Tectonics, Platonics & Logic
The recognition that earthquakes and volcanoes delineate
the boundaries of constantly moving plates at the
Earth’s surface represented an intellectual
about-face of the first order. Plate tectonics has
been one of the most successful theories in the history
of natural science and has revolutionized thinking
in all of the Earth sciences. Yet plate tectonics
remains a largely descriptive and kinematics theory,
albeit a remarkably predictive one. It is even more
powerful than generally acknowledged since it causes
thermal and chemical inhomogeneity in the mantle.
The forces that drive the plates also stress and reorganize
them. In real world plate tectonics, triple junctions
and boundary conditions evolve, and plates interact
and reform when conditions change. Second order features
such as fracture zones, accreted terranes, transform
faults, diffuse boundaries, swells, sutures and microplates
may hold the key to global tectonics and volcanism.
Aristotle Contemplating a Bust
was the first philospher of science and Aristotelian
Logic, both deduction and induction, has dominated
the scientific method for more than two millenia.
Plato believed in the underlying
rationality of the Universe and used discourse, rhetoric
and logic in uncovering it. He believed in the ideal
and abstract world perhaps more than the world
of the senses.
In spite of its successes plate tectonics is widely
regarded as an incomplete theory. Although mountain
belts and continental collisions are accepted as consequences
of plate tectonics, volcanic chains, large igneous
provinces and continental breakup have been rationalized
with separate hypotheses. The concept of rigid plates
offers no explanation for diffuse deformation and
volcanoes not at plate boundaries. The driving mechanism
for plate tectonics is not agreed upon. A homogeneous
isothermal mantle does not explain melting anomalies
- occasional and localized bursts of excess magmatism.
There are two approaches for dealing with these perceived
limitations. One is to introduce phenomena such as
plumes (core-heat driven thermal instabilities) to
break up continents and create volcanic chains. The
other is to drop such adjectives as rigid, fixed,
elastic isothermal, homogeneous, and uniform when
describing plates and the mantle and to push the plate
tectonic theory to the limit to see where it fails.
Small-scale convection, stress variations and cracks
in the plates (consequences of plate tectonics), magma
focusing, and variations in mantle fertility may be
alternative explanations of volcanic chains and melting
anomalies. Lateral variations in temperature and density
(which drive mantle convection) and fertility of the
upper mantle are also consequences of plate tectonics.
Recycling, continental insulation, tensile stress
and slab cooling can explain variations in temperature
and volcanic output from place to place. These options
are not available if the plates are rigid and uniform.
In convective systems cooled from above, instabilities
of the surface drive motions of plates and the interior.
This is the kind of convection involved in plate tectonics.
Yet motions and temperature variations in the deep
mantle, independent of surface conditions, are often
assumed to drive the plates and create volcanic chains.
In one theory the plates control their own fate and
self-organize. In the other, many surface processes
are controlled by deep convective motions and core-heat;
the surface passively responds. On the one hand, we
have ideal plates plus plumes and, on the other, a
motley array of secondary features (cracks, rifts,
volcanic chains), and ideas such as self-organization,
lateral heterogeneity, non-isothermal upper mantle,
and convection driven by the edges of continents and
plate motions. In science ideas grow in strength as
they compete successfully with alternative ideas.
But no alternative concept presently competes with
the simplicity of plume, the word and the image. The
plume hypothesis is seldom challenged.
Topography: the ocean had been removed. Blue
lines: edges of the tectonic plates, yellow dots:
earthquakes 1960-1985, red triangles: volcanic eruptions
Scientific descriptions should consist of small groups
of linked words that convey concepts without fixing
theories. Melting anomaly and midplate volcanism are
neutral words but these have morphed to hotspot and
plume so we now have the Iceland and Hawaiian plumes,
where there used to be volcanoes, and plume or lower
mantle components in oceanic basalts. Alternative
hypotheses for volcanic chains such as propagating
cracks and lithospheric extension were dropped because
of the perceived fixity and high temperatures of hotspots.
Hotspots, however, are not particularly hot and words
like coldspots, crackspots and paradox are starting
to invade the literature. They are also not ‘spots’,
‘fixed’ and seldom in age progressive
chains. Some are built on abandoned ridges, preexisting
fracture zones or sutures between microplates. Although
the belief in mantle plumes is unlikely to be soon
shaken (more scientists believe in plumes than ever
believed in phlogiston, aether or continental fixity)
it is necessary to have alternative theories and also
suitable words. After all, we have steady state, big
bang, inflationary, and accelerating universes and
various versions of gravitational theory (which are
still being tested at great expense although physicists
know the outcome).
One not-so-obvious alternative is simply plate tectonics
itself, with the implied qualifiers removed and the
secondary features elevated to prominence. Plate collision,
separation, reorganization, cracks, incipient plate
boundaries and volcanic chains are parts of plate
tectonics. Only in an idealized or Platonic world
can one expect plates to be perfectly rigid or elastic
with boundaries forever fixed and volcanoes restricted
to the edges. Imperfect (non-ideal) plate tectonics
does not have the semantic appeal or power to compete
with an established paradigm. I propose the term The
General Theory of Plate Tectonics to acknowledge the
imperfections of the real world and to include the
dynamics as well as the kinematics. The Special Theory
of Plate Tectonics can then refer to the instantaneous
or steady-state kinematics of idealized (permanent)
plates. For many purposes this is accurate enough
and all we need. In both cases, all motions are relative
and the concepts of fixity or absolute motions do
Platonics is suggested for the superficial and abstract
version of global tectonics that requires ad hoc assumptions
for many real world plate tectonic features. Sometimes
words, particularly adjectives and metaphors, serve
as mental handcuffs in advancing a science. Rather
than quibble over the definition and scope of the
plate tectonic concept it is useful to have several
concepts in mind, even if they only represent various
levels of abstraction or approximation. It is not
uncommon in science for certain levels of approximation
to be appropriate at some stages but not adequate
for other applications. Newton’s theory can
be regarded as a useful approximation to Einstein’s.
John Wheeler fortified Occam’s Razor by introducing
radical conservatism. It is conservative in its reluctance
to introduce new assumptions. Power is added by taking
a radical approach to the few assumptions that are
adopted. The assumptions must be formulated precisely,
pushed hard and applied to as many situations as possible.
When Nature resists it may be time to explore an alternate
lean theory rather than adding more assumptions. Often,
new hypotheses are needed to undo the damage done
by unnecessary original assumptions. The general theory
of plate tectonics drops most of the assumptions,
adjectives and limitations of the abstract theory
and makes it evident that plate tectonics is more
powerful than generally believed. The general theory
is put forward as a topdown, stress and plate controlled,
largely tectonic and athermal, alternative to the
bottoms-up deep thermal plume hypothesis. The perceived
limitations of plate tectonic theory that are thought
to require ad hoc mechanisms to drive and break-up
the plates and create volcanic chains are semantic,
not real, limitations.
we need a semantic solution and the present proposal
is a modest step in that direction.
argument, rhetoric and fallacies
These are branches of philosophy. Science started out
as a branch of philosophy. Scientific truth is now treated
differently from logical truth, or mathematical truth.
But in the search for scientific truth it is important
not to make logical errors, or to make arguments based
on logical fallacies.
Some of the common arguments in support of particular
models of mantle convection or geochemical box models
can be cast into the form of logical arguments and analyzed
for their validity. Some well known fallacies are categorized
below, with examples from the recent literature.
Circulus in demonstrando
Mid-ocean ridges are able to migrate over hotspots,
which implies that the hotspot source is deeper than
about 200 km.
reconstructions not using the fixed hotspot reference
frame do not demand that ridges cross hotspots.
The association of
"plume heads" [Deccan, Monteragian Hills,
Rajmahal, Siberia] with "plume tails" [Reunion,
Corner Seamount, Kerquelen, Jan Mayen] is speculative,
Argumentum ad populum
"For many geoscientists, the mantle plume model
is as well established as plate tectonics".
Dilemma and Affirming the Consequent, plus rhetoric
"The apparent controversy can be
broken down into two questions. Is there evidence that
deep mantle plumes exist? And do all volcanoes not associated
with plate boundaries require a deep mantle plume? The
answers seem most likely to be "yes" and "no"
A limited number of
options (usually two) is given, while in reality there
are more options (or perhaps only one). A false dilemma
is an illegitimate use of the "or" operator.
Putting issues or opinions into "black or white"
terms is a common instance of this fallacy.
The actual question is, "Is there evidence that
any volcano requires a deep mantle plume? "Deep
mantle plumes, in the sense of thermal instabilities
of a thermal boundary layer, certainly exist but do
they rise to the surface and are they narrow? Pressure
(and chemical layering) at the CMB causes them to be
broad, sluggish, long-lived and slow to form, apparently
consistent with the large features seen by tomography.
The probable existence of a deep mantle TBL is not the
same as the assumption that these must be the source
Also referred to as the "black and white"
fallacy and "false dichotomy", bifurcation
occurs if someone presents a situation as having only
two alternatives, where in fact other alternatives exist
or can exist.
Red herring and fallacy
of Irrelevant Conclusion
The upwelling mantle under Hawaii must also be 200
to 300 K hotter than the surrounding mantle to achieve
the required large melt fractions at depths below the
80-km-thick lithosphere . Such hot rock material must
come from a thermal boundary layer. The core-mantle
boundary is the most likely
source, unless there is another interface within the
mantle between compositionally distinct layers.
These are requirements
of the plume hypothesis, not general requirements.
The Ratio Fallacy
and the Slippery Slope Fallacy
The chemistry and isotopic composition of many hotspot
lavas, especially the high 3He/4He
ratios, indicate that the hotspots sample a part of
the mantle distinct from that sampled by mid-ocean ridge
basalts. High 3He/4He ratios imply
high 3He contents and therefore an ancient
undegassed reservoir and therefore the deep mantle.
of Irrelevant Conclusion
Numerical simulations of plumes reproduce many of the
geophysical observations, such as the rate of magma
production and the topography and gravity anomalies
produced by plume material as it spreads beneath the
lithosphere. Therefore, plumes exist.
Fallacy of Irrelevant
Conclusion, Affirming the Consequent and Permissivity
Theoretical and laboratory studies of fluids predict
that plumes should form in the deep Earth because the
core is much hotter than the mantle. Therefore hotspots
are caused by plumes from the core-mantle boundary.
Confusion of "should"
with "do" or "must".
and Circulus in Demonstrando
The persistence of flow through the plume tail for
100 million years or more (several times the number
of years required for plume heads to rise through the
mantle) implies that the plume is much less viscous
than the surrounding mantle.
This has nothing to
do with whether plumes exist or the characteristics
and requirements of other models.
Continental flood basalts erupt a million cubic kilometers
of basalt or more in 1 million years or less. Therefore
plumes erupt erupt a million cubic kilometers of basalt
or more in 1 million years or less.
is now used to prove that continental flood basalts
are caused by plumes.
Note that the above two conclusions are contradictory.
The rate of plume magmatism is controlled by lower mantle
viscosity while in the plate theory it is controlled
by lithospheric stress (the valve).
or disproof of the plume model
Popper has argued that one can never
prove a scientific idea, one can only falsify (disprove)
it. Other philosophers of science argue that it is no
easier to falsify a theory than to prove it since one
can always use auxiliary assumptions to prop up a failed
theory. One can claim that the proposed phenomena is
unobservable. An issue that lies outside this debate
is the following; Suppose all the evidence that led
to the formulation of a theory is reanalyzed and shown
not to be valid, or to have been overinterpreted? What
should one do with such a theory? Should one look for
new evidence or arguments to support the theory? Or
should one consider or reconsider other theories, even
ones that were abandoned in the face of the now abandoned
of science and logic texts one finds the following example
of a theory that is steadfast in the face of recalcitrant
data. A Newtonian astronomer makes the prediction that
a previously unobserved planet is perturbing the motions
of an observed planet. He receives a grant to develop
a special telescope to search for this planet. The search
is unsuccessful so he proposes that the planet is obscured
by cosmic dust. He develops a new observational program
and concludes that cosmic dust is not the problem. The
next idea to rescue the theory is the presence of electromagnetic
fields, which requires an even more expensive observing
program involving satellites. The field is not found.
He then proposes that the perturbing planet is superdense
and too small to be seen. Alternate theories (relativity)
are not considered. Because of the large number of publications
and grants the Perturbing Planet hypothesis is considered
a huge success.
There are similar examples in Earth
sciences. Hotspots are no longer regarded as "fixed",
in the sense of Ptolemaic astrology, but wander as rapidly
as other elements of plate tectonics such as motions
between some trenches and some continents for equally
long periods of time. Hotspots wander in the geographic,
geomagnetic and biofacies reference systems as well
as with respect to one another, Auxiliary assumptions
used to rescue the fixed plume idea include True Polar
Wander (TPW), mantle roll, westward drift of the lithosphere,
mantle wind, large lateral transport of plume material,
elimination of badly behaving hotspots, hotlines and
large radius hotspots.
often cited as the main tool for solving the plume debate
but the low resolution of seismic techniques is viewed
as making seismology incapable of detecting plume stems.
However, a plume, in contrast to passive upwellings,
spreads out beneath the plate and the various mantle
discontinuities. These large horizontal features and
plume heads are readily detectable by current technigues
including surface waves. Plumes should cause uplift
of the surface and the 650 km discontinuity but none
of these are observed so attention is focused on small
unobserved plume tails. The absence of a clear tomographic
signal has led to proposals for intricate contortions
in the plume stem. NSF is currently spending large amounts
of money on this search. Other (shallow) ideas are not
Helium isotopes are often quoted as
evidence for plumes. The idea originated with the observation
that some samples from regions thought to be affected
by plumes sometimes have "high 3He/4He"
ratios. The definition of "high" is arbitrary
and is sometimes taken as 9 to 10 times the atmospheric
ratio and higher. Iceland, Yellowstone and Samoa have
high ratios but these have straightforward tectonic
explanations and are apparently shallow features. The
3He/4He ratio is taken as a proxy
for "high 3He", which is the so-called
"primordial" isotope. What would it take in
the way of helium isotopic data to prove or disprove
the plume hypothesis? About half the hotspots have "low"
3He/4He ratios. Does this do it?
No. These are now called "low helium plumes"
or are "contaminated". Suppose it is found
that high 3He/4He does not correlate
with high 3He and hotspot basalts really
have very low 3He? Does this do it? No. These
are merely degassed, as appropriate for their shallow
extrusion levels. Can this be tested? If the magma is
degassed the gases from hotspot locales should have
more 3He and higher 3He/CO2
ratios than elsewhere, and the magmas shuld have low
He/Ne ratios because of solubility effects. The opposite
is observed, but helium is still considered to be a
At this point,
one should ask,
tomographic or helium observation would shake our opinion
that a melting anomaly or volcano (the old words for
hotspot) may not be due to a deep mantle plume?"
This is more
in tune with the methods advocated by the philosophers
of science (and quantum physicists, cosmologists and
relativity specialists), than the question,
else can I do to prove the hypothesis?"
The primary developer
of quantum mechanics spent the rest of his life trying
to disprove the theory! Jason Morgan is reported to
have said, after being asked,
plate tectonics and plumes under your belt what will
you do now?",
"Well, try to prove
them wrong, I guess."