92
sometimes fuzzy, at times acute. In the world of British cultural and economic historian/author David Boyle’s book The Tyranny of Numbers: Why Counting Can’t
Make Us Happy
12
our obsession with numbers and statistical vogues, can lead to
fascinating but unmistakably painful, madness. Indeed, the more numbers and equations, the more paradoxes. In an essay for the London Observer (January 14, 2001)
he recalls “the eighteenth-century prodigy Jedediah Buxton in his first trip to the
theatre to see a performance of Richard III. Asked whether he’d enjoyed it, all he
could say was that there were 5,202 steps during the dances and 12,445 words spoken by the actors. Nothing about what the words said, about the winter of our discontent made glorious summer; nothing about the evil hunchback king.”
In physics (particularly with respect to the so-called Copenhagen Interpretation
within quantum mechanics), philosophy, and ecology, this level of analysis strikes
of the famed “Schrödinger’s cat” paradox, in which the cat is simultaneously alive
and dead, depending on the microscopic or macroscopic vantage point; the location
of the observer, and the instantaneous relationship between entropy and probability.
It can, indeed, drive one to a degree of, shall we say, scientific restlessness, as it
must have done for those who tried to puzzle their way through what Bertrand
Russell first envisioned in the late spring of 1901 in his set-theoretical paradox, or
antinomy, one of the origins of naïve set theory.
13
Russell applied strict logic to sets,
and to sets of sets, therein imagining a set of sets adhering to a rule that excluded
any such set of a set from including itself. But if such a set of sets were such a set,
then it must be itself, which, by its own inner logic precluded itself from being a
member of its own set. Hence, a paradox in every way equal to missing the forest
for the trees, or “Richard III” for its meanings.
A very different paradoxical frontier from that of Cicero’s famed Paradoxa
Stoicorum (46 BC) focusing in particular on six paradoxes of the Stoic philosophers
of his time, who gave great exercise to those passions concerning virtue and vice,
wisdom and folly; and of what higher qualities their combining contradictions
might ultimately enshrine. Given the moral confusion in every age, one might be
inclined to embrace cynical idealism, a first order of defense against one’s own
eventual doubts in the face of inevitable mismatches between personal genetics, and
evolutionary principles, for example.
14
12 Harper Collins/Flamingo, London, 2001-2.
13 See Godehard Link (2004), One hundred years of Russell’s paradox, p. 350, ISBN 978-3-11017438-0; See also From Frege to Godel, a Source Book in Mathematical Logic, 1879–1931, edited
by Jean van Heijenoort, Harvard University Press, Cambridge, Massachusetts, 1967.
14 The booke of Marcus Tullius Cicero entituled Paradoxa Stoicorum Contayninge a precise discourse of diuers poinctes and conclusions of vertue and phylosophie according the traditions and
opinions of those philosophers, whiche were called Stoikes. Wherunto is also annexed a philosophicall treatyse of the same authoure called Scipio hys dreame. Anno. 1569. Cicero, Marcus
Tullius., Newton, Thomas, 1542?-1607., Cicero, Marcus Tullius. Somnium Scipionis. Imprinted at
London: In Fletestreate neare vnto Sainte Dunstones Church by T. Marshe, [1569]; See D Mehl
(2002). C Damon; JF Miller; KS Myers, eds. The Stoic Paradoxes according to Cicero (in) Vertis
in Usum. Walter de Gruyter. p. 39. ISBN 3598777108; See M.O. Webb (1985). Cicero’s Paradoxica
Stiocorum: A New Translation with Philosophical Commentary (PDF). Texas Tech University.
9 The Obsolescence of Presuppositions
sometimes fuzzy, at times acute. In the world of British cultural and economic historian/author David Boyle’s book The Tyranny of Numbers: Why Counting Can’t
Make Us Happy
12
our obsession with numbers and statistical vogues, can lead to
fascinating but unmistakably painful, madness. Indeed, the more numbers and equations, the more paradoxes. In an essay for the London Observer (January 14, 2001)
he recalls “the eighteenth-century prodigy Jedediah Buxton in his first trip to the
theatre to see a performance of Richard III. Asked whether he’d enjoyed it, all he
could say was that there were 5,202 steps during the dances and 12,445 words spoken by the actors. Nothing about what the words said, about the winter of our discontent made glorious summer; nothing about the evil hunchback king.”
In physics (particularly with respect to the so-called Copenhagen Interpretation
within quantum mechanics), philosophy, and ecology, this level of analysis strikes
of the famed “Schrödinger’s cat” paradox, in which the cat is simultaneously alive
and dead, depending on the microscopic or macroscopic vantage point; the location
of the observer, and the instantaneous relationship between entropy and probability.
It can, indeed, drive one to a degree of, shall we say, scientific restlessness, as it
must have done for those who tried to puzzle their way through what Bertrand
Russell first envisioned in the late spring of 1901 in his set-theoretical paradox, or
antinomy, one of the origins of naïve set theory.
13
Russell applied strict logic to sets,
and to sets of sets, therein imagining a set of sets adhering to a rule that excluded
any such set of a set from including itself. But if such a set of sets were such a set,
then it must be itself, which, by its own inner logic precluded itself from being a
member of its own set. Hence, a paradox in every way equal to missing the forest
for the trees, or “Richard III” for its meanings.
A very different paradoxical frontier from that of Cicero’s famed Paradoxa
Stoicorum (46 BC) focusing in particular on six paradoxes of the Stoic philosophers
of his time, who gave great exercise to those passions concerning virtue and vice,
wisdom and folly; and of what higher qualities their combining contradictions
might ultimately enshrine. Given the moral confusion in every age, one might be
inclined to embrace cynical idealism, a first order of defense against one’s own
eventual doubts in the face of inevitable mismatches between personal genetics, and
evolutionary principles, for example.
14
12 Harper Collins/Flamingo, London, 2001-2.
13 See Godehard Link (2004), One hundred years of Russell’s paradox, p. 350, ISBN 978-3-11017438-0; See also From Frege to Godel, a Source Book in Mathematical Logic, 1879–1931, edited
by Jean van Heijenoort, Harvard University Press, Cambridge, Massachusetts, 1967.
14 The booke of Marcus Tullius Cicero entituled Paradoxa Stoicorum Contayninge a precise discourse of diuers poinctes and conclusions of vertue and phylosophie according the traditions and
opinions of those philosophers, whiche were called Stoikes. Wherunto is also annexed a philosophicall treatyse of the same authoure called Scipio hys dreame. Anno. 1569. Cicero, Marcus
Tullius., Newton, Thomas, 1542?-1607., Cicero, Marcus Tullius. Somnium Scipionis. Imprinted at
London: In Fletestreate neare vnto Sainte Dunstones Church by T. Marshe, [1569]; See D Mehl
(2002). C Damon; JF Miller; KS Myers, eds. The Stoic Paradoxes according to Cicero (in) Vertis
in Usum. Walter de Gruyter. p. 39. ISBN 3598777108; See M.O. Webb (1985). Cicero’s Paradoxica
Stiocorum: A New Translation with Philosophical Commentary (PDF). Texas Tech University.
9 The Obsolescence of Presuppositions