• Banno
    26.1k
    If it is all syntax, what is semantics? And what of intent? There'd be a lot to fill out in explaining behaviour without making use of intent. Even if it is just a shorthand, that might make it useful enough to keep.
  • Banno
    26.1k
    does ¬∀ have ontological import?Arcane Sandwich

    Well, yes. It hadn't occurred to me that folk might think otherwise. Ux(fx) is just fa ^ fb ^ fc... for every item in the domain. And ∃x(fx) is just fa v fb v fc...

    There's a presumption that we are not dealing with an empty domain. I don't see that as a problem.


    A seperate issue. That ∃!t is defined as ∃(x)(t=x) is a result of the need to maintain extensionality. The SEP article explains how. And extensionality is just the idea that we can swap one name for another that refers to the same thing, presumably becasue it is the thing we are talking about and not the name.

    To say that ∃!t is to say that there is at least one thing in the Domain D - let's call that "x" - which is the very same as t. Which is to say that t exists.

    We could move to non-extensional free logics, but I think we'd be overthinking it. And we would need to rework what it would mean to be consistent in such a logic; and tracking the semantics would be difficult. But go ahead, if you think it would help.

    if I don't accept Bunge's dichotomy between conceptual existence and real existence, then there is no need for me to use subscripts...Arcane Sandwich
    Bunge's dichotomy looks to be much the same as that used in free logic, with conceptual existence taking the place of empty terms. I'm presuming that Bunge would suppose t=t to be true, even if t does not exist - Pegasus is Pegasus. So I'm understanding his idea as an interpretation of positive free logic. So yes we can drop the subscripts. But then "Pegasus does not exist" would be ~∃!(Pegasus); that is, ~∃x(x=Pegasus). This has the advantage of dropping the idea of treating proper names as pretend predicates - dropping parsing "Pegasus exists" as "Something pegasises". This directly gives us
    Bunge's approach also manages to accommodate the idea that proper nouns can be treated as individual constants.Arcane Sandwich
    And seems to me to be an improvement over Quine's idea of simply dropping proper nouns and individual constants.

    Bunge seems to have been anticipating free logic.
  • Banno
    26.1k
    But Quine is saying that you can conceive of different meanings for the same verbal dispositions - that is the example.Apustimelogist
    It might be worth adding "... and get the same result". The same behaviours might be seen with very different interpretations - we get a rabbit stew even if "gavagai" means undetached rabbit leg.
  • Moliere
    5.1k
    Or "dinner time, whatever is near!"

    Just to emphasize that inscrutability falls within common sense uses.
  • Arcane Sandwich
    2.2k
    Bunge's approach also manages to accommodate the idea that proper nouns can be treated as individual constants. — Arcane Sandwich

    And seems to me to be an improvement over Quine's idea of simply dropping proper nouns and individual constants.
    Banno

    But that is precisely where my disagreement with Bunge is to be found, because I think that Quine is actually right in treating the word "Pegasus" in a predicative way. I don't have the space here to explain why I prefer Quine's approach on this exact point, but it has to do with a (hopefully) novel solution to the problem of Material Constitution. Essentially, I agree with Quine's syntax (which is identical to Russellian syntax), but I disagree with Quine's parsing: "something Pegasizes". I also disagree with Russell's parsing, which is based on his theory of definite descriptions (but not because referents are inscrutable). I would just parse the following syntax:

    ∃x(Px)

    like so: "Some particular x is Pegasus".

    Notice that I do not say that some "x" exists. I parse it strictly as "Some particular x". And then, Px is to be read: is Pegasus. In this way, I (hopefully) manage to preserve what is intuitive in the idea that proper nouns successfully refer; that is, they function more or less like Kripkean rigid designators, but I avoid Kripke's (and Bunge's) idea that proper nouns should be treated as individual constants. Instead, I preserve (hopefully) what is intuitive in the Russellian and Quinean approaches, that is, of treating the expression "is Pegasus" as a predicate, because the "is" here is not the "is" of identity, it is the "is" of predication.

    At least this is one of the projects that I'm currently working on, in my day job (professional philosophy is far less glamorous than it sounds to outsiders).
  • Banno
    26.1k
    Yep. It's the simple observation that even if we disagree, we can often get on with the doing.
  • Moliere
    5.1k
    Yes, but if something is not linguistic then it does not constitute a reference of any kind, scrutable or inscrutable, no? Or rather, if we do not recognize something as a linguistic sign, then it cannot be inscrutable, for we would never say, "That non-reference is an inscrutable reference," or, "We will never figure out what that thing is referring to, namely that thing which we do not believe to be referring to anything."

    In fact I want to say that in order to identify something as referential one must already have a foothold of one kind or another. Without such a foothold there is insufficient reason to posit a referential reality (i.e. an intentional sign).
    Leontiskos

    You tempt me into the quagmire of the sign! Back, foul demon! :D

    What I'd commit to is the idea that though reference is inscrutable we can still communicate. If we somehow connected "reference" as a necessary condition of communication then that's pretty damning for the notion of reference always being inscrutable, or whatever.

    What this leads me to is the notion that proper names function differently, at least in English, than nouns. There's no description which "picks out" a reference, yet we are able to refer. I can't tell if it's the nose or the drink or the carpet, at least when talking about the facts before me, but I can tell by "Robert" you're referring to the man on the carpet with a drink. I remember his name and everything!

    So I think the target is more various philosophical notions of reference rather than the whole ability to communicate.

    At least, that's a more interesting thing to think about.
  • Banno
    26.1k
    OK. I'm not seeing a reason for something so complex, but you might be able to make it work.

    Px is to be read: is Pegasus.Arcane Sandwich
    So "P" is much the same as "Pegasus=" in "Pesasus=x"?
  • Arcane Sandwich
    2.2k
    Px is to be read: is Pegasus. — Arcane Sandwich

    So "P" is much the same as "Pegasus=" in "Pesasus=x"?
    Banno

    No, because x is a free variable. Like Quine, I believe that in some cases, we should avoid using individual constants, and we should treat proper nouns (i.e., names) as predicates of some free variable instead. Why? Because it has to do with a hopefully novel solution to the problem of Material Constitution that I mentioned in my previous comment.
  • Banno
    26.1k
    No, because x is a free variable.Arcane Sandwich

    I parse it strictly as "Some particular x"Arcane Sandwich

    I'm not sure how to reconcile these.
  • Arcane Sandwich
    2.2k
    I don't see where the problem is. What is it that you don't understand here?
  • bongo fury
    1.7k
    I assume chatbots and chromosomes are all syntax. Like Chinese rooms. And semantics is the interpretations that we (and future machines conceivably might) add. As Searle argues.

    I agree that this added dimension is what Searle addresses in terms of intention. I grok the "extensionalism" (and nominalism) of Quine and Goodman as trying to bypass the internal psychology. Hence Word and Object rather than Person and Object (as Chisholm had it).

    But no, no one is denying the importance of semantics. (Intentionality if you prefer.)
  • Arcane Sandwich
    2.2k
    Ah, I see what you mean. You're asking how can I say that "x" is a free variable instead of a bound variable. Is that it?
  • Leontiskos
    3.7k
    So I think the target is more various philosophical notions of reference rather than the whole ability to communicate.Moliere

    What I'd commit to is the idea that though reference is inscrutable we can still communicate.Moliere

    "How we manage to refer is mysterious, but what is being referred to is not indeterminate."

    Yes?

    Or:

    "How we manage to refer is inscrutable, but what is being referred to is not inscrutable."
  • Banno
    26.1k
    Well, in "Pesasus=x", isn't x some particular x? And a free variable? So why isn't "P" much the same as "Pegasus=" in "Pegasus=x"
  • Banno
    26.1k
    :up:

    Syntax as pattern, semantics as what we do with the pattern?
  • Count Timothy von Icarus
    3.2k


    You don't need these extraneous interpretations for people to communicate or use words, and the idea that you can coherently assign divergent meanings is something like a reductio to the thought that verbal behavior, language and understanding is anything above the physical events responsible for word-use.

    It seems to me that there is a more effective reductio pointing in the opposite direction. For what could be more obvious then that we do refer to things with our words and mean things by them? And if the reductio is not so obvious, one need only consider that the same sort of arguments are leveled against the existence of qualia and first-person experience. "What need have we for your 'experiencing' pain? Stimuli and response covers all the observations just as well."

    Yet what is said to constitute "all the observations," is doing all the lifting here, since clearly the person in pain observes this fact easily enough. Of course it is true that if one disallows all the evidence for something one will not be able to point to any evidence for it.
  • Arcane Sandwich
    2.2k
    Well, in "Pesasus=x", isn't x some particular x?Banno

    But I don't say "Pegasus=x", because the phrase "is Pegasus", in the case of Px, is not the "is" of identity, it is the "is" of predication. Like when you say: Some lemons are yellow. You're not saying "Lemon = yellow", you're not saying that a fruit is identical to one of its colors. You're saying that some fruit has that color. When I say that some "x" is Pegasus, I mean it like that: some x is Pegasus, in the sense of predication, not in the sense of identity. It's something that I'm working on, so I understand your confusion.
  • bongo fury
    1.7k


    Yes. I guess. Not sure.
  • Banno
    26.1k
    But I don't say "Pegasus=x", because the phrase "is Pegasus", in the case of Px, is not the "is" of identity, it is the "is" of predication.Arcane Sandwich
    Sure. And "Pegasus =" is also a predicate, not an equivalence.

    So we have two ways of parsing "x is Pegasus". As an equivalence, x=p, which is a two-place prediction "=(pegasus, x)"; or as a single-placed predication, "=pegasus(x)".

    But you said that these were not the same "becasue x is a free variable". I just wasn't able to follow that. Not a big point in the context. Leave it if you like.
  • Arcane Sandwich
    2.2k
    But you said that these were not the same "becasue x is a free variable". I just wasn't able to follow that. Not a big point in the context. Leave it if you like.Banno

    Maybe I meant to say "bound" variable instead of "free" variable, but the notions of free and bound variables is also something that I'm currently working on.
  • Arcane Sandwich
    2.2k
    Think of it like this, , if it makes any sense. I believe that in the formula ∃xPx, "x" is a free variable, not a bound variable. Why not, if it's quantified and it has a predicate? Well, because I believe that it's better to define a free variable as any variable that is not identical to an individual constant. Otherwise (and only otherwise) it's a bound variable. So, in this other formula, ∃x(x=p), I believe that "x" is a bound variable, not a free variable. But not because it's quantified, rather because it has been declared to be identical to an individual constant, "p".

    I'm aware that none of this makes sense to you.
  • Banno
    26.1k


    Hmm.

    From Open Logic, 15.8:

    Definition 15.33 (Free occurrences of a variable). The free occurrences of a vari-
    able in a formula are defined inductively as follows:
    1. φ is atomic: all variable occurrences in φ are free.
    2. φ ≡¬ψ: the free variable occurrences of φ are exactly those of ψ.
    3. φ ≡(ψ ∗χ): the free variable occurrences of φ are those in ψ together
    with those in χ.
    4. φ ≡∀x ψ: the free variable occurrences in φ are all of those in ψ except
    for occurrences of x.
    5. φ ≡∃x ψ: the free variable occurrences in φ are all of those in ψ except
    for occurrences of x.
    Definition 15.34 (Bound Variables). An occurrence of a variable in a formula φ
    is bound if it is not free.

    You can change that definition for your own purposes, if you like, but why?
  • Arcane Sandwich
    2.2k
    You can change that definition for your own purposes, if you like, but why?Banno

    Because it seems to be a necessary requirement of the hopefully novel solution that I'm working on in response to the problem of Material Constitution that I was telling you about. If it just so happens that there's no need for a re-definition, even better.
  • Banno
    26.1k
    it's better to define a free variable as any variable that is not identical to an individual constant.Arcane Sandwich
    Wouldn't that just mean that any non-constant was free, and so free variables would just be variables? That'd just be dropping the distinction between bound and free variables.


    I gather its a work in progress, so no need to reply until you have it worked out.
  • Arcane Sandwich
    2.2k
    Wouldn't that just mean that any non-constant was free, and so free variables would just be variables? That'd just be dropping the distinction between bound and free variables.Banno

    It would seem that way. So far, I see no reason for not doing exactly what you just said: to drop the distinction between free and bound variables in favor of the (arguably simpler) distinction between variables and constants. In other words, it seems to me that we can do just fine with constants and variables, there is no work do be done with the tripartite distinction between free variables, bound variables, and individual constants.

    EDIT: But I could be wrong.
  • Banno
    26.1k


    Except that f(x) says nothing, while ∃(x)fx says that something has the property f.


    Definition 15.37 (Sentence). A formula φ is a sentence iff it contains no free
    occurrences of variables.

    So if we drop the distinction between free and bound variables, we no longer have any sentences. Or any formulae is a sentence.
  • Arcane Sandwich
    2.2k
    Except that f(x) says nothing, while ∃(x)fx says that something has the property f.Banno

    Sure, but in saying ∃(x)fx, you're saying two things, you're making two declararions (or declarative speech acts):

    1) you're saying that some particular x (fill in the blanks)
    2) you're saying that (fill in the blanks) x is F.

    There's a sort of synthetic operation here, in a formula like ∃(x)fx. You're not saying "just one thing", you're saying two different things that only make sense when said together, but they're still two different declarations, even though neither can be declared independently of the other.
  • Banno
    26.1k
    There's a sort of synthetic operation here, in a formula like∃(x)fx. You're not saying "just one thing", you're saying two different things that only make sense when said together, but they're still two different declarations, even though neither can be declared independently of the other.Arcane Sandwich

    Not following that. Unless you are saying that ∃(x)fx says there is at least one thing and one thing is f - ie, that the domain is not empty. That might make sense.
  • Arcane Sandwich
    2.2k
    Unless you are saying that ∃(x)fx says there is at least one thing and one thing is f - ie, that the domain is not empty. That might make sense.Banno

    More or less, except that I have no use for the notion of a domain either in this proposal that I'm working on. But that would be more or less the correct parse: 1) there is at least one thing, and 2) that thing is F, in the manner of a variable (not an individual constant) having something predicated of it (instead of predicating that the variable in question is identical to an individual constant).
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