This page is
devoted to display my work on
fuzziness and the sorites
paradox. The theory I try to
develop considers fuzziness as
nothing but
gradual and contradictory. Therefore, my aim is to show that only by
appealing to fuzzy sets, degrees of truth, and by controlling
contradictions, one can make justice to the phenomena under discussion.
Let me be optimistic and hope that the elements
given here serve to vindicate, or at least contribute to a friendly
reassessment of the many-valued, fuzzy, and paraconsistent approach to the
so-called problem of "vagueness" and the heap paradox.
Except as indicated
otherwise, all the following documents
are
in pdf format. In
order to
see them, you probably need the Acrobat Reader.
You
can go to its download page, to get it for
free.
My Ph.D.
Project, approved
on March 2003. It is an overview
of the field, containing all the major proposals, and a summary of my
favorite solution. As I now see my research, it will focus, from the
beginning, on the many-valued, fuzzy, and paraconsistent perspective,
justifying it through a critical dialogue with its rivals.
It contains 6
chapters. See Chapter 7, for a summary.
Comments on,
and criticisms of
my
work
are welcome.
Submitted
Articles
"Paraconsistent
Approaches to Fuzziness and the Sorites
Paradox", paper delivered in the III World Congress on
Paraconsistency,
Toulouse, July 2003. It reviews: a) Hyde's subvaluationism, b) Sylvan's
& Hyde's relevantism, and c) Vanackere's & Van Kerkhove's
pragmatist Adaptive Logic.
"Vagueness
or Graduality?", co-authored with my friend Lorenzo
Peña. I assess Williamson's agnosticism and reply to his
objections to a many-valued approach. Lorenzo concentrates on his
solution to the sorites, exploring three alternative formulations of
the
major premises of the sorites paradox, in terms of: a) disjunction plus
weak negation, b) the
classical conditional, and c) implication. He delineates a nice
anatomy of the argument.
Other Available Documents
My M.A. Thesis: The
Sorites Paradox. General Survey (2002). My first serious
attempt to
deal with the problem. Some original points include the following: a
discussion of
the slippery slope argument (Ch. 1, §2c), a
short allusion to relevant metaphysical doctrines of two presocratic
philosophers,
namely, Anaxagoras and Heraclitus (Ch. 1, §4), and a brief
comparison of the different
conceptions of existence in Parmenides and Plato (Ch. 4, §7). For
more ontological considerations, please see Ch. 4, §2, where the
opposition between continuism and discontinuism is presented. The
core ideas are introduced in Ch. 4: please look at §3,
on degrees, and §5a, for an argument from degrees to a
contradiction.
"Degrees and
Contradiction in
Ancient Philosophy". A brief historical survey about degrees of being,
the relation among the opposites, non-being, in Parmenides,
Heraclitus, Anaxagoras, Plato and Aristotle. It was an historical
appendix to the paper "Contradictorial Gradualism vs. Discontinuism",
which had to be excised to shorten the length of the article.
"Yes and No",
which is a collection of three lists of statements (not real
quotations, but
succinct, simplified, close paraphrases) on several subtopics held by
distinguished philosophers. I have made the selection out of 235 bibliographical
items
reviewed so far. The title of this doxography is
inspired
by Peter Abelard's book Sic et Non, which reflected the
controversy among authorities. In order to highlight the clashing
"intuitions", you may read the contrasting streams simultaneously in
each of the respects enumerated immediately below. It will thus become
clearer that the one affirms what the other denies. Within each
compilation, the opinions
have
been arranged according to the following aspects -if applicable:
Fuzziness: what
is it?, its relation with the principles of excluded middle and
non-contradiction, borderline cases, degrees, supervenience of degrees,
maximalism,
contradiction, ontological fuzziness.
The sorites paradox:
characterization, the soritical series, continuous or
abrupt transitions?,
boundaries,
differences (among adjacent members), major premiss,
agnosticism (so-called epistemicism),
indeterminism, supervaluationism, precisification, pragmatism, nihilism.
NOTE: To save some lines at the moment of printing, I have
shortened the family name of some authors to its three or four initial
letters, and/or the publication year to its last two digits.
Bibliography
at my disposal (611 items). Although the information in
each entry
is complete, there is presently a lack of uniform style from one to the
other.
Free Software to
Download
Thanks to the
courtesy of Prof. Dr. Richard DeWitt.
This is a windows program that shows a real example
of a
soritical series. I quote
his description: it «presents a series of colored rectangles
("cards") moving gradually from "pure" green to pure "red". The VGA
color capability is not terribly fine-grained, but it is sufficient to
produce a series of cards such that any two consecutive members are
observationally indistinguishable in color» (DeWitt [1992], p.
115, n. 2). Actually, the change is from green to blue, in 255 steps.
The size of the installed program is 2.54 Mb. In
order to see the back and forward buttons, and the card number
adequately, you need a screen resolution of at least 800 by 600 pixels.
Instructions to download and install.- First, save
the link target into your computer. After downloading it, unzip the
compressed file, save the decompressed files into a
directory, and then, to start the program, just open the file named:
"Sorites01a.exe". No setup is necessary. Download
the program.