On Sep 22, 2008, at 1:00 AM, Len Yabloko wrote:
First - I want to thank you for the exposition. It is very satisfying to have people like you and John, who takes time to explain and support their position, in contrast to postings which express attitudes and very little substance. I also took time this weekend to carefully re-read the entire thread to see what engineer like myself can learn from it.
My point (I just sent off a long exposition to the thread) was only
that logical semantics relates a logical representation to reality,
not to a representation or "model" (intuitive sense, as in 'model
airplane') or description of reality. John's position is that this
never happens, that logical semantics cannot possibly relate logic to
reality, only to an intermediate abstraction which then must itself be
related to reality by some other means, hence the 'two-stage'
The notion of "model" is one of those paradoxical notions that everyone is using every day without second thought, but if asked would not be able to explain in basic terms (another one ofcource is 'love', but that is entirely different topic). Yet I always thought that it is *not* one of those words with different meanings requiring us to qualify it every time we use it. I don't see that intuitive sense of it (as in 'model airplane') is so very different from formal. Here is the definition I found in your exposition:
"Put another way, the FOL semantic metatheory describes the real world as a relational structure; and for each world so described, it tells how to determine the truth-value (true or false) of any sentence in the FOL representation. It may be referred to as a model theory (the relational structure here being the 'model') or a logical semantics or a truth-functional semantics or a Tarskian semantics, after its inventor."
So according to you formal 'model' is a relational structure which describes the reality
No! The relational structure *is* the reality, described (in this case) in the semantic metatheory. The relational structure doesn't do any describing or representing itself. That's why the use of the word "model" here is so misleading. A model in the normal English sense is always a model OF something, but in model theory, the "model" is the reality being described.
in a way that is suitable for reasoning about real things, which can be done using FOL, and thus can be (some times) execute by computers. Well - a 'model' of airplane is a structure equally suitable for reasoning about real airplane, as some times done by people and computers.
Yes, exactly. The model airplane is a representation of the real airplane. If we were to describe this set-up using the terminology of model theory, however, we would have to say that the model-airplane was the representation, and that the real airplane is the "model": that is, the relational structure which determines if the representation is true or not. As I said, this is almost exactly backwards in its use of "model".
The main difference is that logical model is used for different kind of reasoning than say - differential equation.
Differential equations can be expressed in logic. Logic is topic-neutral.
And here comes another one of these tricky words: 'semantics'. Ordinary use of that word would ascribe to differential equation semantics of differential calculus as a model theory (not *the* Model Theory created by Tarski). Again the main difference is the kind of reasoning. But do we have to qualify this time - that we are not talking about formal semantics, just ordinary one?
Im not sure what 'ordinary' semantics are. Formal semantics tries its best to simply be a formalization of semantic intuition, not a rival or alternative to it.
You seem to be implying that while you can represent knowledge using
model-theoretic semantics - the same can not be said about actuality.
Um, not quite. Knowledge is represented using logic (in the case under
discussion, i.e. a logic-based ontology), and the semantics is an
account of how this representation relates to the reality it describes
(more precisely, to some reality it could be describing.)
So is differential calculus an account of how equations relate to reality it could be describing? I think so.
I think not. Where does the differential calculus talk about semantics, or meaning, or denotation, etc.? LIke most of mathematics, it seems to just take meaning for granted rather than provide any analysis of it.
To me the word 'represents' means the same as 'interfaces' - that is
serves as a conduit for interaction and (limited) comprehension.
Interesting. Im not sure I follow this, but I think I disagree :-)
I purposefully did not use the word 'represents' this time because it seems to be the point of disagreement between John and you. Your claim is that Tarskian semantics are sufficient to reason about the real world, be it limited in power by FOL, but by no means does it make it wrong about real things. And you claim that John implies that such reasoning is incorrect unless augmented with another non-Tarskian theory about possible worlds - each described by its own Tarskian model?
It would have to be something different from Tarski. I have no idea what John thinks is missing, so I'm, not the person to consult on its exact form ;-)
Forgive my interpretation of you differences, but that is about as good as engineer can do, provided he is willing to get into semantics which most engineers don't (and seem to do as well as you do without any non-Tarkian or 'two-stage' semantics)
BTW, of course reality can be comprehended. We do it all the time. We
don't ever get complete comprehension, maybe, if that means what I
suspect you mean by it. But I didn't say anything about being
(in this sense, ie comprehensive, all-knowing). But its still the
actual bridge that falls into the river when the cables break, not
incomplete comprehension of it.
But what difference does it make for us in general and for your's
and John's discussion?
Well, if you had been on the bridge at the time, quite a lot. This
isn't meant to be a joke, by the way. I find it hard to understand how
anyone can say that reality isn't important, when just about all the
things that happen to us happen by virtue of impinging upon reality in
one way or another.
I did not notice anyone saying that reality isn't important, even after re-reading the entire thread couple of times.
Perhaps I misunderstood your point, above (what difference would it make?)
I think the argument arisen from interpretation of 'possible world' as abstraction that has no existence outside particular ontology or Tarskian model (seemingly equated by John?). Again forgive my interpretation! That claim somehow (I can't understand fully how) follows from John's 'metalevel reasoning' thesis. You on the other hand seem to say that all these possible worlds do exist, but only one of them is described by particular FOL ontology. That claim can be interpreted in two different ways:
1) All possible worlds exist side by side occupying the same physical universe, but exposing it from different prospectives given by semantic meta-theory (call it 'dark matter' theory because we have enough of it for few more worlds).
2) All possible worlds exist only in our imagination, but that is the only way we can reason about reality without being completely overwhelmed by it, so each world as real as it gets for all intents and purposes- just can't reason about all of it/them at once (call it 'multiple personality' theory because multiplicity originates when we begin to think).
The truth of any statement depends on initial assumptions and inputs
obtained from some representation.
No, really. The TRUTH depends on how well the representation
corresponds to reality. That is pretty much what truth means, in fact.
What you are talking about, I think, is how we come to know things,
which indeed does have to do with interfaces and transduction.
If I understood you correctly - you are telling me that statement about reality is truthful when semantics of language (used to make it) is fathefull to possible world.
Right, though better to say, faithful to the actual
world. Possible words are a bit of a red herring. They are only needed to give a semantics for modal sentences, like saying something is necessarily
true which is supposed to mean more than just plain true. If we only use plain language without any modalities in it, then nobody needs to consider possible worlds.
So if I make false statement about that world it will be provably and obviously (due to 'truth function') false. Thus we can't hide the truth anymore (from computers :-).
No, being true doesn't mean being provably true, or obviously true. It just means being true. Truth can be hidden, don't worry.
But that is not what I meant by 'truth of statement' - I meant its meaning (if something said about world true or false).
So did I mean that.
The role of semantics is to make a sound connection from later to
former. Moreover, semantics can not be fixed, but must allow for
cycles of expansion and compression to accommodate growth and
physical limits. Isn't that what you call two-stage semantics?
No, thats not what I mean. In fact I cannot follow this stuff about
expansion and compression.
The stuff about expansion and compression is (IMHO) what makes one and only one real world to look like multiple worlds (ie. expansion), but allow interaction with one of your choice (compression).
Hmm, I still don't understand this, sorry. What makes one actual world look like multiple worlds is our ignorance. We don't have all the information about it, so many possible worlds (or if you prefer, possible ways the actual world might be) are consistent with what we know. As it says in the old song: For all we know, this may only be a dream...
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