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To refer to the content of this article, quote: INTERS – Interdisciplinary Encyclopedia of Religion and Science, edited by G. Tanzella-Nitti, P. Larrey and A. Strumia, http://www.inters.org
 Analogy
Alberto Strumia
I. What is Analogy? 1. Common
Meaning of the Word Analogy. 2. Analogy and Logic. 3. Analogy
and Metaphysics. - II. Analogy in the Aristotelian-Thomistic
Logic and Metaphysics. 1. Analogy of Attribution or Simple Proportion.
2. Analogy of Proper or Intrinsic Proportionality. 3. Analogy
of Improper Proportionality, Extrinsic or Metaphorical. 4.
Analogia Entis. 5. The Crisis of Analogy. - III. Analogy
and Theology. 1. The Knowledge of God and Divine Names. 2. Examples
of Analogy in the Scriptures. 3. Uses of Analogy in
Theology. 4. Analogia Fidei. - IV. Analogy and Science.
1. Analogy alongside Scientific Theory: Analogy and Experimental
Science. 2. Analogy alongside Scientific Theory: Analogy
and Mathematical Science. 3. Analogy within Scientific Theories.
4. The First Steps towards a Theory of Analogy. - V. The
"Profundity" of Analogy.
I. What is Analogy?
1. Common Meaning of the Word "Analogy". The
word "analogy" in its usual sense in modern English means
. Recently, the adjectival form of the world "analogy",
"analog", as opposed to "digital" or "numerical",
which is used in reference to two different ways in which electronic
devices work, has become of frequent use. The origin of the word
"analogy", as the Greek root (analoghía) suggests,
is however very ancient and is based on the mathematical concept
of "proportion" (a:b = c:d) which establishes
a similarity based on the equivalence of relations. One may think,
for instance, of the similarity of two triangles whose sides stand
in a fixed relation. The transfer of the word "analogy"
to  mathematics
and to logic
and philosophy dates back to Plato (427-347 B.C.) who, however,
never devised a theory of analogy. Aristotle (384-322 B.C.) would
be the first to give a systematic formulation of it in the field
of logic. In the Middle Ages, Thomas
Aquinas brought to fruition Aristotle’s work with an intention
at once philosophical and theological. In successive periods, beginning
with the Nominalists, analogy became, less and less understood.
It was gradually abandoned in the fields of logic and philosophy,
and restricted in its scope to the point of becoming a simple literary
"metaphor". And it is in this sense that the term is used
today in the context of hermeneutics.
2. Analogy and Logic. The need of introducing analogy in
Greek thought seems to arise from two types of problems: one which
is strictly "logical-linguistic" and the other more properly
"metaphysical". From the logical-linguistic point of view,
Aristotle, and later Thomas Aquinas, begin with the observation
that in common language —which expresses and therefore is a
sign the structure of how thought proceeds— the same term ("predicate")
can be attributed to different subjects in a "univocal",
"equivocal", and "analogous" way. In the first
case, the predicate has exactly the same meaning for the entire
class of subjects it is attributed to: for example, when we say
and , the term "man" corresponds to the same definition
"rational animal" in both instances. In the second case,
on the other hand, the same term is used with completely different
and uncorrelated meanings: as when one says , . In the second case,
the word "bull" corresponds to different definitions in
each of the two examples: in the first example, it involves an "adult
male bovine", in the second, "a communication written
by the Pope". Consequently, the use of the same word to signify
different things is adopted purely by convention, so much that equivocity
can be related to the language one uses and can be lost when one
translates into another language. In the third case, finally, the
same term is used with different meanings, but in a certain way
they have a real correlation and therefore the use of the same term
indicates a real similarity and not a mere choice of convention:
for example, as when one says , . Properly speaking, only a man
can be intelligent, but a theory can be said to be intelligent in
so far as it is an expression and "real effect" of the
intelligence of its author (and not by pure convention!).
3. Analogy and Metaphysics. The second class of problems
which have led to the idea of analogy is not purely logical and
linguistic, but more properly metaphysical, in that it is inherent
in things and is successively transferred to thought and language
with which one attempts to understand reality ( REALISM).
Greek thinkers confronted the problem of reconciling two seemingly
contradictory facts of experience:
the being of things and their "becoming", or in physical
terms, "motion". The "monist" solution — that
is, a solution based on the assumption that reality is founded on
only one constitutive principle (be it material or immaterial) —
requires that one take one of the two facts of experience as apparent:
if one admits only the reality of being, as a single undifferentiated
state, "being" can never be but itself, as it cannot change
into something different from itself; on the other hand, one cannot
explain the phenomenon of motion we observe in everyday experience,
as the passage from one state to another. Therefore, one must say
that this passage is not real but purely apparent (this is the solution
proposed by Parmenides, VI-V century, B.C.). We are then left with
the problem of understanding what produces this illusion in us.
If, on the other hand, one admits the reality of becoming only,
it is necessary to admit the contradiction that becoming, by the
very fact that it is, coincides with being, that multiplicity coincides
with oneness, that nothingness, that is non-being, is a state of
being, and becoming is a continuous oscillation between these two
contradictory states. However admitting this contradiction implies,
in the end, that knowledge is impossible (this is the extreme consequence
of Cratilus, following in the footsteps of Heraclitus, VI-V century
B.C.). To explain human experience completely, it is necessary to
hypothesize that being may exist according to "differentiated
states" that constitute a spectrum of modes of being lying
somewhere between being in its absolute fullness (God, Pure Act)
and its complete absence (nothingness). To understand correctly
the analogy of being we need the help of the accurate latin terminology:
ens means "being" as a subject capable to be, while
esse, is the property of "being". Being (esse)
is the principle by which a being (ens) is: "being"
(ens) is a term which is predicated in a differentiated but
not equivocal way of different subjects.
The notion of analogy of being corresponds, from the logical point
of view, to the metaphysical fact which assumes that being (esse)
is actuated ("participated") in differentiated modes and
degrees in the existing things. Thus, the logical theory of analogy
corresponds to the metaphysical theory of participation.
II. Analogy in the Aristotelian-Thomistic Logic and Metaphysics
In Aristotelian-Thomistic logic, three types of analogy are possible
(even if further distinctions have been introduced by later schools):
analogy of "attribution", or of "simple proportion",
analogy of "proper", or "intrinsic proportionality"
and analogy of "improper", or "extrinsic", or
"metaphorical proportionality".
1. Analogy of Attribution or Simple Proportion. Analogy
of attribution is usually presented with a classic example: "Tom
is ‘healthy’, his complexion is ‘healthy’, this
food is ‘healthy’, the air is ‘healthy’."
By observing this example, we note that the characteristic of being
"healthy" is proper only to Tom who is the only subject
which can be said to enjoy good health, being the only living being
of the things considered in this example. One cannot properly speak
of the other things as being "healthy" because they are
not living beings. One can say that in a certain sense these non-living
beings are "healthy" only in reference to the good health
of Tom, who alone is the subject of the predicate "health"
in the proper sense. For this reason, Tom is called the summum
analogatum or primum analogatum.
As for the other subjects, one can single out the relationship
they have with the healthy state of being of Tom: his healthy complexion
is a sign of his good health, in so far as it is an "effect"
of his good health. Healthy food is that which favors Tom’s
good health as one of its "causes". It must be understood
that the reference to the summum analogatum is neither conventional
nor accidental, but is instead founded on reality and confirmed
by experience (from the fact that healthy food really contributes
to the good health of someone who eats such food and that healthy
complexion is really a sign of good health, and so on and so forth).
For this reason, food, complexion, and climate are considered analogata
inferiora. It is this reference, which is founded on reality,
that makes the concept of attribution more than just "equivocal".
These things and realities are and remain different, but the common
name of the predicate expresses qualities which, even if they are
in themselves different, have, under a certain aspect, a direct
relationship with the quality of the primum analogatum (cf.
Thomas Aquinas, Summa Theologiae, I, q. 13, a. 5).
2. Analogy of Proper or Intrinsic Proportionality. Even
this second kind of analogy is usually illustrated with a classic
example which consists in comparing sight with intelligence. We
often use the idea of "vision" either in reference to
"eyesight" or in reference to the "mind’s understanding".
Thus, we say, for example, "the light of truth illuminates
the mind", "to understand at first glance", "a
philosophical vision of reality". In these examples, we have
a term which expresses an action (seeing) which we attribute to
two different subjects (the eye and the mind). In this type of analogy,
the similarity is established between the "relations"
between predicate and subjects and not between different senses
of the same predicate attributed to different subjects. This similarity
between the relations can be summarized by a formula which recalls
that of a mathematical proposition: . Nevertheless, when we write
a mathematical proportion, we establish two "equal" relations
(2:3 = 4:6), whereas in the case of the analogy of proportionality,
we state that two subject-predicate relations are not the same,
but "similar" (cf. Thomas Aquinas, De Veritate,
q. 2, a. 11). It must be emphasized that the action attributed to
the subjects is really connected with each of them. The faculty
of seeing is intrinsic to the eye and the faculty of understanding
is intrinsic to the mind: in both cases, we are dealing with a natural
capacity, a proper and therefore really possessed faculty. For this
reason, one speaks of analogy of "proper" or "intrinsic"
proportionality. We note that in this type of analogy there exists
neither a primum analogatum nor analogata inferiora:
we have instead a subject-quality relationship which can be applied,
in the proper sense, to a subject (the eye in the case of vision)
and in a "similar" sense to the other subject (the mind).
Seeing is proper of the eye, not of the mind. One can therefore
say that, in a certain sense, what takes the place of the primum
analogatum is not the subject to which the predicate is properly
attributed, but a relation between subject (the eye) and predicate
(able to see).
3. Analogy of Improper, Extrinsic, or Metaphoric Proportionality.
The third type of analogy is that of the "metaphor".
It involves a kind of analogy in which, unlike the two preceding
cases, there is no real basis for similarity, but which is founded
instead on a similarity discovered by the knowing subject who does
not see any cause-effect relation in the nature of the subjects
and the predicate nor any real similarity in their relations. Properly
speaking, it is not a real analogy, but we can consider it as such
in a loose or improper sense. A typical example one can use to illustrate
the concept of this kind of analogy is the following: "Tom
has the courage of a lion". Even in this case there is implicitly
a kind of proportion: we can, in fact, reformulate this example
in the following terms: . We see immediately that the quality "courageous"
through which Tom can be likened to a lion is a quality which can
be found in its highest degree in the lion: in a certain sense,
this recalls the analogy of attribution. Nevertheless, there is
a fundamental difference: there is no cause-effect relation between
the courage of the lion and that of Tom, in that Tom is not courageous
in virtue of a supposed participation in the courage of the lion.
We cannot therefore speak of the analogy of proportion. It is instead
a similarity which the knowing subject recognizes as an external
observer between the courage of Tom and the courage of the lion.
In this case, we have instead a similarity of relations between
the subject and its quality, as in the case of the analogy of proportionality.
Nevertheless, one cannot even speak of a true analogy of proper
proportionality. In fact, in order to have an analogy of "proper"
proportionality, the proportion that one wishes to establish would
have to be: Tom is to the courage (of Tom) as the lion is to the
courage (of the lion), whereas in the analogy of improper proportionality
the same quality of courage proper to the lion (lion-like courage)
is attributed to both Tom and the lion. Properly speaking, Tom has
human courage, while the "lion-like courage" is attributed
to him. We are dealing with a kind of "extrinsic" attribution,
in that one attributes a character which is natural and proper to
the lion to a natural endowment of Tom (cf. Thomas Aquinas, Summa
Theologiae, I, q. 13, a. 3, 1um).
4. Analogia Entis. The fundamental discovery of the metaphysics
of antiquity has probably been that of the analogy of being (analogia
entis). Unlike the different genera which, from the logical
point of view, are formalized in "universal" concepts
predicated in a univocal way of various subjects as "man"
is said with the same meaning of Tom, Dick, and Harry— "being"
is predicated in an analogous way of several subjects and rises
above the genera and universal concepts which describe them
(cf. Aristotle, Metaphysics, 998b, 22-27).
We note here two relevant aspects of the issue: a) in particular,
"being" is said of an object (substance) according to
an analogy of proper proportionality of the object and its properties
(accidents). This is a result of the fact that a property is always
a property of something and can exist only in something else and
not of its own accord. A color, a length, a temperature, etc. exist
always and only in an object, while an object possesses an autonomous
existence. Thus, one must say that a property is to its mode of
being as an object is to its mode of being, but the two modes are
not identical, though they may have in common the fact of being.
b) In addition, "being" is said of a finite object, which
has being by participation, and is said to be so according to an
analogy of proportion with respect to the Pure Act which is being
in itself and is the cause of the being of a finite object. A similar
property to that of "being" is also characteristic of
super-universal notions of "true", "one", and
"good" which, together with "being", are called
"transcendentals".
5. The Crisis of Analogy. The concept of analogy, which
finds its most complete development and use in the philosophy of
Thomas Aquinas, contains, beginning with Thomas Aquinas’ contemporaries,
the seeds of its future downfall. In fact, from as early as the
13th century, the two great schools of philosophical-theological
thought of Paris, where Albert
the Great (1200 ca.-1280) and later his disciple Thomas Aquinas
flowered, and of Oxford, the university of Roger
Bacon (1214-1252), Robert Grosseteste (1174-1253) and later of John
Duns Scotus (1275-1308) and William of Ockham (1280-1349), were
in opposition and would follow two different paths without ever
coming to a mutual understanding. The Aristotelian path of Albert
the Great and Thomas Aquinas, was to be of great importance especially
for Catholic theology and, three centuries later, would be officially
recognized in large part by the Council of Trent (1545-1563). The
Platonic path, prevalent in Oxford, would concentrate on the problem
of the mathematical formulation of the sciences, beginning with
Roger Bacon, creating the methodological premises for the development
of modern science.
In this way, the gradual departure of an ever more univocal and
mathematical scientific way of thinking from metaphysical and theological
analogy-based thought, took root. Duns Scotus would resolve the
analogy of being in a multiplicity of univocals just as William
of Ockham would dissolve the reality of universals in a pure name
(Nominalism) by denying to it a real existence outside of the mind.
This development would then have an influence on the philosophical
thought of Descartes
(1596-1650) and later of Kant
(1724-1805), with the success of Galileian and Newtonian science,
and would eventually lead to the end of the very possibility of
metaphysics as a science and consequently of theology as a systematic
science. Nevertheless, for several decades, we have been witnessing
a new turn in the sciences which seem to seek and in a certain sense
discover anew the concept of analogy with the purpose of confronting
new problems related to the theory of the logical and mathematical
foundation of sciences and to the complexity of self-organizing
structures. Even if it is too early to judge, one could say that
the concept of analogy, which was initially excluded from scientific
thought for fear of equivocity, now claims its place.
III. Analogy and Theology
The recourse to the concept of analogy in theology is necessary
for many reasons. It cannot be otherwise since human reason, which
is by its very nature creaturely, is able to approach the mystery
of God only if it maintains the distance between creature and Creator
by acknowledging that one can speak of God only by analogy and not
in a univocal or equivocal way. In the context of the metaphysics
of being, the analogia entis allows one to approach the problem
of God’s existence as the basis of the being of all things
and to predicate of God’s attributes and perfections starting
from the way in which these perfections are participated in God’s
works. But it is the very language of Revelation as presented in
Sacred
Scripture which uses analogy in its various forms, be they proper
or improper, as for example in the metaphor and even in the "parable",
to express, through human concepts, that which would otherwise remain
transcendent and ineffable in itself. The language of analogy is
then used by theologians (
THEOLOGY) in their attempt to approach, through recourse to images
and comparisons, the mysteries of faith, but also to see relations
between such things, thereby grasping a deeper, inner coherence
of God’s plan of salvation.
1. The Knowledge of God and Divine Names. The various
applications of the concept of analogy to theology lie on different
levels. The first question one asks concerns the knowledge of God,
either through human reason alone (
GOD, IV.1) or by
faith in what God revealed about Himself. Theologians have traditionally
taken two paths to this aim: the first is the "apophatic"
or "negative" way, typical of Eastern Christianity, which
emphasizes the fact that we can only know with certainty what God
is not, rather than what He is. Following this approach, such characteristics
as composition, corporeality, finitude, and so on and so forth,
are excluded from the notion of God. In addition to negative theology,
and inspired by a scriptural passage from Book of Wisdom (cf.
Wis 13,5) in which explicit reference to the concept of analogy
is made (
WISDOM, BOOK OF of, III.3), Western Christianity also developed
a positive theology. On the basis of the analogy of simple proportion,
it allows one to recognize in God a similarity with the perfections
found in creation, as effects whose summum analogatum is
God Himself (cf. Thomas Aquinas, Summa Theologiae, I, q.
12). It involves a cognitive approach which certainly does not dissolve
mystery in that, as the Fourth Lateran Council (1215) recalls, (DH
806).
Another classic theological problem which is closely tied to the
problem of the knowledge of God, is that of the titles one can correctly
attribute to God ("divine names"). This theme, already
treated by pseudo-Dionysius in De Divinis Nominibus, was
given a complete treatment by Thomas Aquinas who would let analogy
play a decisive role. First of all, he maintained that the names
which certainly denote what God is not (imperfections or ontological
or moral limits) cannot be attributed to God. He then states that
we can attribute to God the words we use to describe creatures,
but only by analogy, as our language refers mainly to what we know
of creatures. These are in fact an effect of which God is the cause,
a cause which cannot be known directly by us. We cannot speak of
Him univocally because God is a cause which is infinitely higher
than His effects and transcends their nature as He does not belong
to any genus. We cannot speak of Him equivocally, since there
is a cause-effect relation, real from the creatures towards God,
which distinguishes creatures from Him. Thus, the names signifying
God’s perfections can be used by analogy of proportion, God
being here the summum analogatum. When one says that something
is good, one says so more properly of God, who is good in and of
Himself, than of the creatures, who are good only by participation.
Other names can be attributed to God only metaphorically. This happens
either when one signifies a perfection by means of a name describing
a creature who possesses it or when, instead of the name of a certain
perfection, the creature’s name is attributed to God, having
the intention of attributing to Him that perfection. This happens,
for example, when in Holy Scripture God is called a "rock"
or "lion", with the intention of attributing to Him the
perfections of the rock and the lion (cf. Summa Theologiae,
I, q. 13).
2. Examples of Analogy in the Scriptures. It is proper
of the language of Holy Scripture to offer, through different literary
genres, a great wealth of analogies and metaphors. This is due,
as already mentioned above, to the need of expressing with human
words used primarily to describe creatures, contents regarding the
transcendent reality of God, which reason alone cannot reach and
which is not an object of common experience. It is God who communicates
His will and His plan through images based on analogy. It is asked
of Abraham to try to conceive of the immense number of descendents
of which he is called to be the father, by analogy with the great
number of stars in the sky and grains of sand in the sea (cf. Gen
15,5 and 22,17). Another example is the prophet Jeremiah, who is
invited by God to look at the renewal that God would bring about
in the house of Israel (Jer 18, 1-4), by considering the
analogy of the potter who forms and then destroys the work of his
hands to make it new over again. The prophets themselves were the
ones who spoke to the people through numerous images and analogies,
drawing from what happens in nature, in their own history, and in
the story of different peoples (Ez 31, 1-14; Hos 1,2-9;
Dan 2,31-45).
Jesus would speak in "parables" rather frequently to describe with effective
and coherent images, the reality of the Kingdom, in order to make it more understandable
to his audience. The expression frequently recurs in the Gospels (cf. Mt 13,1-41; Mk
4,1-34; Lk 8,4-18). This comparison is based on the "analogy of
proportionality". The use of images and metaphors establishes a simile between a
known reality and one that it unknown or difficult to understand, favoring the
transposition of properties and relations from the better known to the lesser known image.
The parable is often told in the form of a story whose argumentative force consists in the
narration of a fact (a fictitious but true-to-life fact) which the audience can understand
well and through which the audience can draw the logical conclusions. Such conclusions, by
dint of analogy, can be then applied in this case to the initially unknown reality so as
to understand some of its most important characteristics. The language of the metaphor and
parable, or if you prefer, of "narration", is particularly fitting to the human
mind. We find ourselves in a situation in which it is possible to identify a series of
unchanging relations between human beings and things, or between human beings themselves,
beyond the changing objects of experience. These relations can be used as logical,
cosmological, and anthropological coordinates to communicate a certain message. It is not
surprising, however, that the Word of God, which has also taken on the history and logic
of such a communicative and cognitive structure, taken together with the true humanity of
Christ, has recourse to it as to a kind of "fundamental human language".
From an hermeneutic point of view the language of analogy in Scripture
has a special role, that must be distinguished from the symbolic
one, which is also present. In the case of analogy an analogate
is always referred to, while symbolic language is intended to refer
to a reality beyond the limits of human discourse and language,
requiring completely new non-analogous categories. But
symbol remains incomplete without the help of analogy, since it
recalls a reality independent of symbol itself, with the risk of
conceiving mentally an infinite chain of symbols never attaining
its real object.
3. Uses of Analogy in Theology. Analogies are widely used
in Ecclesiology when speaking of the Church, by resorting to "figures",
as made for example by the Magisterium of the Second Vatican Council
(cf. Lumen gentium, 6). The mystery of the Church, in fact,
participates in the richness and transcendence of God, since she
has her origin in the mystery of God the Father’s plan of salvation
and is revealed and accomplished through the missions of the Son
and the Holy Spirit. To be expressed by words, the reality of the
Church needs the analogy of intrinsic and extrinsic proportionality.
Based on Sacred Scripture and the teachings of the Fathers of the
Church, theology employs different images for the Church: a flock
led by the shepherd, the Lord’s vine, a house built on a keystone
which is Christ, the Kingdom, the family and abode of God, and,
above all, God’s people and the Body of Christ. It should be
also observed that one must use this last analogy not in the metaphorical
but in proper sense (cf. Lumen gentium, 7; Pius XII, Mystici
corporis, 29.6.1943). The relationship between Christ and His
Church is likened, in addition, to the relationship between the
bride and the bridegroom, but also to the relationship of the head
to its body. The peculiarity of such analogy-based images lies in
the fact that none of them alone is adequate enough to express the
mystery of the Church (due to her being both visible and invisible,
temporal and eternal, one, yet present in many places; distinct
from her Bridegroom, and yet one with her Head, etc.), whereas all
of them together can play their part to clarify her character and
properties.
Classic examples of applications of analogy can be found in the teaching concerning the
sacraments: as stages of the "Christian life", they can be compared to the
various phases of the "natural life", be it individual or social, according to
an analogy of proper proportionality. In this way, Baptism is like "birth" to
the Christian life, Confirmation is like "coming of age", the Eucharist
is like nurturing oneself in one’s spiritual journey, and so on and so forth (cf.
Thomas Aquinas, Summa Theologiae, III, q. 65). In the life of grace, then, sin is
compared to death, so that one might understand its effects on the spiritual
soul, in analogy with what death brings about in the body. Even though such
uses come with the limitations inherent in any type of comparison, they have undoubtedly
aided our understanding of the mysteries of faith and facilitated its diffusion.
Concerning the relationship between scientific thought and religious
faith, the theological analogies used throughout history to clarify
the relationship between faith and reason (or between philosophy
and theology), are worth noting. In medieval thought, philosophy
is spoken of as the handmaiden of theology. Such a comparison, which
has been frequently presented in a reductive and instrumental way,
elicited Kant’s ironic response. Kant remarked that the handmaiden
should have preceded her mistress, like a torch, in order to light
the way. But the relationship between faith and reason has been
viewed as a marriage relationship as well, a typical image also
used to describe the relationship between nature and grace, stressing,
however, the greater dignity of the faith-husband pole. Contemporary
theology uses especially Marian and Christological analogies. Following
the first analogy, faith-word-Spirit is accepted and embraced by
reason-listening-Mary, thus "generating" the fruit of
Theology, where theology is used here in the strong sense of a wisdom
which participates, by dint of Revelation, in the uncreated Wisdom
of Christ. In the Christological analogy, reason and faith are seen
in relationship with one another as are human nature and divine
nature in the Person of the Divine Logos made man ( JESUS
CHRIST, INCARNATION AND DOCTRINE OF LOGOS). As Christ’s humanity
gives visible and historical expression to the divine nature and
person, so philosophy and reason give to theology and faith an indispensable
language to express, in a clearly limited and incomplete, but authentic
way, what one knows by faith, belonging to the transcendence of
God.
Concerning the history of theology and its relationship with scientific
thought, the essay of Joseph Butler (1692-1752) entitled The
analogy of natural and revealed religion in the constitution and
course of nature (1736) must be mentioned. In it, the author
presents the course of nature and human history as a great analogy
for the purpose of understanding the language and meaning of Christian
revelation. The work would then become famous for its great influence
on the thought of John
Henry Newman (1801-1890) who would often cite the work of this Anglican
bishop in his books.
4. Analogia Fidei. A different meaning for the word
analogy, at least when compared with its counterpart in Aristotelian-Thomistic
philosophy, is that present in the expression "analogy of faith"
(analogia fidei). It is first found in the letter of St.
Paul to the Romans (, Rom 12,6), where the Greek term analoghía
is used in the sense of "measure" or "proportion".
In the Catholic tradition, this expression has taken on a technical
character and signifies the inner coherence and harmony between
the truths of faith which cannot contradict each other. The recent
Catechism of the Catholic Church has defined it in the following
way: (CCC 114). The analogy of faith guides us in our interpretation
of the Old Testament in light of the New Testament. It is essential
indeed for a correct understanding of what the "development
of dogma" means. Under the guidance of analogy, such a development
must not be viewed as a change of the content of truth, but as a
consistent deepening of understanding of the same revealed truth.
Classic sources for this understanding can be found in St. Vincent
of Lerins (cf. Commonitorium, 53: PL 50, 668) and in John
Henry Newman (cf. An Essay on the Development of Christian Doctrine,
1845).
Reformed theologians, especially Karl Barth (1886-1968), made use
of the expression analogia fidei to indicate the one and
only source of knowledge of God, that of divine Revelation, as opposed
to analogia entis understood as the foundation of the path
that allows natural reason to reach a non-revealed knowledge of
God, a path which, in the Lutheran view, is denied at the root (LUTHER, MARTIN). Refusing the possibility of analogy-based knowledge
of God arising from the experience of creatures, such theologians
attempt to base the possibility and intelligibility of Revelation
solely on the gift of grace. According to Karl Barth, . One might
say of God only what God says of Himself, that is, his Word, Christ.
It should be observed, however, that such a perspective does not
seem to solve in a convincing way the problem of how to ground the
intelligibility and understanding of the revealed word, in that,
even though we are helped by grace, our understanding of God is
always expressed through our own words, which are the only words
we have at our disposal. "It remains true that the notions
chosen by Christ to introduce us to the divine mystery are still
human notions. Christ borrowed them from human language, from the
whole range of created realities. And it is on the basis of these
realities, objects of human experience, that is effected a purification
and development of meaning which are dictated by the necessities
of revelation [...]. If Christ can utilize all the resources of
the created universe to make us know God and the ways to God, it
is because the word of creation has preceded and left a foundation
for the word of revelation; it is because both one and the other
have their principle in the same interior Word of God. The revelation
of Christ presupposes the truth of analogy" (R. Latourelle,
Theology of Revelation, Alba House, New York 1966, pp. 366-367).
IV. Analogy and Science
Up to now, the concept of analogy has never been a part of any
scientific theory even if it has always in fact accompanied the
progress of science from the outside, suggesting new avenues of
research and new interpretations of results. This can be understood
by considering the fact that modern science, which employs the Galilean
method, is as mathematical as possible. In mathematics, as it has
been developed up to now, every symbol used in the same proof must
unambiguously correspond to a single definition. In the second place,
even when direct use of mathematics is not made, univocity is adopted
so as to avoid the possibility of ambiguity or of error. It is however
interesting to observe that in the last decades, research concerning
the science of complexity
and self-reference in different fields seem to show the theoretical
limits of univocity and to suggest an analogy-based approach.
1. Analogy alongside Scientific Theory: Analogy and Experimental
Science. The word "analogy" is often used by scientists
in their qualitative description of their results even if it has
never been a part of any scientific theory. In particular, analogies
have proven to be useful throughout the history of science and have
been used for a two-fold purpose: (a) to suggest a way to build
a theory (a heuristic purpose); (b) to aid in interpreting an already
developed theory which is similar to another theory because it has
a similar mathematical structure (a hermeneutic or interpretative
purpose). In both cases, analogy, however, does not play a direct
part in the mathematical formulation of the theory in that the symbols
used continue to have an unambiguous definition. And it must be
emphasized that from the Aristotelian-Thomistic point of view, we
are dealing with "analogies of proper proportionality",
that is, with similarities between relations. These similarities
lie at the root of any possible model describing certain facts of
experience. In particular, analogies, thus understood, can be said
to be "material", i.e. concerning the "physical structure"
of the systems to be described, or "formal", i.e. concerning
the "mathematical laws" (
LAWS OF NATURE) which describe and explain determined behavior of
physical systems.
"Material analogies" are useful in describing the properties of a system the
internal structure of which is still unknown: one assumes that the unknown structure of
the system may be similar to that of another well known system, governed by a known law.
One says, in that case, that a "model" has been proposed to describe a system. A
familiar example, in physics, is provided by the model of "elastic rigid balls",
which is adopted as an approximated description of the behavior of gas molecules. In such
a case the similarity between the model and the physical phenomenon is established on the
level of the structure, of the material components; as a consequence a similar behavior of
the two systems is also expected, and similar laws are supposed to govern them. It is the
case of analogy of proper proportionality, which can be expressed by the following
sentence: . A similarity between the relationships (balls-dynamics and molecules-dynamics)
is established, which is so tight to legitimate the use of the same law to describe both
systems within an acceptable error margin.
On the contrary, formal analogies are not based on a model of the physical
constituents of a certain system, but on mathematical equations
capable of describing its behavior without any hypothesis on the
material structure governed by such laws (cf. Nagel, 1961). This
way of proceeding is less natural to those who are not used to representing
things in mathematical terms, whereas it is completely obvious to
the mathematical physicist, used to substitute in his or her mind
the physical object with the mathematical equations which govern
its behavior. In certain cases, the formal equivalence of certain
equations, which however have different physical interpretations
of the same mathematical symbols, lead to new theories which are
difficult to formulate without the aid of such a formal analogy.
The most significant example of this can be found in wave mechanics
( QUANTUM
MECHANICS, I-II): the Schrödinger equation, which is the fundamental
equation of wave mechanics, is obtained through analogy with geometrical
optics and classical, analytical mechanics (
MECHANICS, III).
But aside from the heuristic aspect of analogy in the sciences,
there is also a hermeneutic aspect: analogy, in fact, can aid in
the interpretation or explanation of the behavior of a certain system
for which a certain model is adopted as it serves the purpose of
reducing a lesser known phenomenon to a better known one. Suffice
it to think of all of the microscopic models developed to explain
the behavior of a macroscopic system: the kinetic theory, for example,
gives, as a mechanical-statistical model of a thermodynamic macroscopic
system, a detailed understanding of the macroscopic processes involving
the variables which characterize the system. In this case, the analogy
which one forms is the following: . If we accept this analogy and
assume that it is possible to identify the laws of kinetic theory
with those of thermodynamics within an acceptable margin of error,
we can obtain a relationship between the kinetic theory quantities
and those of thermodynamics and thereby obtain a kinetic interpretation
of the latter: one may think, for example, of the conceptual identification
of the absolute thermodynamic temperature with the average translational
kinetic energy of the molecules in a gas. In this case, analogy
proves to be advantageous since it leads to an increase in understanding.
2. Analogy alongside Scientific Theory: Analogy and Mathematical
Science. If in physics, analogy does not play a direct role,
except as a methodology suggesting from the outside how to build
and interpret theories, formal analogy has a similar role in the
development of new mathematical structures. The latter are intended
to be based on simpler models for which one looks for a generalization
which keeps some of their formal properties. It is important to
keep in mind that in both physics and mathematics, analogy does
not directly come into play as an "internal" element of
the theoretical system, but plays a role in the building and interpretation
of science. It is true that in the internal structure of mathematics
there are biunivocal relations between elements of distinct sets
(isomorphisms, homeomorphisms, diffeomorphisms, etc.), but we are
not dealing, in this case, with real analogies of proper proportionality
in the way it is understood above, but instead to structural equivalence.
In these cases, there is a complete equivalence, and not only a
similarity between the relations. For this reason, such sets are
indistinguishable as far as the properties of the structure are
concerned and one says that each of these sets is a "model"
for the structure in consideration. In Aristotelian-Thomistic language,
one could say that these models are like the "species"
of the same "genus". A well-known example can be found
in the so-called "Euclidean models" of non-Euclidean geometry
and, more generally, in any mathematical model with an abstract
structure. Non-Euclidean geometry, for example, can be thought of
as abstractly defined by its axioms, regardless of the fact that
there are different realizations of any one of its models. Nevertheless,
as soon as we realize these models, they are not simply analogous
but completely isomorphic to each other. It is so because every
relation between the elements of the model corresponds to an equivalent
and not only similar relation to the elements of the other model.
In the example of non-Euclidean geometries, we can think of the
hyperbolic geometry of Bolyai which can have as model the Euclidean
model of Klein in the plane (cf. Courant and Robbins, 1996).
Another well-known example of two mathematical models with the
same structure can be found in quantum mechanics which admits a
two-fold representation in two isomorphic Hilbert spaces: that is,
the Schrödinger picture, formulated in terms of wave-functions in
an L2 Hilbert space (functions with a defined
square modulus) and that of Heisenberg,
expressed in terms of l2 vectors expanded on an
orthonormal basis of eigenfunctions (cf. Fano, 1971).
3. Analogy within Scientific Theories. The interest in analogy
and the research devoted to the development of a "scientific
theory of analogy" and a "method of demonstration"
based on the latter, seems to emerge inevitably in the study of
systems, be they biological, chemical, physical, mathematical, logical,
or other, which are organized according to "hierarchical levels".
Some of these levels cannot be reduced to more elementary ones (cf.
Cini, 1994), because they differ not only "quantitatively"
but "qualitatively". They have different natures but,
at the same time, something real in common. In this case, it seems
possible and useful to invoke the analogy of simple proportion or
that of proper proportionality.
Up to now, sciences have involved the search for components which act as fundamental
"parts" or "building blocks" to explain the structure of the universe
as a "whole", assuming that the parts have the same nature as the whole
(matter-radiation). In this scheme, the "building blocks" of the whole,
according to the Standard Model, are "quarks" and "gluons"
which bind them, which form particles once believed to be elementary, which in turn form
nuclei and atoms, which then form molecules, and finally, living cells and more complex
living organisms. Every level of this scale is considered perfectly homogeneous with the
other levels, and is made of the same matter and considered of the same nature. In a sense
which seems to contradict this way of framing the problem, qualitatively diversified (and
hence irreducible to each other) levels have a tendency of emerging in the same system. If
in fact one of these levels of organization (the "higher level") were in some
way decomposable to other, more elementary ones (the "lower levels") and if it
could be reconstructed through an appropriate recomposition of the latter, the higher
level would not be "qualitatively" different, but a simple
"superposition" of the lower levels. These do not represent absolutely disparate
properties which cannot be compared to each other, but instead constitute, different ways
of manifestation and realization of the same property, which can therefore be actuated not
always in the same way (that is, not univocally), but according to differentiated ways
which are really related to each other (that is analogically). In particular, we are faced
with a two-fold modality in the relationship between the whole and its parts: on the one
hand, we have a whole which is not reducible to the sum of the parts, but possesses a new
informative and unifying element which characterizes it as a whole. On the other hand, we
have parts in which there exists something similar to the whole. Such a structure is
commonly described by scientists as "complex" (cf. Nicolis and Prigogine, 1989).
This situation is encountered in every contemporary scientific discipline:
the irreducibility of the levels is none other than a sign of the
insufficiency of
reductionism in the formulation of scientific theories which deal
with complex systems (cf. Dalla Porta Xydias, 1997). The biological
sciences, for example, have always dealt with properties of living
beings not shared by non-living beings, even from the chemical and
physical point of view ( BIOLOGY).
The behavior of a living being, even the simplest, cannot be described
entirely by its constituent parts. On this level, the analysis of
the constituent parts is no longer enough and a study of the new
level of the whole is necessary. A thorough study of a somewhat
complex molecule such as those found in a crystal lattice or a study
of the impurities in a crystal which determine the electric properties
of a semi-conductor (to cite a few examples) have shown that even
in the chemistry of non-living objects the properties of the whole
of a complex, composite structure cannot be deduced from the properties
of the atoms comprising it (
CHEMISTRY, V). The existence of molecular orbitals of shared electrons
cannot be thought of as electrons belonging to a single atom. In
an electric conductor, the conduction electrons are in fact shared
among all the atoms of the lattice. In the field of physics and
mathematics, the problem of the whole and the parts is clearly of
relevance in the two senses alluded to above: in particular, the
"non-reducibility of the whole to the sum of the parts"
is a consequence of the "non-linearity" of the differential
equations which govern complex physical systems, whereas the self-replication
of the whole in each of its parts is none other than a sign of "self-reference"
which is of great relevance to the logician and to the computer
scientist. In fact, it seems that computer scientists were the ones
to revive the by now classical problems of mathematical logic. Take,
for instance, the problems related to Godel’s theorem concerning
the consistency and completeness of axiomatic systems or the problem of displaying sets, in all their beauty,
on the computer screen which up to then seemed to be "mathematical
monsters" due to their infinitely winding boundary (as the
Julia sets). One had to wait for the work of Benoit Mandelbrot to
rekindle interest in these problems. The field of fractal geometry
began to develop when the computer was utilized as a laboratory
in which mathematical experiments could be performed, in a way similar
to the manner in which Archimedes, more than two thousand years
ago, performed mechanical experiments so as to catch a glimpse of
geometrical properties; only later would he seek a logical demonstration
of such properties beginning with a set of axioms. Research in the
field of the so-called artificial intelligence, in addition, has
afforded an understanding of the fact that information can be found
on various levels and that there can be different hierarchies of
information:
the lower level lies in the hardware of the machine, and the higher
levels in the software; the programming language, in turn, contains
the higher-level information related to the goal for which it was
written (which lies in the mind of the programmer and in that of
the user, and so on and so forth). In every scientific discipline,
there seems to be a hierarchical structure of information related
to the degree of complexity —and therefore of unity— of
the structure studied. It therefore seems necessary to widen the
scope of current scientific methodology and rationality so that
the sciences can overcome the barriers erected by impossibility
theorems such as that of Gödel (cf. De Giorgi et al., 1955).
The need for such a widening of scope is felt, first of all, in the study of
"non-linearity". From the mathematical point of view, and therefore, from the
point of view of all mathematical sciences, the impossibility of conceiving the whole as
the sum of parts which are homogeneous with the whole (reductionism), is encountered in
the field of non-linear differential equations for which, as it is well known, the sum of
two or more solutions is not a solution, and conversely, every solution cannot be written
as a linear combination of simpler solutions (which is the case with linear differential
equations). Therefore, it is not possible to reduce the study of any given solution to
simpler and already determined solutions in a non-linear system. Moreover, Nature itself
is described almost completely by systems of non-linear equations and linear solutions are
only a first approximation. Non-linearity, therefore, introduces the concept of the
"irreducibility" of certain solutions to simpler ones. The different solutions,
however, have something in common: they are all solutions of the same equation.
In the second place, the problem of self-reference must be considered.
By "self-referring", a term originating in the field of
logic, but which is now universally used, one means an operation
or system whose "whole" is completely replicated, i.e.,
is completely identical to itself, in its parts. Self-reference
had already been discovered by logicians of Ancient Greece who viewed
it as a possible source of contradictions: one can think of the
famous "liar’s paradox" in its different versions.
For the same reason, modern logicians and mathematicians have carefully
kept self-reference out of their axiomatic systems.
Betrand Russell (1903) had excluded it from his set theory, where
it had emerged (for example, in the idea of "self-inclusion"
of certain sets of elements which contain themselves).
Kurt Gödel (1931) had succeeded, on the contrary, in exploiting
precisely the possibility of creating paradoxes through self-reference
for the purpose of proving the undecidability of certain propositions
of formal systems, such as the Principia Mathematica. He
had deduced the incompleteness of such a system and the impossibility
of demonstrating its consistency from within the system. The use
of the computer, which makes ample use of recursive algorithms,
brought up once again the problem of self-reference in the fields
of logic and mathematics. If it is clear that self-reference can
lead to contradictions, it is just as clear that this does not always
and does not necessarily happen: we have a contradictory self-referring
proposition when the predicate negates the truth of the proposition
itself. For example: "this proposition is not true". In
like manner, we have a contradiction in set theory when we restrict
the set of all sets not to include itself: "the set of all
sets that do not contain themselves" is contradictory because
the definition restricts the set to contain itself and not to contain
itself at the same time. Nevertheless, certain contradictions can
be avoided if one has a clear idea as to how self-reference can
be applied to "differentiated levels" of the same object,
and if one understands that it must be interpreted in an analogous,
and not univocal, sense. In this case, the "whole" cannot
replicate into copies that are "identical to itself" but
only "similar to itself".
4. The First Steps towards a Theory of Analogy. In
this subsection, I shall give a few examples. The first example
involves the acknowledgment of a hierarchy of levels. Where does
the contradiction lie in the self-referential proposition, or in
the definition of the ? The contradiction arises because the "proposition"
() and the subject "this proposition" are identified with
one another, whereas, in reality, they are not the same proposition.
They have the fact of being propositions in common, but they differ
in the "manner" they are propositions. Likewise, the is
not a set in the same manner as the "sets which do not contain
themselves". The fact of identifying them (univocity) does
not take into account the difference in the mode of being of the
sets and therefore gives rise to the contradiction. In order to
eliminate this contradiction at its root, Russell proposed to classify
the sets into "sets of differentiated types". Sets of
simple elements (that is, elements which cannot be themselves sets)
belong to the first level (or type), Sets whose elements can only
be sets of the first type belong to the second level (or type).
Sets of the third type are those whose elements are sets of the
second type, and so on and so forth. In this manner, one obtains
a hierarchy of sets belonging to different well-defined levels.
Thus, the term "set" can be said in different senses depending
on whether or not one is speaking of sets of the first, of the second,
or of another level. A similar classification is made for propositions.
To summarize, we can say that one has made the first small step
towards the concept of analogy from a need arising from within the
system. And this first step consists of introducing levels, or differentiated
senses in which one can speak of the same term; thus the same object
can be realized, as, in our case, a set or a proposition. It must
be observed in point of this kind of analogy that it is possible
to establish similarities between relations of different types of
sets, in a way similar to what happens in the analogy of proper
proportionality.
In connection with the subject of self-reference, another important direction can be
found in the field of fractal geometry. Fractals are geometrical structures which have the
noteworthy property of being "self-similar", that is, they replicate themselves
infinitely in each of their parts. In certain cases, as the curve of von Koch, such
self-similarity is so perfect that it is impossible to determine the scale of
magnification of a given level, since the replicated form is always the same in every part
(cf. Peilgen and Richter, 1986). In other cases, such as the Mandelbrot set, there is not
a complete self-similarity, but an infinite replication of itself into "similar"
copies which are not exactly the same as the whole. Unlike what happens with sets or
propositions, each of the parts of a fractal which replicate the whole is not, however,
identical to the whole. But, though being distinct from the whole, it is nevertheless
similar in form to it. In this case, it is preferable to speak of
"self-reference" instead of "self-referentiality". The latter
geometrical example, even if it only gives a geometrical representation and is only an
informal model, allows us to make a few considerations. (a) The geometrical structure is
"similar" in its whole and in its parts, even if such a structure is actualized
in slightly different ways in each part. Therefore, one cannot speak of complete identity,
but only of similarity, as it so happens in the analogy of terms. (b) Every replicate is
not properly speaking separable from the whole, but always subsists as a part of the
primary whole. For this reason, the whole can be compared to a sort of "analogatum
primum" (as in the "analogy of proportion"), on which every part physically
depends. (c) One can establish relational correspondences between the parts and the whole,
and the parts with each other, as in the "analogy of proportionality".
A further step can be made if we acknowledge the difference between "essence"
and "existence". The decisive leap, which is needed for analogy in the strict
sense, is to begin thinking of "objects" (as the scientist would say) or of
"entities" (as the philosopher would say) which are "similar" but
irreducible to the same "mode of existence". In order to characterize different
"modes of existence", one needs to avoid reducing existence to a simple logical
"non-contradiction", as is the tendency in formal logic. This kind of reduction
makes the very notion of existence univocal, as it postulates that what is not
contradictory, that is, what is thinkable, exists, and exists only because it is not
contradictory and only according to a single mode determined by its non-contradictory
nature. In philosophical language, this position is equivalent to that of "the
identity of essence and existence". One can show that this kind of mathematical
approach proves its own insufficiency using Gödel’s theorem. The first attempt to
refute mathematical formalism through the distinction between existence and essence can be
found in the intuitionist program (cf. Basti and Perrone, 1996). The intuitionist approach
is pushed to the extreme position which denies the universal role of essence and
overemphasizes that of existence. In fact, intuitionism posits the distinction between
essence and existence by denying the "principle of excluded middle": in this
way, proofs by contradiction are insufficient to prove the existence of a mathematical
entity and are only capable of showing its logical impossibility. Existence must be proved
with a constructive, finite method. Only what can be constructed with a finite number of
operations exists: in other words, only this or that particular model can be constructed
and therefore the universal cannot be reached and remains a pure name (Nominalism). It is
interesting to observe how both formalism and intuitionism assume a univocist mind-set,
whereas the analogy-based solution, which acknowledges differentiated modes of existence
of the universal and the particular, seems to be more appropriate (cf. ibidem, pp.
220-223). Research in this direction is still in the development phase.
Another scientific field in which the concept of analogy is being
used is that of artificial
intelligence, or better yet (and more generally), that of cognitive
science, a wider field of study which involves not only problems
dealing with machine learning but more generally problems in psychology,
such as the mind-body relationship and the relationship between
the mind and the brain in particular (
MIND-BODY, RELATIONSHIP). It is important to stress the effort made
to overcome Cartesian dualism, a philosophical position according
to which mind and body are two separate "objects" joined
together in a completely extrinsic way (cf. Basti, 1991, p. 105).
On the one hand, computer science has in practice forced us to revise
such a dualistic-mechanistic view. In fact, information inserted
in a machine by means of software and input peripherals, which allows
the machine to interact with the external world, is not a "thing"
to be placed on the same footing as the hardware, but lies on a
higher plane. The stratification of different levels of information
allows one to establish relationships between entities of different
levels (which recalls the analogy of proportion) and relations between
these relationships (which recall the analogy of proportionality).
In this way, a structure of information emerges which is in a certain
sense analogous. On the other hand, experimental study of the mind-body
relationship of the human cognitive processes has by now convinced
several scientists that the human mind works by analogy and not
simply through an accumulation or extraction of information from
a kind of data base (cf. Hofstadter et al., 1998). Consequently,
with the intent of imitating human intelligence with a computer,
one seeks a way of reproducing this kind of analogy-based operation
and not simply a way of storing a lot of specific information concerning
the problem which the machine is to solve according to a reductionist
mind-set which isolates single parts of an object from all the rest.
Certainly, it is not enough to found a theory on a merely intuitive
notion of analogy taken from its everyday meaning in common language.
A rigorous theory of analogy is therefore needed.
V. The "Profundity" of Analogy
In conclusion, the genius of analogy, for which scientific interest
is gradually but slowly developing, lies in two fundamental aspects:
(a) the fact that it distinguishes between qualitatively different,
but really related, levels of the same entity; (b) the fact that
it is inseparable from a true extra-mental reality that participates
in the being. The Aristotelian-Thomistic concept of analogy, as
we have striven to point out, acknowledges different hierarchic
levels of being which differ by their very nature. For this reason,
there are "things" and "principles" which allow
these things "to be" and "to be what they are".
The "principles" and "things" are irreducible
to each other for the very reason that they have different natures.
At the same time, they are not completely heterogeneous with one
another since they constitute different modes of the same being
they possess in a differentiated way. In Latin terminology, quod
indicates the "thing" and quo the principles by
which the thing "is" and "is what it is", that
is, they possess their own characterizing properties. In the language
of modern physics, we would say that that which is "observable"
is a quod, whereas the quo is not only unobservable
in practice, since it is in a certain sense confined in virtue of
a certain infinite potential barrier (as a quark in an infinitely
deep potential well), but it is not observable in theory, since
it is of a completely different nature from the observable. For
example, if the "thing" is a particle, its constitutive
"principle" is not a particle, or at least not in the
same but in an analogous way. For this reason, the "principle"
is not observable. The unobservable quo is introduced not
as a superfluous element of the theory (as if it were a hidden variable
which could be eliminated), but as a simple principle which is in
a certain sense necessary and inevitable to account for the observable
phenomenon. It is clear that the mathematical sciences, in their
current version, are not yet in the position to introduce into its
language a quo which is irreducible by nature to a quantitative
and relational quod. Nevertheless, in a "broad enough
theory", such an introduction seems possible and plausible.
In this way, one can widen a reductionist theory to a non-reductionist
one which is able to accommodate principles which are irreducible
and analogous to each other, without falling short, for this reason,
of the rigorous demands of a formal theory.
The second characteristic which we cannot afford to ignore in the theory of analogy is
its close link to logic and truth, or in other words, the relationship between
what is thought and extra-mental reality. Analogy can be fully understood only as a
logical description of what is verified in the extra-mental reality of things, only if one
can describe on the logical level what reality is on the ontological level. Consequently,
a broad theory with which one can formalize analogy in the way it is understood here must
be able to accommodate the distinction between both a purely logical-formal mode of
existence (non-contradiction) and different real modes of existence (extra-mental) through
the distinction between essence and existence.
Analogy is one of the tools which allow us to understand why essence and existence are
not reducible to each other. In a certain way, it constitutes a response to the
incompleteness of existential philosophy (the truth of the thing leads only to its
emergence in the stream of existence and not to other questions) and of the essentialist
philosophy (the truth of the thing consists only of the explanation of what it is, that
is, its essence). Analogy also serves as a guide aiding us in the correct use of language
and symbols as it prevents language from ending up in a continuous regress with no
epistemological basis.
Alberto Strumia
(translated by Eric Chang)
See also: COMPLEXITY;
LOGIC; MATHEMATICS, SAPIENTIAL VALUE OF; METAPHYSICS; REASON; SYMBOL;
THEOLOGY.
Documents
of the Catholic Church related to the subject:
Bibliography
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