Jacques Maritain Center :
Studies in Analogy /
by Ralph McInernyIn his recent book The Logic of Analogy,{1} Ralph M. McInerny makes the repeated claim that "'analogy' is analogous." In the pages that follow this claim will be examined in some detail and an attempt made to fill out McInerny's terse account. The issues raised by the dictum "'analogy' is analogous" are extremely difficult and complicated. This present paper, therefore, does not pretend to solve these problems. The reflections of this paper are offered rather in the hope that the problems may be somewhat clarified and the issues at stake brought once again into clear focus.
To
facilitate the examination of
the meaning of "'analogy' is
analogous," we shall take as
our point of departure Austin
Farrer's view that analogy
presupposes complexity in the
things compared.{2} The
adoption of this insight
commits us to the following
general formulation of
analogy: "x
is analogous to y
with respect to z."
If we substitute for the word
"analogy" the word "like" we
shall be further committed, at
least tentatively, to treat
analogy as a species
of likeness. It will somewhat
simplify matters if the
linguistic issues are kept
distinct from the ontological
issues. We have in mind here
McInerny's distinction between
dicuntur and
sunt and
betwen rationes
and entia. This
qualification demands a
revision of the proposed
schema so that it reads: the
expression 'a' is like the
expression 'b' with respect to
C (where C is a property
signified by 'a' and 'b' in a
given context).{3} Such a
general formulation of analogy
is calculated to rule out, at
least for purposes of the
present paper, the need to
consider things
claimed to analogous.
The view of
analogy proposed here is very
much like a definition per
genus et per differentiam in
the following way: both
proceed on the assumption that
some properties signified by
expressions are complex in the
sense of being analyzable into
two or more properties. We
offer as a paradigm for
complex property the
property of being human signified
by the word "man." This
property can be analyzed into
the property of
being animal and the
property of being rational
(signified, respectively, by
the expressions "animal" and
"rational" in terms of which
"man," traditionally, has been
defined).
In addition
to providing a paradigm for
complex property (and
indirectly for complex
expression) demanded by the
rubric "x
is like y
with respect to z,"
the word "man" is useful in
carrying the inquiry into the
meaning of "'analogy' is
analogous" one stage farther.
Employing
the Lxyz formula
let us consider what it would
mean to say "man" and "horse"
are analogous in meaning. Let
"man" signify the properties
of being an animal
and of being
rational (dubbed
respectively A and R) and let
"horse" signify the properties
of being an animal and
being a quadruped
(dubbed respectively A and Q).
We are now in a position to
claim that "man" is analogous
to "horse" with respect to A.
Customarily, however, the
expression "animal" as
predicated of horses and men
is acknowledgedly univocal.{4}
We cannot, therefore,
harmonize the general schema
of analogy with the claim that
"animal" is univocal, for on
the latter assumption the
comparison of "man" and
"animal" is an instance of the
rubric "x
is the same as y
with respect to z"
rather than of the rubric "x
is like y
with respect to z."
Nevertheless our example seems
to meet Aquinas' criterion
that analogy be a via
media between
univocity and equivocity.{5}
To be univocal two expressions
must have exactly the same
signification i.e. signify
exactly the same properties,
(e.g. "a" signifying FG and
"b" signifying FG). By parity
of reasoning two expressions
are equivocal if they signify
no properties in common (e.g.
"a" signifying FG and "c"
signifying LM). The example
offered above avoids both
extremes, the expressions
"man" and "horse" are partly
univocal (i.e. they have A in
common) and partly equivocal
("man" signifies R and "horse"
signifies Q). The admission of
partial univocity, however,
seems to be ruled out by
McInerny's caution (which
seems to be well founded in
the Thomistic tradition)
..."we must never confuse the
ratio communis of
an analogous name with the ratio
communis of the
univocal name."{6} Granted
this proviso, the likeness at
the basis of analogical
comparisons cannot be
univocity. This insight could
be made more explicit in the
case of the example under
consideration as follows:
(1) m and h are analogous in meaning if m signifies A1R and h signifies A2Q and A1 is like but not identical with A2 i.e. [L(A1, A2)] & (A1 ≠ A2).
The clause [L(A1,A2)]
& (A1 ≠ A2)
tells us (a) A1 is
like A2 (in some
undefined sense of "like") and
(b) specifies that however
"like" is to be defined it
must not be defined in terms
of identity. The clause fails,
however, to furnish any
positive clue whatsoever about
the nature of likeness which
would qualify for
incorporation into an adequate
definition of analogy.
In his The
Logic of Analogy
McInerny speaks of the... "commune
analogicum which is
opposed to the genus
univocum."{7} We
shall attempt to understand
this within the framework of
our proposed schema. Could the
ratio communis of
analogous expressions be
analogy?{8} As unpromising as
this idea sounds let us pursue
it a little farther. For [L(A1,
A2)] & (A1
≠ A2)
let us substitute AN(A1,A2).
The introduction of this
clause in (1) would involve
treating the genus of animal
as analogical. McInerny does
speak of treating genus, in
certain contexts, largo
modo, though it is
quite clear that the genus of
animal would not
be included in this category.
At this point we shall persist
in drawing out the lessons of
our chosen example while
recognizing that it
constitutes an extension of
McInerny's genus largo
modo. The
difficulties with treating
analogy as the ratio
communis of analogous
expressions can be brought out
in the following manner.
Generalizing (1) we arive at
the following definition of
analogy:
If for [L(G1, G2)] & (G1 ≠ G2) we substitute AN(G1, G2) we derive the following formula:(2) Two expressions x and y are analogous if x signifies G,F and y signifies G2H and [L(G1, G2)] & (G1 ≠ G2).
(3) Two expressions x and y are analogous if x signifies G1F and y signifies G2H and AN(G1, G2).A number of difficulties emerge in connection with (3). First, the definition is overtly circular in that it defines analogy in terms of itself. Second, if one attempts to avoid the circularity by an appeal to differences of types claiming that the clause AN(G1, G2) is concerned with analogous properties rather than analogous expressions, it is difficult to see what has been gained. Presumably what it means to say G1 and G2 are analogous is that G1 and G2 are analyzable respectively into, say, LM1 and M2N. Such an interpretation is open to two objections. In the first place, even if it does not mean the same to say that properties are analogous as to say expressions are analogous, the notion of analogous properties is no clearer than the notion of analogous expressions. No clarity has been achieved by the introduction of the clause AN(G1, G2). In the second place, the same difficulties recur in the case of M1 and M2 as with G1 and G2. To subject M1 and M2 to the same analysis of G1 and G2 would lead to an infinite regress. nor could the regress be avoided by claiming that the expressions "s" (signifying G1) and "t" (signifying G2) are analogous, since the same claim would now have to be made for, say, "v" (signifying M1) and "w" (signifying M2) and so on ad infinitum.
Third
(and this is directly related
to this last comment) if we
are to succeed in specifying a
meaning for "'analogy' is
analogous," it would seem that
the expression "analogy"
itself must be included among
the possible substitution
instances for x
and y in (3).
Failing this we should be
specifying what it means to
say that two expressions other
than the word
"analogy" (but falling under
the general definition of
analogy) are analogous. The
moral of this being that a
part of what is meant by
"'analogy' is analogous" is
that the expression "analogy"
itself can be a substitution
instance for x
and y in (3). We
shall now explore this
possibility in some detail.
On the
basis of the submission just
made the claim "'analogy' is
analogous" involves a
comparison of two occurrences
of the expression "analogy"
itself. Let us begin with a
comparison of "a1"
and "a2" (two
occurrences of "analogy" in
the sense of analogy of
attribution). We shall first
analyze "a1" along
the following lines. The
expression "healthy1"
and "healthy2" are
analogous by analogy of
attribution. This claim is to
be made good by showing that
"h1" and "h2"
conform to the Lxyz
formula. There is, however, a
prior question that demands
attention, namely: In virtue
of what characteristic or
characteristics are "h1"
and "h2" analogous
by analogy of
attribution? On closer
scrutiny "h1" and
"h2", respectively,
turn out to be elliptical for
"x is the
cause of health" and y
is the sign of health"{9}
where health
in the expanded expressions is
being employed in the primary
sense (i.e. as predicated of
living organisms). We shall
now attempt to specify the
necessary characteristics of
analogy of attribution.{10}
They are: (A) "h1"
and "h2" are dyadic
predicate terms of the form
"...R..."; (B) the first slot
in "...R..." is a place marker
for an individual variable;
"C) the second slot in
"...R..." is a place marker
for a monadic predicate term
employed in its primary sense.
It is not
difficult now to show that "a1"
(the comparison of "h1"
and "h2") conforms
to the Lxyz
formula. The substitution
instances for x
and y are
dyadic predicate terms of the
form "...R..." ("h1"
and "h2" are such
terms) while z
serves as a place marker for
the characteristics ABC.
Making the appropriate
substitutions we get Lh1h2ABC
which is clearly of the Lxyz
form. What it means,
then, to say that "h1"
and "h2" are
analogous by analogy of
attribution is that they are
similar with respect to ABC.
Strictly speaking we should
say that "h1" and
"h2" are the
same with respect to
ABC, but if we do we run afoul
of McInerny's caution..."we
must never confuse the ratio
communis of an
analogous name with the ratio
communis of the
univocal name." Have we not
done this very thing here? But
this is not the only
difficulty. So far we have not
succeeded in comparing "a1"
and "a2". We have
been preoccupied with showing
that "h1" and "h2"
are bona fide
instances of analogy of
attribution. To facilitate a
comparison of "a1"
and "a2" we could
analyze "wealthy1"
and "wealthy2"
along the lines of "healthy"
above and let this count as an
analysis of "a2".
We encounter the same
difficulty as before. Since "a1"
(analyzable into "h1"
and "h2") and "a2"
(analyzable into "w1"
and "w2") share the
characteristics ABC both are
univocal in that respect. We
have worked our way back to a
view of analogy of
attribution, at least, that is
based on univocity, a position
which presumably the dictum
"'analogy' is an analogical"
was originally calculated to
avoid.
Possibly
the difficulty just raised
could be avoided by pointing
out that the dictum "'analogy'
is analogous" does not
legislate for causes where two
occurrences of the expression
"analogy" with exactly the
same signification (viz.
analogy of attribution) are in
question but only for cases
where different though related
senses of "analogy" are
involved. The word "analogous"
in "'analogy' is analogous"
tries to pick up this
"different though related
senses" just alluded to.
Presumably, then, a comparison
of "a1" (analogy of
attribution) and "a3"
(analogy of proper
proportionality) would be a
fairer sample of the situation
for which the dictum
prescribes. We shall now
explore this possibility.
If we take
as definitive Aquinas' claim
that analogy of proper
proportionality is "a
similitude of two
proportions,"{11} we can then
make some headway in preparing
the ground for a comparison of
"a1" and "a3".Both
Aquinas' and Cajetan's
treatment of proper
proportionality is based on
the mathematical model 2:4:3:6
with the appropriate weakening
of identity of relations
(here "half of") to similarity
of relations in fields of
investigation where
mathematical precision is
impossible.{12} In the
familiar proportionality
schema - God's essence is to
God's existence as a man's
essence is to a man's
existence - given St. Thomas'
proviso we are comparing R1
(the relation of the divine
essence to the divine
existence) with R2
(the relation of human essence
to human existence). To
facilitate the comparison one
could substitute "... is
appropriate to ..." for R1
and R2. Granted
difficulties will be
encountered in specifying a
precise meaning for "... is
appropriate to ..."
nevertheless it serves
meanwhile to focus attention
on the fact that we are
comparing two expressions of
the form "... R ...". As with
analogy of attribution we
shall attempt to enumerate the
characteristics of "a3"
and to show that it conforms
to the Lxyz
formula. The characteristics
are: (A)
x and
y in the Lxyz
formula are place-markers for
dyadic predicate terms of the
form "... R ..."; (D) the
comparison of such terms (e.g.
"... is appropriate to1 ..."
and "... is appropriate to2 ..."
is with respect to "... R ...
(contrast this with analogy of
attribution where R1
= "... cause of..." and R2
= "... sign of..."); (E) the
slots in "... R ..." are place
markers for variables ranging
over individuals, properties,
activities and so on. That "a3"
is of the Lxyz
formula can be shown by making
the appropriate substitutions
thus L:(R1, R2)
(ADE). We are now in a
position to compare "a1"
and "a3". They are
similar with respect to A but
different in the following
respects - "a1" has
characteristics BC and "a3",
characteristics DE. We now run
again into the old Phocian
rampart ..."we must never
confuse the ratio
communis on an
analogous name with the ratio
communis of the
univocal name." Working within
the prescribed limits we have
set for ourselves, we are
committed to the view that "a1"
and "a3" are the
same with respect to A and
clearly "the same with respect
to A" or "x
and y in the Lxyz
formula are place
markers for dyadic relations
of the form '...R...'" are as
univocal as one can get.
Perhaps the way around this
difficulty is to attempt to weigh
the characteristics. That "a1"
and "a3" exemplify
the form Rxy
is such a general property,
that given this criterion
alone all dyadic relational
terms are analogous. But
rather than eliminate this
characteristic all together
perhaps one or more of the
other characteristics could be
ranked higher in order of
importance. On the face of it,
it would be a tall order to
arbitrate between BC and DE
(since these are the respects
in which "a1" and
"a3" are claimed to
differ). In principle, one
line of analysis is closed to
us, namely, the unpacking of
AB and DE (treated as complex
properties) in the quest for a
common core. This is not
to say that it is
impossible to arbitrate
between BC and DE or that in
singling out BC and DE that
the last word has been said on
the selection of the
characteristics of analogy of
attribution and of analogy of
proper proportionality. It is
safe to say, however, that the
task of weighting the given
characteristics or the quest
for further characteristics,
if successful, would solve the
problem of analogy. If one can
contribute to that ultimate
solution even if only by
erecting the sign cul
de sac over certain
lines of investigation, then
this will be its own reward.
The reader
is likely to be as
disappointed with this paper
as a freshman with one of
Plato's dialogues. The problem
posed by the dictum "'analogy'
is analogical" is still
unsolved. It may be objected
that the failure to avoid
univocity in the foregoing
account springs from (a) the
classification of analogy as a
species of likeness and (b)
from the choice of the
man-horse model which is
acknowledgedly based on
univocity. This objection is
not without force. By way of
rejoinder, however, it should
be pointed out that the
alternative classification of
analogy as a species of
equivocity does not avoid the
difficulties encountered
above. One would still have to
show that "a1" and "a3" are
not totally equivocal or that
they have some property or
properties in common. We are
at once confronted with our
self-appointed task of finding
"something common" other than
univocity. Furthermore, while
it is true that the man-horse
model is based on univocity,
it primarily functions negatively
to rule out identifying
the ratio communis with
the genus univocum.
John E. Thomas
Philosophy Department
McMaster University
Hamilton, Ontario
* I am grateful to Professor Ralph M. McInerny of the
University of Notre Dame for his helpful criticisms of
an earlier draft of this paper. I must assume full
responsibility for any obscurities that remain
particularly where our views tend to differ.
{0} I am grateful to Professor
Thomas for permission to include here this essay. He
and I are continuing our discussion and expect to
publish more later.
{1} Ralph M. McInerny,
The Logic of Analogy
(the Hague: Martinus Nijhoff, 1961) pp. 4, 33, 166 ff.
It is clear from the last two references that McInerny
is concerned with the expression "analogy."
{2} One can force the problems for this view in the
case of God's nature which, according to tradition, is
simple. We shall have to advocate at least a notional
distinction of, for example, essence and existence in
God if our analogical schemata are to have any
purchase.
{3} The schema focuses attention on the properties as
signified rather than the properties as exemplified.
{4} Speaking "secundum
intentionem."
{5} Summa
Theologiae I q 13 a 5.
{6} McInerny ibid.,
p. 79.
{7} Ibid., p.
135.
{8} Put this bluntly the proposal would be rejected by
McInerny. Since. however, we are seeking to get at the
adjectival form of "analogy" in "'analogy is
analogous," if not analogy then something very much
like it seems to be called for.
{9} For the justification for this analysis see Summa Theologiae I
q 13 a 6, De
nominum Analogia cap. 2 para. 8 and E. L.
Mascall's Existence
and Analogy (London: Longmans, Green and
Co., 1949), p. 101 ff.
{10} I am not here prepared to do battle for these
characteristics. They have been arrived at simply on
the basis of generalizing examples taken from Aquinas,
Cajetan and Mascall for the purpose of illustrating
the sort of thing needed to clarify the meaning of
"'analogy' is analogous."
{11} ..."similitudo
duarum ad invicem proportionem"... De Veritate II,
11 c.
{12} Summa
Theologiae I q 13 a 2 c.f. De Veritate 9 a
12 and 9 a 13 and De
Nominum Analogia cap. 3, para. 24.
© 2011 by the Estate of Ralph McInerny. All rights reserved including the right to translate or reproduce this book or parts thereof in any form.