131
that we are a member of that set, or class of distinctions that does not appreciably
change from the Iron Age to the present.
3
The contrasts between the Burgundian
Renaissance and its unabashed impact upon primary forest cover, and today’s candid
assessment by French authorities regarding the global sixth extinction spasm, and
the modest tools the French can mobilize in defense of remaining ecological integrity both within and outside its political boundaries, are all part of the same subset.
What does that mean in terms of predicting coming years? Enter Bertrand Russell
(1872–1970) and a moment in time, 1902, when he corresponded (now famously)
with German philosopher Gottlob Frege (1848–1925).
4
Their friendship would converge upon the basis of Russell’s curious predilection for a certain phenomenon he
detected in logic, namely, that concerning “the set of all sets that are not members
of themselves. Such a set appears to be a member of itself if and only if it is not a
member of itself”
5
(Fig. 14.2).
14.2 The Confusion Borne of Trichotomy
Russell’s approach to resolving this paradox (also implicating Frege’s “trichotomy”—all numbers are positive, negative, or zero) has been clarified thus: “…we
are confusing a description of sets of numbers with a description of sets of sets of
numbers. So Russell introduced a hierarchy of objects: numbers, sets of numbers,
sets of sets of numbers, etc. This system served as a vehicle for the first formalizations of the foundations of mathematics… Russell’s paradox becomes: let y = {x: x
is not in x}, is y in y?”
6
That is one form of antinomy crucial to understanding the ecological paradox unleashed in the guise of humanity’s own introverted use of biases to enact
calculations that, in turn, build into theories by which we ascribe to the world
3 https://www.diplomatie.gouv.fr/en/french-foreign-policy/sustainable-development-environment/
french-policy-on-biodiversity/Accessed March 16, 2019
4 See http://brianrabern.net/onewebmedia/FregeRussellCorr.pdf, March 16, 2019; See also “The
Russell Paradox,” in Gottlob Frege, The Basic Laws of Arithmetic, Berkeley: University of
California Press, 1964, 127–143; abridged and repr. in A.D. Irvine, Bertrand Russell: Critical
Assessments, vol. 2, New York and London: Routledge, 1999, 1–3; and “Paradoxes, Self-Reference
and Truth in the 20th Century,” in Dov M. Gabbay and John Woods (eds) (2009) Handbook of the
History of Logic: Volume 5 – Logic From Russell to Church, Amsterdam: Elsevier/North Holland,
875–1013. See also, “A Guide to the Jean Van Heijenoort Papers, 1946-1988,” Briscoe Center for
American History, The University of Texas at Austin, https://legacy.lib.utexas.edu/taro/
utcah/00245/cah-00245.html, and most importantly, his edited translations in, From Frege to
Gödel: A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge,
Mass., 1967
5 See https://plato.stanford.edu/entries/russell-paradox/Copyright 2016 by Andrew David Irvine
and Harry Deutsch.
6 “What Is Russell’s Paradox?” by John T. Baldwin and Olivier Lessmann, Scientific American,
https://www.scientificamerican.com/article/what-is-russells-paradox/. Accessed, July 25, 2020.
14.2 The Confusion Borne of Trichotomy
that we are a member of that set, or class of distinctions that does not appreciably
change from the Iron Age to the present.
3
The contrasts between the Burgundian
Renaissance and its unabashed impact upon primary forest cover, and today’s candid
assessment by French authorities regarding the global sixth extinction spasm, and
the modest tools the French can mobilize in defense of remaining ecological integrity both within and outside its political boundaries, are all part of the same subset.
What does that mean in terms of predicting coming years? Enter Bertrand Russell
(1872–1970) and a moment in time, 1902, when he corresponded (now famously)
with German philosopher Gottlob Frege (1848–1925).
4
Their friendship would converge upon the basis of Russell’s curious predilection for a certain phenomenon he
detected in logic, namely, that concerning “the set of all sets that are not members
of themselves. Such a set appears to be a member of itself if and only if it is not a
member of itself”
5
(Fig. 14.2).
14.2 The Confusion Borne of Trichotomy
Russell’s approach to resolving this paradox (also implicating Frege’s “trichotomy”—all numbers are positive, negative, or zero) has been clarified thus: “…we
are confusing a description of sets of numbers with a description of sets of sets of
numbers. So Russell introduced a hierarchy of objects: numbers, sets of numbers,
sets of sets of numbers, etc. This system served as a vehicle for the first formalizations of the foundations of mathematics… Russell’s paradox becomes: let y = {x: x
is not in x}, is y in y?”
6
That is one form of antinomy crucial to understanding the ecological paradox unleashed in the guise of humanity’s own introverted use of biases to enact
calculations that, in turn, build into theories by which we ascribe to the world
3 https://www.diplomatie.gouv.fr/en/french-foreign-policy/sustainable-development-environment/
french-policy-on-biodiversity/Accessed March 16, 2019
4 See http://brianrabern.net/onewebmedia/FregeRussellCorr.pdf, March 16, 2019; See also “The
Russell Paradox,” in Gottlob Frege, The Basic Laws of Arithmetic, Berkeley: University of
California Press, 1964, 127–143; abridged and repr. in A.D. Irvine, Bertrand Russell: Critical
Assessments, vol. 2, New York and London: Routledge, 1999, 1–3; and “Paradoxes, Self-Reference
and Truth in the 20th Century,” in Dov M. Gabbay and John Woods (eds) (2009) Handbook of the
History of Logic: Volume 5 – Logic From Russell to Church, Amsterdam: Elsevier/North Holland,
875–1013. See also, “A Guide to the Jean Van Heijenoort Papers, 1946-1988,” Briscoe Center for
American History, The University of Texas at Austin, https://legacy.lib.utexas.edu/taro/
utcah/00245/cah-00245.html, and most importantly, his edited translations in, From Frege to
Gödel: A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge,
Mass., 1967
5 See https://plato.stanford.edu/entries/russell-paradox/Copyright 2016 by Andrew David Irvine
and Harry Deutsch.
6 “What Is Russell’s Paradox?” by John T. Baldwin and Olivier Lessmann, Scientific American,
https://www.scientificamerican.com/article/what-is-russells-paradox/. Accessed, July 25, 2020.
14.2 The Confusion Borne of Trichotomy