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					                 Conceiving, Conceivability, and Modal Knowledge

                                  Thomas Kroedel
                         Merton College, University of Oxford

‘There could have been flying pigs’ – ‘How do you know?’ – ‘Can you conceive of a
world where pigs fly?’ – ‘Yes’ – ‘There you are’. Dialogues like this show that
conceivability are commonly assumed to play an important role in the explanation of
modal knowledge. However, this common assumption is flawed; or so I shall argu e.
   An explanation of modal knowledge will proceed along the following lines: we
find out whether or not a proposition p is conceivable, come to believe that p is
possible if we find p conceivable, and come to believe that p is impossible (or that
not-p is necessary) if we find p inconceivable. Thus, checking the (in-)conceivability
of a proposition is the method that produces our beliefs as to its (im-)possibility. For
this explanation to work, three conditions have to be satisfied:
   (I)     What is and is not conceivable is knowable without presupposing modal
   (II)    There is a reliable connection between a proposition’s
           (in-)conceivability and its (im-)possibility.
   (III)   What is and is not conceivable does not depend on our prior beliefs as to
           what is and is not possible.
I shall argue that no viable notion of conceiving satisfies all of (I)-(III). In particular,
the notion of conceiving that seems most suitable for explaining modal knowledge
fails to satisfy (III).
    It might be argued that (I) is bound to be false because conceivability is itself a
modal notion: that p is conceivable means that it is possible that someone conceives
that p. However, this problem can be overcome if we come to know about our abilities
to conceive by trying: we try to conceive that p, and, succeeding, we conclude that p
is conceivable, while we conclude that p is inconceivable if we fail. This does not
presuppose modal knowledge since trying, succeeding, and failing are non-modal
    However, analysing the content of conceiving (i.e. what is represented in an act of
conceiving) provides the clue for revealing the difficulties. Many cases of conceiving
involve mental imagery. However, what is represented, in an act of conceiving, by the
imagery itself is fairly limited. I can represent that pigs fly by imagining three pigs
flying towards me in V-shape formation, but, while holding the image constant, I can
also imagine that three robots that look just like pigs are flying towards me. All that
these two cases have in common is that everything ‘looks’ the same in both. Thus, the
imagery involved in an act of conceiving will only be able to represent that things
appear such-and-such a way. How they are represented as being requires an
interpretation of the imagery. This interpretation will consist of the (propositional)
thought that things are represented as being (and not merely appearing) thus-and-so
(e.g. that I represent genuine flying pigs).
   Since almost anything can appear in almost any way, these thoughts are doing the
main work in determining the content of our conceivings. However, what thoughts we
are willing to integrate in our conceivings depends on our prior modal beliefs. To take
a drastic example, we are unable to conceive the following:

                                Box with a non-self-identical beetle inside

But this is merely because we believe that it is impossible that something fails to be
self-identical. Thus, what is (in-)conceivable depends on our prior modal beliefs; (III)
is false. (Even though (I) holds and (II) at least seems to hold as well, since we will
find all and only those propositions conceivable that we believe to be possible. *)
    There are alternative notions of conceiving. On one of them, conceiving a
proposition may just amount to assuming that it is true, in a matter similar to
assuming a proposition in the course of a proof. On this understanding of conceiving,
many impossible propositions will count as conceivable (for instance, one may
assume (p & not-p) in a proof, for applying the ex falso quodlibet rule), and hence (II)
will be false. Also, one may construe conceiving as a success verb, such that per
definitionem only possible propositions count as genuinely conceivable. However, this
notion will fail to satisfy (I). Even if we apply the method of trying in order to find out
what is conceivable and thus circumvent the problem that conceivability is a modal
notion, this method alone will not enable us to decide whether we genuinely
conceived a proposition (in the success verb sense) or whether it merely seems to us
that we conceived it. For whether we believe that we genuinely conceived a
proposition still depends on whether we hold the prior belief that this proposition is
possible. (If someone believed that non-self-identical beetles were possible, she would
also believe that she conceives them, even though, on the success verb reading, they
are inconceivable.) Hence, the former belief cannot constitute knowledge unless the
latter does too; knowing what is genuinely conceivable presupposes modal knowledge
after all.
    In summary, there is no notion of conceiving that warrants the traditional hopes of
founding modal epistemology on conceivability.

     (II) might be false too. If we understand (II) as saying that in possible worlds sufficiently similar
to the actual world a proposition is conceivable if and only if it is possible, and (III) as saying that what
is conceivable does not vary with our prior modal beliefs, failure of (III) will entail failure of (II) if S5
modal logic holds and the following is true: (IV) in some sufficiently similar possible world our prior
modal beliefs differ from our actual modal beliefs. (Proof. Assume (II), not-(III), and (IV): in a
sufficiently similar world where prior modal beliefs differ (which exists by (IV) ), what is conceivable
differs as well (by not-(III) ), so what is possible differs too (by (II) ). But by S5, the modal facts don’t
differ; contradiction.)

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