Abstract
Diagrams are hybrid entities, which incorporate both linguistic and pictorial elements, and are crucial to any account of scientific and mathematical reasoning. Hence, they offer a rich source of examples to examine the relation between model-theoretic considerations (central to a model-based approach) and linguistic features (crucial to a language-based view of scientific and mathematical reasoning). Diagrams also play different roles in different fields. In scientific practice, their role tends not to be evidential in nature, and includes: (i) highlighting relevant relations in a micrograph (by making salient certain bits of information); (ii) sketching the plan for an experiment; and (iii) expressing expected visually salient information about the outcome of an experiment. None of these traits are evidential; rather they are all pragmatic. In contrast, in mathematical practice, diagrams are used as (i) heuristic tools in proof construction (including dynamic diagrams involved in computer visualization); (ii) notational devices; and (iii) full-blown proof procedures (Giaquinto 2005; and Brown in Philosophy of mathematics. Routledge, New York, 2008). Some of these traits are evidential. After assessing these different roles, I explain why diagrams are used in the way they are in these two fields. The result leads to an account of different styles of scientific reasoning within a broadly model-based conception.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 3-19 |
| Number of pages | 17 |
| Journal | Studies in Applied Philosophy, Epistemology and Rational Ethics |
| Volume | 27 |
| DOIs | |
| State | Published - 2016 |
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ASJC Scopus subject areas
- Philosophy
Cite this
Visual reasoning in science and mathematics. / Bueno, Otavio.
In: Studies in Applied Philosophy, Epistemology and Rational Ethics, Vol. 27, 2016, p. 3-19.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Visual reasoning in science and mathematics
AU - Bueno, Otavio
PY - 2016
Y1 - 2016
N2 - Diagrams are hybrid entities, which incorporate both linguistic and pictorial elements, and are crucial to any account of scientific and mathematical reasoning. Hence, they offer a rich source of examples to examine the relation between model-theoretic considerations (central to a model-based approach) and linguistic features (crucial to a language-based view of scientific and mathematical reasoning). Diagrams also play different roles in different fields. In scientific practice, their role tends not to be evidential in nature, and includes: (i) highlighting relevant relations in a micrograph (by making salient certain bits of information); (ii) sketching the plan for an experiment; and (iii) expressing expected visually salient information about the outcome of an experiment. None of these traits are evidential; rather they are all pragmatic. In contrast, in mathematical practice, diagrams are used as (i) heuristic tools in proof construction (including dynamic diagrams involved in computer visualization); (ii) notational devices; and (iii) full-blown proof procedures (Giaquinto 2005; and Brown in Philosophy of mathematics. Routledge, New York, 2008). Some of these traits are evidential. After assessing these different roles, I explain why diagrams are used in the way they are in these two fields. The result leads to an account of different styles of scientific reasoning within a broadly model-based conception.
AB - Diagrams are hybrid entities, which incorporate both linguistic and pictorial elements, and are crucial to any account of scientific and mathematical reasoning. Hence, they offer a rich source of examples to examine the relation between model-theoretic considerations (central to a model-based approach) and linguistic features (crucial to a language-based view of scientific and mathematical reasoning). Diagrams also play different roles in different fields. In scientific practice, their role tends not to be evidential in nature, and includes: (i) highlighting relevant relations in a micrograph (by making salient certain bits of information); (ii) sketching the plan for an experiment; and (iii) expressing expected visually salient information about the outcome of an experiment. None of these traits are evidential; rather they are all pragmatic. In contrast, in mathematical practice, diagrams are used as (i) heuristic tools in proof construction (including dynamic diagrams involved in computer visualization); (ii) notational devices; and (iii) full-blown proof procedures (Giaquinto 2005; and Brown in Philosophy of mathematics. Routledge, New York, 2008). Some of these traits are evidential. After assessing these different roles, I explain why diagrams are used in the way they are in these two fields. The result leads to an account of different styles of scientific reasoning within a broadly model-based conception.
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U2 - 10.1007/978-3-319-38983-7_1
DO - 10.1007/978-3-319-38983-7_1
M3 - Article
AN - SCOPUS:85019644082
VL - 27
SP - 3
EP - 19
JO - Studies in Applied Philosophy, Epistemology and Rational Ethics
JF - Studies in Applied Philosophy, Epistemology and Rational Ethics
SN - 2192-6255
ER -