Aristotle‘s theory of syllogism (in Prior Analytics) is often cited as the origin of modern logic. He also had a theory of analogy (in Poetics), which he put to practical use in reasoning about ethics (in Nichomachean Ethics).
It seems that he believed logic and analogy were both valid forms of
reasoning. The majority view today is that logic is primary and analogy
can be reduced to logic. I believe that, on the contrary, analogy is
primary and logic can be reduced to analogy.
Traditionally, artificial intelligence research has borrowed many of
its foundational ideas from modern logic, and continues to do so. Many
of the efforts to model analogy have reduced analogy to logic (for
example, A Logical Approach to Reasoning by Analogy, Davies and Russell, 1987).
However, there is a minority view that logic reduces to analogy. For example, in Analogical Reasoning, Sowa and Majumdar write:
Logical and analogical reasoning are sometimes viewed as
mutually exclusive alternatives, but formal logic is actually a highly
constrained and stylized method of using analogies. Before any subject
can be formalized to the stage where logic can be applied to it,
analogies must be used to derive an abstract representation from a mass
of irrelevant detail. After the formalization is complete, every logical
step — of deduction, induction, or abduction — involves the application
of some version of analogy.
In Where Mathematics Comes From, Lakoff and Núñez write:
This book argues that conceptual metaphor
plays a central, defining role in mathematical ideas within
the cognitive unconscious — from arithmetic and algebra to
sets and logic to infinity in all of its forms: transfinite numbers,
points at infinity, infinitesimals, and so on. Even the real
numbers are constituted by metaphorical ideas coming out of
the way we function in the everyday physical world.
Note that metaphor is based on analogy (see Metaphor is Like Analogy, Gentner, Bowdle, Wolff, and Boronat, 2001).
I believe that analogy is a more suitable foundation for research in artificial intelligence than logic. I agree with Douglas Hofstadter, who said (Wired 3.11, 1995):
I’ve managed to convince myself that analogy is really at
the core of thinking — not just for myself, but for other people, too.
I’m trying to put forth a vision of thought that involves — if you don’t
want to say “analogy-making” you can say “stripping away irrelevancies
to get at the gist of things.” I feel I’ve discovered something
essential about what thinking is, and I’m on a crusade to make it clear
Tony Veale has applied analogy to ontology development, information retrieval, and other problems. Yves Lepage has used analogy for machine translation, morphology, and other linguistic problems. René Lavie argues that grammar is based on analogy. I have used analogy for classifying semantic relations in noun-compounds. Analogy is the key that will open the door to successful natural language processing.