Pat Hayes wrote:
>> John F. Sowa wrote:
>>> Ingvar,
>>>
>>> My position and Pat's position are compatible and for the same
>>> reasons: we both have propositions, but we admit that their
>>> truth values in different contexts can be different.
>>
>> One could call it 'hard-headed language puristness', but it seems to me
>> that Ingvar makes a valid point (if I understand him correctly); to me,
>> to say (as Pat did) that a proposition has a fixed truth value, which is
>> not a function of anything (or is a nullary function), and then to say
>> (as Pat did) that a proposition may have different truth values in
>> different contexts is plainly confusing.
>
> What I said is that propositions have fixed truthvalues, and that
> propositions may also stand in relations to other entities. One of these
> relations is conventionally denoted by "ist", holds between entities
> called 'contexts' and propositions, and is understood - externally to
> the actual logic - to have the interpretation that the proposition is
> 'true in the context'. This relationship of truth-in-a-context has
> absolutely no relationship with actual logical truth, and is indicated
> in the formalism simply by the ist relation: that is, we say that P is
> 'true in C' simply to mean that "ist(C, P)" is logically true. Now,
> perhaps calling this 'having a different truth-value in a context' is
> confusing, since this truth-in-a-context is not really anything to do
> with actual truth-values: but it is simply an extension of the
> conventional nomenclature. So if you find this awkward, abandon this
> terminology and say instead that P is C-true, or something similar,
> which draws attention to the fact (and it is a fact, even in a context
> logic) that truth and C-truth are different; and the the latter has a
> parameter.
>
>>
>> While in the case of multiple possible worlds -- which seem a purely
>> theoretic device that does not reflect the actual reality we live in --
>> it does sound reasonable to say that a proposition may have different
>> truth values in different worlds, as far as the worlds are truly
>> different possible worlds, rather than consequtive stages of the same
>> actual world (in which case we would have to admit that the truth of a
>> proposition is time-dependent). But it does not seem to me reasonable
>> to say that a proposition may have different truth values in different
>> contexts in the same actual world
>
> My position is that I have no idea what a 'context' is supposed to be
> (and I have spent more mental hours than I want to admit trying find out
> what others mean by this horribly evasive word) and I prefer to do
> without them altogether. There simply is no fact of any matter involving
> the term "context". But if someone wishes to speak of truth in a context
> - and many people do - and has some notion of what a context might be
> (and people do use it to mean possible worlds, by the way, among many
> other kinds of thing), then the IKL stance and formalism provides them
> with the ability to formalize their intuitions by writing axioms about
> some suitable relation between their kind of context and propositions.
> In other words, contexts are hereby brought into the scope of
> ontological engineering, rather than being some mysterious aspect of
> truth itself that we must resolve before we can even get started.
>
>> -- especially after having said it has
>> a fixed truth value. It may be that a context considers, in any sense
>> you like, a proposition to be true or false, independently of its actual
>> truth or falsity, but the proposition does not thereby change its truth
>> value. We end up saying that a proposition is true, but (and?) false in
>> some context, for example. Awkward, as Ken says.
>
> If you think this is awkward (and I agree) then I suggest you would be
> better off without having contexts at all. It is part of the very idea
> of contexts that they can change the meanings of things, so that
> sentences may be true but seem false in a context, or vice versa. They
> are inherently <it>de dicto</it>, inherently opaque, inherently elusive.
> Awkward, I agree, but awkwardness is inevitable when one sets out to
> write axioms (which are by their nature intended to be effectively
> eternal, or at the least long-lived) about such truth-shifting entities
> as contexts.
> (01)
I think we agree. A context, as treated in IKL, corresponds to a
perspective (no cognitive agent implied) on a proposition *as if it
were* true or false, irrespectively of whether it *is* true or false. (02)
And to summarize -- back to the original question: it seems to me that
we agree that the truth of a proposition does not depend on any
conditions other than what is the case in that part of reality
(understood in a 4d manner, I think) the proposition is about. (03)
I think one should be careful to distinguish a proposition's being
eternally true and a proposition's being (still eternally) true about an
eternal fact. (04)
The sentence (P-at x t) would mean (correspond to the proposition) that
x is P at t; if the proposition is true, it is eternally true: it is
true at t, it were true earlier (or of undetermined truth, depending on
how the world is), and it will be true later. (05)
However, the sentence (P x), which does not explicitly refer to time, if
read as not referring (implicitly) to any time instant or interval at
all, corresponds to the proposition that x is P at all times, which
would be (eternally) false for most x's: since most entities we know do
not exist eternally (but who knows?), they cannot be P, or whatever
else, at all times, since there are times at which they are not at all. (06)
But sentences like (forall (x) (if (P x) (Q x))) may well correspond to
(eternally) true propositions, even if sometimes there are no x's which
are P. (07)
vQ (08)
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