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Plate Tectonics, Platonics & Logic

Don L. Anderson

Seismological Laboratory, California Institute of Technology, Pasadena, CA 91125

dla@gps.caltech.edu

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 of Homer
(Rembrandt)

Aristotle 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 1980-1995

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 not arise.

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.

Thus, we need a semantic solution and the present proposal is a modest step in that direction.

Logic, 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.

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.
Plate 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, not evidence.

Argumentum ad populum

"For many geoscientists, the mantle plume model is as well established as plate tectonics".

False Dilemma and Affirming the Consequent, plus rhetoric and Bifircation

"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" respectively."
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 of OIB.

Bifurcation

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.

Fallacy 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".

Ignoratio Elenchi 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.
This characteristic 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).

Proof 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 constraints?

In philosophy 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.

Tomography is 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 funded.

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 plume diagnostic.

At this point, one should ask,

"What 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,

"What 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,

"With plate tectonics and plumes under your belt what will you do now?",

"Well, try to prove them wrong, I guess."

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