o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Where number is irrelevant, regimented mathematical technique has hitherto tended to be lacking.
Thus it is that the progress of natural science has depended so largely upon the discernment of
measurable quantity of one sort or another. Measurement consists in correlating our subject matter
with the series of real numbers; and such correlations are desirable because, once they are set up,
all the well-worked theory of numerical mathematics lies ready at hand as a tool for our further
reasoning. But no science can rest entirely on measurement, and many scientific investigations are
quite out of reach of that device. To the scientist longing for non-quantitative techniques, then,
mathematical logic brings hope. It provides explicit techniques for manipulating the most basic
ingredients of discourse. ]]
Quine, W.V., ''Mathematical Logic'', 1st edition, 1940. Revised edition, 1951.
Harvard University Press, Cambridge, MA, 1981.
☞http://intersci.ss.uci.edu/wiki/index.php/Differential_Logic_and_Dynamic_Systems_2.0#Philosophy_of_Notation_:_Formal_Terms_and_Flexible_Types
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
Jeff, List,
Any line of demarcation between empirical sciences based on the measure of their measure-dependence
long ago faded and fuzzed beyond recognition — largely because function and structure today hold
sway and measures are solely means to those ends — but within many fields of research one still
finds a rough sorting of cognitive styles and personal preferences between qualitative and
quantitative researchers. The work of building bridges between these research modalities has been
one of my special interest since the earliest days of my experience working at all levels of data
archiving and analysis. Peirce's perspective on inquiry, logic, mathematics, and semiotics has been
the steadiest place to stand through all of this work.
Regards,
Jon
Jeffrey Brian Downard wrote:
List,
I'd like to ask another question about the topic of chapter 6. This question is not
about the "Fixation of Belief." Rather, it is about a part of the philosophy
of science that does not figure prominently in Kees's discussion.
In the first half of the 20th century, a methodological dispute arose between those who were engaged in the
special sciences of physics and psychology. At the time, physics was considered a "hard" science
because it was based on observations involving exact measurements. The second was considered a
"soft" science because it appeared to be based on observations that did not seem to be amenable to
such an exact treatment. In time, as the debate came to a head, a expert panel of experts in measurement was
asked to take a closer look at the issues. See, for instance, Stanley Smith Stevens, "On the theory of
scales of measurement" (1946).. In order to sort out a number of the contested issues, Suppes, Luce,
Krantz and Tversky engaged in an ambitious attempt to examine the foundations of measurement in a more
systematic and thorough manner.
Let's state the question in general terms. What position does Peirce take with
respect to the foundations of measurement?
If we look at Peirce's work in mathematics generally and on measurement theory
in particular, we see him trying to provide a coherent framework for
understanding foundations of key conceptions, such as quantity, order,
magnitude. How does his position compare to the accounts that have been
developed in the 20th century by the likes of Stevens, or by Suppes, Luce,
Krantz and Tversky?
--Jeff
--
academia: http://independent.academia.edu/JonAwbrey
my word press blog: http://inquiryintoinquiry.com/
inquiry list: http://stderr.org/pipermail/inquiry/
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
facebook page: https://www.facebook.com/JonnyCache
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
