Descartes and the Philosophical Crisis of Modern Science

The philosophical collapse of science was presaged by Cartesian Dualism, which was itself a radical reformulation of the medieval doctrine of transcendentalism.   This latter doctrine argued for the view that God was a spiritual being (or principle) creative of, yet not ontologically coextensive with, but rather categorically transcendent relative to the physical world.  From this idea, the notion emerged that the spiritual and the physical must exist in two separate and wholly independent realms.   This was the dominant theological doctrine of the Church during the 17th century which regulated all public religious thought during the Enlightenment period.  Descartes, perhaps the most influential Enlightenment thinker, worked vigorously to separate the interests of science from the interests of the Church (which, in the name of religious purity, had persecuted the great Renaissance scientist Galileo Galilei and  burned Giordano Bruno).

In Descartes dualist doctrine, all of nature was divided into two forms of substance: res extensa (matter) and res cogitans (mind).  Most importantly, these two substances were conceived as ontologically independent and separate.  They have absolutely contrary natures and yet are somehow able to interact.  Descartes had very little to say about this contradictory notion except to posit as an ad hoc assertion that they did interact at the pineal gland.  It was essential to assert the interaction between mind and body in order to grant the Church doctrines of the power of the conscience over the actions of the human body.

Descarte-Basso Doctrine: Physical as Extended Body

Descartes’ mind-body dualism did not spring de novo from his own mind, but was greatly influenced by early 17th century Neoplatonic doctrines regarding the question of the proper ontology of mind and body as well as the proper ontology of matter and substance.   Abandoning the Aristotelian conception of the total integrated organism as a unified substance, an animated being, a psyche-somatic unity, the new Neoplatonic physicians, under the powerful influence of Sebastian Basso, conceived of a new radical approach to the ontology of  soul (psuche) and body (soma).

[Basso] saw that what was fundamentally involved in [this new approach] was an entirely new conception of physical existence.  In this conception the physical was body, and body alone.  This meant that body was conceived as shed of soul, and thus of form, and was constituted only of matter.  Matter, that is to say, was now for the first time in history given fully the status of a self-subsistent existent, it alone, separated from soul, being the physical.  Thus, in this position Renaissance Neoplatonism, with its ontological dualism of body and soul, was carried to its furthest consequence of the complete separation of body and soul, which is to say, into the complete bifurcation of the universe. – from The Philosophy of Nature by Ivor Leclerc,1986, pp.53-54.

Once the universe of mind (soul) and matter were separated through Cartesian-Basso dualism into ontologically independent realms, the history of philosophy has had as one of its enduring major themes the accounting for the interaction between mind and body as well as integrating or resolving the contrasting ontologies of these two forms of being.

Descartes Contra Aristotle

Descartes New Science rested upon an explicit and conscious denial of  and opposition to Aristotelian natural philosophy of the physical world, which Descarates (and many moderns) characterized as qualitative as contrasted with the  quantitative ontology of the New Science:

In establishing the ground for science, Descartes was at the same time overthrowing a system of natural philosophy that had been established for centuries—a qualitative, Aristotelian physics. In a letter to Mersenne, dated 28 January 1641, Descartes says “these six meditations contain all the foundations of my physics. But please do not tell people, for that might make it harder for supporters of Aristotle to approve them. I hope that readers will gradually get used to my principles, and recognize their truth, before they notice that they destroy the principles of Aristotle.”  – from Descartes’ Life and Works by Kurt Smith, published in the Stanford Encyclopedia of Philosophy.

The doctrine of quantization of science was essentially a radical restriction of scientific investigation, and indeed the very concept of science, to the process of quantification, more specifically to geometric quantification of all scientific subject matter.

From Cartesian Mind Body Dualism to Cartesian Quality Dualism

Beyond the doctrine of the geometrical as the physical, was the doctrine of the non-objective, non-scientific nature of the so-called  secondary qualities.  This latter was derived from the doctrine, also originating with Descartes, of sensory-quality dualism.  This was the doctrine that divided sensory qualities into two mutually exclusive classes: (1) primary qualities, such as extension, shape, location, body, which mapped to or corresponded to the geometric properties of the objects of perception, and (2) secondary qualities, such as color, odor, tone, warmth/cold, which had (it was argued) no objective correlation or mapping to innate properties of perceived objects, and which were often in contradiction to the properties of perceived physical objects.   [For a detailed discussion of the nature and implications of sensory quality dualism, see the bioperipatetic article entitled A Direct Realist Theory of Sensory Qualities.]

Cartesian versus Platonic Dualism

It is often said that Descartes’ mind-body split was anticipated by Plato, who  advocated the distinction between the body and the soul.  But Cartesian and Plationic dualism, though superficially similar, were in a fundamental way radically different, for whereas Plato viewed the soul as the seat of both intellect and bodily animation, Descartes believed that the body was essentially a machine whose animation was effected by the laws of motion acting on its bodily parts (at least for animals, for he wisely omitted man from this hypothesis).  Plato saw the body (as did Aristotle, who was not a dualist) as the instrument of the soul, that which allows the soul to  realize its values and desires in the world.  For an excellent discussion of Cartesian vs Platonic dualism, see Soul and Body in Plato and Descartes by Sarah Brodie

Descartes rejected the Platonic concept of soul (as a union of thought and bodily control) and reduced the essence of ‘soul’ to consciousness alone, without the power of bodily animation.  Furthermore, consciousness, mind, was reduced to ‘thought’ only, without bodily feeling and sense perceptions, these latter reduced to bodily mechanics or reflexes.

Thus Descartes dualism is far more radical than that of Plato and has had, as a result, a radical and profound influence on the rise of modern science, including the science of psychology. (For a discussion of Descartes’ impact on modern psychology see Reflex Action, by Franklin Fearing).    Dualism has led to the philosophical dispute regarding the proper ontology of the world.  Since res extensa and res cogitans cannot (based upon their hypothesized contrary natures) ever interact, nor either serve as the ontological foundation of the other,  and since their is no third alternative (so it is believed) to these two ontological primaries, according to the modern doctrines of the philosophy of science, the universe must be entirely either the manifestation of matter (materialism) or the manifestation of mind (idealism).

The impact of mind-body dualism cries out for a new systematic examination and thorough reassessment of this doctrine by philosophy.  Ivor Leclerc makes this point and takes this position decisively:

The main point I am concerned to bring out is that in reference to the mind-body problem the fundamental bequest of the Renaissance to the modern period has been the Neoplatonic ontological dualism and the consequent dichotomy of mind and body.  It is this feature of our philosophical inheritance which in our day most urgently requires critical scrutiny. – from The Philosophy of Nature, by Ivor Leclerc, 1986, pp 55-56

Cartesian Mathematical Bridge between  res extensa & res cogitans

Descartes ingeniously and brilliantly conceived of a conceptual bridge between the otherwise contrary substances of res extensa and res cogitans.  That bridge was the realm of the mathematical.

For Descartes the very essence of the physical res was extensiveness; it existed as extensive; its extensiveness constituted its being.  That is, this resin essence was geometrical extensiveness and nothing else. Descartes conceived the other existent, res cogitans, as the mental counterpart of the physical, that is, it was the conceiving, the mental grasping, of what in the other res was the extended mathematical.  This is why for him the knowledge of pure mathematics was the knowledge the essence of physical existence.  – from The Philosophy of Nature, by Ivor Leclerc, 1986, p. 14

One can see in Descartes’ connection of both the physical real and the conceptually real through the idea of mathematics the influence of Plato (himself deeply influenced by Pythagoras), which in Descartes’ time was radicalized as Neoplatonism.

Cartesian Dualism Versus Material Atomism

Under the powerful influence of the Renaissance physician/scientists, there emerged a new embracing of material atomism (first conceived by the ancient Greek philosophers  Leucippus and Democritus).   It was soon realized by Renaissance scientists, including Newton, Gassendi, as well as by Leibniz, that Descartes’ system was incompatible with material atomism.  This contradiction was well-described by Ivor Leclerc:

. . . It was not at the level of pure thought, therefore, that the metaphysical dualism presented Descartes with difficulties in respect of mathematical knowledge of the physical.

What constituted a real difficulty for his contemporaries and thinkers of the following generations was that Descartes’s identification of the physical and the mathematical made material atomism impossible.  Gassendi and Newton both saw that the only way to save material atomism was to separate the mathematical entirely from the physical.  But that made acute the problem of how there can be mathematical knowledge of the physical if the physical be entirely devoid of mathematical features. – from The Philosophy of Nature, by Ivor Leclerc, 1986, pp. 14-15

Modern Material Atomism Abandons Descartes and Newton

Descartes viewed res extensa as a passive spatial geometric material continuum.

Matter in general, res extensa, is a continuum whose only properties are spatial properties, i.e., the spatial-geometrical dimensions of depth, length, and breadth. It is, in effect, a homogenous (hence utterly simple), passive, spatially extended “stuff.” –  Itay Shami , The Myth of Reductive Extensioinalism, p. 171, published in Axiomathes (2007) 17:155-183

Why passive? Because, as Ivor Le Clerc explains:

For the physical as mathematical extension neither entails motion, nor does it require motion.  Motion is thus arbitrarily introduced to account for a diversity and separateness of the parts of matter which matter in its essential nature excludes.  – from The Nature of Physical Existence by Ivor Leclerc, 1972, p. 191,

Newton also conceived of matter as passive, fully independent of motion and incapable of self-motion.

Matter, as Newton explicitly recognized, is moveable but it is incapable of moving itself.  This means that the concept of motion is not entailed by the concept of matter and cannot be derived from it. Accordingly, in this philosophy motion is a completely independent fundamental concept.  from Studies in Philosophy and the History of Philosophy, Volume 14, The Philosophy of Nature, by Ivor Leclerc, 1986, p. 5

Although not analytically derivable from matter, eventually, both Descartes and Newton allowed matter to have additional properties essential for scientific study of the material world.  Motion was still withheld from matter but matter was conceived as subject to being moved (not self-motion or auto-motion).   This passive view of ‘movability’ allowed the new scientists to account for extensive change, i.e., change in figure or shape).   Matter was also asserted  ad hoc  to possess the properties of impenetrability, solidity and passive resistance to movement, i.e., inertia.

[W]hen it comes to particular physical bodies some additional irreducible characteristics (simple natures, in Descartes’s parlance) must be admitted: impenetrability, divisibility, figure, and, in particular, mobility and extensibility (the capacity for configurational change due to relative movements of parts). Similarly, Newton’s atoms were predicated with mobility, impenetrability, solidity, and inertia. –  Itay Shami , The Myth of Reductive Extensioinalism, p. 172, published in Axiomathes (2007) 17:155-183

Materialism required an analysis of the concept of matter — while remaining the essence of res extensa –  decomposing it into its hypothesized irreducible, invisible ‘elements’ and thus emerged the modern atomic theory, wherein the atoms (each unique and irreducible in structure and nature) are the ultimate elements composing the entire universe.

Matter replaced by Fields as the Primary Objects of Physics

Unfortunately (for atomic theory and the irreducibility hypothesis of atoms) science soon was forced to conceive the atoms themselves as composed of still more ‘elementary particles’ (electrons, positrons, protons, neutrons).  With further cracking open of the atom, its ‘elementary particles’ turned out to be composed (or so it seems) of still smaller and stranger subatomic particles called quarks, which manifested themselves in multiple varieties.  As for the originally hypothesized solidity, continuity and extensiveness of the atom, the conclusions of research on subatomic particle physics, encompassing the dynamics of matter below the level of individual atoms, resulted in the solidity, and extensiveness of particles disappearing into a stocastic fog of probabilistic wave forms and wave fields.

Consider first, the notion of an atom. Neither indivisible, nor structureless, nor, indeed, indestructible the atoms of modern physical theory bear little resemblance to the atoms of Newtonian mechanics. The search for the fundamental building blocks of atomistic metaphysics must therefore go further and deeper, into the deep waters of the subatomic realm. Yet, instead of providing a definite support for extensionalism, instead of consolidating the notion of solid, formless, elementary chunks of matter as the ultimate basis of all there is our best contemporary physics seems to steadily and consistently undermine it. –  Itay Shami, The Myth of Reductive Extensioinalism

Matter appeared to manifest itself in the form of waves subjected to the universal influence of fields of force.  What was the ontological nature of these new existents, mater waves and force fields?  Are the waves undulations of a material ether, as the ultra-structure/ultra-substance of the universe? And if so, what is the ontology of  force fields?  Does this all ultimately undermine the basic concept of material atoms as the particulate constituents of the universe?

The first serious crack in the idea of particulate building blocks came with Einstein’s relativity theory. Rejecting the idea that a mechanical substance, the ether, must carry the vibrations of the electromagnetic field, Einstein was driven, in his special relativity theory, to consider the notion of a field as an entity in its own right. In general relativity theory, the structure of space-time itself was identified with a field, the gravitational field . …the reality of relativistic force fields, led Einstein to conclude that fields are the only primary reality. –  Itay Shami , The Myth of Reductive Extensioinalism, p. 177, published in Axiomathes (2007) 17:155-183

Thus fields, not atoms, emerge as the primary objects composing the universe.  In his book The Unity of Nature, Friedrich von Weizsäcker discussed how Einstein merged the concepts of force field with space and matter:

In merging the field of force with space it makes the latter into a physical object in the full sense of the word, an object that produces effects and can in turn be acted upon…Einstein was consistent in trying to overcome the remaining dualism of matter and space by regarding matter, too, as a property of space–particles, for example, as singularities of the metric field. – Carl Friedrich von Weizsäcker,  pp 118-119 of The Unity of Physics So Far, in The Unity of Nature, 1971,  (Translated into English by Francis J. Zucker)

Quantum Theory  Abandons Ontology and Epistemology

So what has happened to solid, continuous, impenetrable, irreducible, passive particles, that were once held by physicists to constitute the substance of the universe?  It all dissolved into fields.  And  as for fields, what are these ontologically, actually, in reality?  Modern physics no longer views ontology from its physical perspective, but only from its mathematical perspective.  Modern theories of the physical world are entirely mathematical.   Thus the ultimate world-view of Descartes’ res extensa as essentially mathematical (geometrical and analytical) was realized by modern physics.  The terms ‘particle’ and ‘wave’ no longer mean anything physical about the real world, but refer instead to elements of mathematical models.

Talk of “particles” and “waves” by physicists today sounds like narrative physical  explanation, but actually it is merely useful modeling terminology for one or another special, isolated context, that is light may be treated as a wave or a particle depending on the context; the situation is confusing, but these modeling strategies do not answer the question as to that light propagation actually is, but rather  stand in place of such an answer in conventional discourse.  – from  Scientific Nihilism: On the Loss and Recovery of Physical Explanation by  Daniel Athearn, Part One, Introduction, p. 5

But quantum physics goes even more radically beyond all of this.  Today physical science is dominated by Quantum Theory with its strange, even bizarre notions of the properties and nature, matter, space and fields of force, manifest as waves, and at the quantum level,  quantum waves, and probability waves, i.e. waves of indeterminateness, of ‘uncertainty’.  Particles at the quantum level of existence are ruled by the uncertainty principle which holds that the position and the momentum of a quantum particle cannot both be known at the same time.  Quantum theory holds that the act of perceiving (qua measuring) one property renders the other indeterminate and its values uncertain, and unknowable.

Some quantum theorists argue that the uncertain properties (or at least their quantitative aspects) by virtue of the fact that they are not (or not yet) perceived actually do not exist or at least do not exist in the particular universe of a given observer.  For to exist and become actual is predicated on the collapse the quantum wave of indeterminateness, this latter being a superimposition of all possible outcomes into a virtual quantum system of multiverse of parallel existence, whose collapse requires the act of measurement.  In addition, quantum theory holds, that there exists at the quantum level of interaction, the ‘spooky’ (Einstein’s term) phenomenon of action-at-a-distance, the strange notion of entanglement, the stranger notion of non-locality.  Stranger than all of these is the quantum theoretic notion that the act of measurement, and ultimately looking at the measurement of a physical quantum property actually causes the value and states of those properties to come into existence!  Thus the classical ontology of matter with its Newtonian mechanics was fully undercut and abandoned by quantum theory and the new quantum mechanics at the subatomic level or matter and its manifestation as discrete particles.

Quantum mechanics shows in unequivocal terms that as we go down the ladder of size and complexity to reach the simplest known “particles”—photons, leptons, and quarks—what we find are not minute material corpuscles but, rather, a whole new kind of reality which, though capable, under certain circumstances, of manifesting particle-like qualities, bear little resemblance to the particles of old. –  Itay Shami , The Myth of Reductive Extensionalism, p. 178, published in Axiomathes (2007) 17:155-183

Thus, due to the impact of quantum theory, physical science has abandoned classical materialism only to embrace quantum idealism (mind-caused reality)!  That is the actual and proudly trumpeted Copenhagen interpretation of the quantum phenomena (most associated with the quantum theoretical ideas of Neils Bohr).

The deep problem of modern science (and of modern philosophy) is its fatal neglect of the Aristotelian perspective of ‘generation and corruption’, of coming into being and going out of being, of becoming and ending.   This topic will be discussed at length in a future blog post, for now it is sufficient to point out the significance of this problem.   In this regard I recommend the paper Mathematics, Explanation and Reductionism: Exposing the Roots of the Egyptianism of European Civilization by Arran Gare.  Here is an excerpt from the Abstract of that paper clearly stating the essence and implications of the problem or neglecting the dimension of ‘becoming’ in modern science and philosophy:

We have reached the peculiar situation where the advance of mainstream science has required us to dismiss as unreal our own existence as free, creative agents, the very condition of there being science at all. Efforts to free science from this dead-end and to give a place to creative becoming in the world have been hampered by unexamined assumptions about what science should be, assumptions which presuppose that if creative becoming is explained, it will be explained away as an illusion. – Mathematics, Explanation and Reductionism, published in Cosmos and History: The Journal of Natural and Social Philosophy, vol. 1, no. 1, 2005, p. 54.

This problem of ‘becoming’, of process and temporal continuity of being, is relevant to quantum mechanics and attempts to overcome the static reality view of the Copenhagen interpretation.   The Copenhagen interpretation of quantum mechanics is not the only embraced interpretation.  There are others, equally or even more bizarre. Some have reduced the degree of strangeness by introducing explicitly Neoplatonic ideas into their interpretation.  Most prominent and widely embraced, and least paradoxical, is the ingenious theory of David Bohm, which is based on the Cusanian idea of the universe as the unfolding (explicatio)  of a transcendent enfolded (implicatio) world whose nature is fundamentally mathematical.   This is the fundamental vision underlying Bohm’s ‘implicate order’, illustrated by his famous thought experiment: the Glycerine Machine. What make David Bohm’s model of ‘the implicate order’ so significant is that it introduces the fundamental missing element of quantum mechanics: process and continuity, what Arran Gare would call the dimension of ‘becoming’.  Here are David Bohm comments about the absence of the concepts of movementprocess and continuity in quantum mechanics:

You see, the present quantum mechanics does not have any concept of movement or process or continuity in time. It really deals with one moment only, one observation, and the probability that one observation will be followed by another one. But there is obviously process in the physical world. Now I want to say that that process can be understood from the implicate order as this activity of re-projection and re-injection. So, the theory of the implicate order, carried this far, goes quite beyond present quantum mechanics. It actually deals with process, which quantum mechanics does not, except by reference to an observing apparatus which in turn has to be referred to something else. — from  Morphic Fields and the Implicate Order: A dialogue with David Bohm, p. 7.

 The Nihilism of Modern Science

This is the current ontological and epistemological crisis of modern physics.  This ontological/epistemological crises has led to the current deeper crisis of explicative nihilism in modern science.  Nihilism being, in this context, the denial that the physical universe can be explained (even in principle) by science through ‘narrative causal explanation’ (as coined by Daniel Athearn) and the denial that narrative causal explanation is even a legitimate goal of physical science.  An excellent analysis and prognosis of the current crisis of nihilism in modern science, see Scientific Nihilism: On the Loss and Recovery of Physical Explanation by  Daniel Athearn

Acausalism about fundamental physical science is only the core of scientific nihilism, around which have accumulated layers of assumptions and methodological doctrines that dominate a scientific/academic community in which philosophy of science has an influence second only to physics itself. … Taken as a whole this institutional dogmatic structure is antithetical to the basic claims of physical ontology; indeed the two outlooks are radically alien to one another. Philosophy of science as theory of science has been largely animated by the project of following out the apparent acausalist implications of twentieth-century physics–essentially a philosophical reaction as if to the decree of an unique authority, partly due to the purely emotional factors of the prestige of “hard” mathematical physics with its technical accomplishments. – from  Scientific Nihilism: On the Loss and Recovery of Physical Explanation by  Daniel Athearn, Part One, Introduction, p. 9-10

A New Philosophy of Science is Needed

What has led to this philosophical impasse?  Where has science gone wrong? Where has philosophy gone wrong?   How do we once again find our way out of this seemingly insolvable maze of contradictory ontologies?   This is where a new philosophy of nature and philosophy of science is beginning to emerge.

Essential to this discussion is a clear reevaluation of the Renaissance Neoplatonic concept of the real as extension, holding that non-extended entities are not real.  By non-extensional properties of entities, modern  philosophy uses the term intensional (in the sense of being internally elaborated as opposed to merely externally conceived). Itay Shami offers and elaborate and brilliant paper that argues strongly against the dominate extensionalist doctrine:

ABSTRACT: Extensionalism, as I understand it here, is the view that physical reality consists exclusively of extensional entities. On this view, intensional entities must either be eliminated in favor of an ontology of extensional entities, or be reduced to such an ontology, or otherwise be admitted as non-physical. In this paper I argue that extensionalism is a mis-guided philosophical doctrine. –  Itay Shami , The Myth of Reductive Extensionalism, published in Axiomathes 2007 17:155-183, p. 155

Ivor Leclerc extends a plea for a revival and resumption of the previously abandoned philosophy of nature.

In our time, I wish to maintain, the development of science has come to require of philosophy as one of its most important tasks the resumption of the inquiry into nature. from Studies in Philosophy and the History of Philosophy: The Philosophy of Nature, by Ivor Leclerc, 1986, p. 11

Daniel Athearn makes a similar plea (although with a different proposed strategy):

The present project seeks to restore this old-fashioned quest for physical or causal explanations (under a sweeping transformation) to a vital and productive condition, rescuing it from its current status as a complete anachronism that was only justified during a more innocent stage of science. – from  Scientific Nihilism: On the Loss and Recovery of Physical Explanation by  Daniel Athearn, Part One, Introduction, p. 3-4

Recovering Aristotle’s Physis

This is where Aristotle, his metaphysics, his categories, and his principles of ontology come into the picture and this is the theme of my forthcoming series of blog articles.  Others have also realized that the return to Aristotle is the key to discovering and rediscovering the proper conception of nature:

It seems that the time is ripe to swing the pendulum away from our radical extensional heritage and back towards a conception of nature, and meaning, which [are] Aristotelian. –  Itay Shami , The Myth of Reductive Extensionalism, p. 181, published in Axiomathes (2007) 17:155-183

Ivor Leclerc, a contemporary scholar of the philosophy of science, argues that modern philosophy of science needs to recover Aristotle’s  profound identifications regarding the the philosophy of nature:

In Greek times Aristotle had brought philosophy back to a necessary concentration upon physis, nature, as the object of philosophical inquiry.  The profundity of Aristotelian insights into the philosophical issues involved are unsurpassed. We need today to come back to this source, more particularly in respect of the fundamental issues and problems. – from  The Philosophy of Nature by Ivor Leclerc, 1986, p. 208

For a detailed discussion regarding the profound content, historical influence, and crucial need for the recovery of Aristotle’s philosophy of nature, see the bioperipatetic article entitled Recovering Aristotle.

List of References in Order of Citation:

  1.  Ivor Leclerc  The Philosophy of Nature, in Studies in Philosophy and the History of Philosophy, 1986.
  2.  Kurt SmithDescartes’ Life and Works, published in the Stanford Encyclopedia of Philosophy, 2014.
  3. Jack Schwartz,   A Direct Realist Theory of Sensory Qualities., bioperipatetic.com, 2015.
  4. Soul and Body in Plato and Descartes by Sarah Brodie , from Proceedings of the Aristotelian Society (hardback), 102, 2001.
  5. Franklin Fearing,  Reflex Action, The Williams & Wilkins Company, 1930.Itay Shami , The Myth of Reductive Extensionalism,  published in Axiomathes, 2007
  6. Carl Friedrich von Weizsäcker,  The Unity of Physics So Far, in The Unity of Nature,  (Translated into English by Francis J. Zucker), 1971.
  7. David Bohm,  Morphic Fields and the Implicate Order: A dialogue with David Bohm.
  8. David Bohm, Wholeness and the Implicate Order, Routledge & Kegan Paul, 1980
  9. Ivor Leclerc,  The Nature of Physical Existence, 1972.
  10. Daniel Athearn,  Scientific Nihilism: On the Loss and Recovery of Physical Explanation Part One, Introduction, State University of New York Press, 1994.
  11. Arran Gare, Mathematics, Explanation and Reductionism, published in Cosmos and History: The Journal of Natural and Social Philosophy, vol. 1, no. 1, 2005
  12. Jack Schwartz,  Recovering Aristotle, bioperipatetic.com, 2014.

Copyright © 2014 by bioperipatetic.  Published on January 29, 2014  3:11 pm

Latest revision:  October 27 , 2015 @ 1:46 pm

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