Page 45 - Studio International - May 1972

consequences of allegiance to the Theory of in terms of its Own status (unspecified, —is art.
Types and of the idea of metalanguage ascent propositional etc.) and so attempts an account and
is a member of the class art.
• should be examined with respect, more of previous paradoxes in terms of its own.
importantly, to art. Whilst it might appear more convenient to
Which in part constitutes a form of
In utilising the notion of a metalanguage to talk of such paradoxes quite apart from a
resolution of this paradox. Later also the
discuss 'all other art entities' no definitive art- particular work of art, as will become apparent,
art-entities will be seen not as particulars but
status is attributable to such intentional forms the existence of the couplets as paradoxical is
as second intentional entities. The question is
without paradox in adherence to the Theory of too intimately related to the art entity 'adn' and
whether the essence of an, apn, and adn is that
Types. Because such work provides no ontology to the relationships between the intended
of being particulars related to the universal
of the work itself, essentially it must rely upon entities an, apn, and adn and to their status as
`art' or whether their relevance is as universals
its implicit inclusion in 'art'. There seems to be intentional forms for such discussion. The
in themselves. The classes implied in the terms
little point in making a distinction such as first following is thus by necessity an informal
an, apn, and adn might be seen as successive
and second order arts because if the function of representation of the paradoxes as they exist
sub-sets of the preceding set, the final set being
the second order art is in discussing the first (formally) in the work of art 'adn'.
a unit set. The question of the status of the
order art then there is no way in which the
entities as particulars or universals results in
• second order activity can attain an art-status— The paradox of an
the paradox of the divided entity in adn and
except implicitly. A paradoxical consequence of The first paradox (of an) is the paradox
`adn'. The complete succession in this respect
the reliance upon an implicit inclusion in art associated with the relationship between 'art is a case of maximum extension, minimum
is that the work depends for its art-status upon in extension' and 'art in intention'. In many
• inclusion as an extension in art, i.e. in extensional ways this paradox is associated with the more intention in an to minimum extension,
maximum intention in adn.
terms. The activity, therefore, in not general paradoxes in the relationship between
• developing an ontology which is capable of set-theory and semantics, but relies more
including the work itself and in not talking particularly on the peculiar relationship The paradox of apn
• explicitly of its status with respect to art, is between art and its entities, such that whilst The paradox of apn, the art-propositional
retrospectively descriptive rather than `art' as an extensional attribute represents the paradox, is more explicitly connected with
• prescriptive and self-referential. Thus whilst class of all art entities the intention of the `adn' and is based upon the implicit inclusion
• there might be an implicit prescription of what art entity is 'art'. Thus whilst dealing with art of apn in art as a real entity, i.e. dealing with
art ought to be and how art entities should be in extension the art entities bear a relationship apn instrumentally or in first intention. The

seen to relate to 'art', there is no means of of class membership to `art'; the 'art' is seen treatment of apn as a 'real' or non-intentional
establishing whether or not the art-entities also to bear a relationship of intentional entity enables the inclusion of the proposition
involved with such a prescription exemplify identicality with the art entity. It is this in the class represented by an in its status in
the prescribed state of affairs. couplet of relations which forms the paradox. reality and in its own universe of discourse (in
The use of the idea of a metalanguage Art entities and art are said to be logical intention). This is partially explained in terms
encourages the paradoxical state of affairs in functions of one another, i.e. each is the of the argument mentioned before which
which a highly developed ontology of art and a predicate in the definition of the other. To defines the class represented by apn as a mere
refined means of assigning art-values relies on a refer again to the propositional form of the sub-set of that implied in an (i.e. in terms of
regressive and unclear means of assigning art- implicit definition an). However the paradox of this state of affairs
values in achieving its own art-status. has already been inferred, and similarly in
is art. terms of apn: in talking of the essentially
The Three Paradoxes of 'adn' : propositional nature of an the entity an
an, apn & adn It is possible to say that the function of the art- qualifies for membership in the class of art-
The art-entity 'adn' in reality is subdivided entity is in disclosing 'art' by means of such a propositions. Each view is capable of including
into three further entities : an, apn, adn, the definition, whilst the propositional form defines the other in its theory. Thus the paradox exists
entities being respectively the nth (unspecified) the entity as art or as a member of the class here of no single exclusive theory, while each in
art entity, the nth art-proposition, and the nth `art'. In talking of art as a class of such predicating the other in its definition maintains
(and only) art definition which defines itself as disclosures of art, the circuitous and a mutually supportive couplet of paradoxical
the sole member of the class 'art'. Each paradoxical state of affairs implied is that in definitions. The paradox exists in the reliance
expresses a paradoxical couplet of definitions which knowledge of art and knowledge of upon inclusion in art in extensional
which are formal representations of the artworks each apparently precede the other. `Duchampian' terms whilst the intention in
paradoxical situations alluded to in the foregoing Later in the resolution of the paradoxes of adn developing art in propositional terms lies in the
introduction. Each successively re-defines art a distinction is made between essentially intentional nature of propositions.
215