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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ ∧UBill wants to have an affair with Tom's wife

␈↓ α∧␈↓␈↓ αTWe␈α
are␈αsurprised␈α
when␈αthe␈α
ambiguity␈αof␈α
the␈αabove␈α
sentence␈αis␈α
pointed␈αout.␈α
 Our␈αcommon
␈↓ α∧␈↓sense␈α
reaction␈α
to␈α
the␈α
ambiguity␈α
and␈αpresent␈α
philosophical␈α
reactions␈α
are␈α
quite␈α
different,␈α
and␈αI␈α
think
␈↓ α∧␈↓the␈α∞common␈α
sense␈α∞reaction␈α∞is␈α
better.␈α∞ The␈α
common␈α∞sense␈α∞reaction␈α
is␈α∞localized␈α
to␈α∞the␈α∞sentence␈α
in
␈↓ α∧␈↓question,␈αwe␈αtry␈αto␈αdetermine␈αwhich␈αreading␈αis␈αappropriate␈αif␈αthere␈αis␈αsome␈αreason␈αto␈αsuspect␈αthat
␈↓ α∧␈↓Bill␈αmay␈α
not␈αboth␈αknow␈α
the␈αwoman␈αby␈α
sight␈αand␈αknow␈α
that␈αshe␈αis␈α
Tom's␈αwife.␈α
 Having␈αdecided
␈↓ α∧␈↓the␈αcase␈αin␈αpoint,␈αcommon␈αsense␈αis␈αfinished␈αwith␈αthe␈αsentence.␈α The␈αphilosophical␈αreaction,␈αwhich
␈↓ α∧␈↓is␈α∂also␈α∂the␈α∂reaction␈α∂of␈α∂AI␈α∂researchers,␈α∂is␈α∂to␈α∂devise␈α∂a␈α∂formalism␈α∂in␈α∂which␈α∂the␈α∂two␈α∂readings␈α∞are
␈↓ α∧␈↓expressed by different formal sentences.

␈↓ α∧␈↓␈↓ αTThe␈α
philosophical␈α
approach␈α
would␈α
be␈αfine␈α
if␈α
it␈α
we␈α
could␈αsolve␈α
the␈α
problem␈α
once␈α
and␈αfor␈α
all.
␈↓ α∧␈↓However,␈α∂it␈α∂may␈α∞be␈α∂that␈α∂ever␈α∞more␈α∂complicated␈α∂examples␈α∞of␈α∂this␈α∂kind␈α∞could␈α∂be␈α∂devised.␈α∞ The
␈↓ α∧␈↓approach␈α∀of␈α∪making␈α∀basic␈α∀revisions␈α∪in␈α∀the␈α∀syntax,␈α∪semantics␈α∀and␈α∀ontology␈α∪of␈α∀the␈α∀logic␈α∪of
␈↓ α∧␈↓intensions␈αseems␈α
to␈αbecome␈α
increasingly␈αpedantic,␈αand␈α
we␈αare␈α
led␈αto␈αspend␈α
our␈αtime␈α
on␈αexamples
␈↓ α∧␈↓that never arise in common sense contexts.

␈↓ α∧␈↓␈↓ αTMaybe␈α∩circumscription␈α∩or␈α∩some␈α∩other␈α∩form␈α∩of␈α∩non-monotonic␈α∩reasoning␈α∩can␈α∩make␈α∩the
␈↓ α∧␈↓common sense approach work, but I don't have a detailed proposal.  The idea is the following:

␈↓ α∧␈↓␈↓ αTShould␈α
it␈αbe␈α
the␈αcase␈α
that␈αBill␈α
wants␈α
to␈αhave␈α
an␈αaffair␈α
with␈αthe␈α
woman␈αand␈α
knows␈α
she␈αis
␈↓ α∧␈↓Tom's␈α∂wife␈α∂and␈α∂the␈α∂speaker␈α⊂does␈α∂not␈α∂wish␈α∂to␈α∂commit␈α∂himself␈α⊂on␈α∂whether␈α∂the␈α∂fact␈α∂that␈α⊂she␈α∂is
␈↓ α∧␈↓Tom's␈α⊂wife␈α⊂contributes␈α⊂to␈α⊂Bill's␈α⊂wish,␈α⊂then␈α⊃the␈α⊂sentence␈α⊂is␈α⊂not␈α⊂␈↓↓ambiguous␈α⊂in␈α⊂the␈α⊃context␈↓,␈α⊂both
␈↓ α∧␈↓readings␈αare␈αtrue␈α
in␈αall␈αpossible␈α
worlds␈αin␈αwhich␈αthese␈α
other␈αfacts␈αare␈α
true.␈α Therefore,␈αwe␈α
try␈αto
␈↓ α∧␈↓say that ␈↓↓the readings are equivalent in the world unless there is a reason why they aren't␈↓.

␈↓ α∧␈↓␈↓ αTMaking␈α~this␈α→work␈α~requires␈α→solving␈α~two␈α~problems.␈α→ First,␈α~we␈α→may␈α~need␈α~to␈α→apply
␈↓ α∧␈↓circumscription␈α∂to␈α∞meaning␈α∂itself,␈α∂i.e.␈α∞two␈α∂phrases␈α∂have␈α∞the␈α∂same␈α∂meaning␈α∞unless␈α∂there␈α∂is␈α∞some
␈↓ α∧␈↓reason␈α⊃why␈α⊂not,␈α⊃and␈α⊃I␈α⊂haven't␈α⊃seen␈α⊃how␈α⊂to␈α⊃write␈α⊃this␈α⊂formally.␈α⊃ Second,␈α⊃if␈α⊂we␈α⊃are␈α⊃to␈α⊂follow
␈↓ α∧␈↓common␈α
sense,␈α∞the␈α
ambiguity␈α
shouldn't␈α∞even␈α
be␈α∞noticed␈α
unless␈α
there␈α∞is␈α
a␈α
reason␈α∞to␈α
do␈α∞so.␈α
 This
␈↓ α∧␈↓suggests␈α
a␈αformalism␈α
in␈αwhich␈α
the␈αsentence␈α
implies␈αthe␈α
the␈αconsequences␈α
of␈αboth␈α
readings␈αunless
␈↓ α∧␈↓there␈αis␈α
a␈αreason␈α
why␈αnot␈α
and␈αis␈α
implied␈αby␈α
anything␈αthat␈α
will␈αimply␈α
either␈αreading␈α
unless␈αthere␈α
is
␈↓ α∧␈↓a␈αreason␈αwhy␈αnot.␈α A␈αcomputer␈αprogram␈αthat␈αworked␈αthis␈αway␈αwould␈αnever␈αproduce␈αtwo␈αversions
␈↓ α∧␈↓of the sentence unless it had to.

␈↓ α∧␈↓␈↓ αTThe␈α∂need␈α⊂for␈α∂this␈α⊂approach␈α∂would␈α⊂be␈α∂obvious␈α⊂if␈α∂we␈α⊂could␈α∂find␈α⊂examples␈α∂in␈α⊂which␈α∂the
␈↓ α∧␈↓modal approach and introducing concepts as objects both led to infinite regress.