Enrique Dussel

 Universidad Autónoma Metropolitana (Autonomous Metropolitan University, UAM) and Universidad Nacional Autónoma de México (National Autonomous University of Mexico, UNAM).

©Macaco Producciones. Luis David Perez Graillet

Analogy and Communication

ABSTRACT

Analogy makes possible the dialogue between people. This dialogue, at the intercultural level and from distinct ontological comprehensions of life, cannot be achieved from

a univocal pretension of meaning. Analogy permits, especially at the rhetoric level of Political Philosophy,  an adequate interpretation of such complex concepts as peoplestate or rights. A semantics of these concepts by similarity allows us to advance in the process towards a better interpretation of the other interlocutor´s expression though never reaching identity.

©Małgorzata Leśniewska

Piotr Leśniewski

Adam Mickiewicz University (UAM), Poznań, Poland

©Jan Hubrich

 

ABSTRACT

 

Analogy has many faces and uses. We have reasoning

by analogy, analogical concepts in the sense of transcendental, analogia legis, analogia iuris, analogical concepts in the ordinary sense, analogical models, analogical computers, etc. Clearly, this variety has something in common,  namely the idea of being similar  Thus, if we say that A and B are analogical, we intend to indicate that they are similar to some to degree. However, the idea of similarity is vague, the same concerns analogy. On the other hand, the concept of analogy is commonly  subjected to logical analysis. The stable result of such attempts is that it is very difficult, or even impossible, to provide precise criteria for assertions that A and B are analogical or not, or that inference by analogy is correct or not. Clearly, some cases of analogy are easy to defining. For example, if say that two ordered sets are similar (analogical), because they have the same order type, it is precise. But to give a general criterion for analogy seems to open a Pandora  box.

 

In order to identify at least some difficulties, I assume

the scheme (*) A is analogical to Bis a basic form of

an analogy-statement, in which “is analogical to” is a binary predicate, but A and B are nominal expressions referring

to objects, properties, relations, etc. We can call them analogata. In general, analogy is a binary relation.

Now, consider sentences (a) A is analogical to B, and (b) B

is analogical to C. Clearly these sentences do not imply (c) A

is analogical to C. This circumstance prevents introducing ordering into the collection of analogical objects, etc. We cannot define the relation of equivalence between analogata.

These facts show that important algebraic constructions

(for instance, forming equivalence classes and mathematical induction), cannot be performed on analogical items.

If we define identity as a special case of analogy, the latter relation is symmetric and reflexive. However, these attributes are too weak to generate powerful mathematical structures. This suggests that correctness of analogy-statements has to remain a conventional issue, at least to some degree.

Perhaps fuzzy logic could improve the situation.

Jan Woleński

University of Information, Technology and Management, Rzeszow, Poland

Logical Problems Related to Analogy

Marcin J. Schroeder

Akita International University (AIU), Japan

Analogy: From Identity, Equivalence and Similarity to Cryptomorphism

ABSTRACT

Analogy, although understood in many different ways throughout the ages of its use in philosophy was always a tool for reducing or eliminating complexity. For instance, Aristotle writing in Metaphysics (1048a25-b17) about the antithesis of potentiality and actuality escaped the trouble to explain the complexity of the concepts involved in it by invoking analogy “[...] we must not seek a definition of everything but be content to grasp the analogy” [1]. In this case the escape from complexity was achieved by building analogy between the relationship opposing concepts of a very high level of abstraction (potential existence and actual existence) and the relationships between particulars coming from our everyday experience.

However, if analogy was simply replacement of that which is abstract, general by that which is particular, it would have been just an illustration, possibly confusing and misleading. So what is analogy and why does it have so important role in philosophical inquiry?  The etymology of its name refers to the Greek word for proportion derived from geometric analysis of figures and therefore apparently to quantitative, metrical analysis of the objects of human experience. But actually it belongs to fundamental concepts of the structural, i.e. qualitative methodology. Even in this original, literal meaning of the Greek word “analogia” as a proportion of geometric measures important is the equality of mutual relationships of the components within a whole, not their numerical values. No wonder that already in the philosophy of Greek antiquity analogy acquired much more general meaning of the equality or similarity in structural relations expressed frequently in terms of non-numerical, intuitive proportions.

This intuitive character of analogy is of special importance. Human capacity to identify structural resemblances which cannot be easily described or formalized is surprising. However we cannot be “content to grasp analogy” as advised by Aristotle, if we leave the judgment of the validity of the analogy exclusively to our intuition. Thus, we should try to identify the function of analogy in the study of structural characteristics. It is quite clear that analogy works through similarity or even equality (as in the case of proportions understood literally). However, even if frequently, but mistakenly analogy is reduced to a binary relation from the type of identity (in logical sense), equivalence (binary relation which is reflexive, symmetric and transitive) or its generalization similarity (in mathematics tolerance relation which is reflexive and symmetric, but not necessarily transitive [2]), it actually describes correspondence between structures. Of course, there is nothing wrong in calling similarity relation an analogy, but considering the special role of analogy in the study of structural characteristics which is lost in the reduction to tolerance relations, it is unnecessary overextension.

If we have predefined structures of particular type (e.g. algebraic structures, partially ordered sets, topological spaces, etc.), then we could consider the description of analogy in terms of functions (homomorphisms, isomorphisms, etc.) between structures which preserve structural characteristics (algebraic operations, order, topology). In this approach structures are primary concepts and analogy is introduced as a secondary concept defined by selected functions determined by the condition of these structures’ preservation. However this approach trivializes analogy. Its main role is as a tool for the inquiry of the structure, for determination of structural characteristics. If the structure is already defined and fully characterized, there is no use for analogy. Moreover, these specific types of mathematical structures mentioned above are just examples of only apparently special importance. There are many other examples of at least equal philosophical, theoretical and practical significance. The general question: ”What is a structure?” is not at all easier to answer than “What is analogy?” Only when we have an answer to the former question, we can try to answer the latter.

Instead of providing the ultimate answers to both, I will present an outline of the attempt to answer the first one and additional questions, which show that the reflection on the general concept of a structure is non-trivial and cannot be easily resolved by existing tools of mathematics, such as morphisms. The same structure (for instance a topological space) can be introduced in a several different, but equivalent ways (topological space can be defined by the class of open subsets, closed subsets, closure operator, or a long sequence of other equivalent operators, base for open subsets, base for closed subsets, etc.) We are expressing this fact by referring to “cryptomorphic presentations of a structure”. How to describe the identity (or cryptoisomorphic class) of the structure independently from the particular choice of the defining concepts and corresponding sets of equivalent axioms? What actually is “cryptoisomorphism”? Thus far this concept is being used without any definition. We are simply “content to grasp analogy”, or rather we are forced to be content.

   

References

[1] W.D. Ross (ed.), «Aristotle: Selections» Charles Scribner Sons, New York, 1955, p.82.  

[2] M.J. Schroeder & M.H. Wright «Tolerance and weak tolerance relations» J. Combin. Math. and Combin. Comput. 11 (1992), 123-160.

Alessandro Minelli

University of Padova, Italy

ABSTRACT

To explain the amazing morphological and biomechanical analogy between two distantly related vertebrates as are a dolphin and a shark, an explanation exclusively framed in terms of adaptation is far from satisfactory. The same is true, of course, of any other comparison between structurally similar, but phylogenetically unrelated organisms. Among the plants, for example, there are succulent species of spurge (Euphorbia spp., fam. Euphorbiaceae) – some of them hemispherical to spherical, other columnar – amazingly similar to corresponding hemispherical to spherical or columnar species of a very different family, the Cactaceae. To be sure, all these forms are well-adapted to survive in arid places (in terms of the Darwinian survival of the fittest), but this does not explain how the developmental processes of their non-succulent ancestors could eventually evolve in such a way as to eventually produce these peculiar phenotypes (the arrival of the fittest). How does Nature play with animal and plant form? To address the issue of the evolution of possible forms, we must take development seriously and adopt the integrated perspective currently known as evolutionary developmental biology, or evo-devo. Paths through the maze of living forms are not satisfactorily explained in terms of pure geometrical transformations (à la D’Arcy Thompson), neither in terms of simple combinatorics, involving archetypical modules such as heads, limbs and segments in animals (an Empedoklean scenario), or leaves, petals and stamens in plants. Evolvable and often recurrent conditions that we can describe as local state variables, such as vegetativeness in Prusinkiewicz’s models of inflorescence evolution, offer instead a promising path into a solid biological explanation of analogy. Plausible scenarios of evolvability of living organisms can not miss to pay attention to the unceasing evolutionary changes in the kind and degree of modularity through which developmental processes operate, subject to constraints dictated by the anisotropy of the landscapes of genotypic and phenotypic change.

An evo-devo perspective on analogy

Olga Pombo

Center of Philosophy of Sciences of the University of Lisbon (CFCUL), Portugal

©António Pedro Ferreira

Science and Art.

Variations upon a Common Ground

ABSTRACT

Our first aim is to signalise some similarities and decisive differences between science and art.  We know that there always has been a deep relationship between science and art. We are able to identify, to remember and to point out some genius of the past who were at the same time great in science and splendorous in art. We are aware that science has had a great impact in art and inversely that many artists took science as inspiration for their work.

But, if we are obliged to acknowledge that science and art have the great proximities, at the same time we know that they exhibit the most crucial distances. We will remember some examples of those divergences.

Now, by questioning, by cross-examining and by putting in danger those similarities and differences, that will allow us to claim, with Paul Valery, that Science and Art are variations upon a common ground. We will finish by trying to clarify such dictum. Science and art are insurmountably distinct in the way they deal with infinite and they are indisputably close in the way they instantiate universality.

Walter Redmond

Austin, Texas, USA

©Teología UC

Logical Analogies/Interpretations,

Oppositions and Probabilism

ABSTRACT

 I present a logical analog common to several interpretations: modality (necessity and possibility), quantification,

truth-functional relations, moral attitudes (deontic logic),

states of knowledge (epistemic logic) and belief (doxastic logic). To display the two underlying logical templates, I call upon the originally scholastic convention, recently put to use again,

of using squares, hexagons and octagons “of opposition”.

A combined epistemic-deontic logic happens to be found

in the traditional “probabilist” theory of the right conscience, and I shall then briefly explain how this is so.

ABSTRACT

 

The usual formalism given today for argument by positive analogy (it should be “from”) is like Copi’s: 'Every analogical inference proceeds from the similarity of two or more things in one or more respects to the similarity of those things in some further respect.' Entities ab, and c share properties F, and a and b also share G, the target property; therefore Gc (Copi, 426). Yet there are problems. Similarity must case be defined as the sharing of relevant properties. I will state and argue for a form for analogical argument which does not use the concept of similarity.  The form under this view is that c as well as a and b is an instance of R (a generalized form of the given "ratio" or "proportion" in the original Greek sense of identity of proportion (ἀναλογία)). Entities ab, and c are instances of Rx, and (x)(Rx  ⊃ Gx); therefore Gc. I will defend the analysis against the criticism that it begs a key question, and two other objections. The form given is not really new; in essence it is Aristotle's, in the Prior Analytics.  I will defend Aristotle's view, discussing the problem of justification, particularly concerning the establishment of the "inductive step" to R, and also discuss three examples of analogical argument based on identity of “ratio”. I end with a few words about Leibniz's views on induction and analogy.

A “New” Form for Analogy?

Jonathan Westphal

School of Cognitive Science, Hampshire College
Amherst, USA

©Hampshire College

 

Homo Compassiblis. The Art of Analogy-Making

ABSTRACT

The therapeutic analogy and the grammatical analogy were used by P. F. Strawson when he explained the concept of analytical philosophy. But the Rylean analogy of a map or charting (i.e. the so-called logical geography of concepts) was invoked in this context. Yet another analogy is explored here. For philosophical analysis, idealizations are considered as construction methods of an appropriate image or rather of a correct caricature (of a given object). Five paradigms of idealization are briefly presented.

A model of a compassionate person is then developed and

analogy-making within the realm of its actions

is described as an art of establishing such deep and

meaningful social relationships as responsibility

(x is responsible for y), gratefulness (x is grateful to y),

love (x loves y), etc.  Leszek Nowak (1943-2009) was one of the founders and main representatives of the Poznań Methodological School. He emphasized the vital role of autonomous social relationships within the framework of the non-Marxian historical materialism. In Property and Power there is the following passage: “The class struggle is possible, if the suppression is painful enough, but not too much, if the autonomous social relations enabling people to act commonly still exist. Pure socialism kills them and kills the society in the people. And the name socialism mystifies this ideologically.”  The book was published in 1983 and after over thirty years the topic of autonomous social relationships is taken up here in erotetic study – it begins with the question: Why did agent X perform action A? It is a natural basis for the development of a political concept of love in the very sense of Commonwealth by Michael Hardt and Antonio Negri.

References

Almond, S. (2012). Introduction. I Was Sugar Once: Lessons in Radical Empathy. [in:] Ch. Strayed.   Tiny Beautiful Things. Advice on Love and Life from Dear Sugar. New York: Vintag   Books: 3-9.

Badiou, A. (2008). What is Love? [in:] A. Badiou. Conditions. Translated by S. Corcoran.

London- New York: Continuum: 179-198.

Gan-Krzywoszyńska, K. & Leśniewski, P. (2013). On Reyes Mate’s Theory of the Victim: A Meta- ethical Sketches on Injustice. Ethics in Progress. Vol. 4, No. 2.: 63-77.

Gan-Krzywoszyńska, K. & Leśniewski, P. (2015). On Non-Rationalities in the Foundations of the  Humanities: A Hexagonal Analysis of the Counterrationality Principle. Studia Metodologiczne.

Vol. 35: 168-182.

Gan-Krzywoszyńska, K. & Leśniewski, P. (2016). Analogies in the Meta-Methodology of the Humanities. Studia Metodologiczne. Vol. 37: 241-254.

Hardt, M.& Negri, A. (2009). Commonwealth. Cambridge MA: The Belknap Press.

Harris, S. (2010). The Moral Landscape. How Science Can Determine Human Values.

New York-London-Toronto-Sydney: The Free Press.

Ikäheimo, H. (2012). Globalizing Love: On the Nature and the Scope of Love as a Form of Recognition. Res Publica 18: 11-24.

Leśniewski, P. (2015). Hacia la siguiente revolución. Contribución a la cuestión de la responsabilidad. Analogía filosófica: revista de filosofía, investigación y difusión. Vol. 29, No. 1: 31-51.

Nowak, L. (1983). Property and Power. Towards a Non-Marxian Historical Materialism.

Dordrecht-Boston-Lancaster: D. Reidel.

Reich, R. B. (2012). Beyond Outrage. What Has Gone Wrong with Our Economy

and Our Democracy, and How to Fix It. New York: Vintage Books.

Sternberg, R. J. (1986). A Triangular Theory of Love. Psychological Review. Vol. 93, No. 2: 119-135.

Sternberg, R. J. (1999). Love Is A Story. A New Theory of Relationships.

New York: Oxford University Press.

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