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Re: [ontolog-forum] from logical intuitions to natural logic2.

To: paoladimaio10@xxxxxxxxxxxxxx
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sat, 17 Oct 2009 15:20:52 -0400
Message-id: <4ADA1914.4000808@xxxxxxxxxxx>
Paola,    (01)

PDM> I would be interested in seeing you and Pieter argue over
 > the contended points in a public discourse arena, and I am
 > hopeful that you could come to some brief conclusion    (02)

A public debate might be exciting, but it's not necessary.
I suggest that anyone interested in the subject should take
a hard look at Seuren's assumptions:    (03)

    http://www.lel.ed.ac.uk/events/lcircle/abs/SeurenPaper.pdf    (04)

Starting on page 1, he makes some points that are not controversial,
but he adds assumptions that make them dubious.  Since I won't comment
on all of Seuren's assumptions, the numbering below is his:    (05)

  1. "Progress in science is contingent upon taking the data seriously."    (06)

     But he follows that with extremely controversial statements:    (07)

     "In the cognitive sciences, the data is experiential intuitions.
     In the semantics of natural language, data consists of semantic
     experiential intuitions, including logical intuitions."    (08)

     Intuitions aren't data.  They are essential for hypotheses, but
     every hypothesis must be tested with publicly observable data.    (09)

  2. "The primary function of any signaling system, including natural
     languages, is for the sign-giver (speaker) to enter a social
     commitment with regard to the truth of a proposition."    (010)

     Social commitment is essential for language, but the assumption
     that propositions and truth are primary is not supported by the
     data of language use.  For infants learning language and for
     adults who have a minimal use of a foreign language, requests
     and questions are primary.  Stating propositions is secondary.    (011)

  4. "The relation between logic and language has been unclear from
     the very beginning and all accepted logical systems violate
     natural intuitions to some degree."    (012)

     The first clause is certainly true.  But the second clause
     contains the dubious term "natural intuitions", which Seuren
     identifies with his own hypotheses.    (013)

  5. "To understand the semantics of natural language it is necessary
     to investigate the possibility of reconstructing NATURAL HUMAN
     LOGIC."    (014)

     He assumes that there exists a fixed propositional system that
     supports NL semantics.  But there are many more reasonable
     assumptions.  Terrence Deacon, a neuroscientist who has been
     working in anthropology for years, has a better hypothesis:
     the human brain has the architecture of a chimpanzee brain
     with an extensive symbol processing system built on top.    (015)

     In his later philosophy, Wittgenstein showed the wide range
     of "language games" that people play with their symbol systems.
     The various logics that logicians construct and philosophers
     and linguists study are different abstractions from the many
     different kinds of language games that people play.    (016)

  5. "A logic can only be a logic when expressed in a (formal)
     language (see (9))."    (017)

     A formally defined syntax certainly helps to clarify the
     operations, but any argument stated in any formal logic can
     be restated in an equally precise way in English and many
     other natural languages.  (I'll avoid making a commitment
     about "all" languages, since some of them may need to add
     vocabulary and possibly some syntax to support all logics.)    (018)

  6. "A proposition is the mental act of assigning a property to
     an entity or n-tuple of entities."    (019)

     First of all, propositions are not acts, and they are
     independent of the minds that conceive them.  Furthermore,
     propositions may relate continuous signs to continuous
     referents that can't be analyzed as n-tuples.    (020)

     Peirce noted that propositions can be made by pointing,
     and they can also be expressed in images.  For example,
     a portrait with "George Washington" underneath states
     "This is a likeness of George Washington."    (021)

  8. "A logic is a formal system for deriving entailments (or:
     defining inconsistencies)."    (022)

     Deduction is only one way of using logic, and it's not
     even the most important way.  Induction and abduction are
     prior to deduction because they're necessary to form the
     hypotheses from which deduction proceeds.  Furthermore,
     hypotheses derived by induction and abduction can often
     be useful without any further deduction.  (If you think
     you see a tiger about to pounce on you, don't waste time
     in testing the hypothesis or deducing the consequences.)    (023)

10. "This discussion is limited to the logical constants ALL,
     SOME, NOT, AND, OR."    (024)

     That limitation and the assumptions about truth and
     propositions (2), formality (5), and entailments (8)
     drastically restrict what Seuren is willing to accept as
     a "natural" logic.  I believe that Seuren is "throwing out
     the baby with the bathwater."    (025)

11. "A sentence of a NATURAL LANGUAGE L is transformationally
     derived from the corresponding S of an underlying LOGICAL
     or SEMANTIC LANGUAGE (LL)..."    (026)

     That was a common assumption in the 1960s and '70s in
     several different fields.  In linguistics, it included both
     the "generative semantics" movement, in which Seuren was a
     participant, and the formal semantics movement, which was
     started by Richard Montague and promoted by Hans Kamp and
     Barbara Partee.  It was also widely assumed in artificial
     intelligence by people who hated logic, such as Roger Schank,
     and by many people who used logic, such as me.    (027)

     Today, many of those people are dead, and others have adopted
     much broader views about language and logic.  For the more
     recent position by Hans Kamp, see    (028)

     http://www.illc.uva.nl/lia/farewell_kamp.html    (029)

13. "Natural logical intuitions are a mixed lot... when separated
     out into basic-natural and strict-natural they make for two
     (or more) consistent systems."    (030)

     I agree with the first sentence.  But for the rest, Seuren
     carefully selects which intuitions he considers natural.
     I have serious doubts about his choices.  See point 10.    (031)

14. "Every logic is definable in terms of a set theory.  Standard
     predicate logic is a direct reflex of standard set theory."    (032)

     If you broaden the term 'set theory' to mean any way of talking
     about collections and referring to their elements, the first
     sentence is true but meaningless.  The second sentence is false.    (033)

15. "Basic-natural set theory (BNST) analyses the cognitive concept
     of PLURALITY."    (034)

     Many linguists and logicians (including anyone who has tried to
     teach conventional set theory to beginners) have observed that
     the usual set theory does not have an obvious mapping to plurals,
     as used in English and many other languages.  For that reason,
     many people have proposed versions of mereology as a better
     foundation.  But there are many more versions of mereology than
     there are of set theory, and none of them have an obvious claim
     to be natural.  I have far less hope for Seuren's BNST.    (035)

16. "Natural human ONTOLOGY must be taken to include INTENSIONAL or
     VIRTUAL ENTITIES, because humans refer to and quantify over virtual
     entities (e.g. Greek gods) with the same ease and naturalness as
     they do with regard to really existing (actual) entities (Seuren
     2009, Ch. 2)."    (036)

     I certainly agree with that point.  But a better citation is
     Ockham's _Summa Logicae_ (1323).    (037)

21. "Extensive data... show that two kinds of negation must be
     distinguished in natural language: MINIMAL NEGATION to correct
     failure to satisfy an update condition and metalinguistic,
     discourse-correcting RADICAL NEGATION to correct failure to
     satisfy a precondition."    (038)

     Those are only two of the many, many ways that negative terms
     are used in natural languages.  It's another example of the way
     that Seuren picks and chooses which "intuitions" he considers
     to be "data".    (039)

As I said about point 11, I had a lot more sympathy with Seuren's
approach in the 1970s than I do today.  In fact, I cited his books
from 1969 and 1974 in my 1984 book _Conceptual Structures_.    (040)

But even in that book, where I presented conceptual graphs as
a candidate for something one might call a "natural logic" or
a "discourse representation," I called Chapter 7 "The Limits
of Conceptualization."  In that chapter and in many of my later
writings, I discussed the numerous problems and issues that any
claims about a "natural logic" must address.  See, for example,
my paper on "The Challenge of Knowledge Soup":    (041)

    http://www.jfsowa.com/pubs/challenge.pdf    (042)

I still believe that conceptual graphs are a useful representation
for many of the purposes that Seuren and others have claimed.  But
in our current work at VivoMind, we use them in much more flexible
ways (of which formal deduction is just one).  See, for example,    (043)

    Two paradigms are better than one and
    multiple paradigms are even better    (044)

The writings by Peirce and the later Wittgenstein had a strong
influence on my 1984 book, and their influence has grown even
stronger today.  I don't believe that Seuren could have made
the assumptions above if he had done either of the following:    (045)

  1. Spent some years working on natural language processing or
     at least collaborating with people who did (as Kamp had done).
     Alan Perlis said "A year spent in artificial intelligence
     is enough to make one believe in God."    (046)

  2. Read Peirce and Wittgenstein and taken their arguments
     seriously.    (047)

As I said in my previous note, every version of logic is an
abstraction from the way reasoning is expressed in ordinary
language.  As Wittgenstein pointed out, there are infinitely
many different "language games" that can be played with the
syntax and vocabulary of any natural language.  I would say
that all of them are "natural" to a greater or lesser degree.    (048)

Furthermore, we have implemented computer systems that use
conceptual graphs to play many of those language games.
Seuren's assumptions about what is natural are too limited
to support the ways people actually use language.    (049)

PDM> could you interpret at a glance the transition from the
 > square to the dodecadron (that would save me having to study
 > the paper for the mo)    (050)

The square is sufficient to make the point.  The dodecahedron
is an extension that incorporates more of Seuren's assumptions,
which are interesting, but dubious hypotheses.    (051)

John    (052)

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