Re: Analytic/Synthetic distinction in modern inference engines?

On Mar 24, 7:05 pm, martinobal <martino...@xxxxxxxxx> wrote:
but what about the logical frameworks that some philosophers (or even
logicians) develop for their semantic investigations, like Montague's
Intensional Logic or, more recently, Pavel Tychy's Transparent
Intensional Logic

"Developing logical frameworks for semantic investigations"
is not even important, really. Anybody can develop whatever
framework they want for whatever application they want;
no one mode of doing that is privileged over any other, nor
is any domain of application.


I was asking something like "aren't *they* closely related to logic,
even if natural language itself may not be?"

Since they ARE logics, OF COURSE they are closely
related to logic. This was a stupid question.

It is important to note, for *everything*, however, that if it is more
complicated than 1st-order logic (this very much INcludes 2nd-order
classical logic), then it really CANnot be "logic" AT ALL. It simply
fails of the *purpose* of logic.

Could you elaborate on that sentence?

FOL has some tractability properties that more complicated
logics lack. It is basically a dividing line between what is
simple enough to be applicable in practice and what is too
complicated to be of any practical use.

When you say "this very much
INcludes 2nd-order classical logic" do you mean SOL is included with
FOL, or is it included with those things that are more complicated
than FOL?

The latter.

And what is, in your view, the purpose of logic

Logic exists to help you avoid inconsistency as you
pile up new knowledge (new axioms).

and how those other things fail to accomplish it?

Implication is too complex to enable you to pragmatically
CONFIRM when you have fallen into inconsistency.

Any examples?

Not off the top of my head. All the real-world examples
have the property that they could NOT be CONFIRMED to
be examples except BY PERFORMING this inference that
was "too complex" TO BE performed.



or Carl Pollard's Higher Order Grammar?

I'm not so interested in distinguishing
the provable from the unprovable, as I am in distinguishing what can
be proved using *only* definitional axioms (axioms from the T-layer,
in my terminology) from what can be proved using non-definitional
axioms (axioms from the A-layer).

That IS NOT the analytic/synthetic distinction.

This is what I called the a/s
distinction. If you don't agree with calling it the a/s distinction,
I'm open to other designations.

You will not get any, because that isn't even a valid distinction
AT ALL. The NON-distinct part is that they BOTH involve
WHAT CAN BE *PROVED*. The nature and the kind of PROOF
occurring on BOTH sides of your purported distinction IS THE
SAME. So there simply IS NO difference TO distinguish.

I just want a logical framework where definitional axioms
and axioms about facts are not mixed in one big
pool.

That simply cannot happen.
What you ACTUALLY want is a framework wherein
a proposed axiom can be properly categorized as either
"definitional" or not so. In mathematical theories,
that doesn't make a whole lot of sense, since EVERY
axiom is a partial restriction and critical component of
the "definition" OF EVERY predicate it uses.


If you equate being analytic to being inferable, you are using a
framework where the distinction I seek is not expressible,

It's not JUST ME, kiddo. YOU equated being analytic to being
inferrable.

hence your
conclusion that my request is silly. I want it to distinguish an
analytic inference process from a synthetic one,

There is no synthetic inference. Inference is analytic by definition.

based on whether all the axioms involved are definitional.

You are speaking in terms of some sort of mixed theory from some
other discipline (was it DL, originally?). I have been speaking from
a mathematical point of view. Obviously if you are talking about
formal language for describing some real-world events then you
can separate the sentences describing observed truths about
individual objects (which could have been otherwise, logically)
from the axioms of your theory of the physics of the world.

But in an abstract logical context, that distinction does NOT arise.
Even when A is NOT analytic or logical, the fact that A->B is
necessarily so, if A does in fact imply B. If A is merely true and
B is as well, or A is false, then A->B can be true without being
analytic, but again, that depends on whether you can PROVE B
from A. Your distinction between "definitional" and "other" axioms
is truly not well-motivated "locally". At this point, YOU are the one
who needs to come up with "examples".


A physicist can't forbid the colloquial usage of "work" for anything
that is not force times displacement. Why would a logician have a say
in the colloquial usage of "definition"?

Because misusing "work" won't stop you from doing it, but
misusing "definition" really CAN prevent you from properly
using definitions, and thereby from reasoning consistently.
NObody wants to be inconsistent. That really is deadly
FOR EVERYBODY IN ALL endeavors.

I took a methodological approach, as if one is building an ontology
(in the I.T. sense) one axiom at a time, but the end result would show
a "topological" partial ordering, as you say, independent of what
axioms were introduced first. Whatever is inferable from the T-layer
alone would be "analytic", and the rest (involving the A-layer) would
be "synthetic".

The important thing for you here is simply the distinction between
the layers. In the mathematical theories that we are usually talking
about in this room, THAT DISTINCTION DOES NOT EXIST.
You really do need 1) to motivate the distinction, and 2) to be clear
about what it MEANS to USE an axiom "from the A-layer(synthetic)".
In the real world, those axioms almost don't get "used"; rather,
people simply worry about what follows ("using" axioms FROM THE
T-layer) FROM them.

.

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