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“Free rides” in Mathematics

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“Free rides” in Mathematics. / Carter, Jessica.

In: Synthese, Vol. 199, No. 3-4, 12.2021, p. 10475-10498.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

Carter, J 2021, '“Free rides” in Mathematics', Synthese, vol. 199, no. 3-4, pp. 10475-10498. https://doi.org/10.1007/s11229-021-03255-9

APA

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MLA

Vancouver

Carter J. “Free rides” in Mathematics. Synthese. 2021 Dec;199(3-4):10475-10498. doi: 10.1007/s11229-021-03255-9

Author

Carter, Jessica. / “Free rides” in Mathematics. In: Synthese. 2021 ; Vol. 199, No. 3-4. pp. 10475-10498.

Bibtex

@article{2aec6c2773d7427ba307887b040164c9,
title = "“Free rides” in Mathematics",
abstract = "Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima (Artif Intell Rev 15: 5–27, 2001), is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima{\textquoteright}s (informal) framework as a tool to analyse the occurrence and properties of them. I consider a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams.",
keywords = "Diagrams, Free rides in mathematics",
author = "Jessica Carter",
year = "2021",
month = dec,
doi = "10.1007/s11229-021-03255-9",
language = "English",
volume = "199",
pages = "10475--10498",
journal = "Synthese",
issn = "0039-7857",
publisher = "Springer",
number = "3-4",

}

RIS

TY - JOUR

T1 - “Free rides” in Mathematics

AU - Carter, Jessica

PY - 2021/12

Y1 - 2021/12

N2 - Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima (Artif Intell Rev 15: 5–27, 2001), is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s (informal) framework as a tool to analyse the occurrence and properties of them. I consider a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams.

AB - Representations, in particular diagrammatic representations, allegedly contribute to new insights in mathematics. Here I explore the phenomenon of a “free ride” and to what extent it occurs in mathematics. A free ride, according to Shimojima (Artif Intell Rev 15: 5–27, 2001), is the property of some representations that whenever certain pieces of information have been represented then a new piece of consequential information can be read off for free. I will take Shimojima’s (informal) framework as a tool to analyse the occurrence and properties of them. I consider a number of different examples from mathematical practice that illustrate a variety of uses of free rides in mathematics. Analysing these examples I find that mathematical free rides are sometimes based on syntactic and semantic properties of diagrams.

KW - Diagrams

KW - Free rides in mathematics

UR - http://www.scopus.com/inward/record.url?scp=85109266377&partnerID=8YFLogxK

U2 - 10.1007/s11229-021-03255-9

DO - 10.1007/s11229-021-03255-9

M3 - Journal article

AN - SCOPUS:85109266377

VL - 199

SP - 10475

EP - 10498

JO - Synthese

JF - Synthese

SN - 0039-7857

IS - 3-4

ER -