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\title{24.03 Paper on Conceptual Schemes}
\author{Matthew Gray}

\begin{document}
\maketitle

\section*{Introduction}

This paper will discuss some of the formulations of conceptual schemes
and try to evaluate wether these formulations are coherent.
Primarily, the focus will be on Davidson's notion and examination of
conceptual schemes and some serious potential problems that arise from
this formulation.

\par

\section*{Davidson's Conceptual Schemes}

Generically, a ``conceptual scheme'' is a complete set of concepts, a
complete view of the world.  Kuhn's paradigms could be considered one
form of conceptual scheme, while others, like Davidson, take a less
subtle definition.  Davidson presents the notion of a conceptual
scheme which is reflected by and wholly embodied by a language.  While
this point itself may be the subject of some contention, it is first
necassary to accept Davidson's equivocation of a ``conceptual scheme''
and a ``language''.\footnote{Though, more specifically, Davidson does
not seem to want it to be a one to one mapping, but a one to many
mapping, where a ``conceptual scheme'' is in fact an equivalence class
of languages under the equivalence relation ``is intertranslatable
with''.}  Given that a language is (according to Davidson) a complete
conceptual scheme, and that any language intertranslatable with
English shares the same conceptual scheme, Davidson generalizes the
conceptual scheme of English speakers to be that of all speakers of
natural language.

\par

In fact, Davidson further expands on this notion to claim that it is
impossible to have a conceptual scheme (and therefore, a language)
which is not wholly translatable into English.  Davidson seems to
admit the possibility that there could be disjoint conceptual schemes
which are subsets of the conceptual scheme associated with English,
but does not seriously explore this.

\section*{An Argument Against Davidson's View}

There are two pricniples which form a basis for a possible argument
against Davidson's view that there are no conceptual schemes distinct
from our own.  Those principles are:

\par

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If we can clearly imagine that {\bf p}, then this is good (but not conclusive) reason to think that it is possible that {\bf p}.
\par
\end{singlespace}
\end{newmargins}
and
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\begin{singlespace}
\par
If we can clearly imagine having good evidence for the proposition {bf p}, then this is good (but not conclusive) reason to think that the proposition that {\bf p} is possible.
\end{singlespace}
\end{newmargins}

\par

This yields an argument which shall involve the following symbols:

\begin{itemize}
\item{\sE} is the conceptual scheme the corresponds to our own, as embodied by English.

\item{\sS} is the conceptual scheme of a hypothetical set of beings
dubbed the ``Saturnians''

\item{\sP} is the conceptual scheme of a hypothetical set of beings
dubbed the ``Plutonians''

\end{itemize}

The argument presents a proposition {\bf x} that {\sE} is a subset of
{\sS} and that {\sP} is a subset of {\sS} and that {\sE} and {\sP} are
wholly disjoint.  It seems reasonable that humans could encounter the
Saturnians who could converse with humans without (conceptual)
difficulties after all the translation issues were resolved.  

\par

This argument is presented as a scenario in which humans encounter
some Saturnians who do in fact engage humans in translatable
conversation.  These Saturnians would explain to us that they also
knew of beings, the Plutonians, with whom they can also converse
fluently, but the Plutonians can not converse with humans at all.
Hence, {\sE} and {\sP} are disjoint subsets of {\sS}.

\par

This seems to allow for two disjoint conceptual schemes ({\sE} and
{\sP}) which satisfy the above principles, in that the scenario
described in the previous paragraph can be ``clearly imagined'' and we
therefore have good reason to think that it is possible.

\section*{The Nature of Disjoint Schemes}

Davidson argues agains the case of complete failure of translatability
by debunking some specific examples, such as, Whorf's claim that the
Hopi language contains untranslatable metaphysical concepts which
Whorf proceeds to describe in English.  Davidson's case here seems to
be strong, but it does not eliminate the possibility that there are in
fact schemes that have a complete failure of translation into {\sE}.

\par

The problem with such a scheme is it is inherently indescribable, in
English.  A scenario which would at least present a plausible nature
for such an alternate scheme follows:

\par

There is an experience {\bf e}, which, if experienced enlightens one
to a conceptual scheme ({\sN}) wholly disjoint from our standard scheme,
{\sE}.  The nature of this experience is, of course, indescribable,
just as explaining the experience of ``opening ones eyes'' may be
impossible to relate to a blind man.

\section*{Failure of Evidence}

One of the fundamental problems with this seeming argument against
Davidson is that it requires that one ``clearly imagine that there
exist concepts which are unimaginable in our conceptual scheme''.  The
question of whether one can clearly imagine that there are things that
are unimaginable, is dubious, at best.

\par

Davidson, it would seem, would want to discount the ability to
concieve of such things, or at least place them outside the realm of
the ``clearly imagined''.  More important, Davidson most definitely
wants to claim, that even given the scenario above describing
experience {\bf e}, if there were beings which held {\em only} the
conceptual scheme {\sN}, that any beahavior of theirs would not in
fact be interpreted as reflecting an alternative conceptual scheme,
but as simple incoherence of their behavior.  Hence, there would not
be evidence for distinct conceptual schemes, only evidence for
incoherent behavior.

\par

Davidson's reaction to the possibility of a human individual who has
experienced {\bf e} and therefore understands both schemes {\sE} and
{\sN} is unclear.  Most likely, he would want to claim that either the
individual could, in fact, describe the things in {\sN} in English, or
that if they couldn't that they were simply being incoherent.

\section*{Other Cases For Alternative Conceptual Schemes}

There seems to be a great amount of concrete evidence for concepts
which are fully out of the bounds of those expressible in English.
For example, though it is certainly possible to describe the process
of riding a bicycle in English, there certainly seems to be some
concepts associated with this that are not describable, as someone is
unlikely to learn to ride a bike by mere instruction in English.

\par

Further, there seems to be a great amount expressed in body language
and facial nuance that cannot be translated into word.  Additionally,
in a great many physical activities such as dance, or martial arts,
there are concepts learned such as ``frame'' and ``ki'' which are not
completely describable in English yet can be used to communicate and
require experience to fully grasp.

\par

One might counter-argue that these are in fact not ``concepts'', but
``skills'' in the case of the bicycling and other physical arts and
``feelings'' in the case of facial expressions.  This argument appears
weak as it seems difficult to formulate a definition of ``concept''
which does not include any of these things but includes most things
that we would qualify as ``concepts''.

\par

Another counter-argument to the above cases might be to claim that the
conceptual scheme {\sE} in fact includes all forms of communication of
an English speaker, not just the verbal.  This is contrary to
Davidson, but perhaps a reasonable admission.  It is however, weakened
by the fact that in order to deny the existence of alternative
conceptual schemes, the definition has to be further extended to
include not only all forms of communication of an English speaker, but
all the forms of communication that an English speaker might
learn.\footnote{If not, are these non-verbalized conceptss learned by
some individuals, but not others, indications of alternative
conceptual schemes?}  This, however, threatens to degenerate into a
discussion of the capacity of the human brain, such as discussing
whether or not it has the capacity to conceive of large cardinals.

\par

Using again Davidson's formulation of conceptual schemes, one could
counter the counter-Davidson argument\footnote{Though the result is
not in accordance with Davidson.} by stating that though there is a
set of concepts {\sN}, it does not constitute a conceptual scheme
which a being could actually hold because there are certain
fundamental concepts (perhaps such as object identity and infinitive
forms) contained in a {\em minimal conceptual scheme} {\se} which are
contained in all other conceptual schemes.  That is, there is a set
{\se} (comprised of concepts $\epsilon_1, \epsilon_2, \epsilon_3,$
...) which is a subset of all conceptual schemes {\sX} (comprised of
concepts $\epsilon_1, \epsilon_2, \epsilon_3,$ ..., $x_1, x_2, x_3,$
...).

\section*{Conclusion}

Conceptual schemes, as Davidson initially claims, seem to be fraught
with peril.  It is indeed difficult to improve intelligibility of
conceptual relativism through conceptual schemes, but Davidson's
argument against alternative conceptual schemes has similar problems
of intelligibility.

\par

It is the opinion of the author that both Davidson's argument and it's
counter-argument are incoherent by fault of the equivocation of
language and conceptual schemes.  However, given this requirement, the
counter-argument seems a strong one and Davidson's response alleging
the failure of the evidence is weak.

\end{document}
