


The Quine–Duhem paradox, which highlights the contradiction between the need to isolate known and unknown hypothesis, in order to test a given hypothesis, and the inability to do so, poses complications, both scientific and philosophical. The Bayesian response is the preferred corrective by the scientific community, but one encounters a tradeoff between the positing of meaningful–verifiable experience, and, the type of limiting self–referential implicit in the use of self–credences. In fact, the Bayesian response to the methodological and epistemological issues posed by the Quine/Duhem paradox begs the question of the significant role played by various types of structural creative thought, including: synthesis, blind spots, thin places, inversions, poly–holism, and wild and divergent strands, many of which often stand outside the purview of investigating scientists. In contrast to the Bayesian model, the paper offers a non a priori grounding and/or functional and explanatory set of principles founded in the pattern of historical–interdisciplinary structural creative thought, evident in the history of the physical sciences, at large, and in particular scientific histories of physics, biology and political economy. Via this critical methodology, the self–referential nature of the Bayesian model is significantly tempered and its experimental and theoretical verification process objectively broadened.



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John F.  DeCarlo
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John F.  DeCarlo
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                                                        trópos • anno X • numero 2 • 2017 – ISBN 978-88-255-1253-3
                                                         DOI 10.4399/97888255125334 – pag. 39-62 (dicembre 2017)




                        Transcending Bayesian Self–Credences
                                                                              John F. DeCarlo*




Abstract: The Quine–Duhem paradox, which highlights the contradiction
between the need to isolate known and unknown hypothesis, in order to
test a given hypothesis, and the inability to do so, poses complications, both
scientific and philosophical. The Bayesian response is the preferred correc-
tive by the scientific community, but one encounters a tradeoV between
the positing of meaningful–verifiable experience, and, the type of limiting
self–referential implicit in the use of self–credences. In fact, the Bayesian
response to the methodological and epistemological issues posed by the
Quine/Duhem paradox begs the question of the significant role played
by various types of structural creative thought, including: synthesis, blind
spots, thin places, inversions, poly–holism, and wild and divergent strands,
many of which often stand outside the purview of investigating scientists.
In contrast to the Bayesian model, the paper oVers a non a priori grounding
and/or functional and explanatory set of principles founded in the pattern
of historical–interdisciplinary structural creative thought, evident in the
history of the physical sciences, at large, and in particular scientific histories
of physics, biology and political economy. Via this critical methodology, the
self–referential nature of the Bayesian model is significantly tempered and
its experimental and theoretical verification process objectively broadened.

Keywords: Quine–Duhem Paradox; Bayesian Self–Credences; Structural
Forms of Creative Thought; Historical–Interdisciplinary Methodology; Non
a priori grounding and/or functional and explanatory set of principles.


1. Statement of Problem: Bayesian Response to Quine–Duhem Para-
   dox

The Quine/Duhem Paradox is fairly straight forward: No hypothesis can
be tested in isolation from an indefinite set of auxiliary hypotheses; and in
   ⇤
       Hofstra University and SUNY Farmingdale; john.f.decarlo@hofstra.edu.


                                                                                                              39
40    John F. DeCarlo


order to show that a hypothesis is mistaken, is it necessary to isolate that
hypothesis from its set of auxiliary hypotheses; therefore, no hypothesis
can be shown to be mistaken. The Bayesian response is to introduce the
notion of degrees of belief that an investigator has for a hypothesis, relative
to others. Then, as new information emerges, one reevaluates the likelihood
of that information being compatible with each original possibility. In other
words, the Bayesians solve the Quine/Duhem paradox by rejecting the
claim that in order to show that a hypothesis is mistaken it is necessary
to isolate that hypothesis from its set of auxiliary hypotheses by asserting
that it can be determined whether the set of auxiliary hypotheses should
be rejected based on the degree to which those auxiliary hypotheses are
believed to be true.
    In addition to the problem of confirmation bias, in all its philosophical,
sociological, political, professional, even personal aspects, which looms
largely over the Bayesian notion of self credences, the dilemma emphasized
by Quine–Duhem is that not all of the possible auxiliary hypothesis are
completely apparent; in fact, their claim is that no hypothesis can be ade-
quately separated from an — indefinite — set of auxiliary hypotheses, in
terms of possible inferences, data, and conditions. By the same token, while
evidence should move toward consensus, especially as evidence that favors
one alternative automatically disfavors others, what happens to a startling
new claim in the absence of a corresponding theoretical explanation at hand?
In this respect, Wittgenstein notes in the Tractacus Logico–Philosphicus,
probability is a generalization for it is always based on a given circumstance,
for while a related proposition is always a complete picture of something, it
may well be an incomplete picture of a situation. Whatever we see, whatever
we describe, could be other than it is.
    Scientists, of the rank of Sean Carroll at Cal–Tech, also acknowledge
that the Bayesian Model of scientific inquiry and verification, complete with
its notion of prior credences or beliefs, stands on shaky grounds. Carroll
also admits that emphasis on priors is subjective, and that some people
have certain views that they are just never going to change. Nonetheless,
he hopes they will be honest and change their mind as it becomes clear
(Carroll 2016: 80–83). However, in April 1900, Lord Kelvin proclaimed that
“our understanding of the cosmos was complete except for two “clouds”
— minor details to be worked out” (Livio 2013: 131). Those clouds had to
do with radiation emissions and the speed of light, and they pointed to
two major revolutions in physics: quantum mechanics and the theory of
relativity. By the same token, Vera Rubin observed that the stars on the
outskirts of galaxies were not slowing down; if anything, they were speeding
up. Scorned by authorities in the field that such observations did not have
significance, her team observed more galaxies, only to find that the eVect
                                         Transcending Bayesian Self–Credences   41


persisted, implying that other new types of subatomic particles were left
over from the Big Bang and floating around the universe in clouds. Hence,
the birth of theories of dark energy, which accounts for some 73% of the
known materiality in the universe, that is not only expanding, but at an
accelerating rate.
    Notwithstanding Carroll’s assertion that prior credences need to be
subjected to critical scrutiny, he begs his own question/methodology in
his recent book: The Big Picture (2016). More specifically, for Carroll, the
Core Theory, which posits assertions regarding the fundamental nature
of reality, is in a sense prior to our particular prior credences, in that, it
contains the information that we must use to “update” all other credences.
In other words, the Core Theory becomes its own fundamental priority,
which by other competing theories are being evaluated, which is contrary
to an open–ended science; for example, he rules out the negative analogy,
of immaterial entities, and as well as the synthetic proposition, of a world
with both material and immaterial entities.
    In this respect, Margaret Cunzo notes in her book, Paradox (2014), that
“to determine when an anomalous result requires that the main hypothesis
or some auxiliary hypothesis to be rejected requires more than subjective
degrees of belief of the scientist prior to the experiment. What is required
is evidence that the auxiliary is the faulty assumption and an account of
why this evidence is not mistakenly taken as evidence that the auxiliary is
to blame” (ivi: 79). In this regard, Mario Livio, author of Brilliant Blunders:
From Darwin to Einstein — Colossal Mistakes by Great Scientists That Changed
Our Understanding of Life and the Universe (2013), cautions against having faith
in one’s own beliefs.
    It is in relation to this two–fold lacking that the Bayesian Model is
being up–graded by using a new historical interdisciplinary approach,
whereby the patterns of structural forms of creative thought could im-
prove qualitative methodologies of exploration and analysis, leading to
new scientific insight.


2. The Interdisciplinary–Historical Methodology

The history of scientific ideas has demonstrated the provisional nature of
even those theories and laws which seemed to be certain and true in a given
historical epoch. The pioneers of the great modern sciences, including
Newton, Darwin, and Freud, have been moderately falsified (in keeping
with Lakatos’ revision of Popper theory of falsification), in terms of them
subsequently receiving considerable modification based on other conditions,
or, changing conditions.
42    John F. DeCarlo


    It was Goethe, who first conceived science as the history of science, in that,
a hypothesis is always within a historical setting, influenced by needs, interests
and circumstances of the time. In these respects, his philosophy of science
anticipates Kuhn’s notion of paradigm, which addresses and temporarily solves
the questions and problems of a particular social–scientific community. By the
same token, just as a paradigm is initially refined to accommodate anomalies,
but eventually needs to be replaced by a more inclusive theoretical frame-
work, Goethe likens a theory to an old castle which can be “patched up” but
eventually becomes “uninhabitable” (Kaufmann 1980: 71).
    The philosopher Immanuel Kant also asserted that the sensuous forms of
time and space, along with the conceptual categories of substance, causality
and reciprocal relationship are human constructs, which can not necessarily
be extended beyond known empirical data. It is in keeping with this rea-
soning that NASA continues to consider the theories of special and general
relativity — as theories — and not as laws. Wittgenstein also notes how
the whole modern conception of the world is founded on the illusion that
the so–called laws of nature are the explanations of natural phenomena,
and there is no a priori order of things. As such, the law of causality is
not a law, but the form of a law. In fact, what the law of causality is meant
to exclude cannot even be described (Tractatus Logico–Philosophicus: 6.1 –
6.3). For example, the Newtonian conceptual depiction of space and time,
reigned supreme for hundreds of years, and the corresponding formulas are
still used, under certain conditions, for their ease and quickness. Yet, they
are founded on a fundamental error, regarding the nature of space–time
and mass and energy. It is within this epistemological historical context that
Cartwright envisions science as a patchwork of domains with various math-
ematical and theoretical commitments, and their corresponding equations
indicating capacities, dispositions, and causal relations to be borne out by
local experimental and theoretical contexts: to do otherwise, is to commit a
methodological mistake.
    While Goethe’s conception of science was borne in the pre–specialization
period of the sciences, his emphasis on the history of science is echoed by
Noam Chomsky, who notes that philosophy of science is best borne out by
examining the history of science in terms of: what do the sciences do; what
do they do to achieve their accomplishments; what are paths that often lead
to errors? Chomsky also cautions that while statistical data is not inherently
wrong, more than an error caused by a formal theoretical misconception,
is the error caused by just taking in Big Data into a massive computer, and
converting it into probabilistic statistical models, and then generating an
approximation of what happened. In addition to there being no real expla-
nation, without a theory to guide the data review, there will be a dismissal
of the conceptualization of the data/units that are not yet confirmed, or,
                                         Transcending Bayesian Self–Credences   43


not even yet in view. Hence, Chomsky advocates a Pre–Galilean state of
mind: not knowing what we are looking for, and embracing puzzlement,
and moving beyond initial intuitions. Chomsky also notes that historically,
the sciences have achieved some of their greatest achievements when they
relied on unification or poly holism, as opposed to reductionism (Katz 2012).


3. Prior Literature: Structural Forms of Creative Thought

The project is, in part, in debt to the groundbreaking work of Mary Hesse,
which employs the justificatory sense of analogy not to determine whether
a scientific hypothesis is theoretically viable, but to establish whether it
merits the accolade of even being called scientific at all. A theory has to be
able to be put into a formal correspondence with some appropriate model.
In fact, Hesse thus employs the justificatory sense of analogy, not to uphold
the integrity of science, but to define it (Statile 2008).
    However, unlike Hesse’s methodology which is limited to positive and
negative analogy, related to known areas of experience, and what she called
neutral analogy, which explores unknown areas of thought and research,
the current project reviews several types of analogy and creative intuition,
including: positive and negative analogy, blind spots and thin places, synthe-
sis and inversion, and poly holism and wild and divergent thought, which
explore unknown areas of thought and research.
    In these respects, the hope is that in our post–post–modern world of
science and technology, in which new truths emerge which both tran-
scend our conventional categorical structures of space, time, causality and
co–existence, and permanence and substance, and appear to us as being
counter–intuitive — as in the cases of curved space, indeterminacy and
spooky entanglement, relative time and the lack of material substance —
a new set of mental categories associated with various structural types of
creativity can both help to guide scientific explorations and evaluate new
theories and models and related experimental data.
    It should be noted that these structural forms of creativity stand apart from
the psychology and sociology of the creative process, which betrays any type
of logic of discovery. Take for instance the work of Howard Gardner, who,
integrating his theory of multiple intelligence, examines the personal and col-
lective creativity/intelligences of Einstein, Picasso, Stravinsky, Eliot, Graham,
and Gandhi in Creating Minds: An Anatomy of Creativity. The Rise: Creativity,
The Gift of Failure, and The Search for Mastery, by Sarah Lewis, also examines
the creative process in terms of the inherent experience of failure along the
way, and actually advocates that the creator surrender to such failures, learning
what they can from them (2014). To this effect, Carlo Rovelli characterizes
44     John F. DeCarlo


the time leading up to Einstein’s theory of general relativity as: “Ten years of
frenzied studies, attempts, errors, confusion, mistaken articles, brilliant ideas,
mis–conceived ideas” (2015: 5). Richard Feynman also notes that Dirac tried
everything before happing onto the 4x4 matrix needed to derive his quantum
relativistic theory. In this respect, in Zig–Zag, creativity research psychologist
Keith Sawyer suggests that one accept the chaotic process of creativity, and do
their best to master it by understanding it. Sawyer also comforts the reader:
“this book is your personal trainer, coaching you through the eight zig zagging
steps of creativity, consisting of asking, learning, looking, playing, thinking,
fusing, choosing, and making” (2013: 5–7). And yet, he honestly notes that as
psychology and neuroscience are showing, the creative process is far richer
than that, and far less rigid, hence even after mastering the eight steps, the
need to zig zag between them (ivi: 8).
    Instead, the intent of this categorical classification consisting of: positive
analogy, negative analogy, the thin place, blind spot, synthesis, poly holism,
inversion, and wild and divergent thinking is twofold:

     a) to augment, and possibly supplant the traditional modes of verifica-
        tion and proof;
     b) in the absence of a logic of discovery, to supplement the Bayesian
        model of judging the probabilistic reliability of a given hypothesis.

    In this respect, the foundational research of this paper is primarily in the
modern and post–modern historical development of the physical sciences of
physics and biology, with a particular focus and emphasis on the pattern of
scientific insight, breakthroughs, and revolutions that have occurred among
the various disciplines. These scientific advancements are, in turn, classified
relative to the type of creative thought that brought the new idea into exis-
tence. Thus, while past, present, and cutting–edge scientific theory and data
will be supplied in atomic theory, the theory of special relativity, and Dar-
winian/Neo–Darwinian biology, the purpose is not to inform the reader of
these developments, but rather to present them as categorical illustrations
of various types of structural creative insights. The first section, of atomic
theory, ranging from initial conceptions to quantum theory and issues of dark
matter, will also bear fundamental definitions of the various types of structural
creative thought. We also start with the history of atomic theory because its
development contains all the types of structural thought, metered out in a
nearly perfectly logical format.
    It should also be noted that historical–structural analysis has also been done
in the Newtonian theory, general relativity, and political economy, but that
particular data will be not presented in this paper, due to the constraints of
proper length.
                                          Transcending Bayesian Self–Credences   45


4. Results I: The Emergence of Atomic Science

4.1. Positive Analogy

Positive analogy can be likened to a grafting process, whereby a model
or framework that is similar in nature is applied to an area of exploration.
Science is, as noted by both Richard Feynman and Lisa Randall, for the
most, conservative in nature. If a straight forward and clear–cut explanation
is available that can explain and predict, so be it. The role of positive analogy
also plays the role of Falsification in terms of Popper’s notion that a theory
that can be tested is entitled to be considered a theory; a theory is not a
theory if it cannot be tested and falsified. For Popper, this was the case with
Freudian theory and Marxist theory. In this respect, N.R. Campbell and E.
Negel argue that all scientific theorems require an analogous framework or
model. Thus, it is not argued that analogy establishes whether a hypothesis
has been proven, but rather that it is necessary in the justification of a theory.
    In the case of the scientific narrative of the emergence of the subatomic
world view, the heliocentric model was used as a positive analogous approx-
imation in terms of understanding the nature of the atom and its sub–atomic
particles. But not everyone was in agreement about this: Lord Kelvin and
Maxwell initially thought that the atom could not be divided any further,
and ruled out sub–atomic particles (electrons). In all fairness, Kelvin hints
at a connection between electricity & magnetism and molecular vortex the-
ory of spherical & concentric rings, which does foreshadow Solar System
Analogy (Giles 2008: 98).
    With Thompson’s discovery of electrons in 1897 (Giles 2008: 102), it
was suggested by Lodge that subatomic particles orbit the nucleus like
the planets around the sun. Another positive analogy was constructed by
Maxwell comparing the electrons to the concentric rings of Saturn; in other
words, like the stable satellites, rather than orbits. In terms of Maxwell’s
suggestion, we see that some positive analogies are better than others. By
the same token, take the Wright brothers engineering feat of constructing a
viable airplane. Unlike others who relied on the physics of bird flight, often
resulting in deadly crashes, they relied on the physics of riding a bicycle in
terms of maintaining balance not only in the center relative to left and right,
but in terms of front and back. Consequently, it is suggested to start the
scientific process with a positive analogy, and then consider when to hold
on to that with patience and persistence, and when to move on to the next
phase, in this case, a negative analogy; and yet, to caution that the scientific
process cannot be turned into any type of formulistic prescription.
46    John F. DeCarlo


4.2. Negative Analogy

This is essentially oppositional in nature, comparing the areas of interest to
something which is diVerent from what one would expect, and corresponds
to the fact that the potential shortcoming of positive analogy is that it is too
pact, for it can be too close to an existing truth, oVering a false positive. As
a result, just as the verification principle cannot be verified, in that, it cannot
prove that which cannot be empirically verified does not exist or does not
apply under certain conditions, the positive analogy might be working for
the wrong reason(s).
    While the Hypothetical Deductive is more inclusive than positivism, in
that, the latter does not recognize all known auxiliary hypothesis, and rules
out unknowns as even less meaningful, the hypothetical–deductive method
cannot entertain all possible inferences. Hence, the negative analogy, ac-
cording to Popper, is one way to falsify a theory by developing a viable
negative analogy which the current theory cannot explain. Such a theoret-
ical assertion can then be stronger, although it can also be over–stated. In
other words, the negative analogy can open things up to a new conception,
but can also stray too far, and will eventually be in need of correction, itself.
    Lodge plays with a more opposing analogy: the idea of asteroids, which
unlike planets — can strike at any moment; thus, hinting at quantum theory
and its unpredictable nature. This, of course, played out with Niels Bohr
contra Einstein, with the former emphasizing the erratic quantum leaps
of electrons, and Einstein famously noting that God does not play dice
with the universe. As it turned out, they were both right, in a sense. We
now know that electrons orbit the nucleus, but also jump from one energy
level, or ring, from another, depending on their energy level; and as will
be noted below, both Schrodinger and Dirac devised models to predict the
probability of sub–atomic particles.

4.3. Synthesis

Simply put, synthesis is a blending or melding of opposites in keeping
with shortcomings and strengths of both positive and negative analogies.
In this way, one both eliminates the shortcomings, and elaborates on the
strengths. Much of 20th physics is centered on the debates between Einstein
and the Copenhagen School regarding: certainty, realism, spooky action at a
distance, the nature of time–space, and the measurement problem. Notwith-
standing Einstein’s assertions that a new and improved mathematics would
eliminate uncertainty, and restore Newtonian explanation and prediction,
such an assertion is now conceived as a category mistake. Heisenberg’s prin-
ciple of uncertainty, states that in principle, regardless of human procedure
                                         Transcending Bayesian Self–Credences   47


or observation, the quantum world is essentially filled with uncertainty: the
electron does not have an exact position/momentum. At best, there is a
fundamental trade–oV between measurements of momentum and location,
the probability equal to square of the over–all wave function, as developed
by Schrodinger.

4.4. Synthesis, with Positive and Negative Analogy

Atomic physics was subject to a second major synthesis, consisting of Dirac’s
equation of quantum mechanics and relativity, in 1928, which takes into account
the speed of motion of electrons according to special relativity. In this regard,
attempts to make the old quantum theory compatible with the theory of
relativity based on discretizing the angular momentum stored in the electron’s
possibly non–circular orbit of the atomic nucleus, had failed.
    Dirac, who had been working on the foundation of Heisenberg’s matrix
mechanics, realized how the matrix could be transferred, or positively
grafted. In doing so, he also nullified two other theoretical models: Wave
function has multiple components, and 4 x 4 matrices, not two as in the
Pauli phenomenological theory of spin, or one, as in Schrodinger’s. Thus,
he explains the behavior of the relativistic moving electron, which is capable
of speeds close to the speed of light, allowing the atom to be treated in a
manner consistent with relativity. It also oVers an explanation of spin ½
massive particles as a consequence of the union of quantum mechanics and
relativity.

4.5. Blind Spots

The synthesis can be deceptive, for its act of combining and melding of
opposites seems to be all in–compassing. However, the histories of the
sciences suggest that there is often something that no one even expects or
anticipates, and it is usually revealed years after the initial exploration and
investigation; it also has lasting implications. In this respect, Bohr was wrong
about his rejection of realism: the discovery of cooper pairs and boson pairs
in 1970 strongly supported Einstein’s claim for realism, contrary to the
Copenhagen School’s epistemological emphasis on human observation and
the collapse of the wave function. To this eVect, Schrodinger’s meditation of
the proverbial Cat (in the box) scenario represents how abstract conceptual-
ization can both represent and potentially solve a vexing theoretical issue. It
put to rest two theoretical contentions:

   a) unlike the Copenhagen school it indicated that the cat would be dead
      or alive independent of human observation;
48     John F. DeCarlo


     b) unlike Einstein’s contention that the quantum world could be in-
        tegrated into a unified theory, current findings reaYrm the initial
        postures articulated by Schrodinger, who, unlike the Copenhagen
        school, not only rejected a subjective interpretation of quantum
        events, but asserted that such quantum measurements extended to
        the macro level, would lead to absurd scenarios, such as two dead
        cats suspended in superposition. Nonetheless, his equation, the ana-
        logue of Newton’s law is a partial diVerential equation that describes
        how the single non–relativistic particle/quantum state of a quantum
        system changes with time.

    Regarding the tension between Einstein and the Copenhagen School,
the discovery of the inverted and yet reciprocal nature of fermions and
cooper pairs, where the former (which obey Fermi–Dirac stats) cannot
occupy the same space, thus preventing mass/the universe from collapsing
into itself (as in the case of stars and supernovae), and cooper pairs (which
obey Bose–Einstein stats), which can occupy the same space, preventing
space–time from breaking into disjointed chucks (Cowen 2015), was not
anticipated, and totally altered the discussion regarding atomic physics: there
were diVerent types of electrons; they had very diVerent types of behavior
and related functions; and cooper pairs might even play a role in gravity.
    They also had philosophical implications in that the inverted–reciprocal
relationship between cooper pairs and fermions justifies the violation of
the Ontological Principle of Indiscernibles (in that, while initially separate,
entangled cooper pairs take on all the same properties) on the basis that the
functional significance of their inverted physical roles fulfills the principle
of suYcient reason.
    Frost notes: “There’s always something else in my poetry. . . I’m al-
ways saying something that’s just the edge of something more”. In a
similar vein, Dirac did not at first fully appreciate the importance of his
results: the explanation of spin as a consequence of the union of quantum
mechanics and relativity — and the eventual discovery of the positron —
represents one of the great triumphs of theoretical physics. The equation
also implied the existence of a new form of matter, antimatter, previously
unsuspected and unobserved and which was experimentally confirmed
several years later.

4.6. Inversion

Beyond a reversal, as found in the negative analogy, inversion involves rever-
sal with a convoluted twist. Such a creative leap usually does not resemble
anything, and in this way, can take a big leap, which will either prove to be
                                        Transcending Bayesian Self–Credences   49


revolutionary, or misguided. In regard to this cognitive adjustment, Ricoeur’s
clarification/correction of Aristotle’s concept of metaphor is instrumental:
dismissing its nature as a noun, just playing the role of substitution, he
emphasizing its verbal power to metaphorize and “Bring forth before the
eyes. . . ” (Ricoeur 1975: 91). More importantly, it shifts one’s perception to
a sudden apprehension of similarity. In this regard, Frost aptly notes: No
surprise in the writer, no surprise in the reader.
    Lodge startlingly and intuitively realized if quantum leaps were the case,
related to his negative analogy of electrons being like asteroids, there must
be a lot of empty space, anticipating the discovery made by Rutherford,
years later, that underling the discovery of a strong atomic center, there
exists an empty shell. In other words, in a contrary and yet strangely, and
almost absurdly twisted notion the building block of matter is essentially a
void.
    It would also take decades of development of both science and tech-
nology and the super collider at Cern to demonstrate the existence of the
Higgs Boson which, in eVect, provides the mass of matter; and quantum
field theory which suggests that fundamental particles, in the form of en-
ergy, become variably excited, thus emerging out the underlying field as
particles, only to slip away back into the field.
    Also, as early as 1856 Kelvin wondered how could atomic forces be strong
and yet the atom is composed of empty space? It turns out that a rather
counter–intuitive explanation came into light: as opposed to Newton’s law
regarding gravity being stronger the closer two objects are in relation to
each other, nuclear strong forces are stronger when far apart. Here again, a
reversal, with a strange twist.

4.7. Thin Place

According to Irish folklore the thin place is that very short and narrow tem-
poral–spatial opening that allows for insight and revelation, and then forever
disappears. In the scientific world, it is the subtlest points of theoretical
leverage that looms between positive and negative analogy. Various histories
of science do suggest a certain pattern in keeping with the scientific temper-
ament of being concrete and reserved, and siding with the positive analogy,
and only resorting to more abstract and extreme theoretical speculations of
the negative analogy, as need be. In the case of the exploration of the atomic
world, the thin place relates both to dark matter and the neutrino.
    First, dark matter is thought to comprise 85% of all the gravitational
force in the universe. Its name is reflective of the fact that we know very
little about it, except that it does not interact with light, hence its double
nature of darkness. Then again, this ghostly class of undiscovered particles
50    John F. DeCarlo


interacts with matter via gravity, but otherwise interacts with matter or
light only weakly, or perhaps, not at all.
    In this respect, dark matter is like neutrinos, which were predicted and
eventually discovered, even though they interact extremely weakly with
ordinary matter. In fact, each night and day, a hundred billion neutrinos
pass through each thumbnail patch of your body, every second, without a
trace of interaction with your body’s atoms — or, more amazingly, they
might manifest via forces other than the strong nuclear force, weak nuclear
forces, and electromagnetism (Tyson 2017: 76–93). Thus, as in the cases of
these two sub–atomic particles, the investigative scientist must generally
consider whether one lingers in the camp of the known via positive analogy,
or, venture out into the oppositional unknown via the negative analogy.

4.8. Far–Reaching Poly–Holism

Whereas synthesis resolves the tension between two competing theories,
by melding them together, the reach of poly–holism is even wider. In a
sense its role is to pick up all the pieces, including the hidden blind spots
and the peculiar types of inversion. In this respect, nearly all physicists
admit that the Standard Model is insuYcient, and that there might be
a fourth generation of fermions, but that no replacement has yet to be
devised. In fact, while the Standard Model stands at the best model for the
explanation and prediction of things operating in the universe, it does not
account for dark matter, or for gravity as described in the general theory of
relativity as the curvature of space–time. As a result, it describes a number
of fields interacting among themselves with certain forces each determined
by certain constants showing certain symmetries, but does not explain why
the particular fields, forces, values, and symmetries exist (Rovelli 2015: 34).
Thus, the grand unifying field theory, which Einstein felt he was close to,
and which he worked toward the latter years of his life at the Institute of
Advanced Study, remains an ideal for the physics community, as a whole.

4.9. Wild and Divergent

One thinks of a Jackson Pollack painting composed in his quasi–trance
like state in which he pours gallons of paint across an open canvas, not
knowing nor really controlling how it will manifest itself. By the same token,
divergent thinking is the term psychologists use when you generate multiple
possibilities because your mind diverges and pushes past the obvious to
explore a broad range of options, especially when there is no censor on
what to leave in and what to leave out (Sawyer 2013: 133–134).
                                          Transcending Bayesian Self–Credences   51


    Similarly, the way in which the equations of the Standard Model make
predictions about the world is absurdly convoluted. Used directly, these
equations lead to nonsensical predictions where each calculated quantity
turns out to be infinitely large, and to get meaningful results, it is necessary
to imagine that the parameters entering into them are themselves infinitely
large.
    Part of the diYculty, if not impossibility of directly measuring fields, is
the relationships between various forces and elemental particles in those
respective fields. As the old adage goes, the whole is greater than the sum
of the parts. However, in field theories diVerent configurations of the un-
observable fields such as charges, energies, and velocities, can result in
identical observable quantities; and so, a transformation from one such
field configuration to another is called a gauge transformation, and the
lack of change in measureable quantities is a property called gauge invari-
ance, and is considered a gauge symmetry. In this respect, the potential
importance of gauge theory is its ability to provide a unified framework
to describe the quantum–mechanical behavior of electromagnetism, the
weak force and the strong force. As such, gauge symmetry makes quantum
electrodynamics a renormalizable theory, one in which the calculated pre-
dictions of all physically measureable quantities are finite. However, while
the procedure of “renormalization” is relatively eVective, as Paul Dirac, the
first and principle designer of the Standard Model, noted: “we have not yet
solved the problem” — implying that theory had not yet be married to the
wild and divergent nature of reality (Rovelli 2015: 35).


5. Results II: Biology (Darwin to Epi–Genetics)

Not unlike the study of history and astronomy, where it is diYcult to
construct realistic experimental labs, it is diYcult to see Darwinian evolution
in action, no less to repeat it for verification. For this reason, both fruit flies
and bacteria, which move from generation to generation in short amounts
of time, are favorite study populations. The emergence of biology as a
science was also haunted by the specter of the Judeo–Christian mythology,
with its representative creation myths in both Genesis I and II. In this respect,
the development of Darwinism is inherently filled with negative and positive
analogies, from the outset.

5.1. Negative Analogy

Not unlike Copernicus and Galileo in relation to the Roman Catholic
Church, the stakes were quite high: Divine creation versus Darwinian
52     John F. DeCarlo


evolution. In his Dialogues Concerning Natural Religion David Hume strongly
suggested that there is a substantial diVerence between a designer and our
traditional notion of God, but he did not yet have a plausible explanation for
the emergence of the diverse world of nature in terms of an eYcient and
correspondingly material set of causes.

5.2. Positive Analogy

While not generally known, or discussed, Goethe’s first discovery is made
in the field of comparative anatomy. In that day is was established that the
inter–maxillary bone, which is located between the bones of the maxilla,
and unites them, is found in animals including monkeys, but not at all in
man. But his research leads to the insight that man does have a rudimentary
form of the inter–maxillary bone, fused with the adjacent parts of his facial
structure.
    Others had written about the plan and order of nature, the fitness of
plants and animals to meet the challenges of the natural world. For example,
Charles Lyell discussed and addressed how the movement of water had
carved out major geological modifications, over great periods of time. It
was also a family interest in that Darwin’s grandfather theorized that all
varieties of living things evolved from an original type.

5.3. Inversion

Darwin not only nullifies or reverses the metaphysical notion that God is
the designer, but also proposes the concept of design without a designer. It
is a theory about ends being served by variation but not contrived by some
providential super–intelligence. In contrast, Darwin carefully observes and
classifies the creative natural process, minus, the creator. Variations do not
consciously strive to reach any future goals, and neither can individual
organisms influence them by their actions. Variations that fortuitously
improve an organism’s chances of passing on its genetic heritage will be
more likely to survive than those that are harmful or neutral.
    Darwin also nullifies the notion that homo sapiens have some type of
superior and privileged position and status in the larger scheme of things.
Not only is this reversed, but man is associated with the primates, the two
being in close biological relationship. It is now known that some 97 % of the
human genome is in common with the genome of the primates, which can
be interpreted two diVerent ways: we are very, very similar, and, 3 percent
makes a big diVerence. In any case our commonalities are underscored in a
way that Victorian Society found to be both disturbing and insulting.
                                        Transcending Bayesian Self–Credences   53


5.4. Negative Analogy

To some degree, it can be assumed that the Judeo–Christian myth implies
that the changes due to the hand of god, are relatively immediate, whereas
Darwin addressed the slow and gradual evolutionary changes that take place
over multiple generations, if not eons. However, as developed by Gould,
the dynamics of punctuated equilibrium, whereby long–term evolutionary
trends are understood as the distinctive and relatively sudden success of
some species (or members of a species) versus others, rather than as a
gradual accumulation of adaptations of a continuing evolving population,
seems to be highly relevant. In other words, change occurs not in terms of
evolutionary time, but ecological time, putting extreme pressure on species
to progressively adapt, or die away. This is especially true considering that
there have been 4 major extinctions on the planet, with 17 to 54 percent
of the species being eliminated during each event. One can easily imagine
losses within species as well, so that fitness is determined both between
species, and across a given species.

5.5. Synthesis

Darwin didn’t know about DNA or RNA, or even of genes. In fact, Mario
Livio notes how he relied on the widely–held belief of his day that the
characteristics of the two parents became physically blended, not unlike
colors of paint, in their offspring (2013: 149). The development of Dar-
winian biology would be reliant on Mendel who established the basic
rules of heredity through a set of experiments crossing different varieties
of pea plants. In the early mid–period of the 20th century biologists devel-
oped the modern synthesis, combining natural selection with Mendelian
genetics. The synthesis includes the difference between evolution and
natural selection, the former referring to the change in the complete set
of genetic information contained in the genome, and the latter to specific
cases where changes in the genome are supported by different amounts
of reproductive success.

5.6. Positive Analogy and Hypothetical Deduction

Schrodinger postulated that a collection of atoms could fit together in a
reproducible way, with the capacity for carrying substantial amounts of
information. Likewise, Crick and Watson deduced the double–helix form
of DNA, the molecule that essentially all known living organisms use to
store the genetic information that guides their functioning. Not surprisingly
each strand contains the same information, as the nucleotides in one strand
54    John F. DeCarlo


are paired up with the complimentary ones in the other, which allows
for a possible copying mechanism for the genetic material (Carroll 2016:
265–266). The two strands of DNA can unzip from each other and then act
as templates, with free nucleotides fitting into the appropriate places on
each separate strand.

5.7. Blind Spots

The passing on of specific genes for specific behaviors and physical traits is
not as simple as it was initially conceived. Rather than having one particular
string of nucleotides as an agent, there is actually an interplay between
diVerent factors working simultaneously. Consequently, selective pressure
acting on one trait may end up aVecting another one, if they depend on
common sets of DNA sequences. Such secondary adaptations as coined by
Gould and Lewontin consist of traits that arise for one reason and then end
up being used for something quite diVerent.
    The concept of Genetic Drift has also been introduced as forces that do
not directly relate to adaptation: mutations that neither increase nor decrease
the fitness of an organism. In fact, a single trait can be brought to life by
multiple, separate mutations, which may not individually have much no-
ticeable impact; the randomness in sexual reproduction; and unpredictable
features of the environment.

5.8. Inversion

Epi–Genetics involves genes being passed on to the oVspring other than
through reproduction. There are cases where the chemical structure of
inherited DNA is modified during development by influences such as the
nutritional intake of an organism and the maternal environment in which
the embryo develops. Since there is not an actual change in the inherited
gene structure, but rather in its gene expression (if the gene gets expressed,
when, and to what degree), it is currently unclear how much such changes
can be inherited by subsequent generations. However, research by Azim
Surani at Cambridge University and colleagues, has recently shown that
some epigenetic tags escape the cleaning process at fertilization, slipping
through the net. More specifically, in the cases where traits that are not
contained genetically in the fertilized egg, that are still passed on to the
oVspring, research examines the germ cell, of either the sperm or egg,
which might have a tag or marker attached to it. In the case where the
marker is attached to either the sperm or egg, but not both, the cleansing
process that takes place shortly after fertilization might be circumvented.
                                       Transcending Bayesian Self–Credences   55


    There are also cases, where environmental pressures exerted on the
oVspring eVect if and when a gene gets turned on or oV, but this does
not exactly entail a modification of the genetic code. This is especially
true with respect to epi–genetic tags, where “cultural scars” of the parents
seem to be passed down, chemically, to their children both in terms of
hormonal disposition and traumatic memories. This has also complicated,
if not thwarted the eVorts toward gene therapy, for it is not always clear
how a gene relates to later development, as the development is mediated by
the phenotype, just as it is aVected by the genotype.

5.9. Wild and Divergent

With the initial discovery of the DNA molecule, it was believed that the
DNA replication process by which the entire gene pool is essentially copied
was the major force of mutations. This stemmed from the fact that despite
proofreading chemical actions, designed to stabilize the genetic inheritance,
errors occur in the replication process. Contrary to the prevalent view
for much of the 20th century, that genes were a stable entity arranged in
an orderly linear pattern on chromosomes, in 1950 Barbara McClintock’s
observational studies of chromosome breakage in maize led to her discov-
ery of a chromosome–breaking locus that could change position with a
chromosome. Moreover, transposons revealed that these mobile elements
could reversibly alter the expression of other genes. In fact, more opera-
tive than mutational change, is the process of transposition, or, jumping
genes, by which the gene structure is not directly altered, but significantly
re–arraigned in terms of how genes are associated with each other.

5.10. Inversion

Another theoretical reversal has occurred, but this is more radical. Whereas
Gould’s concept of ecological time, still contains the notion of evolutionary
pressure, the microscopic marine bacteria called Prochlorococcus, which is
one of the tiniest organisms on Earth, and also one of the most abundant,
can add one more superlative to its list of attributes: It evolves new kinds
of metabolites called lanthipeptides, more abundantly and rapidly than
any other known organism. Moreover, while most evolution takes place
through tiny incremental changes, while preserving the vast majority of
the genetic structure, the genes that enable Prochlorococcus to produce these
lanthipeptides do just the opposite. They somehow undergo dramatic,
wholesale changes all at once, resulting in the production of thousands of
new varieties of these metabolites (Chandler 2017).
56    John F. DeCarlo


6. Results III: Special Relativity

6.1. Positive Analogy

Galileo’s principle of relativity is based on the example of seamen below
deck who can’t discern whether the ship set in smooth waters is in motion,
or, stationary relative to the movement of the water. Two inertial frames
are related by a Galilean transformation, which involves the addition or
subtraction of velocities relative to some absolute reference frame. Thus,
it preserves 3 dimensional Euclidean distances, in that, distance is purely
spatial and time diVerences are preserved.

6.2. Positive and negative analogy

By the late 19th century the eVects of the not yet formulated theory of special
relativity had been noted: FitzGerald — bodily contraction 1887, Lorentz
— same idea elaborated, 1892, Lorentz & Larmor — time contraction, too,
1900. Hence, in 1905, the Poincare Group via rotation of the coordinates of
Euclidean geometry develops transformations that preserve a space–time
interval, with time as an imaginary fourth unit or coordinate. More specifi-
cally, they restate the Maxwell electro–magnetic equations in four dimen-
sions, showing directly their invariance under the Lorentz–Fitzgerald trans-
formation equations. In doing so, when dealing with non–simultaneity they
resorted to depicting space and time as fictional variables, thus insuring
proper time and length contraction.

6.3. Negative Analogy

Whereas Poincare is not prepared to make a complete commitment to a
space–time metric, Minkowski, via hyperbolic rotation, develops a single
metric with the Poincare transformation. In this respect, he relies on the
Euclidean three dimensional spaces, and melds it with a fourth dimension
of time. But this too, does not have a complete realism about it. It will take
Einstein’s boldness to declare it as an actual reality.

6.4. Synthesis & Hypothetical Deduction

Einstein is still wrestling with the scientific findings of Michelson and
Morley (in 1887): light has the same velocity, regardless of its directional
movement around the earth, and whether its source or the observers are in
motion. In other words, the speed of light is a universal constant, regardless
of one’s speed of movement. Hence, the relative velocity between 2 inertia
                                        Transcending Bayesian Self–Credences   57


frames is bound by the speed of light, which is diVerent from Maxwell’s
electro–magnetic current. Thus, instead of universal time, each inertia
frame has its own temporal measurement: time and space are relative to a
particular observer. He deduces that the temporal duration of an event is
dependent of the state of motion of the system of reference in which the
duration is measured.

6.5. Inversion

Special relativity: (a2 — b2 = C2); Based on the Cartesian coordinates
contained in c–squared factor of the Pythagorean equation, Einstein, in a
sense, simply inverts a plus sign to a minus sign: a2 — b2 = c2/D2 —T2
= S2, and in doing so, introduces the absolute parameter of space–time in
that length is no longer measured in terms of a straight line, but rather as
a curved line by which the length is measured by time; consequently, the
curved line which is actually longer than the straight line, measures time
as shorter than the straight line. Imagine a merry go round: people seated
near the center have a shorter distance to transverse compared to those
who are seated at the outer edge, but both complete a full circle in the same
amount of time. Why? Those on the outer edge must travel faster, slowing
down the relative passage of time. While this represents a basic reversal
of the Pythagorean equation, it is also a radical inversion of the notions of
space and time. The notion that time is relative to the motion of one’s frame
of reference is a revolutionary idea.

6.6. Negative Analogy

In 1908, Minkowski posits a real time coordinate within an absolute four–di-
mensional space–time continuum based on experimental physics, which
confirmed Einstein’s theory. Minkowski space–time is a combination of
Euclidean space and time into a four–dimensional manifold where the
space–time interval between any two events is independent of the iner-
tial frame of reference in which they are recorded. While the individual
components in Euclidean space and time will often diVer due to length con-
traction and time dilation relative to one’s frame of reference, in Minkowski
space–time, all frames of reference will agree on an invariant: the total
distance in space–time between events.

6.7. Inversion

Notwithstanding Einstein’s revolutionary theory of special relativity, current
data in quantum mechanics conceives of space–time to be an emergent qual-
58    John F. DeCarlo


ity, not an inherent geometric structure. More specifically, due to the lack
of diVerential between time dilation between constant motion and accelera-
tion, the arrow of explanation has been conceptually reversed by Harvey
Brown in terms of the geometric structure of Minkowski’s space–time
being the result of the dynamic–emergent quality of certain key aspects
of the behavior of particles, and on the conceptual notion that a curved
line is a series of short straight lines (2007). But more radically it calls the
very notion of space time into question: rather than being a fundamental
geometry, inherent to reality, it is an emergent quality.

6.8. Blind Spot

The Equivalency principle, known as Einstein’s fondest thought in 1907,
represents analogy as a structural similarity, namely that: Limits of Special
Relativity, it did not consider acceleration. A basic postulate of general
relativity is that at any point of space–time the eVects of a gravitational field
cannot be experimentally distinguished from those due to an accelerated
frame of reference.

6.9. Holistic and Extended Analogy

Special relativity and gravitational forces aVect time. Hence, even before he
develops the concept of curved space–time, Einstein combined the equiv-
alence principle with special relativity in 1911 to predict that clocks run at
diVerent rates in a gravitational potential, and light rays bend in a gravita-
tional field.


7. Discussion

As a seeker of certain, universal, and verifiable truths, science is inherently
a slow and cautious process; hence, it is not surprising that positive analogy
is often the first step toward new insight, and eventual breakthroughs, and
even revolutionary visions. In terms of negative analogy, Popper seems to
be right that the history of science/the sciences is the history of falsification,
in that, prior myths, beliefs, and even solid theoretical frameworks are
often refined, if not, overhauled. In this respect, for Popper, echoing Hume’s
critique of the inductive method, no theory can be proven, for there is
always a particular case that can be raised that can undermine the theory;
therefore, all one can do is falsify an existing theory.
    Moreover, just as positive and negative analogies, as well as synthesis,
and even inversion and holism, have been regular and essential parts of
                                         Transcending Bayesian Self–Credences   59


the scientific process, blind spots, along with wild and divergent elements
seem to be part of the accepted expectations. In fact, as in the case of atomic
science, notwithstanding the synthetic integration of various theoretical
assertions, not one but two blind spots emerge in biological theory. All these
histories also include revolutionary inversions, which required a radical
re–imagining. In these respects, the limitation of the Bayesian response to
the Quine–Duhem paradox is noteworthy, for such aspects of nature have
not yet been tapped, by the natural sciences, at large; intricate and dynamic
puzzles have probably not yet been fully discerned, and challenges remain.
    The results of three–fold analysis of atomic theory, biology, and special
relativity, are two tiered: on one level, while the structures of creative
thought do not identify specific causal–mechanical dynamics, the structures
are explanatory, in that, a diverse group of historical scientific systems have
consistently displayed the same large–scale developmental pattern. More
specifically, while the history of atomic theory includes all eight of the
creative structural forms, biological history includes seven, and special
relativity, which stands as a more particular strain, contains five of them.
This continuity implies that the patterns demonstrate how the structural
forms of creative thought can be used as grounding and/or functional
principles to explain and predict data driven systems.
    Close examination of the particular scientific histories, relative to their
particular observed data, indicates that the structural creative schema cor-
relate with the nature of the system that is being examined, and its con-
nection(s) with other systems of data. For example, the history of atomic
theory, which aims to plummet the basic parts and connections of the
physical world, has exhibited the logical sequence of: positive and nega-
tive analogy, culminating in synthesis, and yet followed by blind spots and
inversions, culminating in a quasi–holism, with remaining wild and diver-
gent strands. In contrast, owing to the presiding theological assumptions
about the creation of the natural world, the history of biological science is
prompted by negative or oppositional analogies. Moreover, owing to the
dynamic and creative nature of biological organisms, which required the
cleansing of mind–sets to fully understand, two inversions precede the ma-
jor synthesis. But as in the case of atomic theory, there are blind spots, and
wild and divergent strands linger, and there is even a third inversion, after
synthesis. Lastly, the history of the theory of special relativity, more closely
follows the logical structure of atomic theory of: positive and negative analo-
gies, culminating in synthesis, but rather than the blind spot immediately
following, this does not emerge until two inversions have placed things in
proper perspective. In these respects, the three respective histories and their
corresponding creative structural forms, represent logical axioms and rules
that pertain to the given historical science and its respective data.
60    John F. DeCarlo


    Hence, on both levels, the patterns of the structure of creative thought
could guide current and future scientific explorations and evaluate new
theories and models and related experimental data. For example, in light of
the series of radical inversions in biological theory, which calls into question
the conceptual borders of a gene, cell, organ, organism, and environment, a
unifying holism is in order. By the same token, considering the limitations
of the Standard Model in physics, relative to dark matter, gravity, and theory
of special relativity, the grand unifying field theory which Einstein felt
he was close to, remains an ideal for the physics community, as a whole.
Moreover, it might require prior points of synthesis between two sets of
strange bedfellows, such as general relativity and quantum theory, and high
energy physics and condensed matter physics.
    Looping back to the initially stated tradeoV between meaningful–verifiable
experience being posited, and, the type of limiting self–referential implicit in
the Bayesian model and its instrumental use of self–credences, the pattern(s)
of creative structural thought in both the broad history of the sciences, as
well as the histories of particular sciences, allows the practicing scientist
to transcend and objectify, to some degree, the limitations of the their
Bayesian approach, with its use of self–referencing prior credences. By the
same token, the awareness of the dual pattern of blind spots, thin places,
and inversions, even after substantial cases of theoretical synthesis, guards
against the exclusion of currently vague and unknown parameters.


8. Implications

The structural categories which have been introduced and examined in the
contexts of atomic, biological, and special relativity science, in a somewhat
logical fashion, seem to represent a phenomenological structure of scientific
pursuit. Hence, it seems incumbent upon scientists to be aware of these
creative structural forms, as well as how and when they have manifested
in the course of their particular scientific history. For example, chemists
working on the extraction of hydrogen from water seem to be at an impasse:
there are two schools of thought, which basically contradict each other, with
each deriving limited results (although one has better results, but with less
understanding of the process). In such a case, it would seem that a synthesis
of the two approaches is ripe, if not begging for implementation. A similar
state exists in the science of political economy (which has been closely
examined, but excluded from this study due to publications constraints),
where the field is still attempting to reconcile the competing assertions of
Colbert and Adam Smith, whose seminal works are still being extended
and fully developed, exposing contradictions and shortcomings in both
                                            Transcending Bayesian Self–Credences   61


theoretical camps. Hence, it is hoped that such awareness can both help
to guide scientific explorations, and evaluate new theories and models and
related experimental data.


9. Conclusion: Limitations and Future Research

In order to provide a fuller and more representative account of the history
of the sciences, and their general and particular pattern(s) of structural cre-
ative thought, further publication will include: Newtonian physics, general
relativity, and political economy, for the histories of these sciences seem
to manifest similar patterns, supporting the assertion that future scientific
insights and breakthroughs could be pursued and monitored, accordingly.


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