Pat Hayes wrote:
>> Pat Hayes wrote:
>>
>>>>> Why do you assume that 'rains' is logically false? I have no idea
>>>>> what its actual logical truth-value is;
>>
>> Of course.
>>
>>>>
>>>> because I take
>>>>
>>>> (that (rains))
>>>>
>>>> to be a proposition that it rains, without any indexicals, that is,
>>>> that it rains everywhere, at all times.
>>>
>>> I don't think that is how it should be understood.
>>
>> Why? As John says, that's my choice. Perhaps if I chose otherwise,
>> (that (rains)) would be false. Why can't I decide that 'rains' means
>> that it rains at all times and in all places?
>
> Sorry. Yes, of course you can. You can in fact state it as an axiom in
> IKL, if you wish:
>
> (iff (rains)(forall (s)(ist (that (rains s))))) (01)
Well, no. (rains) means, say, that it rains at all times and in all
places. But the axiom above does not justify, explain, or sanction
that: it merely says that iff it is true that it rains in all places
and at all times, then in every context (including your and mine
beliefs, for example) the proposition that it rains always and
everywhere is seen as if it were true -- but the two sides of the
equivalence speak of quite different truths. You can state such an
axiom, of course, but it does not mean what you suggest it means. (02)
I can decide that (rains) means that it rains everywhere and always, and
yet still meaningfully assert that there is a context in which (that
(rains)) is not in-that-context-true. (03)
>
> or more radically
>
> (= rains (that (forall (s)(ist (that (rains s))))) )
>
> But it is not a *logical* truth. That is, this choice is not necessary,
> or forced upon one by the inherent structure of contexts or
> propositions. One could just as well, and just as consistently, assert
>
> (iff (rains)(exists (x)(and (madeOf x cheese)(Orbits x Earth)))) (04)
Sure. (05)
>
>> This, of course, is
>> inessential.
>>
>>> After all, that can be stated explicitly:
>>>
>>> (forall (c)(ist c (that (rains))))
>>
>> Well. Again, this says that in every context, the proposition that it
>> rains (whatever it means, according to my wish) is context-true in that
>> context.
>
> Right. Bearing in mind that as far as IKL is concerned, "p is
> context-true in c" is just an English gloss for "the relation ist holds
> between c and p" (06)
Of course. (07)
>
>> It is not about raining (whatever 'rains' means).
>
> Well, it is about it to the extent that it determines it's ist-relation
> to c. (08)
Well, but the ist relation does not relate to truth in any way.
It is about raining to the same extent as "I don't think it was raining"
is about raining. (09)
>> I admit that talking about context-dependent truth of sentences sounds
>> more natural to me than talking about truth-independent context-truth of
>> propositions.
>
> I agree, which is why I tend to slip into that way of talking myself.
> But the formalism treats it the second way. The surprising fact (and it
> is a fact) is that this works: that is, that (modulo the complication
> regarding opaque names) the two readings coincide. (010)
I have no problems with the formal semantics of IKL. (Or maybe I just
think so.) Just the human-IKL interface seems a bit sandpapery to me. (011)
>
>> This may be an unfortunate mindset.
>>
>> I am also suspicious about the distinction between a proposition's being
>> non-contextually true a proposition's being true in all contexts.
>
> It sounds as though you would like the above equivalence to be logically
> true. (012)
Quite the opposite; I oppose, it seems (what a discovery) to the idea
of context-independent meaning of sentences (and context-dependent truth
of propositions). (013)
> IKL could have been constructed in this way; but to do so would
> have required that 'ist' be given a logical status, and not be a mere
> relation between contexts and propositions. That would have made the
> actual logic more complicated, and made it into a species of context
> logic. Whereas our mandate (and scholarly interest) was in keeping it as
> simple as we could, and we wanted to avoid making our interlingua into a
> context logic. (014)
I appreciate and admire your work. But if I am not the most silly or
picky person who has ever read, or who will have read the IKL manual,
you may expect problems. (015)
>> What
>> is the difference between being true independently of context and being
>> true whatever context is chosen?
>
> Er... they have nothing to do with one another? What is the difference
> between a duck and a camel? (016)
My guess: the first starts with a 'd'? (017)
Right: if you *must* have both in one logic, they may have nothing to
do with each other. (018)
>>
>> If
>>
>> (dead osama)
>>
>> "asserts that Osama-Bin-Laden simply has a property, without any
>> qualification as to time or circumstances"
>
> But that way of phrasing it is misleading, since it suggests that having
> a property is something that CAN be qualified by time or circumstance.
> IKL does not admit that notion of qualification as a logically
> meaningful kind of expression. This sentence in IKL means simply that
> osama has a property. (019)
This is your way of phrasing it. Live from IKL guide. (020)
>
> In any case, time and circumstance are not enough. One has to allow
> other kinds of contextual qualification (or at least, the context
> logicians claim this), including spatial locations (It is true in France
> ...) beliefs (Joe believes ...), fictional narratives (In the Conan
> Doyle novels, ...), provenances (According to Hoyle, ...) and even
> purely 'formal' kinds of "context" such as "It is consistent with set
> S13 of sentences that ..."
>
> .
>> , then
>>
>> (ist t1 (that (dead osama)))
>>
>> asserts that c and (that (dead osama)) are ist-related, without any
>> quantification as to time or circumstances. If you add a bit of
>> ontology and interpret ist as a is-true-in relation between a context
>> and a proposition, then the above asserts that the proposition that
>> osama simply has a property is-true-in c.
>
> Right. And that is the IKL way of modelling what would be stated in a
> context logic as the claim that osama has a property is contextually
> true in c. (021)
You're the boss, but I guess that the corresponding statement in a
context logic would actually mean that the *sentence* 'dead osama' is
contextually true. 'Claim' is amiguious here -- do you mean a sentence,
or a proposition? (022)
>> It is still about osama's simply having a property (it is about the
>> proposition about osama's simply having a property), only that viewed
>> from the perspective of a context.
>
> But what does this 'viewing from a perspective' mean, logically? (023)
Logically in IKL it means ist-relatedness. (024)
> How
> shall we represent this in a formalism? Are we obliged to go beyond
> classical logic to do an adequate job of encoding this kind of meaning?
> Many have claimed that this is inevitable, and that the presence of such
> perspectives or contexts means that classical logic is inadequate.
> The
> formal adequacy of the IKL encoding of such forms suggests however that
> this assumption is wrong, or at any rate needs to be re-examined
> critically. (025)
You are certainly right. I do not discuss formal adequacy of IKL, but
the somewhat counterintuitive interpretation of contextualization of
propositions. (026)
>>>>> but in any case that would be irrelevant to its *contextual* truth,
>>>>> which is modelled in IKL by the ist relation. "True throughout an
>>>>> interval" and "standing in the ist relation to an interval" are
>>>>> just two ways to say the same thing. Or perhaps, if you feel that
>>>>> truth at a time is something fundamental, by all means say that the
>>>>> ist-formulation is IKL's way of modelling or describing or
>>>>> representing the notion of truth at a time.
>>>>
>>>> But are we not taking a round here, saying that (ist c p) *does*
>>>> mean that p *is true* in c, even if it is false?
>>>
>>> My point is that truth in a noncontextual classical logic such as FOL
>>> or CL or IKL - logical truth - on the one hand; and 'truth at a time'
>>> or 'truth in a context', on the other, are two *distinct* notions.
>>> They have different meanings and different logics, and support
>>> different notions of interpretation and of proof. They can be related
>>> in various ways, which are well-understood, but they are not the same
>>> notion. In particular, if I can warp the English for a moment and
>>> write L-truth for the first notion, contextual truth is *not* L-truth
>>> at a time or L-truth in a context, since it is quite literally
>>> meaningless to relativize L-truth to a context. So if we look at a
>>> simple English present tense sentence such as "gusty winds exist", it
>>> can be understood in two different ways: as uttered in the present
>>> (and perhaps a particular place, ie with an implicit 'now, here') and
>>> referring to it, or as uttered timelessly.
>>
>> But what would 'gusty winds exist' mean uttered timelessly?
>
> What it says: gusty winds exist. In fact, they do, so it is true. (027)
But what does 'gusty winds exist' mean, then? That there is an
instant/interval in time such that gusty winds exist at that time? (028)
>
>> What would '2+2=4' mean uttered timelessly?
>
> I take it be uttered timelessly, usually. I certainly don't usually mean
> it say, two plus two equals four *now*.
>
>> What would it mean in the real world?
>
> That discussion would take us into the foundations of mathematics and
> mathematical philosophy, and Id rather not venture there. Im quite happy
> to be a robust Platonist for ontological purposes. So, I will claim that
> 2+2=4 is simply timelessly true in the real world. (029)
OK (030)
>>> In context logic, "ist" defines a context-relative notion of truth.
>>> In IKL, "ist" is simply a relation which holds between C and the
>>> proposition (that <sentence>) precisely when <sentence> is true-in-C
>>> in the context logic.
>>
>> But true-in-c in context logic means, as far as I get it, 'the
>> proposition which is the meaning of <sentence> in c is true'.
>
> true *in c*. (031)
The *sentence* is true *in c*. The *proposition* which is the meaning
of the sentence in c is *simply* true. (032)
>> This is the same -- the only -- notion of truth, the L-truth, in the
>> logic. What is contextual, is the mapping from a sentence to a
>> proposition. No need for different notions of truth.
>
> Oh no, it really does assume a context-dependent truth. Meanings can
> change, but they also can remain the same but truth-values change. I
> agree, your notion would not require such a radically different logic. (033)
No, right. (034)
>>> I believe you may feel that truth is often, or perhaps always, best
>>> understood as being relative to a context,
>>
>> Depends on what you now mean by 'truth'. The truth of a proposition,
>> no; this was one of my primary questions on this thread, and we seem
>> to have agreed here that propositions have fixed truth values. The
>> truth of a sentence, yes, is relative to a context.
>
> Ah, I see. No wonder we are having trouble communicating. The primary
> authorities on the context logic we were referring to insisted on the
> following, when we asked them what 'ist' meant:
>
> 1. The syntactic form is "ist( <context-name> <sentence>)" (Not the IKL
> form, note)
> 2. The first argument denotes a context. What a context is, is not
> specified in the logic. Anything that satisfies the logical axioms can
> count as a 'context'.
> 3. The second 'argument' denotes a proposition, but the proposition it
> denotes may be dependent on the context denoted by the first argument.
> That is, the mapping from sentences to propositions is itself
> contextual, and so opaque. Or at any rate it may be. In this respect,
> ist(c ...) acts rather like a modality with c as a parameter.
> 4. The truth-value of a proposition may itself be different in different
> contexts. That is, it may be that all the names in the language refer in
> the same way in two contexts c1 and c2, and still it be the case that
> ist(c1 p) and ist(c2 p) differ in truth-value. (035)
Doesn't sound good. Seems as if they accepted indexical propositions
(propositions like 'it rains now'). (036)
> When pressed on what exactly they meant by a proposition, we were not
> able to get a clear answer, other than it is clear that a sentential
> syntactic form is able to denote one. About the only universally agreed
> axiom was the distribution of ist over conjunction, which has to be
> stated as an axiom schema or an inference rule in a first-order context
> logic:
>
> (forall (c)(if (ist c (and <P> <Q>)) (and (ist c <P>)(ist c <Q>)) )) (037)
So they at least do not contextualize 'and'. (038)
> but in IKL is an axiom:
>
> (forall (c p q)(if (ist c (that (and (p)(q)))) (and (ist c p)(ist c q)) ))
>
>
>>
>>> so that truth-in-a-context is an objective matter and context logic
>>> is the most appropriate formal vehicle for meaning.
>>
>> Yes, proviso that 'truth-in-a-context' means truth of a sentence in a
>> context.
>>
>> My suspicion about non-contextual truths is that
>>
>> a) when it comes to propositions, all are non-contextually true (or
>> false), so it makes no sense to talk about their truth in a context;
>>
>> b) when it comes to sentences, all are true (or false) only in a context.
>>
>> A context logic addresses the latter
>
> The context logics we were dealing with claimed both kinds of contextual
> relativity, and addressed both. (039)
No wonder you haven't liked it. (040)
> The IKL translation uses IKL ist to
> handle the former (relativity of truth to context) and the
> contextual-naming device to address the latter (relativity of sentence
> meaning to context). (041)
Which (the latter) is very fine and clean. (042)
>>> Hope this helps.
>>
>> I appreciate that you make that much effort to answer my (...)
>> questions -- thanks. Whether this helps, I am not sure yet. If not,
>> surely the fault is mine.
>
> If someone of your obvious insight can be muddled by our exposition, we
> have some more explanatory work to do. (043)
Happy to help. (044)
vQ (045)
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