Although the approach you are suggesting might entertain some
philosophical questions, and therefore be entertaining to philosophers, it has
little or no relevance to real engineering problems, which almost never are
applied to the actual universe of every possible entity - i.e. infinite
supplies.
In engineering applications, Ex(...) would normally apply only
to finite sized, or traversably infinite sized, problems. The importance of
scope in engineering, i.e., where you draw the lines around what is a system, which
contains all the entities, enumerators of variables, constants and functions in
real problems.
Even unbounded engineering problems have limits to the possible
types that can be used, though mechanisms like stacks, or even Turing machines
with infinite square supplies, attempt to approximate boundless sizes.
So I suggest your title should be A Question About Mathematical
Logic, since engineers who consider themselves logic designers would find the
ideas impractical, though linguists might be more interested.
Sincerely,
Rich Cooper,
Rich Cooper,
Chief Technology Officer,
MetaSemantics Corporation
MetaSemantics AT EnglishLogicKernel DOT com
( 9 4 9 ) 5 2 5-5 7 1 2
http://www.EnglishLogicKernel.com
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Thomas
Johnston
Sent: Tuesday, October 13, 2015 8:59 AM
To: Thomas Johnston; [ontolog-forum]; [ontolog-forum]
Subject: Re: [ontolog-forum] A Question About Logic
Suppose someone else asserts,
instead, that "No dogs are renates". Certainly, to do that, that
person must believe that there are such things as dogs and, in addition,
believe that none of them are renates (a false belief, of course).
On Tuesday, October 13, 2015
11:57 AM, Thomas Johnston <tmj44p@xxxxxxx> wrote:
My intuitions tell me that
anyone who asserts "All dogs are renates" believes that there are
dogs (i.e. is ontologically committed to the existence of dogs) just as much as
someone who asserts "Some dogs are friendly".
Suppose someone else asserts,
instead, that "No dogs are renates". Certainly, to do that, that
person must believe that there are such things as dogs and, in addition,
believe that some of them are not renates (a false belief, of course).
Now for "Some dogs are
friendly", and also "Some dogs are not friendly". In both cases,
we all seem to agree, someone making those assertions believes that there are
dogs.
Now I'm quite happy about all
this. If I make a Gricean-rule serious assertion by using either the
"All" quantification or the "Some" quantification, I'm
talking about whatever is the subject term in those quantifications – dogs in
this case. I'm particularly happy that negation, as it appears in the
deMorgan's translations between "All" statements and "Some"
statements, doesn't claim that a pair of statements are semantically
equivalent, in which one of the pair expresses a belief that dogs exist but the
other does not.
But in the standard
interpretation of predicate logic, that is the interpretation. In the standard
interpretation, negating a statement creates or removes the _expression_ of a
belief that something exists. My beliefs in what exist can't be changed by the
use of the negation operator. Apparently, John's beliefs can, and so too for
everyone else who feels comfortable with predicate logic as a formalization of
commonsense reasoning, and with the interpretation of one of its operators as
"There exists ....".
I usually don't like getting
into tit for tats. Those kinds of discussions always are about trees, and take
attention away from the forest. But I'll make exceptions when I think it's
worth taking that risk (as I did in my response to Ed last night).
From John Sowa's Oct 12th response:
TJ
> why, in the formalization of predicate logic, was it decided
> that "Some X" would carry ontological commitment
Nobody made that decision. It's a fact of perception.
Every
observation can always be described with just two operators:
existential quantifier and conjunction. No other operators can
be observed. They can only be inferred.
(1) If all ontological
commitments have to be based on direct observation, then we're right back to
the Vienna Circle and A. J. Ayer.
(2) And what is it that we
directly observe? A dog in front of me? Dogs, as Quine once pointed out, are
ontological posits on a par with the Greek gods, or with disease-causing
demons. (I am aware that this point, in particular, will likely serve to
reinforce the belief, on the part of many engineering types in this forum, that
philosophy has nothing to do with ontology engineering. That's something I want
to discuss in a "contextualizing discussion" I want to have before I
pester the members of this forum with questions and hypotheses about
cognitive/diachronic semantics. What does talk like that have to do with
building real-world ontologies in ontology tools, in OWL/RDF – ontologies that
actually do something useful in the world?
(3) I wouldn't talk about
some dogs unless I believed that some dogs exist. And if some dogs exist, then
all dogs do, too. Either there are dogs, or there aren't. If there are, then I
can talk about some of them, or about all of them. If there aren't, then unless
I am explicitly talking about non-existent things, I can't talk about some of
them nor can I talk about all of them, for the simple reason that none of them
exist. To repeat myself: if any of them exist, then all of them do.
(4) And I am, of course,
completely aware that trained logicians since Frege have been using predicate
logic, and that, at least since deMorgan, have been importing to negation the
power to create and remove ontological commitment.
(5) Here's a quote from Paul
Vincent Spade (very
important guy in medieval logic and semantics):
"This doctrine of
“existential import” has taken a lot of silly abuse in the twentieth century. As
you may know, the modern reading of universal affirmatives construes them as
quantified material conditionals. Thus ‘Every S is P’ becomes (x)(Sx ⊃ Px), and is true, not false, if there are
no S’s. Hence (x)(Sx ⊃ Px) does not
imply (∃x)(Sx). And that
is somehow supposed to show the failure of existential import. But
it doesn’t show anything of the sort .... "
So Spade approaches this as
the issue of the existential import of universally quantified statements. He
points out that, from Ux(Dx --> Rx), we cannot infer Ex(Dx & Rx). The
rest of the passage attempts to explain why. I still either don't understand
his argument, or I'm not convinced by it. Why should "All dogs are
renates" not be expressed as Ux(Dx & Rx)?
From John's reply, I think he
would say that it's because we can only observe particular things; we can't
observe all things. But in the preceding points, I've tried to say why I don't
find that convincing.
(6) Simply the fact that
decades of logicians have not raised the concerns I have raised strongly
suggests that I am mistaken, and need to think more clearly about logic and
ontological commitment. But there is something that might make one hesitate to
jump right to that conclusion. It's Kripke's position on analytic a posteriori
statements (which I have difficulty distinguishing from Kant's synthetic a
priori statements, actually -- providing we assume that the metaphors of
"analytic" as finding that one thing is "contained in"
another thing, and of "synthetic" as bringing together two things
first experienced as distinct, are just metaphors, and don't work as solid
explanations).
All analytic statements are
"All" statements, not "Some" statements. Kripke suggests
that the statement "Water is H2O" is analytic but a posteriori. In
general, that "natural kind" statements are all of this sort. Well, a
posteriori statements are ones verified by experience, and so that would take
care of John's Peircean point that only "Some" statements are
grounded in what we experience.
I don't know how solid this
line of thought is. But if there is something to it, that might suggest that if
we accept Kripke's whole referential semantics / rigid designator / natural
kinds ideas (cf. Putnam's twin earth thought experiment also), then perhaps we
should rethink the traditional metalogical interpretation of "All dogs are
renates" as Ux(Dx --> Rx), and consider, instead, Ux(Dx & Rx).
Well, two summing-up points.
The first is that Paul Vincent Spade thinks that my position is
"silly", and John Sowa thinks that it's at least wrong. The second is
that such discussions do indeed take us beyond the concerns of ontology
engineers, who just want to get on with building working ontologies.
As I said above, I will
address those concerns of ontology engineers before I begin discussing
cognitive semantics in this Ontolog (Ontology + Logic) forum.
On Monday, October 12, 2015 10:49
PM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
Tom, Ed, Leo, Paul, Henson,
TJ
> why, in the formalization of predicate logic, was it decided
> that "Some X" would carry ontological commitment
Nobody made that decision. It's a fact of perception. Every
observation can always be described with just two operators:
existential quantifier and conjunction. No other operators can
be observed. They can only be inferred.
EJB
> I was taught formal logic as a mathematical discipline, not
> a philosophical discipline. I do not believe that mathematics
> has any interest in ontological commitment.
That's true. And most of the people who developed formal logic
in the 20th c were mathematicians. They didn't worry about
the source or reliability of the starting axioms.
Leo
> most ontologists of the realist persuasion will argue that there
> are no negated/negative ontological things.
Whatever their persuasion, nobody can observe a negation. It's
always an inference or an assumption.
PT
> on the inadequacy of mathematical logic for reasoning about
> the real world, see Veatch, "Intentional Logic: a logic based on
> philosophical realism".
Many different logics can be and have been formalized for various
purposes. They may have different ontological commitments built in,
but the distinction of what is observed or inferred is critical.
HG
> I keep wondering if this forum has anything useful to offer the
> science and engineering community.
C. S. Peirce was deeply involved in experimental physics and
engineering. He was also employed as an associate editor of the
_Century Dictionary_, for which he wrote, revised, or edited over
16,000 definitions. My comments below are based on CSP's writings:
1. Any sensory perception is evidence that something exists;
a simultaneous perception of something A and something B
is evidence for (Ex)(Ey)(A(x) & B(y)).
2. Evidence for other operators must *always* be an inference:
(a) Failure to observe P(x) does not mean there is no P.
Example: "There is no hippopotamus in
this room"
can only be inferred iff you have failed to observe
a hippo and know that it is big enough that you
would
certainly have noticed one if it were present.
(b) (p or q) cannot be directly observed. But you might
infer
that a particular observation (e.g. "the room
is lighted")
could be the result of two or more sources.
(c) (p implies q) cannot be observed, as Hume discussed at
length.
(d) a universal quantifier can never be observed. No matter
how many examples of P(x) you see, you can never
know that
you've seen them all (unless you have other
information
that guarantees you have seen them all).
TJ
> But now notice something: negation creates and removes ontological
> commitment. And this seems really strange. Why should negation do this?
The commitment is derived from the same background knowledge that
enabled you to assert (or prevented you from asserting) the negation.
> I'd also like to know if there are formal logics which do not
> impute this extravagant power of ontological commitment /
> de-commitment to the negation operator in predicate logics.
Most formal logicians don't think about these issues -- for the
simple reason that most of them are mathematicians. They don't
think about observation and evidence.
CSP realized the problematical issues with negation, but he also
knew that he needed to assume at least one additional operator.
And negation was the simplest of the lot. Those are the three
he assumed for his existential graphs. (But he later added
metalanguage, modality, and three values -- T, F, and Unknown.)
John
PS: The example "There is no hippopotamus in this room" came
from
a remark by Bertrand Russell that he couldn't convince Wittgenstein
that there was no hippopotamus in the room. Russell didn't go
into any detail, but I suspect that Ludwig W. was trying to
explain the point that a negation cannot be observed.
|
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (01)
|