof, but it's not clear to me how to propagate this back to the main proof and thereby establish the desired result.

For example, exercise 2.3(c) in Garson is to prove that <><>A <-> <>A in S4. Here's my attempt to prove the forward implication (<><>A -> <>A):

|<><>A 
|----- 
||~<>A 
||---- 
||[]~A       (~<>) 
||[][]~A     (4) 
||<><>A      (Reit) 
|||[], <>A   (<> Out) 
|||------- 
|||[]~A      ([] Out) 
||||[], A    (<> Out) 
||||----- 
||||~A       ([] Out) 
||||#        (# In) 

Here I would like to write

|<>A         (IP) 
<><>A -> <>A (CP) 

Is that legitimate? Does the # (contradiction) in the sub-sub-subproof license IP at the top level?

Thanks for any insight!

I thought Kripke semantics were for modal logic (only), but I looked on its Wikipedia [https://en.wikipedia.org/wiki/Kripke_semantics] and read that it is also for intuitionistic logic and other non-classical logics. But how can this be? I thought the use of "necessity" and "possibility" were what defined modal logic and made it distinct from all other logics?

So, my question is: how could Kripke semantics be used for any logic other than modal logic?

Three Questions;

1. Is the only alternative to adopting a modal interpretation of logic (i.e. Tarsky Models) proof-theoretic-semantics (i.e. inferentialism)?
2. Am I correct in thinking that proof-theoretic-semantics doesn't given you a notion of truth but rather correctness?
3. Are Tarsky Models only considered modal because they define validity in terms of all possible interpretations?

Please go easy on me in terms of the logic, I am very much first and foremost a (undergraduate) philosopher who has some knowledge of logic (taken undergraduate courses in intermediate logic and set theory). Writing a paper in metaphysics on modality and Genuine Modal realists get very angsty about anti-realists falling back on logic as a resource since it's obviously under standard interpretations modal itself. Been having a hard time understanding why they don't just fall back on a proof-theoretic-semantics (I know about the Tonk thing but I've seen good arguments via Brandom against it) I'm guessing it's because of proof-theoretic-semantics not giving you a notion of truth? Thus makes trying to justify logic giving you underlying metaphysical truths a bit harder???

Edit: So /u/boterkoeken gave me the answer I was looking for, over at r/logic. Just going to copy his response in incase anyone else stumbles across this. (Also I apologise to other responders as it turns out I was a bit confused about what it was exactly that I was confused about)

"Let me see if I understand the debate you are talking about. I believe you are referring to debates about modality itself, right? People like David Lewis are realists and people like Robert Stalnaker are anti-realists about metaphysical necessity.

If this is the context you are referring to: The reason why realists dislike 'falling back on logic' generally speaking is because it implicitly involves modal judgments. As you point out, each Tarskian model represents a possible way the world could be. However, if we know that already when we define Tarskian models, then we are using our grasp of modality to define logic. The problem for anti-realists is that they often want to go the other way around. They will say things like 'all we mean by "possibility" is a logically consistent description of things'. But if we use our grasp of modality to define logic, we can't use logic to define modality or it is just circular.

This is not an issue that specifically has to do with Tarskian