The 'Is' of Identity
By Jon
Neivens
The 'is' of Identity.
The 'is' of identity refers to sentences
of the type "The Morning Star is the
Evening Star, " "Mark Twain is
Samuel Clemens, " or "Carl XVI
Gustaf is the King of Sweden. " But
it can also be seen within sentences like
"Seeing is believing" or, the Wittgensteinian's
favourite, "meaning is use." This
is usually interpreted as meaning that, since
the *is* can be taken as stating
*is the same as, * in way that wouldn't be
possible for predication, the *is* here has
an entirely different function. At the same
time, this aspect of identity statements
means it also has a *substitution property*
which, again, distinguishes it from predication.
For example, the sentence: "Carl XVI
Gustaf is the King of Sweden, " can
be interchanged to give: "The King of
Sweden is Carl XVI Gustaf." The resulting
sentence, whilst not identical, has a definite
and strongly related sense. This *substitution
property* cannot be seen as operating within
a sentence like "Carl XVI Gustaf is
eating," and it is largely this fact
upon which the distinction between *the 'is'
of predication* and *the 'is' of identity*
is based. BUT, and this is the crucial point
here, once we introduce the AIT notion of
the Modal Switch, this distinction proves
not to be cut and dried. This is seen when
you introduce a sentence like "Carl
XVI Gustaf is eating the apple. " This
would be analysed as follows: "Carl
XVI Gustaf' <Extantal Imbuant 'is' <Modal
Processant 'eating' <Modal Informant 'the
apple' <Extantal Objectant" Here,
the Extantal Objectant serves to establish
that the apple is the object to which the
Imbuant is referred, in such a way that the
mode of existence of the Imbuant is also
that of the Objectant.
This means that a *substitution* can also
occur in this case, to give "The apple
is being eaten by Carl XVI Gustaf."
Here, the mode of existence is transformed
from active to passive with regard to the
switched Imbuant, in order to preserve the
original relation wherein the Objectant is
referred to the Imbuant. Thus, the *substitution*
at work within the identity statement can
be seen as a particular form of Modal Switch.
The difference is that with the substitution
of "Carl XVI Gustaf is the King of Sweden,
" to "The King of Sweden is Carl
XVI Gustaf," the original relation is
preserved with no resultant change from active
to passive tense. It is the difference between
these two forms of Modal Switch that is important
here. This is because, in any form of identity
statement, the Modal Informant consists of
an Extantal Objectant alone. The Processant,
in this case 'is,' only has to perform its
standard function of initiating a separable
pertaining correspondence between the Imbuant
and the Informant.
In its more standard function, the Objectant
is a secondary sentential instantiation.
On the one hand, it extantialises something
separate from the Imbuant. But on the other
hand, in terms of the way it is related to
the Imbuant through a mode of the Imbuant's
existence that is also that of the Objectant.
This relation is maintained in the identity
statement, but here the Informant function,
created by the Processant, is focused directly
onto the Objectant. Thus the relation between
Imbuant and Objectant is necessarily compressed,
and is far more limited in scope than it
would be if mediated through a distinct mode
of existence. Consequently, the Modal Switch
has the same compressed form, appearing as
the *substitution property.* However, it
should be noted that not all sentences where
the Modal Informant consists of an Extantal
Objectant alone display this *substitution
property.* An example of this would be a
*generic implication* type sentence like:
"The whale is a mammal." So, where
the Modal Informant consists of an Extantal
Objectant, the correspondence function of
the Processant has a *compressed form, *
where there is no scope for tense adjustment.
The Modal Switch either produces sentences
that make sense, and thus have a *substitution
property,* or do not. Therefore, identity
statements depend upon three things.
1) They depend upon the Processant, which
is only required to work in EXACTLY THE SAME
WAY AS WITHIN PREDICATION STATEMENTS.
2) They must have a Modal Informant which
consists of an Extantal Objectant alone.
3) There must be a SEMANTIC EQUIVALENCE between
Imbuant and Informant/Objectant, which allows
them to display the *substitution property.
*
The Processant function itself has to do
with *correspondence* which has nothing to
do with identity, rather, it allows for two
semantic correspondences to refer to the
same thing (whatever is extantialised within
the Imbuant) in such a way as to be separable.
What is important as far as AIT is concerned,
is to show that beyond its reliance on this
basic correspondence, all other characteristics
specific to identity statements can be accounted
for by reference to semantic/syntactic factors
other than the Processant function.
With identity statements, and, more generally,
any kind of sentence where the Informant
consists solely of an Objectant, the correspondence
function of the Processant
ensures that the Objectant functions as an
Informant, and hence limits its capacity
to be a secondary Extantal Imbuant. In other
words, whatever is marked out in the Objectant
phrase applies to whatever is extantialised
by the Imbuant.
This means that a *substitution* can also
occur in this case, to give "The apple
is being eaten by Carl XVI Gustaf. "
Here, the mode of existence is transformed
from active to passive with regard to the
switched Imbuant, in order to preserve the
original relation wherein the Objectant is
referred to the Imbuant. Thus, the *substitution*
at work within the identity statement can
be seen as a particular form of Modal Switch.
The difference is that with the substitution
of "Carl XVI Gustaf is the King of Sweden,
" to "The King of Sweden is Carl
XVI Gustaf, " the original relation
is preserved with no resultant change from
active to passive tense. It is the difference
between these two forms of Modal Switch that
is important here. This is because, in any
form of identity statement, the Modal Informant
consists of an Extantal Objectant alone.
The Processant, in this case 'is, ' only
has to perform its standard function of initiating
a separable pertaining correspondence between
the Imbuant and the Informant. In its more
standard function, the Objectant is a secondary
sentential instantiation. On the one hand,
it extantialises something separate from
the Imbuant. But on the other hand, in terms
of the way it is related to the Imbuant through
a mode of the Imbuant's existence that is
also that of the Objectant. This relation
is maintained in the identity statement,
but here the Informant function, created
by the Processant, is focused directly onto
the Objectant. Thus the relation between
Imbuant and Objectant is necessarily compressed,
and is far more limited in scope than it
would be if mediated through a distinct mode
of existence. Consequently, the Modal Switch
has the same compressed form, appearing as
the *substitution property. * However, it
should be noted that not all sentences that
where the Modal Informant consists of an
Extantal Objectant alone display this *substitution
property. * An example of this would be a
*generic implication* type sentence like
"The whale is a mammal. " So, where
the Modal Informant consists of an Extantal
Objectant, the correspondence function of
the Processant has a *compressed form, *
where there is no scope for tense adjustment.
The Modal Switch either produces sentences
that make sense, and thus have a *substitution
property, * or do not. Therefore, identity
statements depend upon three things.
1) They depend upon the Processant, which
is only required to work in EXACTLY THE SAME
WAY AS WITHIN PREDICATION STATEMENTS.
2) They must have a Modal Informant which
consists of an Extantal Objectant alone.
3) There must be a SEMANTIC EQUIVALENCE between
Imbuant and Informant/Objectant, which allows
them to display the *substitution property*.
The Processant function itself has to do
with *correspondence* which (as I hopefully
made clear in Part One) has nothing to do
with identity. Rather, it allows for two
semantic correspondences to refer to the
same thing (whatever is extantialised within
the Imbuant) in such a way as to be separable.
But what is important as far as AIT is concerned,
is to show that beyond its reliance on this
basic correspondence, all other characteristics
specific to identity statements can be accounted
for by reference to semantic/syntactic factors
other than the Processant function. With
identity statements, and, more generally,
any kind of sentence where the Informant
consists solely of an Objectant, the correspondence
function of the Processant ensures that the
Objectant functions as an Informant, and
hence limits its capacity to be a secondary
Extantal Imbuant. In other words, whatever
is marked out in the Objectant phrase applies
to whatever is extantialised by the Imbuant.
This can be seen most clearly within direct
statements of non-identity. For example,
in the sentence "Carl XVI Gustaf is
not the King of France, " the Objectant,
which does not correspond to the Imbuant,
has a far more explicit extantialisation,
and this becomes a statement concerning two
definite entities, as is not the case with
"Carl XVI Gustaf is the King of Sweden.
" Nevertheless, the statement of non-identity
still displays the
*substitution property. * In fact, here,
the *substitution property is more explicit,
* inasmuch as the relation between "Carl
XVI Gustaf is not the King of France, "
and "The King of France is not Carl
XVI Gustaf, " since it pertains to two
separate entities, says substantially the
same thing in a way which the two possible
statements of identity, "Carl XVI Gustaf
is the King of Sweden, " and "The
King of Sweden is Carl XVI Gustaf, "
does not. But, to reiterate, it is the Processant
function which allows the identity statement
to be about one entity, and not two. Nevertheless,
not all sentences where the Informant consists
of an Imbuant are identity statements. In
order for this to be the case, the Objectant/Informant
must have an equivalent particularity to
the Extantal Imbuant, either through the
use of a definite article, or of proper nouns.
A proper noun can have a definite article
phrase as its equivalent, and vice versa,
because the definite article always extantialises
a particularity, in such a way as to allow
the subsequent nouns or adjectives that are
syntactically linked to it to define this
particularity, and not each to have their
own referent. (I'll say more about the distinction
between the definite and indefinite articles
in the next section. ) that the identity
statement depends upon this equivalent singularity
of reference can be seen shown within such
sentences as: "The Munsters are the
Adams Family" or "Stan and Ollie
are Laurel and Hardy. " Again, the way
in which these kinds of sentences depend
upon the Processant function is such that
they either display or do not display correspondence.
But within a sentence like "Stan is
the Adams Family, " this correspondence
is rendered semantically impossible. Again,
this has to do with the limitation placed
upon the correspondence function, which has
a *compressed form, * wherever the Informant
consists of an Objectant alone.
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