César Frederico dos Santos

The field of numerical cognition provides a fairly clear picture of the processes through which we learn basic arithmetical facts. This scientific picture, however, is rarely taken as providing a response to a much‐debated philosophical question, namely, the question of how we obtain number knowledge, since numbers are usually thought to be abstract entities located outside of space and time. In this paper, I take the scientific evidence on how we learn arithmetic as providing a response to the philosophical question of how we obtain number knowledge. I reject the view that numbers are abstract entities located outside of space and time and, alternatively, derive from the scientific evidence a novel account of the nature of numbers. In this account, numbers are reifications of the counting procedure and arithmetic statements are seen as describing the functioning of counting and calculation techniques.

No Discurso sobre as Ciências e as Artes, seu primeiro discurso, Rousseau defende a polêmica tese de que o progresso das ciências e das artes, contrariamente ao que pretendia o Iluminismo, estava contribuindo mais para a degeneração dos costumes e da sociedade do que para seu aperfeiçoamento. O Primeiro Discurso foi escrito em 1749, há quase 300 anos. Nesse período, a ciência e a nossa compreensão sobre ela mudaram profundamente. Mais importante, nesse período surgiu da ciência algo imprevisto para Rousseau no Primeiro Discurso: a tecnologia moderna. A proposta deste trabalho é, pois, revisitar as críticas de Rousseau à ciência com um olhar contemporâneo, buscando avaliar o quanto daquelas críticas ainda faz sentido nos panoramas científico e social atuais. Para tanto, classificamos esquematicamente as críticas de Rousseau em dois grupos: as que acusam a inutilidade das ciências e as que acusam como nociva a sofisticação que as ciências produzem na sociedade. Defenderemos que o surgimento da tecnologia moderna tornou obsoletas as críticas quanto à inutilidade ao mesmo tempo que potencializou as críticas quanto à sofisticação. Assim, uma parte importante de suas críticas à ciência pode ser recuperada, vestida em nova roupagem e aplicada justamente na crítica à tecnologia.

No Discurso sobre as Ciências e as Artes, seu primeiro discurso, Rousseau defende a polêmica tese de que o progresso das ciências e das artes, contrariamente ao que pretendia o Iluminismo, estava contribuindo mais para a degeneração dos costumes e da sociedade do que para seu aperfeiçoamento. O Primeiro Discurso foi escrito em 1749, há quase 300 anos. Nesse período, a ciência e a nossa compreensão sobre ela mudaram profundamente. Mais importante, nesse período surgiu da ciência algo imprevisto para Rousseau no Primeiro Discurso: a tecnologia moderna. A proposta deste trabalho é, pois, revisitar as críticas de Rousseau à ciência com um olhar contemporâneo, buscando avaliar o quanto daquelas críticas ainda faz sentido nos panoramas científico e social atuais. Para tanto, classificamos esquematicamente as críticas de Rousseau em dois grupos: as que acusam a inutilidade das ciências e as que acusam como nociva a sofisticação que as ciências produzem na sociedade. Defenderemos que o surgimento da tecnologia moderna tornou obsoletas as críticas quanto à inutilidade ao mesmo tempo que potencializou as críticas quanto à sofisticação. Assim, uma parte importante de suas críticas à ciência pode ser recuperada, vestida em nova roupagem e aplicada justamente na crítica à tecnologia.: In the Discourse on the Arts and Sciences, his first discourse, Rousseau supports the polemical thesis according to which the scientific and artistic progress were contributing more to moral degeneration than to the improvement of society. The First Discourse was written in 1749, almost 300 years ago. Since then, science and our understanding of it have changed completely. More important, in this period something new and unpredictable from Rousseau's view point has emerged from science: modern technology. In this essay, thus, we intend to review Rousseau's criticisms of science from a contemporary perspective to evaluate if they are still appropriate in face of our transformed society and science. To do so, we classify Rousseau's criticisms in two groups: those which claim that science is futile and those which blame science for the sophistication of society. We argue that the emergence of technology has become obsolete the criticisms of the first group meanwhile has made powerful those of the second group. Consequently, as we intend to show, an important part of his criticisms of science can be useful to criticize modern technology. Keywords: Science. Technology. Rousseau.

In 1939, the influential psychophysicist S. S. Stevens proposed definitional distinctions between the terms ‘number,’ ‘numerosity,’ and ‘numerousness.’ Although the definitions he proposed were adopted by syeveral psychophysicists and experimental psychologists in the 1940s and 1950s, they were almost forgotten in the subsequent decades, making room for what has been described as a “terminological chaos” in the field of numerical cognition. In this paper, I review Stevens’s distinctions to help bring order to this alleged chaos and to shed light on two closely related questions: whether it is adequate to speak of a number sense and how philosophers can make sense of the claim by cognitive scientists that numbers are perceptual entities. Moreover, I offer further support to Stevens’s distinction between numerosity and numerousness by showing that they are relational properties that emerge through different relationships between agents and their environments. The final conclusion is that, by adopting Stevens’s distinctions, numbers do not need to be seen as perceptual entities, since the so-called number sense is better described as a sense of numerousness.

Anti-exceptionalists about logic claim that logical methodology is not different from scientific methodology when it comes to theory choice. Two anti-exceptionalist accounts of theory choice in logic are abductivism and predictivism. These accounts have in common reliance on pre-theoretical logical intuitions for the assessment of candidate logical theories. In this paper, I investigate whether intuitions can provide what abductivism and predictivism want from them and conclude that they do not. As an alternative to these approaches, I propose a Carnapian view on logical theorizing according to which logical theories do not simply account for pre-theoretical intuitions, but rather improve on them. In this account, logical theories are ameliorative, rather than representational.

In the literature on enculturation—the thesis according to which higher cognitive capacities result from transformations in the brain driven by culture—numerical cognition is often cited as an example. A consequence of the enculturation account for numerical cognition is that individuals cannot acquire numerical competence if a symbolic system for numbers is not available in their cultural environment. This poses a problem for the explanation of the historical origins of numerical concepts and symbols. When a numeral system had not been created yet, people did not have the opportunity to acquire number concepts. But, if people did not have number concepts, how could they ever create a symbolic system for numbers? Here I propose an account of the invention of symbolic systems for numbers by anumeric people in the remote past that is compatible with the enculturation thesis. I suggest that symbols for numbers and number concepts may have emerged at the same time through the re-semantification of words whose meanings were originally non-numerical.