Seminarium Filozofia Kognitywistyki: Cognitive Artifacts for Geometric Enculturation
Zapraszamy na kolejne posiedzenie Seminarium Filozofia Kognitywistyki IFiS PAN, które odbędzie się dnia 26 stycznia 2018 (piątek) w Pałacu Staszica (ul. Nowy Świat 72) w sali 161 o godz. 12.00.
W trakcie seminarium dyskutować będziemy draft artykułu “Cognitive Artifacts for Geometric Enculturation” autorstwa prof. Marcina Miłkowskiego i dr. Mateusza Hohola.
In this paper, we focus on the development of geometric cognition. We argue that the proper account of mathematical enculturation should not only include the evolutionary timescale, to which Menary (2015) confined himself, but also the historical timescales, at which the development of mathematical cognitive artifacts can be traced. In particular, we will claim that the development of Greek mathematics, enshrined in Euclid’s Elements, Archimedes’, Spiral lines or Pappus’ Collectio, was driven by the use several tightly intertwined cognitive artifacts; one was the use of lettered diagrams, and another the creation of the linguistic formulae, namely non-compositional fixed strings of words used repetitively within authors and between them, which formed professional language of geometry.
Together, as Netz (1999) pointed out, they have contributed to making geometrical practice both reliable and learnable. Lettered diagrams, on one hand, contribute to specification of objects, they are full-blooded components of geometric arguments and provide a substitute for ontology by creating the universe of geometric discourse. Linguistic formulae, on the other hand, facilitate the acquisition of the geometric conceptual framework, the reconstruction of the logical structure of geometric proofs, the transfer of results from one geometric problem to another, and understanding the structure of discourse. In this sense, formulaic language constitutes the vehicle for abstract geometric concepts.
To understand how geometric cognition has been constituted, as we argue, we need to appreciate not only individual cognitive factors, such as phylogenetically ancient and ontogenetically early core systems of geometric knowledge (localized, as Spelke et al., 2011 claim, in hippocampal formation and lateral occipital complex) and gene-culture co-evolution but also the social history of the spread and use of cognitive artifacts. In this respect, the case of Greek geometry clearly shows that cognitive explanations of geometrical reasoning have to go beyond the confines of methodological individualism to account for how the distributed practice of artifact use has stabilized over time. This practice, as we suggest, has also contributed heavily to the understanding of what mathematical proof is; classically, it has been assumed that proofs are not merely deductively correct but also remain invariant over various individuals sharing the same cognitive practice.
Ogólnopolskie Seminarium Filozofia Kognitywistyki organizowane jest w ramach projektu NCN „Kognitywistyka w poszukiwaniu jedności: unifikacja i integracja badań interdyscyplinarnych”, DEC-2014/14/E/HS1/00803.