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␈↓ ↓H␈↓␈↓βS␈↓∧ Artificial Intelligence Laboratory, STANFORD UNIVERSITY, Stanford, California 94305

␈↓ ↓H␈↓∧Telephone 415 497-4430␈↓ 	TDecember 14, 1978 




␈↓ ↓H␈↓Professor Barbara Partee
␈↓ ↓H␈↓Department of Linguistics
␈↓ ↓H␈↓University of Massachusetts
␈↓ ↓H␈↓Amherst, MA 01003

␈↓ ↓H␈↓Dear Barbara:

␈↓ ↓H␈↓Here are some more thoughts suggested by your "Semantics - Mathematics or Psychology?

␈↓ ↓H␈↓1.␈α The␈α
word␈α"psychology"␈αrequires␈α
clari≡cation.␈α Does␈α
it␈αapply␈αonly␈α
to␈αpeople␈α
or␈αto␈αmachines␈α
also?
␈↓ ↓H␈↓Your␈α⊂main␈α⊂example␈α∂of␈α⊂a␈α⊂psychological␈α∂limitation␈α⊂-␈α⊂non-substitutability␈α∂of␈α⊂logical␈α⊂equivalents␈α∂-
␈↓ ↓H␈↓applies␈αto␈αmachines␈αas␈αwell␈αas␈αpeople,␈αso␈αlong␈αas␈αwe␈αrequire␈αthat␈αwhat␈αis␈αknown␈αbe␈αsayable.␈α This
␈↓ ↓H␈↓is␈α
a␈α∞consequence␈α
of␈α
the␈α∞undecidability␈α
of␈α
logical␈α∞equivalence,␈α
but␈α
practically␈α∞buildable␈α
machines
␈↓ ↓H␈↓have limitation far tighter than those imposed by these theorems.

␈↓ ↓H␈↓2.␈α∞ I␈α∂think␈α∞it␈α∂␈↓↓may␈↓␈α∞be␈α∂fruitful␈α∞to␈α∞extend␈α∂psychological␈α∞considerations␈α∂to␈α∞machines,␈α∂i.e.␈α∞to␈α∂have␈α∞a
␈↓ ↓H␈↓"generalized psychology".

␈↓ ↓H␈↓3.␈α
 As␈α
far␈α
as␈α
I␈α
know,␈α
the␈α
Chomskyans␈α
don't␈α
distinguish␈α
performance␈α
limitations␈α
imposed␈α
by␈α
the
␈↓ ↓H␈↓fact␈αthat␈αa␈αhuman␈αis␈α
a␈αmaterial␈αsystem␈α-␈αfurther␈αlimited␈α
in␈αspeed␈αand␈αmemory␈αperformance␈α-␈α
from
␈↓ ↓H␈↓evolutionary␈α
accidents.␈α
 To␈α∞put␈α
the␈α
matter␈α∞positively,␈α
it␈α
seems␈α∞that␈α
allowing␈α
phrases␈α∞rather␈α
than
␈↓ ↓H␈↓just␈α
single␈αwords␈α
in␈αcertain␈α
sentence␈αpositions␈α
is␈αrequired␈α
for␈αcommunication␈α
between␈αany␈α
physical
␈↓ ↓H␈↓systems with limited ability to see through each others eyes.

␈↓ ↓H␈↓It␈α
may␈αbe␈α
very␈α
di≠cult␈αto␈α
decide␈αwhether␈α
a␈α
feature␈αof␈α
human␈αlinguistic␈α
behavior␈α
is␈αfunctionally
␈↓ ↓H␈↓required␈αbefore␈αwe␈αcan␈αbuild␈αprograms␈αthat␈αcommunicate␈αwell␈αwithout␈αthe␈αfeature.␈α For␈αthis␈αto␈α
be
␈↓ ↓H␈↓a good test, we must subject the programs to corresponding speed and memory limitations.

␈↓ ↓H␈↓4.␈α
 I␈α
believe␈α
that␈αlinguistics␈α
can␈α
and␈α
should␈α
become␈αless␈α
theological␈α
just␈α
as␈α
metamathematics␈αhas
␈↓ ↓H␈↓made␈α∞the␈α∞foundations␈α∞of␈α
mathematics␈α∞less␈α∞theological.␈α∞ Namely,␈α∞we␈α
will␈α∞need␈α∞to␈α∞study␈α∞for␈α
many
␈↓ ↓H␈↓years␈α⊂the␈α⊂characteristics␈α⊂of␈α⊂di≥erent␈α⊂formalizations␈α⊂before␈α⊂we␈α⊂can␈α⊂discard␈α⊂all␈α⊂but␈α⊂one␈α⊂kind␈α∂of
␈↓ ↓H␈↓system␈α∂(if␈α∞ever).␈α∂ In␈α∂particular␈α∞formalizations␈α∂of␈α∂propositional␈α∞expressions␈α∂in␈α∂which␈α∞expressions
␈↓ ↓H␈↓equivalent␈α∀under␈α∀many␈α∀kinds␈α∀of␈α∃equivalence␈α∀relations␈α∀are␈α∀intersubstitutable␈α∀will␈α∃be␈α∀useful.
␈↓ ↓H␈↓Sometimes␈α⊂the␈α⊂relations␈α⊂will␈α⊂be␈α⊂logical␈α∂extensional,␈α⊂sometimes␈α⊂intensional␈α⊂in␈α⊂varous␈α⊂ways,␈α∂and
␈↓ ↓H␈↓sometimes psychological or computational in various ways.

␈↓ ↓H␈↓5.␈α∞ One␈α∞reason␈α∞why␈α
I␈α∞believe␈α∞that␈α∞many␈α∞theories␈α
will␈α∞be␈α∞found␈α∞useful␈α
is␈α∞my␈α∞idea␈α∞that␈α∞they␈α
are
␈↓ ↓H␈↓ascriptive␈αanyway.␈α
 [See␈αmy␈α
␈↓↓Ascribing␈αMental␈α
Qualities␈αto␈αMachines␈↓.]␈α
If␈αthat␈α
be␈αgranted,␈α
it␈αseems
␈↓ ↓H␈↓likely␈αthat␈αdi≥erent␈αsystems␈αfor␈αascribing␈αbelief␈αwould␈αbe␈αuseful␈αdepending␈αon␈αcircumstances.␈α To
␈↓ ↓H␈↓put␈α⊂this␈α⊂idea␈α⊂as␈α∂a␈α⊂bold␈α⊂contention:␈α⊂ Humans␈α∂could␈α⊂be␈α⊂brought␈α⊂up␈α∂to␈α⊂use␈α⊂di≥erent␈α⊂systems␈α∂in
␈↓ ↓H␈↓αProfessor Barbara Partee␈↓ ¬ODecember 14, 1978␈↓ 
nPage 2␈↓ 

␈↓ ↓H␈↓natural␈α⊃language␈α∩comfortably␈α⊃in␈α∩conversation␈α⊃with␈α∩similarly␈α⊃brought␈α∩up␈α⊃people.␈α∩ They␈α⊃could
␈↓ ↓H␈↓probably switch from one system to another especially if di≥erent vocabularies were used.

␈↓ ↓H␈↓6.␈α∞ I␈α∂have␈α∞on␈α∂major␈α∞di≥erence␈α∂in␈α∞taste␈α∂from␈α∞Montague.␈α∂ He␈α∞likes␈α∂to␈α∞regard␈α∂a␈α∞proposition␈α∂as␈α∞a
␈↓ ↓H␈↓function␈α
from␈α
possible␈α
worlds␈α
to␈α
truth␈α
values.␈α
 I␈α
would␈α
prefer␈α
to␈α
regard␈α
propositions␈α
as␈α
abstract
␈↓ ↓H␈↓entities␈αand␈αhave␈αa␈αfunction␈α␈↓↓holds(proposition,world)␈↓␈α-␈αassuming␈αI␈αwere␈αusing␈αpossible␈αworlds.␈α My
␈↓ ↓H␈↓approach reduces to Montague's if I have an extensionality axiom

␈↓ ↓H␈↓(1) ␈↓↓∀w.holds(prop1,w)≡holds(prop2,w) ⊃ prop1=prop2␈↓

␈↓ ↓H␈↓and

␈↓ ↓H␈↓(2) means establishing the existence of a proposition corresponding to every Montague predicate.

␈↓ ↓H␈↓        As you see, I found your paper very stimulating.

␈↓ ↓H␈↓        Many thanks for your hospitality in Amherst, and I am looking forward to March.


␈↓ ↓H␈↓Best regards,



␈↓ ↓H␈↓John McCarthy
␈↓ ↓H␈↓Director
␈↓ ↓H␈↓Professor of Computer Science

␈↓ ↓H␈↓P.S.␈αConsider␈α␈↓↓"He␈αtook␈α
a␈αspoonful␈αof␈αsoup␈α
and␈αfound␈αa␈α∨y␈α
in␈αit"␈↓.␈α It␈αis␈α
not␈αat␈αall␈αsuggested␈αthat␈α
he
␈↓ ↓H␈↓only␈α
took␈α
one␈α
spoonful␈α
of␈α
soup.␈α
 It␈α
is␈α
suggested␈αthat␈α
he␈α
only␈α
found␈α
one␈α
∨y.␈α
 It␈α
seems␈α
to␈α
me␈αthat
␈↓ ↓H␈↓␈↓↓"John␈αtook␈αa␈αspoonful␈αof␈αsoup.␈α He␈αfound␈αa␈α∨y␈αin␈αit".␈↓␈α has␈αthe␈αsame␈αproperty.␈α The␈αuniqueness␈αis
␈↓ ↓H␈↓provided by the sentence containing ␈↓↓"it"␈↓.