SYLLOGISM: Or is the internal
combustion engine an example of
‘bad science’?

First syllogism: If the epoch of the
mathematical sciences coincides with the dissolution
of the planet, And mathematics is the sine qua non
of the sciences, Can we assume that the mathematical
sciences are the key to the dissolution of the
planet?

Second syllogism:
Mathematization/quantification/formal
systems/digitization etc.= science and technology.
Science and technology = the dissolution of the
planetary paradigm.
Mathematization/quantification/formal
systems/digitization etc. = the dissolution of the
planet.

Introductory
Notes:

*”These advances in scientific knowledge, it will be
noted, are largely an inheritance of the mathematization
of science that accelerated after Galileo and Newton,
and is now the sin qua non, if
not the ne plus ultra of rational knowledge creation and
validation, replacing the previously satisfactory
mechanical and 'embodiable' forms of proof .” --- from
The First Eternal Hypothetical Conference on Everything.

**You can argue all you like about the double-edged
sword of good science and technology vs. evil science
and technology, but the net effect so far is a rush
toward planetary dissolution. As Vandana Shiva has
pointed out, Unintended Consequences are but a
conscious/visualizable manifestation of the ‘explanatory
gap’ between the mathematized/quantified version of
Nature and Nature itself.

***Thus it stands that mathematization/quantification
is an indispensable condition for science and technology
and therefore an indispensable condition bringing about
the dissolution of the planet.

****Hence, a moral and ethical caveat pertaining to
the tools of mathematized/quantitfied sciences appears
obvious, ‘ad oculos’, or as James Joyce named it ‘the
ineluctable modality of the visible’. The fact that few
if any alternative epistemologies have been proposed
much less allowed to survive is just tough shit. It is a
product of the short sightedness of a
mathematical/science based imperialism and a
narcissistic epistemology that prompted by ‘mathematical
universals’ remains brutally disqualified to express any
empathy for the ‘other’.

*****Locked into the syllogism above, planetary
dissolution is simply carrying forward the condition
created by the gap between western scientific
epistemology or ‘the way we can know’ the world and
Nature itself, a gap that western science and technology
claimed to be closing even as they opened it and left it
festering like a wound.

******”JBS Haldane, speaking of certain aspects of
20th century physics, famously remarked that 'The
universe may not only be queerer than we think, but
queerer than we can think'.” Though, like planetary
dissolution this is an epistemological certainty, the
above comment is a somewhat unrelated matter to the
above syllogism, so here not central to the discussion.
However, the inevitable conclusion of a ‘quantized’
reality is the implication that all things are
‘thinkable’ formally.

Propositions:

1.1 It should be noted that it’s no small irony that
the same epistemology that pointed up the ignorance and
confusion of Biblical chronology should also be the one
to bring it to a finite, wholly secular end by that same
consciousness.

1.2 The control that must be exhibited in the
‘discovery’ of forces that go beyond control (and
comprehension) bring those forces into play via their
misinterpretation of them.

1.3 It’s the imposition of a substitute quantified,
mathematized quasi-nature for its naturally evolved
archetype which is harmful, not the act of
quantification etc. itself. However, the imposition has
long ago become the quantized case.

1.4 Nature must be quantized in order to be understood
incrementally. Thus, science has little to do with
Nature itself and everything to do with the act of
substitution utilizing a series of techniques for
implementing quantized substitutes. This also reflects
the sciences ‘cumulative’ nature as put forth by Noam
Chomsky et al.

1.5 But how would Chomsky answer David Bohm when we
“begin with traditional Cartesian notions of order and
then try to impose the dynamics of quantum theory on
this order by using the algorithm of 'quantisation[?]"

1.6 Passionate conviction in mathematical analytics
does not ring false here. Or reason has its passions
that the heart cannot know assuming as Ludwig
Wittgenstein did in the Tractatus that mathematics is
the most reliable form of reason if not the only one.

1.7 “The belief that the underlying order of the
Universe can be expressed in mathematical form lies at
the heart of science and is rarely questioned.” But
mathematics is only an expression of that Universe not
its substance or source as Hegel points out. Mathematics
is considered substantive and substantial within western
epistemology to the point where it long ago began
serving as a substitute for objects of the actual world
from which it is said to seek expression.

1.8 Despite its shadow
success as it relates to
what the dominant epistemology regards as the
‘actual’, mathematics remains
existentially suspect. Given, for the present, the
essentially sensate nature
of our existence, this should come as no surprise.

1.9 But mathematics as an
ontological threat,
though this threat was contextualized by earlier
thinkers such as Giordano
Bruno, William Blake, William Wordsworth et al, has
more recently come into
intense focus with the existentially visceral
acknowledgement of global climate
change.

1.10
In the literature, global climate change is
perceived as
existential. But through formal systems of
quantification solutions to Global
Climate Change are invariably manifest through the
mathematical sciences. These
mathematical sciences comprise the very set of
disciplines which created the
weather anomalies we now know as global climate
change.

2.1 Most cultures and religions contain an apocalyptic
literature. But not one foresaw the precise matter by
which the world would end because the dynamics of the
dissolution of the world was in direct or oblique
contra-distinction to the manner in which they
understood the world and its apocalyptic potential.

2.2 This is no small matter since it seems incumbent
upon culture and religion, especially religion, which
has made so much racket about the world’s end, to get
the end time’s agent at least partially right. Instead,
the majority religions, especially of the West, for the
most part abet the scientific/technological dissolution
of the planet even while denying some of science’s most
obvious truths, thereby appearing merely buffoonish.

2.3 Religion in the West has embraced this role as
cultural buffoon even as its very existence has become
inextricably tied to western/global quantized science
and technology. Hypocrisy, irony, parody --- all are
rampant in this milieu and western religion is the
rightful victim to the most obvious taunts and
criticisms.

2.4 It is therefore unlikely that western religion
would discover the source of their so-called Armageddon,
the agent behind the Apocalypse, though sclerotic
institutions like the Catholic Church were face to face
with advocates of a deeply formalized science by way of
its numerous pogroms and inquisitions.

2.5 The churches reacted badly to the results of
scientific discovery while remaining woefully ignorant
about how those results were achieved. Sciences
dependent on observation are attacked such as evolution
whereas the Higgs Boson and its overwhelmingly
mathematical foundation poses as the ‘God Particle’ with
nary a whimper from the religious community. Why?

3.1 The buffoon element is already present in the term
‘God Particle.’ For science, because the Higgs Boson
will give way to a different set of suppositions as its
mathematics becomes more and more untenable. This is the
cumulative effect of science neither named or noted in
its reliance on the syntax of Being e.g. the Higgs Boson
IS when in reality high energy collisions indicate that
under highly controlled conditions a ‘particle’ can be
observed that has some of the already limited properties
required to be considered a Higgs Boson. As the famous
mathematical chauvinist, John Von Neumann expressed it,
“Full knowledge of the object is not requisite, but only
those quantities we believe to exist.” Or as Roger
Penrose counters, “conflating reality with lawfulness.”

3.2 As time passes, the ‘reality’ will become far more
messy as through mathematical calculation supported by
recorded observation under rigidly controlled
conditions, mathematicians attempt to describe how the
now hundreds of sub-atomic particles ‘interact’ to
create our reality and dozens of alternative realities
that touch upon Haldane’s universe of events which are
‘queerer than we can think.’

3.3 Somehow, even though we cannot entirely
conceptualize such phenomema, or ‘visualize’ them to use
Niel s Bohr’s term for quantum events like wave/particle
paradox, they are part of what we are as humans
according to the cumulative and most sophisticated set
of concepts resulting from 500 years of
mathematical/quantized science. We are left
unincorporated into our own being by our own
consciousness, the source of our mathematical/quantized
understanding.

3.4 When a Standard and Poors’ analyst writes apropos
Wells Fargo mortgage derivatives that “Level 3 asset
values use inputs that are unobservable and are often
based on internal modeling “ the ‘unobservable’ inputs
are literally an fubar of mathematical expressions
derived from quantum theory. So it shouldn’t be
surprising that physicists and mathematicians have
flooded Wall Street brokerages converting/brokering
physical nature into intangible assets hidden from
traditional observation. Of course, we should also throw
von Neumann’s Theory of Games into the mix since both
quantum and quantized ‘modeling’ amply supply the
denouement.

3.5 At first historical glimpse around 1500, it’s the
numerical objectification of greed rather than the
delinquency of numbers that appears to hold sway here.
But with the rapid rise of the mathematical sciences in
their role as epistemological ne plus ultra that the
shift occurs.

3.6 This presents a bigger buffoonery than religious
millennialism because it can be supposed that if it had
not had technology with which to become so ‘sinfully’
enamored, religion would play no role in planetary
dissolution. As it stands now, religion’s embrace of
technology (and science by extension) put an end to all
that and made it a wiling dupe.

3.7 Science does not have that luxury. The apocalypse
brought about by the success of science and technology
is very real. And there is no substitute for its core
‘evil’ if you will.

3.8 The “mathematization of science that accelerated
with the [advent] of Galileo and Newton [et al], and is
now the sin qua non, if not the ne plus ultra of
rational knowledge creation and validation, replacing
the previously satisfactory mechanical and 'embodiable'
forms of proof .”

4.1 Is ‘evil’ too strong a term to apply to
mathematics, formal systems, systems of quantification?

4.2 Certainly, evil as regarded as magic does not
apply here.

4.3 The notion that such tools are now indispensable
for the pursuit of science certainly has a ring of
habituation. And habituation certainly has a long
association with evil.

4.4 One does not speak of being ‘habituated’ to God.

4.5 But certainly mathematics habituates science
through its long and largely uncriticized usage. Anatol
Rapoport writes “All purely mathematical theories are of
the sort [a system of theorems built up from a set of
postulates]and, as such are practically immune from
criticism.”

4.6 Mathematics is like logic. It is both insular and
fungible. (In this, its shares a number of traits with
religion like ‘catholic e.g. universal and an interior
logic.)

4.7 The more you quantify the world around you the
more it becomes isolated from criticism and fungible
with more and more applications and potential
substitutions. Why is this?

4.8 The most obvious answer is that a quantized set is
a simpler tool. It can be readily organized among its
elements and easily communicated having a set of agreed
upon symbols which take into account a wide swath of the
actual world or, at least, sets of gleaned properties of
the actual world.

4.9 What’s rarely noted is this utility comes at a
cost. The ‘real’ from which it is derived and which was
far more complex than its quantized caricature would
yield different results if it was the source or, more
likely in its authentic ontological sense, it would
produce no results at all, much less utile ones.

4.10 When the ‘utile’, stripped down, quantized entity
becomes the norm, the ‘real’ source ceases to exist in
the consciousness of the user, but persists in its own
ontic realm.

4.11 Blanket terms for the negative results from such
a system are called unintended consequences (sometimes
unanticipated consequences or unforeseen consequences).
These are merely outcomes that are not the ones intended
by a purposeful or telic action.

4.12 Terms such as unintended consequences etc. are
usually reserved for the social sciences or the social
dimensions of large technological projects.

5.1 But it’s no bother to trace this term back from
the social sciences to the hard sciences, say via John
von Neumann/Oskar Morgenstern’s Theory of Games and
Economic Behavior, published in 1944 by Princeton
University Press.

5.2 And from there it’s even less bother to apply the
‘law’ of unintended consequences to the hard sciences.

5.3 The hard sciences or, more accurately their
purported analytic ‘certainty’, was the object of von
Neumann/Morgenstern’s book, to bring mathematical rigor
to the social science of economics.

5.4 The main tool for this outcome was in the title,
the Theory of Games a highly quantized and, I might add,
idealized, approximation of the ontic. Game theory is
simply designed as the study of strategic decision
making. More formally, it is "the study of mathematical
models of conflict and cooperation between intelligent
rational decision-makers.

5.5 In biographical recollection and critiques,
authors insist that Morgenstern had a more ‘human’ or
‘humane’ sense of his subject than von Neumann who was
content to dwell in the manipulation of statistics and
probabilities, applying the cold hard mathematical
approach. However, Morgenstern largely went along with
von Neumann’s more analytic approach and it is the
mathematical/quantized emphasis of the book which is
considered ground breaking. One could ask what kind of
person warms to such a work? Later, ‘subjective
probability’ primarily through such instruments as
Bayesian logic were applied to such efforts to more
conform to a reality and humanity which had taken a
severe beating under Von Neumann’s rubric. But still the
blows come.

5.6 The answer is von Neumann’s position is more
expressive of Reason or the rational, a hot
Enlightenment term we have not yet evoked. In today’s
ethical marketplace, Reason is highly prized and seldom
scrutinized.

5.7 Von Neumann’s game theoretical reason is
mathematically based between assumed rational decision
makers. This presumes no passionate decision makers need
apply. The analytical approach itself wipes away the
furbelows of emotion and its presumed error.

5.8 It is therefore assumed that after the ground
rules are laid the only error that can occur are errors
in judgment within the framework of the game.

5.9 Therefore, reality has no place in von Neumann’s
mathematical role playing, much as the Prisoner’s
Dilemma Game requires its objects act like numbers when
they are decidedly not. These are indeed games.
Apocalyptic ones in many respects.

5.10 But far more importantly, it justifies a limited
set of outcomes from situations which need not morally
exist and merely describes one set of game theoretical
‘pain’ as more desirable than another set by virtue of
the pain’s quantity and no other factor.

5.11 Thus Hegel writes in the Phenomenology of Mind:
“The evidence peculiar to this effective way of knowing
--- an evidence on the strength of which mathematics
plumes itself and proudly struts itself before
philosophy --- rests solely on the poverty of its
purpose and the defectiveness of its material, and is on
that account of a kind philosophy must scorn to have
anything to do with. Its purpose or principle is
quantity. This is precisely the relationship that is
non-essential, alien to the character of the notion.”
Trans. J.B. Baillie

6.1 The law of unintended consequences not only
describes the historicity of any science you care to
name through the paradox of accumulation or change of
the discipline over time and use of the syntax of Being
which implies permanence.

6.2 there would be little or no problem with this
approach except that such scientific activities are
designed for implementation. They have a far greater
chance of success if they lead to industrial
application. If they lead to profits through commercial
systems set up in tandem to exploit discoveries in the
pure sciences. Is the internal combustion engine an
example of ‘bad science’?

6.3 Tie this to the inherent limitations of the
mathematical/quantized approach which was accelerated
500 years ago and that we have already pointed to and
you have your recipe for global disaster.

6.4 It also becomes apparent why the situation is now
so unique and dire.

7.1 A simple set of propositions professes a simple
irony.

7.2 First, one accepts that the so-called scientific
discoveries display a certain efficacy. Whether this
efficaciousness is universal or relative remains a
matter of debate. Actually, this debate is one of the
engines that drives the sciences.

7.3 Further, one accepts the precept that ”These
advances in scientific knowledge, …, are largely an
inheritance of the mathematization of science that
accelerated after Galileo and Newton, and is now the sin
qua non, if not the ne plus ultra of rational knowledge
creation and validation, replacing the previously
satisfactory mechanical and 'embodiable' forms of proof
.”

7.4 Finally, if the above pervasive and primary tools
of quantification and mathematization indeed dominate
the sciences as is easily demonstrated, those same tools
have an essential role in the dissolution of the planet.

7.5 Thus, to continue to use such tools, while they in
the short term may prove useful, in the long term will
bring about the end of the world as we know it.

8.1 In recent decades we have witnessed or more
accurately glimpsed the planet’s demise.

8.2 Pundits like Gross and Levitt point out that we
would not even be aware of planetary dissolution if it
weren’t for the science’s ‘discovering’ the danger. But
they didn’t ‘discover’ the occurrence of planetary
dissolution itself. They ‘discovered’ some of the
phenomena behind it largely because they through the
mathematical sciences created it.

8.3 The fact that G&L proposition is western
chauvinist horse shit of the first order is not
difficult to suss out. Do Gross and Levitt think that
the people of the Maldives or Bangladesh cannot
‘observe’ their country’s being overwhelmed by rising
sea levels?

8.4 Cultures living there may not have been able to
pin point the problem as carbon emissions, green house
gases et al as the melting of the polar ice caps
submerge their homes. But I’m certain, like hundreds of
minority cultures around the world, they have observed
quite accurately, the exploitation, waste and neglect
that surrounds western science and technology. The
litter-ature is ubiquitous.

8.5 The world knows Gross and Levitt are killing Mama.
Gross and Levitt know it too. But they take solace in
the fact that they, through science, have ‘discovered’
the deadly effects the nature destroying weapons science
has wrought and still wields, leering out from this or
that academic podium.

9.1 A core assertion would be then that positivism
along with its telic dimension is at its heart
nihilistic.

9.2 The proof of this assertion lies no further away
than the abandon with which the positivist gospel is
applied and defended in the face of its obvious dangers.

9.3 Until recent environmental history, there had been
little to say against the materially and spiritually
progressive nature of scientific positivism.
Environmental devastation though apparent in dozens of
instances had yet to reach detectable global dimensions.
Indeed, who bothered or had the wherewithal to detect
any apocalyptic negatives at all. For those who mattered
in, Western Europe and America, it was a material Utopia
of sorts.

9.4 As stated in their book Higher Superstition, it
wasn’t until the likes of Gross and Levitt, like Lenny
Small in Steinbeck’s ‘Of Mice and Men’, had felt Nature
go limp under the positivist grip of their hands around
her throat that they realized and belatedly reported her
imminent demise. Yet, they continue to squeeze because
that’s all they know how to do.

10.1 Of course, wealth has and continues to play a
major role in advocating for the dissolution of the
planet. The acquisition of wealth always trumps good
judgment.

10.2 The connection between corporate wealth and
standards of living are too obvious to reprise here.
Like a quantum paradox, the current corporate agitprop
insists that there is a conflict between jobs and the
environment. Then corporations make the jobs less
desirable by scuttling unions, reducing wages,
eliminating pensions and health care by holding the
workforce hostage to global trade agreements and foreign
outsourcing.

10.3 That such quantum paradoxes as wave/particle and
position/momentum may have provided the metaphysical
underpinnings to the lies behind, say, the
job/environment paradox may seem a stretch. But is it
really? The quantum paradoxes are not ‘embodiable’ or
‘visualizable’ while the job/environment paradox, it is
insisted by the bought off whores and pimps of capital,
is equally intractable.

10.4 But all that is intractable in the corporate
dimension is the headlong pursuit of wealth. If the
ethos of the Kalahari Bushmen proved to be the path
toward vast material wealth, power and luxury, the Koch
Brothers would be wearing a strip of animal hide about
their dicks, chowing down on Hoodia Gordonii.

10.5 In fact, for Hoodia, which has proven to be an
appetite suppressant, the San bushmen have been
ostensibly awarded royalties for their indigenous
knowledge. The San have yet to profit from this
agreement, as P57 has still not yet been legally
developed and marketed.

11.1 Of course, there is close connection between the
modern positivist sciences and modern banking.

11.2 In fact, all western taxonomies have striven to
introduce positivist ‘accuracy’ and the purported
universal indisputability of mathematics.

11.3 This has given rise to the irrelevant notion that
behind every machine error is a human error which can be
overcome by a more sophisticated protocol or software.

11.4 But if the apocalyptic nature of the
science/environment interface has its roots in the 500
year habituation of mathematics such concerns as
communications protocols and software design are mere
furbelows in the headlong plunge into planetary
dissolution.

12.1 Quantum is an approximation of all number sets
because like all number sets each marker must
quantified, discrete, or remain invisible.

12.2 Quantum mimics the gaps in number sets between
values. These ‘gaps’ cannot be eradicated only
minimized.

12.3 Like the gaps between numbers in number sets,
quantum phenomena is not ‘visualizable’ or ‘embodiable
as a continuum.’

12.4 Thus quantum is not only best expressed through
mathematics, it is a set of phenomena inextricably tied
to mathematics.

12.5 Without mathematics quantum would not exist. And
this is not commutative.

12.6 Without the most primitive and rigid forms of
discretion, quantum would not be conceivable much less
‘non-embodiable.’

12.7 Quantum is a mathematically posited reality and
we are fine with that because of its myriad material
uses.

12.8 The relation between the energy and frequency in
a Planck relation is discrete or not at all.

12.9 The packets of energy have only a discrete value.
No others. The movement from one ‘orbit’ of energy to
another takes place instantaneously. There exists no
value in between these orbits, neither in time nor in
space.

12.10 Likewise numbers can never reflect anything but
a discrete value even when attempting to approximate a
smooth curve by reducing the number packet by a smaller
and smaller value.

12.11 Visualize the attempt to make digitized sound
conform to analog sound. The step effect in the interior
of the curve can never be wholly obliterated e.g.
analoged but most audio-files are satisfied with the
approximation of Nature and many even prefer the digital
result to the limitations of the transposition of
reality which will inevitably occur in a mechanical
process like analog recording.

12.12 This is true of the infinitesimals in the
Calculus which are far better suited to mathematical
expression while remaining mere approximations in
perpetuity as regards the objects being expressed.

12.13 What would be the result if the mathematical
expressions for their ur-objects were allowed to
accumulate in the applied literature?

12.14 How would we acknowledge a mathematical
simulation, an approximation of its real corollary that
had been raised to the status of a real or actual
object?

12.15 Is mathematics, at least applied mathematics, a
simulation of the real?

12.16 Does not any object qua mathematical application
retain some aspects of simulation? Or does it become a
wholly new and real entity?

13.1 Majority interpretation sees a mathematical
application that gives a predictable and coherent
result, an entity.

13.2 Sub-atomic particles such as the Higgs Boson or
so-called God particle began life as an explanatory gap
in primarily math driven arena of sub atomic physics.
This already smacks of a fait accompli. As Brian A.
Silver writes of similar experiments in subatomic
physics, "We put in some physical facts, follow the
rules for obtaining the needed results, and almost
always get what we want. The comparison between the
theoretical results and experiment is rarely
disappointing."

13.3 To qualify as the Higgs Boson, a candidate
particle must reflect a set of properties predetermined
by mathematical formula which have a predisposed history
of simulation of a long abandoned ‘vizualizable’ or
‘embodiable’ reality.

13.4 It’s the math, numbers, that now drive our most
essential, being oriented, appreciations of what exists
and what is actual. This is not intended as a critique.
After all, modern material existence would not be
possible without such a compromise between the real and
the ‘artifactual.’

13.5 In myriad applications, from cell phones to
nukes, the math works. And formality has long ago become
normality.

14.1 The particle ‘discovered’ or created at Cern need
not exactly conform to its mathematical prediction. And
it certainly does not and certainly will not. Thus, once
again, a physical entity such as the Higgs Boson is only
a simulation of its mathematical parentage or math has,
once again, only simulated a reality. In either case
more research and funding is urgently needed.

15.1 With the advancement and success of quantitative
system the problem of scale takes on a new dimension.

15.2 Earth’s resources are, of course, finite. That we
are fast approaching the upper bounds of the capacity of
our planet made obvious by some quarters’ desperate
interest in terra forming the moon and other planets.

15.3 Aside from commercial interests’ intense desire
to purchase an object denial of global climate change,
such interests’ burgeoning investment portfolio in terra
forming projects and exploiting other planets belies
their true feelings toward the future of earth. If man’s
ingenuity could solve such problems as energy in
perpetuity here on earth one would suspect fewer scarce
resources would be allocated toward the exploitation of
space. On a smaller scale the same logic applies to the
exploitation of the poles made possible by the very
degradation of the planet commerce denies is occurring.

15.4 But this is not the core issue here. Here we are
concerned with the sine qua non, ne plus ultra, of the
process, mathematization/quantification.

15.5 History won’t have it both ways. It won’t lay
claim to the great leaps, even new paradigms, in
mathematics especially with the advent of the Calculus
and deny mathematics role in the dissolution of the
planet.

15.6 Even if this dissolution is attributed to the
abuse of the few fortunate enough to partake of the
material well-being that resulted from these
mathematical/industrial advances, shouldn’t the
subsequent nature of the unintended consequences as laid
out by scholars such as Vandana Shiva give one pause
about the role of mathematics in this dissolution?

15.7 Nevertheless, the dissolution of the planet in
the manner in which we are now experiencing it would
most certainly not have been possible without its sine
qua non, its ne plus ultra, the mathematization of the
sciences.

15.8 Barrow and Tipler went to great lengths in their
book The Anthropic Cosmological Principle to trace a
seemingly preordained set of cosmic circumstances that
resulted in creation of mankind and his environment.

15.9 Could mathematization/quantification as now
practiced be a ‘virus’ that brings about the specie’s,
if not the planet’s, denouement?

15.10 Certainly, after humans the earth will go on in
some fashion for another 5 billion years or so.

16.1 The mathematization of the sciences has been a
great success. They have predicted the dissolution of
our sun at approximately 5 billion years. This precision
is based on no known sentient being’s ability to
physically alter the sun.

16.2 It has created an evolution that runs parallel to
Nature’s. Change is generally accelerated and
occasionally slowed.

16.3 The mathematical sciences orbit about Nature
picking bits to exploit.

16.4 There is no choice but to let the success of the
mathematical sciences play out. Whether it can outrun
its own manifest denouement is doubtful. As the old
adage goes, if it appears too good to be true, it
probably is, the pun on probability within ‘probably’
notwithstanding.

17.1 Now one might say, now lad, mathematics since
1500 is like any other mathematics. It’s merely a tool.

17.2 But can ‘merely a tool’ also be a sine qua non
and ne plus ultra. A perfectly good house can be built
without a hammer.

17.3 Sine qua non implies a fundamental involvement ,
a metastization if you will, with the subjects of the
sciences.

17.4 A critique of the Ne Plus Ultra implies something
more sinister than an encroaching pathogenic.

17.5 But perhaps these two qualities do not actually
inform much less drive the sciences. But one would be
hard pressed to tease away the mathematics from its
object and have anything left. In most cases there would
attain no ‘object’ at all.

17.6 It’s safe to say that math = science and that
science = math. This is of course why they are called
the mathematical sciences.

17.7 But this framework (math = science/ science =
math) is not commutative. For example, we accept the
adjective noun combination mathematical sciences, but
rarely use the term scientific math except in the most
clumsy and ignorantly iterative way.

17.8 There is no true equivalency here. Here the
adjective ‘mathematical’ defines and denotes the inner
processes of those sciences which benefit from it and
are now often derived from it including their ‘objects’
of study. It is not commutative and given the progress
within the sciences in general the term ‘mathematical’
holds primacy science now being an unnecessary addendum.

17.9 What physicist cannot look at a series of
equations and not immediately recognize the subject
within the ‘objects’ to be plasma physics or string
theory.

17.9 It is almost virtually impossible to speak of any
human endeavor as being scientific if it does not have
its basis in mathematics

18.1 Let us reprise, the tantalizing coincidence of
the birth of calculus accelerating the Age of
Exploration/Exploitation and the meteoric rise of the
scientific discoveries and instrumentation that has
propelled us toward our current denouement.

18.2 Such an approach gets you nowhere.

18.3 You can discuss elements of scale such as
over-population, the rise of the use of coal, the
internal combustion engine etc. and a tipping point for
all such toxins.

18.4 Scale is not an answer but a symptom.

18.5 Once we realize that scale is a symptom complex,
quasi-ethical concerns about good versus bad science
evaporate.

18.6 For example, there is little doubt that the
internal combustion engine and the burning of fossil
fuels produce atmospheric toxins. It is equally true
that transport of goods via internal combustion vehicles
over greatly improved roadways has improved the lives of
much of the world’s population.

18.7 Was the invention of the internal combustion
engine bad science? Would we be better off if science
and engineering had safeguards against such a planetary
toxin once discovered being exploited?

18.8 Such are the conundrums one faces when one does
not consider the root of the problem.

18.9 The Age of Exploration/Exploitation dovetails
nicely with the nascent sine qua non of mathematics.

18.10 But it is safe to say there would be no Age of
Exploration/Exploitation if not for the mathematical
sciences.

18.11 It therefore appears that the mathematical
sciences are the ne plus ultra which has brought us to
our current global state.

19.1 Generally, the elements of calculus are not
discrete in themselves. But their results issue a
discretion, say the distance between A and B.

19.2 Thus a symbolized entity illustrates a ‘property’
of Nature.

19.3 But this property,’ distance’, does not operate
in Nature itself the same way as it does in calculus.

19.4 In Nature the distance contributes to what we
might now refer to as an ecosystem though the use of the
word system has its own limitations.

19.5 The distance derived from calculus draws nothing
from a notion such as ‘ecosystem’ until its techne and
telos are revealed, say a road grade.

19.6 Then reflexively the distance derived from the
calculus can apply ecological principles. But, by then,
it’s too late. The choice of ‘distance’ is limited and
in and of itself discrete. The discretion may be limited
to one but since the entity itself is derived from
properties which are limited to the calculus answering
to it and not Nature, it is at best a discretion of 1.

19.7 This entity derived from properties limited to
the calculus such as distance bears little relationship
to the Nature it is drawn from.

19.8 Yet when the mathematical sciences are ne plus
ultra, Nature is strangled even when the science has the
best intentions.

19.9 Its therefore not surprising that the success of
the mathematical sciences as regards its manipulation
and utility of the natural world measures that success
in the framework from whence it arose.

19.10 Thus the internal combustion engine has been a
startling success. And the internal combustion engine is
a bane to the planet.

20.1 We have not yet said “Nature has outlived its
usefulness.’

20.2 However, one could say that the internal
combustion engine powered by fossil fuels has outlived
its usefulness.

20.3 We are not willing to say that Nature has
outlived its usefulness because we erroneously believe
that Nature is revealed through the mathematical
sciences.

20.4 But this ignores the hermeneutical dimension of
mathematics.

20.5 As implied before, mathematics has very powerful
hermeneutical properties. All of the entities that fall
under its aegis give up their heuristic interpretation
in order to conform to a set of hermeneutical properties
which define the mathematical object. Most often this
process goes entirely unnoticed.

20.6 When scientific anomalies occur or experiment s
fail then the hermeneutical process undergoes scrutiny.

20.7 Though not of Nature, these mathematical objects
prove far more efficient in eliciting certain properties
from the natural world. Thus mathematical objects are
often mistaken for their natural counterparts.

21.1 Several questions.

21.2 What constitutes ‘bad science?

21.3 Does ‘bad science’ alone explain planetary
dissolution?

21.4 Do ‘unanticipated consequences’ fall under the
rubric of bad science, good science or good science gone
bad?

21.5 Do currently discarded theories of science such
as the ‘aether’ or ‘phlogiston’ constitute bad science?
If so is all of the history of science in some sense bad
science? Is the sum?

21.6 Aren’t coal burning plants, atomic fission and
the internal combustion engine examples of ‘good
science’ in that they are inherently utile, their
deleterious effects notwithstanding?

21.7 In the way we are using science here aren’t we
simply referencing whether the science ‘works’ without
the consideration of ‘unanticipated consequences’?

21.8 Will ‘unanticipated consequences’ persist? Do
‘advances’ such as binary orientation and computer
modeling reduce ‘unintended consequences’ or increase
them?

21.9 What study or discipline is endemic to all of
these questions? What epistemology?

21.10 You can hardly call them mathematical sciences
without admitting the role of mathematics.

21.11 You can hardly claim that nuclear fission is not
a product of the mathematical sciences.

21.12 So isn’t it reasonable to ask the role of
mathematics in the conception and acceleration of
technology which in turn is responsible for global
climate change.

21.13 Take nuclear power. Pollution wise it is not at
present seen by most as imminent a threat to the planet
as, say, burning fossil fuels. Of course, spent fuel
rods and nuclear waste remain strong candidates. If the
Wipp or Waste Isolation Pilot Plant were such a fine
example of the progress of the mathematical sciences why
has there been so much public resistance to it. Then
there are nuclear accidents and nuclear war that
currently or potentially play a role in pollution and
climate change. At best, they represent poor
alternatives.

21.14 Given the relative ‘cleanliness’ of nuclear
power it provides little solace as an energy solution as
Three Mile Island, Chernobyl and Fukushima have so
graphically demonstrated.

21.15 Despite avoiding some of the problems associated
with global climate change, alternative energy
technologies have their own negative consequences.

21.16 This suggests that the mathematical sciences
incapable of producing anything other than negative
unintended consequences at odds with the environment.

21.17 Perhaps, the epistemology of mathematics itself,
the ne plus ultra of the mathematical sciences, is
double edged. On one hand it represents rapid
technological progress and dominant, faux- universal
epistemology. This on the other hands excludes the
mathematical sciences from our cultural and
epistemological concerns when at heart it gives every
circumstantial indication that it’s is leading us to
planetary dissolution.

21.18 Once again having said this it appears to refer
to matters of scale. But it must be recalled that
pollution of such scale that it would threaten the
planet is a symptom, not the source of the problem.

21.16 The source remains the instrument itself. In
this case the mathematics of the last 500 years.

21.17 This is not a result apposite Wittgenstein’s
Tractatus. Wittgenstein’s result may suggest certainty
but in context mathematics is too narrow for reality.
Perhaps, consistency, precision, efficiency, were
exactly what was not required for the continued
blossoming of the planet. If so, too late now.

21.18 Much could be said here about the spread of the
mathematical sciences into all other aspects of our
culture from Von Neumann and Morgenstern’s Theory of
Games and Economic Behavior to Frederick Winslow
Taylor’s Scientific Management.

21.19 Taylor’s theories certainly raised efficiency on
the factory floor if not elsewhere. But their inhuman
side has become a source of parody with their outright
ignorance of what constitutes a human. You’d be hard
pressed to divorce the inhuman side of Taylor’s
scientific management from the mathematical sciences
themselves.

21.20 What makes Taylorism such an apt example is its
close proximity of theory to action and the instant
revulsion it created in the humanity that was rendered
subject to it. Now, modern methods of scientific
management or more subtle, more coercive and more
authoritarian. Much of this is due to the reduction of
psychology to mathematical principles.

22.1 Western epistemology? The organism has a
mechanism. That’s all we know. That the organism is lost
in the search for the mechanism is of no consequence. As
Lacan puts it, "Flip through [Descartes On Man] and
confirm that what Descartes is looking for in man is a
clock." To calibrate Taylor’s time/motion studies no
doubt.

22.2 Western epistemology absolutely does not credit
thinking ‘outside the box.’ One could joke ‘No money in
that’ and not be wrong. Other cultural restraints are,
of course, at play and perhaps we’ll get to them later.

23.1. The purpose of this paper is not to deny that
mathematics through the mathematical sciences can reveal
underlying ‘structures’ within reality. It’s simply to
state several caveats.

23.2 First, these ‘underlying constructs’ are and
remain mathematics in so much as they are mere
constructs and not the ding an sich.

23.3 Secondly, such constructs are comprised of
mathematical ‘idealizations’.

23.4 Thirdly, mathematical constructs are at best
approximations of real or actual phenomena. Now, most
studied, ‘relevant’ phenomena are simply mathematical
entities which conform to a limited number of properties
required to confirm the equations.

23.5 Fourthly, these idealized qualities account for
the iterative nature of mathematics as opposed to the
less predictable phenomena they attempt to mimic.

23.6 Fifthly, the readily repeatable or iterative
nature of mathematics makes it a far more attractive and
simple route for the study of nature than, for example,
mere observation. Here think of Goethe’s Zur
Farbenlehre.

23.7 Convenience, utility and success at revealing
underlying constructs accounts for the sine qua non/ne
plus ultra dominance of the mathematical sciences
especially, as cited many times in my earlier work such
as Tale of the Tribe: Deconstructing the Demiurge.

23.8 This success, this reliance on the mathematically
utile, cannot be denied. But at the risk of sounding
melodramatic, at what price.

23.9 I would argue that because it is processed, that
is an easily or easier iterative idealization, all
mathematics is discrete that is can only yield the utile
by being diced into conformal units which have no analog
in the Natural world reaching a real expectation in
Planck’s quantum ‘wave packets.’

23.10 Our world is now largely comprised of these
mathematical idealizations. These idealizations have
superceded and overwhelmed objects in the natural world.
Virtually, all of our determinations are dependent on
these idealized constructs and have little or nothing to
do with the natural world.

23.11 But they do not comprise an evolved, holistic
world ergo are insufficient for the sustainability of
the planet. Stop gap technological measures based on the
mathematical sciences appear daily and are just as
quickly found wanting.

24.1 Of course, without the mathematical sciences in
all likelihood we would not be approaching ecological
disaster. I think it’s equally true that few of us would
want to go back or explore alternatives which do not
embrace the mathematical sciences.

24.2 Not god, but the calculus has created the best of
all possible worlds. From the perspective of western
epistemology, suffering is diminished in our modern
world to the degree that we can embrace Leibniz’s
supposition and reject Voltaire’s.

24.3 The planetary dissolution that results from the
embrace of mathematical sciences introduces a kind of
apocalyptic suffering that may be manifest for just a
few generations and primarily affect those least
responsible for climate change.

24.4 But already a new era of suffering has affected
the west, witness Chernobyl, Yakushima, Katrina, Sandy
etc.

24.5 To any reasonable observer it is now obvious that
the relevant institutions intend to do little or nothing
to slow global climate change. As regards this paper
this matters not at all.

24.6 The observation put forth in this paper is that
relevant institutions intend to do little or nothing to
slow the mathematical sciences.

24.7 Once stated in this context, the term relevant
institutions shifts dramatically from the political and
economic to the scientific. Greed and self-interest may
be the driving forces ensconced within the political and
economic arenas, but mathematics is the self-interested
tool among the scientific institutions.

24.8 One might say on moral and ethical grounds,
though little heed is paid, greed and self-interest can
be debated. The same cannot be claimed for mathematics
within the sciences.

25.1 Theories in the mathematical sciences are both
true and not true. They are not true in the historical
sense because they are usually superceded or utterly
falsified by later research. This Chomsky calls the
cumulative effect where later science builds on earlier
science whether good or bad. There is always a lesson to
be learned.

25.2 But scientific theories are true in a critical
sense before history overtakes them in that they are for
a time, for their time, ‘existential.’ A muon remains a
muon as long as it serves a set of mathematical
properties which constitute a muon, ”internally
identical until the instant of decay.” The theory of
General Relativity is reinforced as true only as further
experimentation and calculation benefit from its tenets.

25.3 If it is indeed too late to stem some kind of
global apocalypse, it cannot be attributed to the
symptoms of the mathematical sciences alone e.g. the
myriad polluting technologies. The mathematics behind
the technology has created the fait accompli.

25.4 The mathematical sciences are not only the sine
qua non and ne plus ultra within its own paradigm but
epistemology wide. It is the ruling epistemology.
Advanced weaponry, the byproduct exclusively of the
mathematical sciences and now attainable worldwide, has
carried on the long tradition of western and now
American hegemony. It is quite clearly ‘how we know the
world’ e.g. our epistemology.

25.5 Who knew each and every limited mathematically
driven success had concealed within it the very symptoms
that would lead to planetary dissolution as sure as if
an large asteroid were headed our way?

25.6 From this perspective there is no good science or
bad science. At best, for several hundred years, the
mathematical sciences provided a minority of the world’s
population comfort beyond that of Medieval European
royalty while it rushed to destroy the planet.

25.7 But here we are not casting blame on the symptoms
whether those symptoms be military, like unexploded
ordnance, depleted uranium bombs, gas and germ warfare,
drones etc. etc. ad nauseam or just plain old green
house emissions.

25.8 Science, religion, philosophy much less economics
and politics never got down to focusing ethically and
morally on the core science, the driving epistemological
source. Mathematics always got an ethical by. It was
immune from ethical judgment even as its cultural and
historical roots were exposed. Irrelevant caveats such
as numbers never lie were our bromides for a planet at
the mercy of a highly destructive mathematics based
epistemology.

25.9 Even as mathematics and the mathematical sciences
got this ‘by’ of utter objectivity, no one made the
connection that by such an exception it implied
mathematical science is something other than a human
activity and beyond ethical scrutiny except at the level
of product or symptom.

25.10 The mathematical sciences do provide a higher
level of truth, and a higher level of falsehood. A level
of falsehood so high it can lead to the dissolution of
the very species which became dependent upon it.

25.11 Who knew? After all the mathematicians,
scientists and engineers regarded mathematics as
providing a glimpse into a higher order of reality, even
god. Problem is a glimpse into something real becomes
not ‘real’ when subjected to the discrete limitations
that makes mathematics possible, makes mathematics what
it is.

25.12 With mathematics for a while you’ve got
something that works. Is utile. And in march the
engineers.

25.13 But little or no account is taken for what other
aspects of the ‘real’ may be affected by the initial
mathematical exposition. This is usually detected when
inconsistencies or symptoms appear. A new look at the
math may occur but no thought given to the existing
epistemology can ever be given to the whole picture,
only the parameters of the isolated, discrete problem.
Those parameters may change but they remain parameters
because with the mathematical sciences that is the way
we know the world.

26.1 As even a casual reader of this paper will now
understand, its core thesis is that no matter how
progressive, how eco-friendly a technology is, if it is
derived though the mathematical sciences it will simply
accelerate the dissolution of the planet.

26.2 However, this thesis probably will not be tested
for several reasons.

26.3 One is the greed and perfidy displayed on the
part of the corporate entities. Millions are spent on
propaganda designed to block international pollution
reduction goals and regulation. Greed will continue to
cloud the picture and obscure the case against the
mathematical sciences.

26.4 Second, in a one epistemology world model like
that presented by the mathematical sciences, there is
little or no way to test the thesis.

26.5 Thirdly, in this atmosphere of greed and from the
myopia of one epistemology even if true, the dissolution
of the planet through the mathematical sciences simply
becomes a fait accompli. Who cares if humankind gets the
reasoning wrong? In this instance even notions of reason
are either muddied by money or limited by the tools
available.

27.1 For example, a ‘description’ (definition) of a
muon from Wikipedia reads thus:

The muon (pron.: /'mju??n/; from the Greek
letter mu (µ) used to represent it) is an elementary
particle similar to the electron, with unitary negative
electric charge (-1) and a spin of 1/2. Together with
the electron, the tau, and the three neutrinos, it is
classified as a lepton. As is the case with other
leptons, the muon is not believed to have any
sub-structure at all (i.e., is not thought to be
composed of any simpler particles).

The muon is an unstable subatomic particle with a
mean lifetime of 2.2 µs. This comparatively long decay
lifetime (the second longest known) is due to being
mediated by the weak interaction. The only longer
lifetime for an unstable subatomic particle is that
for the free neutron, a baryon particle composed of
quarks, which also decays via the weak force. Muon
decay produces three particles, an electron plus two
neutrinos of different types.

27.2 There are a few more properties associated with a
muon, but with the inclusion of these you have for all
intents and purposes a full description.

27.3 With highly specialized instrumentation precisely
calibrated a pseudo-visualization of an object that fits
these properties also is possible.

27.4 Would this sort of ‘description’ be a primary way
of describing an apple? Such a mathematically scientific
description certainly exists. In fact, numerous ones
exist depending on the experimental goal and through
which discipline. But none of these reductionist derived
mathematical objects is an apple. We call it a
scientific description and it would entail those
properties of an apple applicable to the scientific
experiment and, most importantly, an anticipated result
or property of said apple.

27.5 With an ‘object’ such as a muon that has only a
mathematical numeration of properties to comprise its
description, its reality, mathematical prediction even
of its existence beforehand becomes if not easy,
preordained. Either an object exists with said
properties or it does not.

27.6 An apple has such ‘properties’ but they were not
intended to comprise all that is ‘apple.’

27.7 But much of our current world, especially in the
field of communications, operates on principles derived
from the properties of mathematically defined objects.
Objects which are comprised only from their scientific
properties and do not exist as such outside those
properties.

27.8 Thus the conundrum: On the one hand, the object
is said to have been derived from the world. But it has
no authenticity except in the man altered world of
mathematics.

28.8 When such mathematical conditions are placed on
the natural world, a substitution takes place between
the actual object in the natural world and its
mathematical approximation. With the mathematical
sciences we have rapidly, within a 500 year span,
reached a tipping point where the mathematical world is
not only our primary descriptive tool but the foundation
upon which all description functions. This is solely
because of the short term utility of observing the world
in this manner.

29.1 There is some debate over whether Hegel and other
philosophers were in error when they required that
calculus required infinitesimal quantities. Whether this
error was of commission e.g. an error in understanding
the calculus or omission e.g. simply being born too soon
to have been privileged to later developments in
mathematics is also debated.

29.2 But is Hegel in error at all. Or are there not,
no matter how cleverly concealed, gaps between numerical
valuations, even infinitesimal gaps.

29.3 Quantification is fundamental to the mathematical
sciences. Reduction occurs essentially during
quantification. As Hegel says mathematics “purpose and
principle is quantity.”

29.4 Hegel goes on to call mathematics “alien” and
states that mathematical knowing “does not affect the
concrete fact itself…”

29.5 In the immediacy of “comprehending” this is true.
But in reality the mathematical sciences through their
myriad applied states have a most profound affect on the
concrete fact. In our current world, that fact is being
reshaped to respond to the quantities and values the
mathematical sciences can work with while discarding or
ignoring others.

29.6 What the mathematical sciences require is that
the ‘objects’ of the natural world be rendered fungible
that is rendering objects or entities down to where they
are capable of mutual substitution. This requires a
reduction or series of reductions and must be able to
homogenize both the individual entity via its
properties, and sets or series of objects or entities.

29.7 In a set requiring apples and oranges a reduction
we refer to as fruit creates a situation by which the
objects become more mathematically fungible. No
distinction between apples and oranges is necessary. The
obvious differences between apples and oranges are for
the most part ignored to achieve say another set of
values called ‘fruit’ or ‘lunch’.

29.8 This makes things in Nature equal which are not
so. Thus, Nature must be discarded for various forms of
homogeneity which resemble aspects or properties of the
natural world in order for the mathematical sciences to
flourish.

29.9 We have long ago past the tipping point where the
natural world is the primary source of discovery whether
even by reduction and certainly not as ding an sich.

29.10 For experimental purposes, we have become
accustomed to calling a scientific reductio of an apple
an ‘apple.’ If it conforms to several pre-established
properties it is for all intents and purposes an ‘apple’
we are talking about. It goes through the mathematical
process and it comes out an ‘apple’ as well as a list of
properties that conform to an apple. This is a
consequence of the mathematical sciences being the
dominant epistemology.

29.11 In its ‘scientific’ state an ‘apple’ is more
fungible that an apple from the natural world. For
example, apples have been shown to reduce the risk of
some cancers. It is now believed that apples have and
ACE inhibitor quality. An ACE inhibitor (or
angiotensin-converting-enzyme inhibitor) is a scientific
reductio found in many natural sources such as apples
and specially fermented milk and synthetic ones such as
Captopril. However, few would take Captopril for its
apple like taste. The fermented milk lies somewhere
between an apple and Captopril as an expression of the
natural world. But the ACE inhibitor has become the
marker for what constitutes an ‘apple.’

29.12 There is no need to belabor this point. Western
epistemology has demonstrated its preference for the
‘idealized’ object through its reliance on the
mathematical sciences as the core mediator and
transformer of its natural source. Further, that the
natural world can be actualized by its mathematical
counterpart is not in doubt. It’s the outcome of such a
formulation that remains in doubt.

29.13 Quantification as demonstrated in the
mathematical sciences is the ne plus ultra of the ne
plus ultra. If such a dominant quality is, after all,
not satisfying the conditions of reality wouldn’t that
reality, for example the natural world as opposed to the
mathematical one, be expected to respond negatively?
29.14 And binary processes are just an acceleration of
the quantification. They have in short order made
themselves indispensable and have proven havens of
banality.

29.15 Walter M. Elsasser writes "Clearly, the
Cartesian Method fails," analyzing complex systems by
dicing them into "smaller and simpler components";
assuming discretion; threading them mentally. "[T]his
identification of a phenomenological concept (memory)
with its special, mechanistic form, storage, is the
point at which the mechanistic-reductionist
interpretation of organic life is most readily attacked
and can be laid open to an epistemological critique."

30.1 Even with man’s penchant to anthropomorphize
everything, investing any and all objects with human
qualities, Nature in its harshest moments used to be
itself, a matter of cold indifference. In turn, many
cultures took on qualities of nature and their immediate
environment, still a fundamental staple in the
pharmaceutical industry.

30.2 Meanwhile in western epistemology, with the
advent of a plethora of scientific ‘successes’,‘god’s
will’ and even god himself became untenable even a
nuisance.

30.3 Now, Nature appears downright hostile in an
entirely new way. Instead of appearing indifferent but
brutal or poorly anthropomorphized and inscrutable,
Nature seems to have entered into a life and death
struggle with the mathematical sciences. At no time in
man’s history have the ‘intentions’ of Nature been less
inscrutable. This is because it’s the mathematical
sciences, our only surviving epistemology that’s in
direct conflict with it. As standup comic George Carlin
joked, “The planet’ll shake us off like a bad case of
fleas.” And if you quantify what is unquantifiable with
the zeal of our current computerized culture, you might
quantify yourself right out of the lexicon with an
incomprehensible suddenness.

30.4 Certainly, the most obvious source of this end is
our heavily industrialized, mechanized, digitized world.
And the mathematical sciences are the ne plus ultra of
that world, that world’s only apocalyptic possibility.

30.3 The Nobel Prize winning atmospheric chemist,
Frank Sherwood Rowland, once wrote to his wife from the
field, “The work is going well, but it looks like it
might be the end of the world.” That statement rather
sums up the macroscopic conclusion of this brief paper.

31.4 The other dimension is the obvious reality
nothing that can be done to prevent what appears to be a
rapidly approaching environmental apocalypse. Good
science, bad science. It’s all mathematical science in
the end, the ne plus ultra.

31.5 With the mathematical sciences and western
epistemology, you can’t win for losing.

31.6 The final proposition of Wittgenstein’s Tractatus
reads “What we cannot speak about we must pass over in
silence.” Proposition 31.5 of the Syllogism is not quite
so elegant. But it is also not quite so wrong. We
remained silent before the awe of the mathematical
sciences for too long. Now for our denouement.