Analogy suggests several things: similarities, proportions, attributions, even identity and difference. There are hexagons of opposition to express the relationships among these components. Metaphor is more difficult to characterize, although it is relatively easy to detect a metaphor when we pay attention to the language of everyday life and language in other areas, especially in fiction and poetry. Metaphor has been characterized as a trope, a shift in the meaning of an expression, and in this sense, it is considered one among several figures of speech, such as synecdoche or metonymy. Many times we use the same word to signify different things due to a certain similarity that we find in the named things. That is why we can speak of the foot of the bed or the foot of the mountain, and utter metaphorical sentences with these types of expressions: in this sense, metaphor is related to analogy. The similarities can be taken for granted, as in the sayings or proverbs, which try to draw a moral.

George Lakoff and Mark Johnson, in their work Metaphors we live by, argue that metaphor consists in understanding one thing in terms of another thing, and that that it is not just a matter of rhetorical issue, but that thought itself is a metaphorical process. In fact, metaphor encompasses at once three dimensions: language, thought, and action. In this talk, we will pay attention to this book’ view of metaphor trying to understand its links to analogy.

"Good mathematicians see analogies between theorems or theories, the very best ones see analogies between analogies" is Banach’s famous phrase, which we know thanks to Stanisław Ulam. This maxim indicates a certain way of developing investigations, and not only mathematical ones. With the development of knowledge, the domains in which analogical reasoning occur naturally expand and relevant theories of such a reasoning are created.

But Feyerabend warned: ‘Progress of knowledge’ meant in many places killing of minds. We do not want the humanities to be a scene of further murders, maybe even serial killings.