Analogy: Encyclopedia II - Analogy - Models and theories of analogy

Analogy - Models and theories of analogy

Analogy - Identity of relation

In ancient Greek the word αναλογια (analogia) originally meant proportionality, in the mathematical sense, and it was indeed sometimes translated to Latin as proportio. From there analogy was understood as identity of relation between any two ordered pairs, whether of mathematical nature or not. Kant's Critique of Judgment held to this notion. Kant argued that there can be exactly the same relation between two completely different objects. The same notion of analogy was used in the US-based SAT tests, that included "analogy questions" in the form "A is to B as C is to what?" For example, "Hand is to palm as foot is to ____?" These questions were usually given in the Aristotelian format:

It is worth noting that while most competent English speakers will immediately give the right answer to the analogy question (sole), it is quite more difficult to identify and describe the exact relation that holds both between hand and palm, and between foot and sole. This relation is not apparent in some lexical definitions of palm and sole, where the former is defined as the inner surface of the hand, and the latter as the underside of the foot. Analogy and abstraction are different cognitive processes, and analogy is often an easier one.

Analogy - Shared abstraction

Greek philosophers as Plato and Aristotle actually used a wider notion of analogy. They saw analogy as a shared abstraction (Shelley 2003). Analogous objects shared an idea, a pattern, a regularity, an attribute, an effect or a function. They also accepted that comparisons, metaphors and "images" (allegories) could be used as valid arguments, and sometimes they called them analogies. Analogies should also make those abstractions easier to understand and give confidence to the ones using them.

The Middle Ages saw an increased use and theorization of analogy. Roman lawyers had already used analogical reasoning and the Greek word analogia. Mediaeval lawyers distinguished analogia legis and analogia iuris (see below). In theology, analogical arguments were accepted in order to explain the attributes of God. Aquinas made a distinction between equivocal, univocal and analogical terms, the latter being those like healthy that have different but related meanings. Not only a person can be "healthy", but also the food that is good for health (see the contemporary distinction between polysemy and homonymy). Thomas Cajetan wrote an influent treatise on analogy. In all of these cases, the wide Platonic and Aristotelian notion of analogy was preserved.

Analogy - Special case of induction

On the contrary, Bacon and later Mill argued that analogy be simply a special case of induction (see Shelley 2003). In their view analogy is an inductive inference from common known attributes to another probable common attribute, which is known only about the source of the analogy, in the following form:

This view does not accept analogy as an autonomous mode of thought or inference, reducing it to induction. However, autonomous analogical arguments are still useful in science, philosophy and the humanities (see below), which makes this reduction philosophically uninteresting. Moreover, induction tries to achieve general conclusions, while analogy looks for particular ones.

Analogy - Hidden deduction

The opposite move could also be tried, reducing analogy to deduction. It is argued that every analogical argument is partially superfluous and can be rendered as a deduction stating as a premise a (previously hidden) universal proposition which applied both to the source and the target. In this view, instead of an argument with the form:

We should have:

This would mean that premises referring the source and the analogical relation are themselves superfluous. However, it is not always possible to find a true universal premise to replace the analogical premises (see Juthe 2005). And analogy is not only an argument, but also a distinct cognitive process.

Analogy - Shared structure

Contemporary cognitive scientists use a wide notion of analogy, extensionally close to that of Plato and Aristotle, but framed by the structure mapping theory (See Gentner et. al. 2001). The same idea of mapping between source and target is used by conceptual metaphor theorists. Structure mapping theory concerns both psychology and computer science.

According to this view, analogy depends on the mapping or alignment of the elements of source and target. The mapping takes place not only between objects, but also between relations of objects and between relations of relations. The whole mapping yields the assignment of a predicate or a relation to the target.

Structure mapping theory has been applied and has found enough confirmation in psychology. It has had reasonable success in computer science and artificial intelligence (see below). Some studies extended the approach to specific subjects, such as metaphor and similarity (see Gentner et. al. 2001 and Gentner's publication page).

Holyoak and Thagard (1997) developed their multiconstraint theory within structure mapping theory. They defend that the "coherence" of an analogy depends on structural consistency, semantic similarity and purpose. Structural consistency is maximal when the analogy is an isomorphism, although lower levels are admitted. Similarity demands that the mapping connects similar elements and relations of source and target, at any level of abstraction. It is maximal when there are identical relations and when connected elements have many identical attributes. An analogy achieves its purpose as much as it is fit for the problem at hand. The multiconstraint theory faces some difficulties when there are multiple sources, but these can be overcome (Shelley 2003).

A problem for the multiconstraint theory arises from its concept of similarity, which, in this respect, is not obviously different from analogy itself. Computer applications demand that there are some identical attributes or relations at some level of abstraction. Human analogy does not, or at least not apparently.

Analogy - High-level perception

Douglas Hofstadter and his team (see Chalmers et. al 1991) challenged the shared structure theory and mostly its applications in computer science. They argue that there is no line between perception, including high-level perception, and analogical thought. In fact, analogy occurs not only after, but also before and at the same time as high-level perception. In high-level perception, humans make representations selecting relevant information from low-level stimuli. Perception is necessary for analogy, but analogy is also necessary for high-level perception. Chalmers et. al. conclude that analogy is high-level perception. Forbus et. al. (1998) claim that this is only a metaphor. It has been argued (Morrison and Dietrich 1995) that Hofstadter's and Gentner's groups do not defend opposite views, but are instead dealing with different aspects of analogy.

Adapted from the Wikipedia article "Models and theories of analogy", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki