Fuzzy Pictures as Philosophical Problem and Scientific Practice: A Study of Visual Vagueness

192 Pages·2017·2.064 MB·English

by  Jordi Cat (auth.)

Studies in Fuzziness and Soft Computing
Jordi Cat
Fuzzy Pictures
as Philosophical
Problem and
Scientific Practice
A Study of Visual Vagueness
Studies in Fuzziness and Soft Computing
Volume 348
Series editor
Janusz Kacprzyk, Polish Academy of Sciences, Warsaw, Poland
e-mail: [email protected]
About this Series
The series “Studies in Fuzziness and Soft Computing” contains publications on
various topics in the area of soft computing, which include fuzzy sets, rough sets,
neural networks, evolutionary computation, probabilistic and evidential reasoning,
multi-valuedlogic,andrelatedfields.Thepublicationswithin“StudiesinFuzziness
and Soft Computing” are primarily monographs and edited volumes. They cover
significant recent developments in the field, both of a foundational and applicable
character. An important feature of the series is its short publication time and
world-wide distribution. This permits a rapid and broad dissemination of research
results.
More information about this series at http://www.springer.com/series/2941
Jordi Cat
Fuzzy Pictures
as Philosophical Problem
fi
and Scienti c Practice
A Study of Visual Vagueness
123
Jordi Cat
Department ofHistory
andPhilosophy ofScience
Indiana University
Bloomington
USA
ISSN 1434-9922 ISSN 1860-0808 (electronic)
Studies in FuzzinessandSoft Computing
ISBN978-3-319-47189-1 ISBN978-3-319-47190-7 (eBook)
DOI 10.1007/978-3-319-47190-7
LibraryofCongressControlNumber:2016953208
©SpringerInternationalPublishingAG2017
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In memory of Patrick Suppes
and Richard Wollheim
Acknowledgments
I am grateful to Cathy Helgason for having introduced me to her research in the
medical application offuzzy set theory, especially after I had studied the method-
ological role of imprecision and uncertainty in Otto Neurath’s philosophy of sci-
ence. I am also indebted to Enric Trillas and Rudolf Seising for their continued
patience,tolerance,generosityandencouragement.Anearlierversionofthecontent
ofPartIIwaspublishedintheAugustandDecember2015numbersofArchivesfor
the Philosophy and History of Soft Computing; I wish to thank the editors for
permission to reproduce the material that I haven’t revised or developed further in
thisbook.Finally,IamindebtedtoGeorgeClerkforhelpwiththephotographsand
Omar Sosa Tzec for help with the diagrams.
vii
Contents
Part 1
1 Introduction: Visual Uncertainty, Categorization,
Objectivity and Practices and Values of Imprecision ... ..... .... 3
References. .... .... .... ..... .... .... .... .... .... ..... .... 15
2 From Ordinary to Mathematical Categorization
in the Visual World… of Words, Pictures and Practices..... .... 17
2.1 Categorization and Linguistic Representation.. .... ..... .... 17
2.2 Pictorial Categorization... .... .... .... .... .... ..... .... 20
2.3 Mathematical Categorization... .... .... .... .... ..... .... 23
2.4 Objective Categorization.. .... .... .... .... .... ..... .... 25
References. .... .... .... ..... .... .... .... .... .... ..... .... 28
3 Vagueness and Fuzziness in Words and Predication ... ..... .... 31
References. .... .... .... ..... .... .... .... .... .... ..... .... 36
4 Representations: From Words to Images .... .... .... ..... .... 39
References. .... .... .... ..... .... .... .... .... .... ..... .... 44
5 Epistemology, Aesthetics and Pragmatics of Scientific
and Other Images: Visualization, Representation
and Reasoning. .... .... ..... .... .... .... .... .... ..... .... 47
5.1 A Note on Practice-Dense Data Visualization.. .... ..... .... 61
References. .... .... .... ..... .... .... .... .... .... ..... .... 66
6 Visual Representation: From Perceptions to Pictures... ..... .... 69
Reference . .... .... .... ..... .... .... .... .... .... ..... .... 72
7 Vague Pictures: Scientific Epistemology, Aesthetics
and Pragmatics of Fuzziness; From Fuzzy Perception
to Fuzzy Pictures... .... ..... .... .... .... .... .... ..... .... 73
References. .... .... .... ..... .... .... .... .... .... ..... .... 81
ix
x Contents
8 Blur as Vagueness: Seeing Images Vaguely and Seeing
Vague Images; Perception and Representation.... .... ..... .... 83
References. .... .... .... ..... .... .... .... .... .... ..... .... 90
9 Vague Pictures as Pictures .... .... .... .... .... .... ..... .... 91
References. .... .... .... ..... .... .... .... .... .... ..... .... 99
10 Vague Pictures as Vague Representations and Representing.. .... 101
References. .... .... .... ..... .... .... .... .... .... ..... .... 109
11 The Cognitive Values of Imprecision: Towards a Scientific
Epistemology, Aesthetics and Pragmatics of Fuzziness;
Contextual Lessons from the History of Picture-Making
Practices.. .... .... .... ..... .... .... .... .... .... ..... .... 111
References. .... .... .... ..... .... .... .... .... .... ..... .... 123
Part 2
12 Introduction: Fuzzy-Set Representation and Processing
of Fuzzy Images; Non-linguistic Vagueness as Scientific Practice;
ScientificEpistemology,Aesthetics,MethodologyandTechnology
of Fuzziness... .... .... ..... .... .... .... .... .... ..... .... 127
References. .... .... .... ..... .... .... .... .... .... ..... .... 130
13 Application of Mathematics in the Representation of Images:
From Geometry to Set Theory. .... .... .... .... .... ..... .... 131
References. .... .... .... ..... .... .... .... .... .... ..... .... 132
14 Cognitive Framework of Set-Theoretic Methodology
of Analysis and Synthesis: Categorization, Classification
and Many Faces of Digital Geometry ... .... .... .... ..... .... 135
References. .... .... .... ..... .... .... .... .... .... ..... .... 138
15 Conceptual Resources and Philosophical Grounds
in Set-Theoretic Models of Vagueness: Fuzzy, Rough
and Near Sets . .... .... ..... .... .... .... .... .... ..... .... 139
15.1 Set Theory Enters the Picture.. .... .... .... .... ..... .... 139
15.2 Philosophical Motivations. .... .... .... .... .... ..... .... 143
References. .... .... .... ..... .... .... .... .... .... ..... .... 146
16 Analytic and Synthetic Forms of Vague Categorization. ..... .... 147
References. .... .... .... ..... .... .... .... .... .... ..... .... 149
17 From Intrinsic to Extrinsic Vague Categorization and Content.... 151
References. .... .... .... ..... .... .... .... .... .... ..... .... 154
18 Pictorial Representation and Simplicity of Categorization.... .... 155
References. .... .... .... ..... .... .... .... .... .... ..... .... 160
Contents xi
19 Fuzzy Visual Thinking: Interpreting and Thinking
with Fuzzy Pictures and Fuzzy Data .... .... .... .... ..... .... 161
19.1 Visualized Thinking ..... .... .... .... .... .... ..... .... 162
19.2 Visual Thinking from Perception to Pictures .. .... ..... .... 166
19.3 Reasoning with Visual Analogies and Pictorial Evidence.. .... 168
19.4 Problem-Solving in and with Pictures.... .... .... ..... .... 171
19.5 Final Remarks. .... ..... .... .... .... .... .... ..... .... 173
References. .... .... .... ..... .... .... .... .... .... ..... .... 176
20 Pictorial Approximation: Pictorial Accuracy, Vagueness
and Fuzziness.. .... .... ..... .... .... .... .... .... ..... .... 179
References. .... .... .... ..... .... .... .... .... .... ..... .... 186
21 Pictorial Vagueness as Scientific Practice: Picture-Making
and the Mathematical Practice of Fuzzy Categorization ..... .... 187
References. .... .... .... ..... .... .... .... .... .... ..... .... 191
22 Conclusion.... .... .... ..... .... .... .... .... .... ..... .... 193
Reference . .... .... .... ..... .... .... .... .... .... ..... .... 194