• Problem with the view that language is use

    I had begun to wonder if you were just talking about words and dictionary-meanings. Bleh.
  • Problem with the view that language is use
    Where occasion sensitivity might play a role, among other places, is where determination of some determinable has established membership in an equivalence class that is thereby fine-grained just enough to satisfy some practical purpose (including the founding of a meaning convention for effective communication, in some cases."Pierre-Normand

    That makes perfect sense to me. Equivalence is variable.

    Maybe this idea provides the sought after stopping points for Strap Tasmaner's "cofinal tails". Determinable properties and dummy sortals don't determine such tails, but substance-sortals and event-types possibly do since they determine as fully as one might want *what* something is. Further, specifications (or further determinations of determinables) beyond such a natural stopping point only achieves the specification of merely accidental properties (including such things as the accidental microphysical realization or material constitution of events or substances.Pierre-Normand

    So the idea would be that this is how you know you only have the tail of an entailment-poset -- maybe you're starting around "Something happened to him" and "Something" couldn't generate such a set, so you know there's there's something more determinate further up.

    Here, we've been talking at length about a particular event and its accidental properties. If we want to know whether it was a killing, we might stop at one point in the determination process; if we want to know whether it was manslaughter or homicide, we would have to go further; if we only care that there was a death, we can stop before getting to "killing." And if we just want to know as much as possible about an event, as an historian might, we might determine everything we possibly can. If you're doing research on violent death in America, then you might employ pretty unusual sortals, such as "Death by stabbing, assailant known to victim but not immediate family."

    If stopping points are all occasional, we don't need a way to tell we've only got the tail of the entailment-poset, we already know we do. We always do. The point of calling one "just a tail" is to highlight that it is insufficient for our current purpose, and that we need to further determine it.

    What the ontological import of all that is, I couldn't say.

    ADDED: What I haven't addressed here is how you match sortal to purpose.
  • Problem with the view that language is use
    If you want to say that convention of use exists at the moment of it's birthStreetlightX

    No I absolutely don't. I'm just trying to follow your thinking here, badly it seems. I'll take one last shot at it.

    by convention I mean already-established use (of language), and not grammatical regularityStreetlightX

    Maybe if you could give me an example of each, that would be clearer: an example of an already-established use in English that is not what you would call a grammatical regularity (I assume you mean this in a wide sense); and an example of a grammatical regularity in English that is not an already-established use. (Since you use "regularity" in one and "use" in the other, I did too, but that's not an endorsement.)

    It's a measure of my confusion that I have absolutely no idea what your examples will be. I hope it's plain as day to you.
  • Problem with the view that language is use

    Suppose you do attempt to teach John Cakese. Let's suppose also that none of the words of Cakese exist yet; you intend to make them up as you go, and then use them consistently, and you may also distinguish different sorts of words and consistently use those different sorts of words in different ways. Is that the idea? And to you, there is no convention here because you're making it all up.

    (I take it we are not to imagine Cakese as your native language.)

    Isn't Cakese experienced by John as something that already exists by the time he hears it? And if regular, etc., etc., then as conventional?
  • Problem with the view that language is use

    Let's call it "Cakese". You said I could call it what I like, and I've decided.

    As it turns out, you never meant to imply that Cakese actually exists. Fine. It was, let's say, an imagined language, like Builders(2). Your post included no actual use of Cakese -- you were just explaining what it would be if it were a language and how it might be used. Fine.

    On this reading, John's request for "a 'new usage' that bears absolutely no association or link whatsoever to the conventional usages of the time in which it arose" could be satisfied simply by imagining a new language and imagining using it. Since Cakese has just been (imagined to be) invented, it is, by definition, not conventional, not as you use the word "conventional," i.e., it wasn't a language that already existed. Huzzah!

    You may be satisfied, but I seriously doubt John will be. I think he would expect to see something that counts as a use of Cakese, while having no link to the conventions of Cakese.

    Is there something peculiar about English that makes it impossible to produce the sort of unconventional usage John requested in English?
  • Problem with the view that language is use
    these criteria must be 'lived', and the only thing that that guarantees their uptake (or not) is the 'form-of-life', the 'whirl of organism' in which they operate. Meaning is use means: look at the practices in which language is embedded in ("the speaking of language is part of an activity, or of a form of life"), and language or meaning cannot be grasped apart from that activityStreetlightX

    Incidentally, it is just this rarefied, intellectualist, and 'thin' approach to language - in which meaning can only ever find its ground in more language ("meaningless... unless they are given meaning as being equivalents to words..."), shorn of any reference to human practice, lived context, and worldly action - in short, the entire order of the performativeStreetlightX

    The only ground for the supposed meaning of your supposed use of language that you indicated was more language, that is, the translations you provided. We have been given no reason to believe there are practices in which your supposed language is embedded. You didn't even bother to fake it: you could have made up scenarios where you say "koijnufbab" to the postman each day, etc.

    You might have said, here are some arbitrary strings of letters and some gestures that could conceivably be part of a language. Fine. You might have noted that the lived context of those strings and gestures includes the use of English, and that it is possible to treat those strings and gestures as loanwords from a language that happens not to exist. But by claiming there is such an unnamed language, that a few strings and gestures and their translated meanings is all it takes to have a language, it is you who have failed to take Wittgenstein seriously.

    In fact, it's clear that what undergirds your claim that those strings and gestures were a use of language is something you will not say: that they were meant as language.

    If I had some cake, and you were in the same room as me, and neither of us could speak to each other in terms other than in my made-up-on-the-spot language (assuming I was consistent with grammar), I wager you'd 'get' my invitation to eat cake eventually (this would be the 'rough ground' of language - life and it's being lived, language bound up with action - that secures meaning). This is how we teach children, no? Does it matter if we teach them with an already-established - i.e. conventional - language, or not?StreetlightX

    This is a tough sell because it's extremely difficult to imagine the "no other terms" part. I think we all reach in our minds for some foundational gestures we pretend are transparent and self-grounding. (If the goal is to share the cake, the thing to do is cut each of you a piece. That's what Wittgenstein would say.)

    But the most important word in here is "consistent." What you teach someone when you teach them a language, the practice you invite them to join, is precisely the consistent and regular actions (not only the utterances, but the matching of utterance to occasion, and so on) that constitute its use, in short, its conventions. No regularity, no convention, and no language.
  • Problem with the view that language is use

    Supposing, just for the sake of argument, you have a provided a criterion for what could or should count as a use of language, what would lead me to think the criterion had been met in this case?
  • Problem with the view that language is use
    At a minimum one would have to grant that the phrases and gestures have a grammar particular to them (such that there would be different kinds of lexemes employed), and that this grammar would be transposable to other words or gestures that could belong to that same languageStreetlightX

    I'm sorry, are you saying I have to grant this, in the present case? Or are you saying that if this were an instance of language use, this is what I would be granting?
  • "True" and "truth"
    without interpretation there is no difference between meaningful and meaninglessMetaphysician Undercover

    I'm a little puzzled by this.

    If I speak to you in a language you do not know, it would make sense for you to say, "That's meaningless to me." "Meaningless to me" would mean "I can't understand this." But even if it were meaningless to you, it could be and is meaningful to me and to anyone else who knows that language.

    But you seem to have something very different in mind. If I say something to you in a language you know, must you interpret what I said for it to be meaningful to you? I'll grant that conversation usually involves some ambiguity, some ellipsis, and so on, and sometimes those have to be cleared up to understand what someone is saying. I suppose you could call that interpretation.

    But that's by and large a matter of clarifying which of several meanings the speaker meant. You could say that until one meaning is settled on, what was said does not have a meaning. But it doesn't look much at all like the case of speech in a language you don't know. If there's an interpreter on hand, she could transform the meaningless into the meaningful for you, but that's not much at all like the problem of selecting one among several meanings.

    What the two cases do share is an asymmetry: there is no reason to think I do not understand what I say to you, whether I speak in a language you don't know, or speak ambiguously in a language you do know, or speak with the exemplary clarity of a post such as this one. I have no need of an interpreter to understand what I say; nor do I need to disambiguate it or fill in whatever was elliptical in it. So I cannot see that my own speech was ever meaningless to me in any sense, even without either of the two sorts of interpretation.
  • Problem with the view that language is use

    Fair enough. What I'm wondering though is in what sense your typing was a use of language.
  • Problem with the view that language is use
    My uses may be idiosyncratic, but they are not private, by dint of their being uses of language at all.StreetlightX

    What language would that be?
  • Problem with the view that language is use
    The issue is ontological and not directly tied with issues of knowledge or reference.Pierre-Normand

    If by this you mean, can we imagine a theory in which the distinction you are contemplating is deployed to pick out different entities, I suppose that would be fine, but you're not suggesting there is something like a "bare" ontological question here, outside the context of any particular theory, are you? That would seem very strange to me indeed. What's more, it seems to me the motivation for preferring either a theory that distinguishes actions from, say, occurrences, or one that doesn't, would be precisely its utility in dealing with issues of knowledge and reference. And of course the issue arose in this thread precisely as a question of reference.

    At any rate, I'm not sure we are compelled to reach the ontological issue at all: clearly one could be in a position to assert that there was a death and not in a position to assert there was a murder; one could dissemble; one could be interested in the event only qua death and indifferent otherwise (the lawyer executing Caesars will). I suppose some of this is the sort of thing you would count as occasion-sensitivity.

    And the unavoidable fact is that if Caesar does not die, there is no murder. Do we have a problem with theories where the existence of one entity (a murder) requires the existence of another (a death)? What about when the required entity is of a different type?
  • Why am I in that body ?
    Strawson writes about the problem of what makes a particular body my body in Individuals and has this crazy thought experiment -- which someone should turn into a flash game -- in which you have three different bodies: one you see out of, one that determines which horizontal direction your visual field is facing, and one that determines which angle up and down your visual field is pointed, IIRC. I may have the details wrong. I remember that if you try to see your own face in a mirror, you end up looking at the back of your head.
  • Proof of nihil ex nihilo?
    "¬p→p" has an obvious countermodel when p is false, which happily you assumed in (1).
  • Problem with the view that language is use

    I appreciate your response because what I have is not so much an idea at this point as the 'aura' of an idea that has not quite yet arrived! I have classes on the brain, because of my quandary over how we make the leap from particulars to types.

    My first thought was a little like what Harry's saying nearby, that "Caesar was murdered" is a fuller description of the event in question than "Caesar died," and one way to express that would be to compare the cofinal sets of propositions each entails. There are many propositions that will be true whether Caesar was stabbed to death or suffered a massive heart attack.

    Suppose A has a private audience with the Emperor behind closed doors. After half an hour, A comes back out.
    A: "He's dead."
    B: "What do you mean? Was he sick?"
    A: "I don't know."
    B: "What did he die of?"
    A: "His wounds."
    B: "What wounds?"
    A: "The ones I gave him."
    One way to imagine this process, is that B initially grasps a set of propositions that he knows to be the cofinal tail of some more complete set, and there are several different candidates for what that larger set is. The process is to try out various propositions in order to more fully to determine what set you have the tail of: is it, for instance, the cofinal set of "The Emperor was sick" or the cofinal set of "The Emperor was killed"?

    Thinking of this as a "more complete description" led me almost immediately to the concern you noted, that I would need to posit "fully determinate facts" at the head of such sets, and that seems a bit dubious. (They might still do as theoretical entities somehow.) But it then occurred to me that this process need not be imagined as how we pick out the unique, fully determinate facts that make up the world, but simply as comparative, that the use of the procedure could be precisely in what we've been at here, which is deciding whether two descriptions pick out the same thing or not.

    It should be clear by now that in essence what I'm contemplating doing is substituting the classes of entailed propositions for concepts. (I'm testing my Fregean assumptions. Do we need concepts? Do we need propositions for that matter or will equivalence classes of sentences do?)

    In your pigeon experiment, for example, it's clear that to determine whether you have the cofinal tail of "Responds to red" or "Responds to crimson," you had better test some other shades of red.1

    Your example of Pat's height is curious. (For the record, I'm just under 5'10".) I feel a little like I've wandered into the Wittgenstein-Moore conversation, because I want to say that I know every human being who has ever lived and every human being who ever will live is shorter than the Eiffel Tower. It's common sense! But how do I know that? When did I come to know that? The explanation I'm entertaining is this: it's somewhere out in the cofinal tail of "The Eiffel Tower is really tall" and I've never even looked out there.

    So it's just something I'm fooling around with. No doubt something like this has been tried before and I'll discover why it doesn't work soon enough...


    1. I once had a heat pump quit because it turned out there was a relay jammed with ants that had committed mass suicide on it. The repair guy told me he had seen this several times, and had actually asked an entomologist what the deal was. The explanation (hypothesis?) was that the ants happen to be attracted to the particular frequency this device hums at, not to all humming sounds.


    EDIT: Should have noted that the Emperor may have accidentally brutally stabbed himself in the stomach while shaving.
  • Problem with the view that language is use
    Having dragged in convention, I'll do another: I think it's worth noting that the word "representation" has barely appeared in this thread at all. We talk about beliefs, about utterances and propositions, about truth, but representation is nowhere to be seen. I suppose Harry has sometimes been arguing for language as representational, but for the most part it seems to be the farthest thing from everyone's minds.

    Is that down to philosophical fashion? Or is there something we know that most of cognitive science doesn't?
  • In defence of weak naturalism

    Sorry, man, there's no way I'm going to discuss whether "Nothing comes from nothing" is true. Best of luck to you, Sam.
  • Problem with the view that language is use
    Likewise, (1) the fact that Pat is shorter than Chris isn't the same as (2) the fact that Pat is shorter than the Eiffel Tower. And neither of those facts are the same as (3) the fact that Pat is 5 feet tall. For all that, the properties ascribed to Pat in (1), (2) and (3) stand pairwise as determinable to determinate.Pierre-Normand

    I keep thinking, as I suggested in the other thread, that what we want here is sets of propositions ordered by entailment, but it looks like that would have to be relative to a set of assumptions or background knowledge or something. I want Pat's being 5 feet tall to buy you, as a single fact, everything it entails. A separate fact for everything Pat is taller or shorter than seems less than optimal.

    It's also beginning to seem to me that what's going on in these threads is paradigmatic: that insofar as there is a problem to be solved, it's not exactly the problem of uniquely picking out an entity or meaning or event, but deciding whether two (or more) propositions or descriptions pick out the same one. And it seems to me you could do that by looking at what they entail.
  • In defence of weak naturalism

    I expressed no opinion on the apples and don't intend to. It's just logic: "I can eat something" is not equivalent to and does not entail "I can eat anything" or "I can eat everything."
  • "True" and "truth"
    In fact, it seems most natural to say that a fact, such as Caesar having been murdered in 44 BC, should buy you not just a single proposition, but a cofinal set of propositions, ordered by entailment. It is after all the occurrence of this one event that makes it true that Caesar was still dead last week and was still dead yesterday, and on and on. Whatever the problem with correspondence theories, it can't be this trivial addition of true propositions.
  • "True" and "truth"
    Well either a proposition corresponds to an entity or it doesn't, what other options are there?Fafner

    A proposition such as "Caesar died" might be true not because it has a truth-maker of its own, but because it is entailed by a proposition such as "Caesar was murdered" that does have a truth-maker.
  • Problem with the view that language is use
    Since I'm the one who brought convention into this, I should clarify that I'm talking about Lewis's approach in Convention where the conventions are specifically not agreed to, but "emergent" as the solution to coordination problems.Srap Tasmaner

    It occurs to me that since Lewis is avowedly Humean, he might have chosen the word "custom" instead of "convention". He chose the latter to see if there was an answer to Quine.
  • Problem with the view that language is use
    Yes! This, exactly. I reckon if one can grasp the import of this passage, almost the entirety of the PI falls into place.StreetlightX

    Let's assume we have achieved the Right Understanding of what Wittgenstein Really Meant.

    What I want is an account of how language is possible and how it works.

    I would expect a certain sort of challenge:
    (1) What I want is impossible.
    and/or
    (2) What I want shows I am prey to a certain misunderstanding or illusion.
    and/or
    (3) I should really want something else.

    Assuming I can run that gauntlet, then my questions would be:

    (A) Does Wittgenstein provide the sort of account I'm interested in?
    (B) Is it a good one?
  • In defence of weak naturalism
    "It is possible for something to come from nothing" is not the same as "It is possible for anything to come from nothing."
  • Problem with the view that language is use
    Since I'm the one who brought convention into this, I should clarify that I'm talking about Lewis's approach in Convention where the conventions are specifically not agreed to, but "emergent" as the solution to coordination problems.
  • Problem with the view that language is use
    I don't think of conventional usages of language as "contractual" at all. I believe that linguistic usages become established in a 'live' way; that is, in, and in accordance with, lived experience.John

    I completely agree.
  • Problem with the view that language is use
    What grounds meaning in his (quite agreeable view) is not convention (which is easy to think), but "forms of life" far more generally, like what is universal to the human conditionWosret

    That undersells convention, and what motivates convention, rather dramatically. We're not talking about which fork goes to the right of which, but the prospects for communal life and communal aspiration.
  • In defence of weak naturalism
    For the hypothesis 'Something can come from nothing', a necessary consequence is that 3 apples could logically result from 2 apples;Samuel Lacrampe

    It's so not a necessary consequence. I thought you knew how to use quantifiers.
  • Problem with the view that language is use
    One more thought on convention: if the worry is that people will think saying x is just following convention, that it's like playing a word game, that, in short, saying x doesn't mean anything, then the antidote is right there: you say x when you mean y, and by saying x meaning y, you're doing something - - making an assertion, giving a command, asking a question, christening a ship, etc.
  • Problem with the view that language is use
    But the challenge is not make it sound too anti-realistic or conventionalist. We want our sentences to have objective truth conditions at the end, don't we?Fafner

    Absolutely agree, and you're right that even using the word "convention" can send people in the wrong direction. (It's not a word I would have used much until recently and I had forgotten this.)
  • Problem with the view that language is use

    I'm not really sure what you're saying here. If you thought I was offering an interpretation of Wittgenstein, then I could see you thinking I had botched it pretty badly. I wasn't offering a version of LW though; it was Grice and a bit of Lewis.
  • Problem with the view that language is use

    Agreed.

    The sort of example Grice uses (and the above is just Grice lite) is my saying, "The truck is out front," because I believe the truck is out front, and I want you to believe that I believe that on the basis of my saying what I said, and I want you also to believe it, because I do, etc. It's notoriously torturous.

    At any rate, yes, the next step is to look at the occasion of utterance, the context of the utterance, and so on. Do we agree on that?
  • Problem with the view that language is use
    But still, I don't think that shifting the burden to communal conventions can tell you the whole story of how sentences can mean what they mean. What kind of facts make it the case that a given community uses certain words to mean X rather than Y?Fafner

    Are you thinking of the context or occasion of utterance, the language-game being played, that sort of thing? I don't think I would have a problem with that at all. Above, I spoke of wanting to mean something - - but that's honestly pretty silly. It's only there to be distinguished from wanting just to utter a particular string of sounds. The intentions we actually want are intentions to do something that can be done linguistically. For that sort of thing, language-games are a pretty reasonable place to start.

    Is that the sort of thing you had in mind?
  • Problem with the view that language is use
    And what makes it appropriate to use a sentence such as "it is raining" on certain circumstances and not some others, is not decided solely by what one intends. So I think that intention by itself is not a plausible explanation of linguistic meaning.Fafner

    Words are what we use to effect our intentions, that much is clear. What do we say about the meanings of words though? It doesn't seem right to say that we use the meanings of words to effect our intentions. We want to say that we use the particular words we do to effect our intentions because of what those words mean.

    If our intention is to say, to utter, "It rained yesterday," we need only find the words "it," "rained," and "yesterday" in our lexicon and we're all set. If our intention is to mean, "It rained yesterday," we have more choices, because there's more than one way to say that.

    Suppose it has not rained in a while; it finally rains one day and then again the next. A, on this second day, is still emotionally caught up in waiting for rain, and says to B, "Thank God it's finally raining." B could respond, "What was that yesterday? Snow?" and I would submit that what B means by that is, among other things, that it rained yesterday.

    But suppose B did not want to mean anything else by what he said -- not "There's something wrong with you," for instance -- but only "It rained yesterday." Then it seems natural to say that "It rained yesterday" is the right thing to say when that is all you mean, because "It rained yesterday" means, in some special sense, "It rained yesterday." That special sense is something like "literally," because obviously just as there are many things you can say and mean "It rained yesterday," there are many things you can mean by saying "It rained yesterday."

    When searching your lexicon for words you can use to mean something, it is the meaning rather than the shape of words that matters. Whether the words can be used to mean what you mean is what determines whether they are candidates for being used now by you. In many cases there will be a specially favored choice, because the words -- or, let's say, particular words arranged in a particular way to form a sentence -- mean what you mean. If you want to say something that means, "It rained yesterday," then you say, "It rained yesterday," because "It rained yesterday" means "It rained yesterday."

    But we could also say that "It rained yesterday" means, literally, "It rained yesterday" in the following sense: it is what members of your speech community say when they want to say something that means "It rained yesterday," and only means that. It is how your speech community uses these words. It is what they mean by these words, and therefore it is what these words mean in your speech community.

    On this account, the meanings of words are traceable to our meanings. But it is the convention of meaning y by uttering x within your speech community that makes x mean y, not your individual meaning y by uttering x on some occasion. If you are a member of this speech community and want to say something that means y, the simplest way to do that is to utter x, to follow the convention. (But also: you may have some options that are simply less popular than x, or you may find a new way of following other conventions to mean y without uttering x. Uttering x is just the simplest way to go both for you and for your hearer, who can also be expected to be familiar with x and how it is used.)
  • Fitch's paradox of Knowability
    The real problem is supposed to come a few steps later, because you can show that all true propositions are actually known. That result is quite congenial for you, but not for everyone.
  • In defence of weak naturalism
    Substitute rabbits for apples and you can have the Fibonacci sequence. What could you prove with that?
  • Is it possible to categorically not exist?

    Something way back in my memory tells me what you're talking about here as B is what Aristotle called substance, that of which properties are predicated.

    The question here is whether your particular take on such a metaphysics is reasonable.

    You say the Empire State Building exists as an idea and then exists as building. I suppose when it's torn down, it goes back to existing as an idea. It seems perfectly clear to me that there are ideas of the building existing before, during, after the Empire State Building's existence as a building. None of them are the Empire State Building itself, and it is not any of them.

    If it really bothers you that the Empire State Building can come into and go out of existence, then you should look at that. What does it mean to say that? We're not talking about miracles. All we really have here is the rearrangement of stuff that already exists, on the one hand, and how we talk about it, on the other.

    Do you know the sorites paradox? the problem of the heap? You've got a pile of sand. Take away a grain, still a pile of sand. Take away another, or another ten, or another hundred, and it's still a pile of sand. But how far can that go? When you get down to a hundred grains, is it still a pile of sand? Maybe. Down to ten? Doesn't seem like a pile, maybe a very small pile. Three? At what point did it stop being a pile? Was there a number? Is it plausible that there's a cutoff -- 256 is a pile, but 255 isn't?

    Do you see here a pile of sand springing into existence and disappearing? Or the pile of sand being first a physical thing and then an idea as we take away grains? What idea? How many grains of sand in the idea of a pile?
  • One italicized word

    I think psychologism is prima facie implausible as an account of how we talk about mathematics, for one thing. Now the psychologismist, if they weren't just going to deny this -- I expect you will -- could respond that Frege's machinery was developed especially to formalize mathematics, and so there's no surprise that it works there, but also no reason to think it works at all anywhere else. But then the question is, what's different about mathematics? If the response is that mathematics is just convention, that it's all true by definition, something like that, that leaves unexplained how such conventions could possibly arise, conventions for which Frege's account does actually work. And if you could have such conventions as the basis for mathematics, why not for other things, why not for natural language?

    There's nothing wrong with that as such, as long as we acknowledge that it's just a fiction that we're engaging in to make it easier to talk about the topics at hand.Terrapin Station

    Talking as if something were something else is very close to something counting as something else, and I still want to know how that works. As I've said, I think there's a kind of start in the way phonemes work -- there's a whole range of sounds that will count as the phoneme. That involves selecting certain features and ignoring others. Pitch, for instance, is irrelevant in English.

    That "selecting certain features" part makes it sound like we're headed right back toward the Fregean machinery. But maybe not, or not only that. At the very least, we're talking about counting numerically distinct objects or events as instances of the same thing, and in a sense it doesn't matter how "objectively" similar or different they are -- counting two things apparently identical in every way, that as far as we can tell are copies of each other, as instances of some thing-type is still a leap. And it's that leap that is the basis for whatever else we do.

    So I'm still stuck at the move from utterance to utterance-type, belief to belief-type, thing to thing-type.
  • Fitch's paradox of Knowability
    I'm still working on it. (I've been reading Dummett off & on for a while now, so I've acquired some sympathy for his program, and this is an interesting challenge.)

    My current, unfinished thoughts follow:

    "Kp→p" is abhorrent. That's semantics intruding on syntax. "p" should only show up because it's assumed or derived (according to introduction and elimination rules), not because you have applied a specific predicate to p. That's insane.

    So treat "K" as an operator, a primitive. We already have an elimination rule, so how about an introduction rule? No idea. But it still seems like an awful idea to me because it should be (a) shorthand for something else (the way "↔" is, for instance), or (b) orthogonal to the other primitives. It is neither.

    I think if you wanted a formal epistemic logic, you'd have to build that from scratch taking Known in place of True.

    Maybe K is more like the modal operators and will only make sense there. So how does it interact with the others? I've played with that a little but I'm not even sure what the goal here is. And modal logic is not my strong suit anyway.

    I think all of the writing about Fitch's paradox looks like it's taking place in some deductive system that includes the predicate "K" but it isn't really. I think it's just notation.
  • Fitch's paradox of Knowability
    I tried explaining it to my son, and of course his reaction was that if you know p then nobody knows p is just false. When I explained how the conjunction is supposed to work, his feeling was that there's a problem here with the expression of human thought rather than with knowledge itself. (Admittedly, my son is not exactly the man on the street.)