Analogy and Logic

Posted on January 26, 2007 by Peter Turney

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 to everybody.

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.