67
are each subjects of debate. A Rembrandt is a Rembrandt is a Rembrandt. Yet, hagiographies and explanations about Rembrandt conflict.
As with heuristics and exegesis, a subjective variable will always prove to be the
most tantalizing and efficacious. Explanations and conclusions drawn from personal conviction are untroubled, as a class, in their predictions and presumptions.
The personal attestation is the one that most readily transcends blocking juggernauts of logic. And these are the heart and soul of a useful paradox.
With paradox, a vastly more substantiated ballast of logic, concern, ethic, or
physical circumstance is intimated, than with a fallacy, whose contours and implications, at worst, are no more significant than a lie, or contradiction lacking shelf life.
But the paradox level of confusion and skewed prospect involve any number of
serious manifestations both in mind and physical being. Counter-intuition cascades
across all mathematical and physical barriers; blurred horizons are transformed into
pellucid, graspable precision; new perspectives abet old paradigms; until it proves
impossible to witness the world without the assurance of antimony and the contradictory delusion of any and all resolution.
A paradox accounts for, and then moves beyond, the level of fallacy. Most distressing and appealing of all, paradox tutors liberation to move beyond past ages of
constraint and the tyrannies of logic. There is no philosophy without paradox. No
science in absence of contrasts. What was despair is to become possibility; and
where whole ecosystems had been vanquished by our kind, the existential impulses
and subjective ecological qualia that lend us pertinacity in the face of obliteration
also turn toward the devising of probabilities for the biosphere we never even considered. Hence, the everlasting compulsions of exobiology.
On the cusp of a paradoxical frontier, one knows that fallacy turns to likelihood,
much in the manner of that most simplistic of all basic equations, that
1 = 0.9999999…. Such higher-power infinitesimals were simply ignored by
Renaissance mathematicians, and the greatest atomic timekeepers of our age—
those measuring radioactive decay and half-lives—for whom the concept of “almost
zero” has been sufficient. Indeed, a pure concept of one, the equivalent of an argument in favor of a scientific limit, was not fully addressed until the emergence of the
“sequential compactness theorem” first postulated in 1817 by Bernard Bolzano and
fully articulated by Karl Weierstrass (1815–1897) with its language of consequences, substrings, bounded finitudes, “probabilist inference,” limit points, closed
intervals, and deducibility.
2
Not unlike the formal acceptance in logic of the number
one, zero has its own remarkable concatenation of paradoxical frontiers, from art to
physics. Writes Robert Kaplan in his engaging book The Nothing That Is—A Natural
History of Zero, “One physicist says: ‘The reason that there is Something rather
than Nothing is that Nothing is unstable’”.
3
2 See Bar-Hillel, Yehoshua (1950) “Bolzano’s Definition of Analytic Propositions” Methodos,
32–55. [Republished in Theoria 16, 1950, pp. 91–117; reprinted in Aspects of language: Essays
and Lectures on Philosophy of Language, Linguistic Philosophy and Methodology of Linguistics,
Jerusalem, The Magnes Press 1970 pp. 3–28.
3 Kaplan, Oxford University Press, New York, 2000 p. 180.
8.1 Intra-Fallacy
are each subjects of debate. A Rembrandt is a Rembrandt is a Rembrandt. Yet, hagiographies and explanations about Rembrandt conflict.
As with heuristics and exegesis, a subjective variable will always prove to be the
most tantalizing and efficacious. Explanations and conclusions drawn from personal conviction are untroubled, as a class, in their predictions and presumptions.
The personal attestation is the one that most readily transcends blocking juggernauts of logic. And these are the heart and soul of a useful paradox.
With paradox, a vastly more substantiated ballast of logic, concern, ethic, or
physical circumstance is intimated, than with a fallacy, whose contours and implications, at worst, are no more significant than a lie, or contradiction lacking shelf life.
But the paradox level of confusion and skewed prospect involve any number of
serious manifestations both in mind and physical being. Counter-intuition cascades
across all mathematical and physical barriers; blurred horizons are transformed into
pellucid, graspable precision; new perspectives abet old paradigms; until it proves
impossible to witness the world without the assurance of antimony and the contradictory delusion of any and all resolution.
A paradox accounts for, and then moves beyond, the level of fallacy. Most distressing and appealing of all, paradox tutors liberation to move beyond past ages of
constraint and the tyrannies of logic. There is no philosophy without paradox. No
science in absence of contrasts. What was despair is to become possibility; and
where whole ecosystems had been vanquished by our kind, the existential impulses
and subjective ecological qualia that lend us pertinacity in the face of obliteration
also turn toward the devising of probabilities for the biosphere we never even considered. Hence, the everlasting compulsions of exobiology.
On the cusp of a paradoxical frontier, one knows that fallacy turns to likelihood,
much in the manner of that most simplistic of all basic equations, that
1 = 0.9999999…. Such higher-power infinitesimals were simply ignored by
Renaissance mathematicians, and the greatest atomic timekeepers of our age—
those measuring radioactive decay and half-lives—for whom the concept of “almost
zero” has been sufficient. Indeed, a pure concept of one, the equivalent of an argument in favor of a scientific limit, was not fully addressed until the emergence of the
“sequential compactness theorem” first postulated in 1817 by Bernard Bolzano and
fully articulated by Karl Weierstrass (1815–1897) with its language of consequences, substrings, bounded finitudes, “probabilist inference,” limit points, closed
intervals, and deducibility.
2
Not unlike the formal acceptance in logic of the number
one, zero has its own remarkable concatenation of paradoxical frontiers, from art to
physics. Writes Robert Kaplan in his engaging book The Nothing That Is—A Natural
History of Zero, “One physicist says: ‘The reason that there is Something rather
than Nothing is that Nothing is unstable’”.
3
2 See Bar-Hillel, Yehoshua (1950) “Bolzano’s Definition of Analytic Propositions” Methodos,
32–55. [Republished in Theoria 16, 1950, pp. 91–117; reprinted in Aspects of language: Essays
and Lectures on Philosophy of Language, Linguistic Philosophy and Methodology of Linguistics,
Jerusalem, The Magnes Press 1970 pp. 3–28.
3 Kaplan, Oxford University Press, New York, 2000 p. 180.
8.1 Intra-Fallacy