An Extended Mind Perspective on Natural Number Representation

Cruz, Helen De

doi:10.1080/09515080802285289

Cited by 45 publications

(41 citation statements)

References 55 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The phrase "memory techniques" may be used for internal mnemonics. A striking example are Japanese students who have learned to visualize the structure of an abacus and to internally manipulate the beads in their mind's eye as to perform calculations (de Cruz 2008). In this case, the actual material abacus is no longer needed as its mnemonic functions are fully internalized.…”

Section: Metaphysicsmentioning

confidence: 99%

The philosophy of memory technologies: Metaphysics, knowledge, and values

Heersmink

Carter

2017

Memory Studies

View full text Add to dashboard Cite

Memory technologies are cultural artifacts that scaffold, transform, and are interwoven with human biological memory systems. The goal of this article is to provide a systematic and integrative survey of their philosophical dimensions, including their metaphysical, epistemological and ethical dimensions, drawing together debates across the humanities, cognitive sciences, and social sciences. Metaphysical dimensions of memory technologies include their function, the nature of their informational properties, ways of classifying them, and their ontological status. Epistemological dimensions include the truth-conduciveness of external memory, the conditions under which external memory counts as knowledge, and the metacognitive monitoring of external memory processes. And lastly, ethical and normative dimensions include the desirability of the effects memory technologies have on biological memory, their effects on self and culture, and their moral status. Whilst the focus in the article is largely philosophical and conceptual, empirical issues such as the way we interact with memory technologies in various contexts are also discussed. We thus take a naturalistic approach in which philosophical and empirical concepts and approaches are seen as continuous.

show abstract

Section: Metaphysicsmentioning

confidence: 99%

The philosophy of memory technologies: Metaphysics, knowledge, and values

Heersmink

Carter

2017

Memory Studies

View full text Add to dashboard Cite

show abstract

“…Second, our best scientific theories are supported by a series of cognitive artefacts (e.g. mathematics, providing us with a formal system to represent and process quantitative information) and various notation devices, enabling us to store huge amounts of information and work out complex mathematical equations (De Cruz 2008). The leverage provided by these scaffolds can hardly be overestimated.…”

Section: The Foundationalist Fallacymentioning

confidence: 99%

Natural Selection Does Care about Truth

Boudry¹,

Vlerick²

2014

International Studies in the Philosophy of Science

View full text Add to dashboard Cite

True beliefs are better guides to the world than false ones. This is the common-sense assumption that undergirds theorizing in evolutionary epistemology. According to Alvin Plantinga, however, evolution by natural selection does not care about truth: it cares only about fitness. If our cognitive faculties are the products of blind evolution, we have no reason to trust them, anytime or anywhere. Evolutionary naturalism, consequently, is a self-defeating position. Following up on earlier objections, we uncover three additional flaws in Plantinga's latest formulation of his argument: a failure to appreciate adaptive path dependency, an incoherent conception of content ascription, and a conflation of common-sense and scientific beliefs, which we diagnose as the 'foundationalist fallacy'. More fundamentally, Plantinga's reductive formalism with respect to the issue of cognitive reliability is inadequate to deal with relevant empirical details.

show abstract

“…Some scholars (e.g., Clark, 2006;De Cruz, 2008) have explored the possibility that external media play an important part in mathematical cognition. Humans regularly supplement their internal cognitive resources with external support: hard discs and books serve as non-biological memory devices, and slide rulers and calculators make difficult tasks more tractable.…”

Section: Symbols and Mathematical Cognition 41 The Role Of External mentioning

confidence: 99%

Mathematical symbols as epistemic actions

Cruz

Smedt

2010

Synthese

Self Cite

View full text Add to dashboard Cite

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.

show abstract

An Extended Mind Perspective on Natural Number Representation

Cited by 45 publications

References 55 publications

The philosophy of memory technologies: Metaphysics, knowledge, and values

The philosophy of memory technologies: Metaphysics, knowledge, and values

Natural Selection Does Care about Truth

Mathematical symbols as epistemic actions

Contact Info

Product

Resources

About