Euclid completed his geometrical proofs in the Elements (c. 300BC) with the abbreviation “QED” (quod erat demonstrandum). This phrase was not only used in mathematics in the early modern period, but also in deductive proofs in physics, astronomy, philosophy, and ethics. This chapter is a cognitive- historical interpretation of the axiomatic-deductive ideal that consists of some widely accepted propositions or statements about geometry and mathematics: i) Mathematics is objective, its truths are universal, absolutely certain; it is abstract and independent of the human body, and transcends the reality of human beings; ii) Mathematics’ efficiency as a scientific tool leads to the assumption that it exists in the physical structure of the universe. To learn mathematics was simultaneously to learn the language of nature. It is the scientific ideal; and iii) Mathematics characterizes logic and rational thinking. This axiomatic-deductive ideal could, however, be studied from a cognitive perspective stating that mathematics is created, obviously, by humans, and can be seen as a product of the bio-cultural coevolution of human cognitive abilities. These views of thinking and human rationality expressed, in particular, during the scientific revolution are some of the most beautiful dreams of humanity; the dreams of objectivity, certainty, a transcendental reality independent of human beings, an ideal, reliable method of thinking. The conclusion is that these “inventions” of the human mind, that thinking could be objective, certain, universal, transcendent, abstract, and should form the ideal for science and human thinking, are an important and crucial stepping stone in the history of human rationality which occurred during the scientific revolution from the sixteenth to the eighteenth century. In this period of transformation of human rationality, new tools for thinking were invented that have since had a significant impact on human life and cognition.
This chapter outlines a few themes related to the role of language and communication in cognitive-historical processes, in combination with a discussion of the role of cognitive-linguistic analysis as a tool to understand such processes. The first and second sections of the chapter treat cognition and communication from a semiotic perspective. It provides a discussion of how cognition is related to the three basic semiotic modes of representation (index, icon, and symbol), focusing especially on the symbolic mode and human language. The third, fourth, and fifth sections discuss ways in which cognitive linguistics and linguistic-communicative data can provide tools for historical research. This is done in the third and fourth sections by considering different types of linguistic data that can be useful in exploring cognitive history. The following types of data are considered: the vocabulary of a language and its role for our categorization of reality and historical changes in this categorization. We will also explore the role of grammar, metaphors and similes, common phrases and proverbs for studies of how our organization of reality changes our attitudes to animals, expression of gratitude, individual self-sufficiency and the value of family bonds. The fifth section discusses the role of more communication- oriented data for cognitive history. The following types of data are discussed: body, interaction and interpretation, forms of address and personal reference, turn management and communicative feedback and interpretation, as well as understanding and implicit information. The sixth and seventh sections explore the relation between cognition and language somewhat further, both on an individual and on a collective level, and discuss patterns of historical maintenance and change in cognition and language, with an interest in how such change, in relation to different types of cognitive content, might be related to other features of historical change, considering both factors that facilitate change and factors that restrict and slow down change.
What makes human beings, and their way of thinking, unique in the biosphere of the earth is not just the biological-genetic evolution of human cognitive capacities, but also the interaction in historical time with the environment, the socio-cultural Lifeworld, and particularly human semiotic skills; that is, the ability to learn from other thinking beings, and to transfer experiences, knowledge, meaning, and views to new generations. Traditionally, history has been the singular telling of stories of our particular spatio-temporality; and the theory of evolution has consisted in studying the specific way human biology has evolved. According to the evolutionary scheme proposed by Merlin Donald, human specificity proceeds from biological to cultural evolution, from the episodic over the mimetic and the mythic stage to that of theory, that is, it transcends (natural) evolution into history. Such a continuity is taken for granted by recent historians and anthropologists turning to “deep history”, quite in opposition to the singular histories of mentalities holding the stage through most of the twentieth century. But, if we take Donald’s scheme seriously, there may still be a qualitative difference between biological evolution and cultural evolution as history. It might be suggested, following, notably, Stephen Jay Gould and David Hull, that the theory forged by Charles Darwin is not only involved with natural evolution, but is concerned with all sequences of events leading to the generation of variants, as well as the mechanism operating the choice between these variations. Though history emerges out of bio-cultural evolution, it still needs to be qualitatively different from (natural) evolution if it is going to account for many of the traits that are specific to human beings. Peter Richerson and Robert Boyd, who systematically worked out the parallels between natural and cultural evolution, still presented it as a metaphorical extension. Nevertheless, they neglected to reckon with the way in which cultural evolution is necessarily different from biological evolution, in that it is played out in a world in which humanity has already created the semiotic structures for the conservation of memory resulting from mimetic and mythic stages, while they are in the process of producing theoretic structures. Such structures are not only stepping stones underlying certain historical paths taken, they are also stumbling blocks on the way to others not taken, as we may learn from pondering the obstacles set to the extirpation of heresy, as the colonists saw it, in post-conquest America.
The last decades have seen a noticeable increase in cognitive science studies that have changed the understanding of human thinking. Its relevance for historical research cannot be overlooked any more. Cognitive history could be explained as the study of how humans in history used their cognitive abilities in order to understand the world around them and to orient themselves in it, but also how the world outside their bodies affected their way of thinking. In focus for this introductory chapter is the relationship between history and cognition, the human mind’s interaction with the environment in time and space. The chapter discusses certain cognitive abilities in interaction with the environment, which can be studied in historical sources, namely: embodied mind, situated cognition, perception, distributed cognition, conceptual metaphors, categorization, intersubjectivity, and communication. These cognitive theories can give deeper understanding of how - and not only what - humans thought, and about the interaction between the human mind and the surrounding world. The most ambitious aim of such a cognitive history could be to inform the research on the cognitive evolution of the human mind.