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To try to "explain" why the liar sentence is "logically dangerous" whereas the Gödel sentence is "logically helpful," I tried out contrasting the differing "effect" that these sentences would have if "absorbed" into a Fregean One True Fact (). The idea was/is that if a parathetic sentence corresponds to a fact, then when this fact is "absorbed" into the , the gets "rewritten" such that it (the ) itself proclaims, of itself, whatever the parathetic sentence claims. So if the eats the liar sentence, then the goes on to say, "I, the , am false," or if it eats the Gödel sentence, it then proclaims, "I, the , can't be proved by method X."

The liar sentence, then, is (metaphorically) like a demon, when demons are not defined as fallen angels. But, "This sentence ought to be true," is like a fallen angel, for if it is eaten by the , then the says of itself that it ought to be true, i.e. that even the evil truth-parts of the ought to be truths of this world, but that is absurd.

So let us go to another deontic parathesis: "I vow that this sentence will be true." If the devours this vow, then it makes the very same vow, albeit pointlessly: all the truth-parts of the are already true, and to some extent necessarily so (not that there are no contingent truths, but rather that the necessity of the past, which is relevant to a vow about what will be true, renders (from the eternal vantage of the ) every subfact to be "pastwise" necessitated: once a possible fact is absorbed by the (and any possible fact that is actualized is so by said absorption), then the necessity of the now-actual fact is a kind of "necessity of the past"). But also, the parathetic vow seems like another "fallen angel," for even were there the contingency required for the vow to not be pointless, yet again it is a "sin" for the to intend that all its subfacts be as they are, for among those are various evil subfacts.

Does, "I vow that this sentence shall be true," fail also? I mean "shall" here as in the future-tense counterpart of "should." My uncertainty is over whether the making this vow is tantamount to the vowing that its evil subfacts become obligatory, or if instead this vow conflicts with evil, as if the is vowing to purify itself of its evil subfacts. This would be so if this vow would mean that the is promising to make all of its subfacts into fulfilled obligations, and so it would be hoped that the has some way to "defeat" the evil within itself. But I wonder if I need a more complex version of this promise, in order for this hope to go through. Maybe, "I vow that this sentence will or shall not be true if it is an evil sentence"? (I know, I myself am chuckling at this phrase "evil sentence," but again, maybe lies are evil sentences, and maybe the liar sentence is a demon, after all.)

Kristian Berry
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  • You are conflating sentences with propositions. If you include the Liar proposition into the OTF proposition, then "this sentence" does not change its reference to refer to the OTF because you are not adding to the sentence but the proposition. To get that effect, you would have to construct the OTF as a single sentence with uncountably many clauses and include the Liar as a clause. I'm not sure the concept of such a sentence makes any sense. – David Gudeman Feb 09 '23 at 18:39
  • @DavidGudeman the "translation" of my talk of "absorption" is Frege's claim that all true assertoric functions are true by referring to one ultimate "the True." So if the liar sentence were true, it would be true by referring to the True. Beyond that, this bizarre/absurd/surreal metaphysical fantasy story could be taken for a peculiar version of logical fictionalism (paraconsistently logical modal fictionalism, say), occurring in an extremely counterpossible domain of discourse. But so yes, there's a huge risk of this parable being ridiculous to the point of semantic impossibility. – Kristian Berry Feb 09 '23 at 18:45
  • It isn't clear from your response that you got my point. You do understand the difference between a sentence and proposition, don't you? You do realize that a proposition contains no words, and in particular doesn't contain the word "this", right? – David Gudeman Feb 09 '23 at 19:16
  • @DavidGudeman I don't know if I believe in propositions. I know many of the arguments for them, for their possible existence as "abstract objects," but just the same, in everyday life it is sentences, spoken or written, that we think are true. And in the case of the liar sentence, there is no proposition to its name, or if there was, it would be a proposition as bizarre in nature as the entities of the fantasy. Overall, I countenance at least sentence *types* beyond concrete sentences, but I'm not sure I'm willing to go farther. – Kristian Berry Feb 09 '23 at 19:20
  • I mean, a lie, as a deliberate falsehood for the sake of misleading someone, is a sentence. Abstract propositions are neither honest nor dishonest (or are such things in only a metaphorical sense). And the moral issue of lying is more important to us than metaphysical questions about mysterious transworld truthbearers, so it seems as if the important truthbearers are physical assertions, not Platonic ones. – Kristian Berry Feb 09 '23 at 19:24
  • Think of it this way: if Frege's the True is the condition of truth, and is a matter of abstract propositions first and concrete sentences only derivatively, then the liar sentence is not just meaningless but *anti*meaningful. Maybe that's a neat solution to the liar paradox, maybe not, but it doesn't affect the premises of an axiomized fantasy story. The story is, "Counterpossibly, if sentences were the primary truthbearers and their truth-conditions were absorbed into the OTF, what would be the result based on the differences between different self-referential sentences?" – Kristian Berry Feb 09 '23 at 19:29
  • First, it is not difficult to come up with a multi-value logic where the Liar is well-formed and is properly handled by the logic. It's not anti-meaningful; it's just not handled by traditional logic. Second, if you view the OTF as a sentence, it is impossible to add the liar as a sentence because the indexical "this sentence" changes its meaning. You would have to change it to something like "this atomic clause", and then your comments about how "this" applies to the rest of the OTF would still be false. – David Gudeman Feb 09 '23 at 19:47
  • I'll have to leave off with this comment, since I'm getting the, "Go to chat?" prompt. But no, the OTF is not (just) a sentence, it is a fact to which all true sentences correspond/refer. The factivity of the liar sentence is, however, sentential (because self-referential), so when absorbed, it turns *part of* the OTF into a sentence. But the indexical is absorbed too, per the truth conditions of the liar sentence; that's the point of the general exercise. As for multi-value logic solutions to the liar paradox, the problem with those is that they fail revenge-sentence tests. – Kristian Berry Feb 09 '23 at 19:51
  • what is revenge-sentence tests? a deliberate falsehood is the truth for liar. liar created conversion world with another axiomatic. do you know parable about an old man, the snake and the fox? – άνθρωπος Feb 09 '23 at 22:56
  • One shall not make vows one cannot keep. Whose is the "I", God's? – Conifold Feb 10 '23 at 06:52
  • @Conifold I am supposing that we too can make such a vow, but the vow is perhaps trivial in that swearing it is the same as fulfilling it. But the significance of this—if there is any—is a story for another time. – Kristian Berry Feb 10 '23 at 09:48

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Let's begin at the beginning. Let's suppose that parathetic sentences correspond to facts (though correspondence is usually used in conjunction with references to "states of affairs"). I guess the state of affairs rests in the logical appraisal of the OTF, and therfore condition, obligation, propriety, expediency, futurity, probability, expectation, and polite request must in some case apply to it. But am I even on the right path? That's quite the assortment of states of affiars, no? Let me presuppose so you are clear that I'm clear on this metalogical framework you're proposing, and then I'll resume.

You take the OTF to be some sort of collection of logical propositions evaluated with a truth-conditional semantics in which the propositions themselves are inserted into some monsterous conjunction that is self-denoting. Hence any claims about sentences, what you label parathetic claims, are absorbed if they pass a filter to ensure they don't somehow create paradoxes. You believe the vow something will be true in the future fails the filter based on the claim and then go on to look at the modal "should".

Alright, let's appraise.

First, I see no reason why you can't have a OTF that absorbs generated conjunctions of the parathetic variety. To maintain truth, I guess your filter would be nothing more than parsing a candidate parathetic proposition to ensure that either syntactically or semantically, it does not anger the Law of Non-Contradiction. Although, apparently there would be ways of assuaging such a claim by invoking non-classical logics. In any event, the problem I have with your analysis is as follows:

  1. The avowal is a performative act. In truth-conditional semantics, "I vow" is logically empty because it is a pragmatic act of performativity. And even if your OTF were to include in the "filter" you mention some way to address this, what would it even mean for a OTF to vow anything?
  2. The claim that something will be true doesn't logically entail it was ever false. I can vow that I will be faithful to my wife, but that speech act, as far as I construe it, does not logically entail me having ever being unfaithful. As an implicature (again, something awkward within the OTF's project as a truth-conditional metastatement) unless there were additional facts as part of the OTF that provided some sort of context to defeasbily reason to an implicature otherwise, no such implicature exists in the same manner the logical implication doesn't exist.

Furthermore, oh, English modals! Will, shall, should, might, could, can, may, how little clarity you grant me! This is a question that rears its head in English SE in various forms.

I mean "shall" here as in the future-tense counterpart of "should."

I think it all depends on how you interpret should, and in this sense, I see two interpretations. Merriam-Webster has 5 entries for should. Have you given thought to which of these you mean?

1 —used in auxiliary function to express condition
2 —used in auxiliary function to express obligation, propriety, or expediency
3 —used in auxiliary function to express futurity from a point of view in the past
4 —used in auxiliary function to express what is probable or expected
5 —used in auxiliary function to express a request in a polite manner or to soften direct statement

You seem to explicitly excise 3 from definitions, and the rest of them are pragmatic conditions. 1 is a normative claim. Do normative claims bear any weight in regards the OTF making assertions about claims? How are such claims of truth or falsity even justified by a reader of OTF? 2 Is a stronger, perhaps deontological claim. What does it mean for a clause of OTF to obligate something (perhaps other than logical conditions) in a truth-conditional appraisal? 4 interjects probabilistic statements. Is this allowed given that it seems OTF now needs to have the ability to tolerate uncertainty. 5 is just a question of manners.

In short, if should differs from will as an expression of the evaluation of state with the future relative to the present (another question being how does OTF handle temporal logic), then which of these is meaningful?

Of course, this whole exercise is stimulating in that it challenges the intellect to understand what you are even attempting to accomplish. I understand this as an exercise to impose a potentially unlimited number of self-referential truth-conditional claims onto a single proposition; that is, it's building some meta-liar's paradox and then applying the principles of dissolution to it?

Anyway, I hope my objections help you answer your question, because I'm not sure I can. :D

J D
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    This is a very helpful answer. Depending on whether anyone else posts an answer, and how helpful their answers are, it might not end up being the accepted one, but I am definite in thinking that this is a candidate for the accepted answer. I realize this talk of a parasentient universal factoid borders on schizophrenic everything-is-intentionally-connectedness, but then again, from reading through overviews of the actualist-possibilist debate (for example), I get the impression that philosophy is given to such madness by the by. – Kristian Berry Feb 09 '23 at 19:43
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    Re: your specific points: (A) yes, the OTF is a "Big Conjunctive Fact" (the SEP article on the cosmological argument for God qualifies this notion as a "Big Conjunctive *Contingent* Fact," and in the actualist-possibilist debate, the counterpart phrase is usually "world-stories" or "world-books"). (B) by "should," I mean as in your (2), an expression of duty; or, then, something parallel to "ought." (3) I'm glad you mentioned temporal logic, since now I recognize how that destabilizes the story-so-far to an extreme degree; to improve the story, I'll have to reckon with those parameters better. – Kristian Berry Feb 09 '23 at 19:47
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    Some examples of where temporal logic makes all this so much trickier: "This sentence *was* true," "This sentence was false, is true, and will be false in the future," etc. – Kristian Berry Feb 09 '23 at 19:58
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    I don't see OTF as that crazy. It seems that it's a formulation of what philosophers attempt to achieve by vetting their logical claims. I just skimmed what you have here, but again, it's something to think about, because I think like the pluralist notion of a set-theoretic theory, it illustrates the wider program that the conscious mind institutes in an attempt to construct a logically consistent reality. Where it falls short of practice is it's abandonment of paraconsistency which besides defeasibility, are the primary characteristics of functional worldviews. – J D Feb 09 '23 at 20:25
  • I would constantly give thought to how you are grounding the semantics of your process. I don't think that the "filter" is something incidental to OTF, but rather constitutes an adequate characterization of it. – J D Feb 09 '23 at 20:27