Artificial Languages Across Sciences and Civilizations

Staal, Frits

doi:10.1007/s10781-005-8189-0

Cited by 12 publications

(2 citation statements)

References 35 publications

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“…It is therefore not surprising that symbolic notation systems are widespread across cultures. Indeed, artificial languages are nearly as universal as natural languages, and have emerged independently in many civilizations, including Mesopotamia, India and Maya (Staal, 2006). Interestingly, cultures with strong oral traditions such as Homeric Greece, Vedic India or Old Norse culture often drew on fixed formulaic expressions (strings of words) that could be flexibly combined, such as the phrases 'swift-footed Achilles' in Homeric prose or 'steed of the sea' in Norse eddas.…”

Section: Costs and Benefits Of Symbol Usementioning

confidence: 99%

Mathematical symbols as epistemic actions

Cruz

Smedt

2010

Synthese

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Recent experimental evidence from developmental psychology and cognitive neuroscience indicates that humans are equipped with unlearned elementary mathematical skills. However, formal mathematics has properties that cannot be reduced to these elementary cognitive capacities. The question then arises how human beings cognitively deal with more advanced mathematical ideas. This paper draws on the extended mind thesis to suggest that mathematical symbols enable us to delegate some mathematical operations to the external environment. In this view, mathematical symbols are not only used to express mathematical concepts-they are constitutive of the mathematical concepts themselves. Mathematical symbols are epistemic actions, because they enable us to represent concepts that are literally unthinkable with our bare brains. Using case-studies from the history of mathematics and from educational psychology, we argue for an intimate relationship between mathematical symbols and mathematical cognition.

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Section: Costs and Benefits Of Symbol Usementioning

confidence: 99%

Mathematical symbols as epistemic actions

Cruz

Smedt

2010

Synthese

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“…As such, they involve predominantly (but perhaps not fundamentally) our visual capacities. Equally important is the observation that formal languages came into existence only after a very long and gradual process going through the use of schematic letters and the development of mathematical notation (algebra in particular), spanning over many centuries and different continents [Staal 2006], [Dutilh Novaes 2012, chap. 3].…”

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confidence: 99%

Towards a Practice-based Philosophy of Logic: Formal Languages as a Case Study*

Novaes¹

2012

philosophiascientiae

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Résumé : Au cours des dernières décennies, les travaux portant sur les pratiques humaines réelles ont pris de l'importance dans différents domaines de la philosophie, sans pour autant atteindre une position dominante. À ce jour, ce type de tournant pratique n'a cependant pas encore pénétré la philosophie de la logique. En première partie, j'esquisse ce que serait (ou pourrait être) une philosophie de la logique centrée sur l'étude des pratiques, en insistant en particulier sur sa pertinence et sur la manière de la conduire. En deuxième partie, j'illustre cette approche centrée sur les pratiques au moyen d'une étude de cas : le rôle joué par les langages formels en logique, en particulier dans les pratiques des logiciens. Ma thèse est que les langages formels jouent un rôle opératoire fondamental dans le travail des logiciens en tant que technologie pratique du crayon et du papier, génératrice de processus cognitifs -et qui plus spécifiquement vient contrebalancer certains de nos schémas cognitifs « spontanés » peu adéquats à la recherche en logique (ainsi que dans d'autres domaines). Cette thèse sera appuyée sur des données empiriques venant de la recherche en psychologie du raisonnement. Avec cette analyse j'espère montrer qu'une philosophie de la logique centrée sur l'étude des pratiques peut être fructueuse, en particulier si elle est complétée par les réflexions méthodolo-giques nécessaires.Abstract: In different subfields of philosophy, focus on actual human practices has been an important (albeit still somewhat non-mainstream) approach in recent decades. But so far, no such practice-based turn has yet taken place within the philosophy of logic. In the first part of the paper, I delineate what a practice-based philosophy of logic would (could) look like, insisting in particular on why it can be relevant and how it is to be undertaken. In the * . This research was supported by a VENI grant from the Netherlands Organization for Scientific Research (NWO). I would also like to thank two anonymous reviewers for detailed comments, and the audience at the 'From Practices to Results' conference in Nancy (June 2010) for valuable feedback.

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On the Construction of Śivasūtras-Alphabets

Petersen

2008

Lecture Notes in Computer Science

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Artificial Languages Across Sciences and Civilizations

Cited by 12 publications

References 35 publications

Mathematical symbols as epistemic actions

Mathematical symbols as epistemic actions

Towards a Practice-based Philosophy of Logic: Formal Languages as a Case Study*

On the Construction of Śivasūtras-Alphabets

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