Light and Transcendence

If you glance through the liturgy of the hours and the divine office, you will notice the frequency that the word light is used.  Of course, it is in the context of prayer, and it is an attribute of Jesus Christ and of all the persons of the Holy Trinity.  It is not by accident.  Light in the physical world is the closest analogy to the spiritual that is found.  Aristotle recognized that sight is the most liberated of the senses and the one that is closest to the nature of the human mind, especially what he called the Agent Intellect and Plato called the light of Being that illumines our minds and allows us to search out and then gaze out upon the world of being that is behind and beyond the world of appearances.  St. Augustine also picks up on on this light and expands it from the light of being to the light of conscience, the light of faith, and the light of glory.  Light is at the very essence of the human soul.  St. Theresa Benedicta (Edith Stein) picks up on this in her book The Science of the Cross, and recognizes that this inner light is the essence of the human soul, and it is the inner region of the soul where God dwells, and unfortunately, the place from which we as human beings tend to be exiled.  Which means we are exiled from our selves.  But Christ wants us home, to return to abide with Him forever.  God is light. And so are we.

In terms of the transcendental notions then, these are the differentiate lights that Lonergan has articulated in an explanatory manner.  As long as we exist, that can be actuated. But they can also remain merely as a capacity for self-transcendence.  When the interior question for understanding arises with regard to an experience, then this light has awakened.  It is the same quest in which an insight emerges, and this can then be described as an illumination or an ah-ha experience.  Notice how this parallels physical light.  When light shines off into space with nothing to illumine, it seems dark. But as soon as something comes into its realm, like a moon, then it illumines the object, and suddenly our eyes have something to see.  The same with the quest for understand. And insight (act of understanding) allows the eye of the mind (as Augustine frequently uses the term), and eye intrinsic to the quest (a question is intrinsically conscious and intentional) to see (intend) something.  Furthermore, once seen, then we can speak it, and this parallels the need to conceive of the insight.

Once the insight is conceived, then a new transcendental notion can be actuated in our capacity for self-transcendence.  There are two sequences of actuated quests here. The first regards the correctness of the insight.  Is my insight into a representative democracy correct?  The second is whether we have a factual object understood by the insight.  Is our country a representative democracy? The first has to be answer correctly before the second can be answered factually.  Both arise in the quest for truth or being.  To answer this quest for truth, first one needs to gather evidence and then reach a kind of insight into whether the evidence is sufficient. Lonergan calls this a reflective insight, which traditionally is named a grasp of sufficient evidence.  Such an insight then allows one to answer the quest and pronounce a judgment.  Yes, that is the meaning of democracy.  Or yes, we live in a representative democracy.  Or maybe I realize that I do not understand the nature of a democracy, or that we do not live in one. These too are judgments, answers the that quest “Is it so?”

As the mind rises into the world of truth and being through judgment, then the possibility of a new light or transcendental notion emerges.  Judgments of fact attune us to the world that is.  Judgments on the correctness of insight not only make possible a grasp of judgments of fact, but also these open up to us worlds of possibility and even probability.  We can then wonder about doing something in light of the possibilities that could become factual.  There is as Lonergan articulates a scale of feeling that intentionally awakens to objects of fact and objects of possibility.  Naturally, these response to the greater possibility (the greater intelligibilities and factualities) with more vibrancy or more commonly, with more energy. This can become vastly disordered of course.  But nonetheless, our entire souls awaken within this light of goodness, of value, to the possibilities of our creative free participation in the coming to be of this world, and even facets of our own existence.  Appreciation, thankfulness, and love respond to this world of intelligible facts that are good.  Free decision is the possible response to intelligible possibilities and probabilities that then brings about factual goods.  This light is that of conscience.  It is the full realization of the transcendental notion of value. As the landscape of intelligibility grows, the landscape of possibility, probability, and factuality grows.  That is the growth into an entire scale and horizon of the good.

Ultimately it also is the expansion of the actuation of the entire capacity for self-transcendence that then awaken to the question about unrestricted answers to the potentially unrestricted quests. That is as Lonergan articulates in chapter 4 of Method in Theology, the emergence of the question of God.   If one has been appropriating one’s own interiority, one realizes as well that this is also an awakening to the very inner essence of one’s own soul, to the capacity for self-transcendence.  As that capacity becomes actuated, its full actuation, the full actuation of the transcendental notions, which is aptly described as an unspeakable illumination through God’s outpouring love who gives himself as a Triune self to the subject, is then a state of being in love without conditions.

I want to bring this back to the liturgy of the hours and divine office now.  This unfolding of this liturgy throughout the year cultivates the human subject, and through it, God tills the landscape of one’s horizon at all levels of conscious intentionality, from experience up through moral acts to purify the totality of one’s soul so that it is more and more permeated by the transcendental notions. Then one becomes more and more a light in this world.

The liturgy of the hours and divine office however as liturgical however revolve around an even more potent set of lights.  Those lights correctly understood and entered are the sacraments.  The sacraments are gifts from God that literally started in the motor sensory world that if rightly received permeate the entire human subject from the lowest to the highest levels of conscious intentionality, and these do so by actuating the capacity for self-transcendence in its state of being in love without restriction.  This state as long as it lasts and as much as it is lived from then increases the realization of each transcendental notion as it awakens along the paths of emerging conscious intentionality, and it transforms the entire landscape of conscious intentionality.  The Eucharist is the supreme realization of all of this.  One literally is moving into the inner reaches of the Holy Trinity. This is why it is described as an eternal banquet.  At a mass, one’s motor-sensory being literally participates in a physical encounter with that which has been transubstantiated into the ascended incarnate Son of God who opened the doors for humanity to enter the inner life of the Holy Trinity. We are literally able to move closer in space and time to this reality.  This reality though emerges into all levels of conscious intentionality through acts of faith and gifts of grace.  The Father sends His Son into us through their Holy Spirit, literally and spiritually. Is this necessary?  No.  It is a gift and promise.  God makes it possible for us to receive him into our beings in a manner similar to how Mary when Gabriel came to her and she proclaimed her fiat.  The Son was then literally conceived in her.  When we sit in the physical presence of the Holy Eucharist, the body-soul-humanity-divinity of the Son, God promises to enter us if we are rightly ordered, receptive, and pure.  It reaches its height when we say and Amen to Him, and we are feed physically and if rightly purified, spiritually with Him. As incarnate beings, this way of being given the Son then illumines the totality of our conscious intentionality in a manner like nothing else. We can then understand what someone like John Henry Newman meant when he said that our presence in and reception of the Holy Eucharist is the closest we get to heaven while on earth. It is heaven, the eternal banquet.  Now that is a light.

Just some thoughts.

The Conversion of Memory and Intentionality in St. Augustine’s Confessions

by David Fleischacker

Last night, I met a seminarian who had been reading Saint Augustine’s Confessions and was discussing how much he liked the last section (book 10 and on) on memory, time, and eternity.  It brought to mind some of my own memories about the book and about Saint Augustine’s City of God.  Memory is that by which a person is oriented in the present and toward the future.  Amnesia helps to point this out – without memories we would not know the people around us, or even our own names, or the language that we speak.  A priest friend of mine pointed out another thing that was even more important to Augustine that is linked to memory, namely commemoratio. Notice that it has the word memory in it.  As well it contains “co-“ and “ratio”, which points to living in the truth with each other.  Fr. Matthew Lamb writes on this term. Commemoratio articulates the public nature of truth and how living in that truth as a member of the one human race results in a mutual indwelling.

In the Confessions, it is illuminating to read the first nine books as an account of the conversion of Augustine’s own memories, a conversion that awakens him in a more comprehensive biographical manner to the eternal love and forgiveness and justice of God.  Even the simplest memories that he has, such as stealing fruit (something like Adam and Eve had done) are transformed into forgiven acts by which God’s glory shines upon him and the world, and he is elevated into the light of God’s loving forgiveness as a son of God the Father.  Throughout those nine books, Augustine recalls with God’s help the multitude of memories of relationships with family and friends and teachers.  In each case, these memories are transformed in God’s loving light.  One sees how Augustine discerns the dialectic of sin and grace operative in his life, and how God’s grace was working at every moment, even those that were the result of his own sin as he was tossed or tossed himself into the storms of life.  He came to apprehend God’s pursuit of him even in those dark and descending moments in his life.

For Augustine, after his conversion, recalling every memory as he does in the  Confessions involves a transformation of his presence with the others in his life.  They come to dwell in him as creatures and as part of God’s loving providence, as individuals in a fallen world whom God calls out like He did in the Garden of Eden…. Where are you? Why are you hiding? If you have read the Confessions you know that before Augustine’s conversion, he was in the “out of doors” and enslaved in his disordered desires.  He could not think of God or of other human beings except in material images (God as a kind of infinite matter with an infinity of space).  God allowed him to travel through a multitude of experiences (including his travels into the Manichean religion) that constantly included God’s response — sometimes one of desolation that was a result of his fleeing from God, other times one of consolation in which God was awakening him to the truly good.  These moments, especially those that awoke him to the question of good and evil, eventually brought him to a moment in which his mind was elevated to apprehend reality that was beyond the material (see book 7, chapter 10), and that his sinful state was far from the light above.  Even with that experience, he was not free.  His will had to be liberated from the world of lust and disordered desire, a liberation which he recounted in the details of book 8.  After God frees him,  Augustine is able to join in a new commemoratio with his own Mother before she dies.

These transformed memories allow Augustine to grasp, live, and dwell from the totality of his life, his friends, family, and enemies within a commemoratio of God’s eternity and love. That is the real commemoratio of the human race.  Years after writing the Confessions, Augustine’s City of God expands his commemoratio to include a transformation of how one should live in the totality of history as a dialectic between the city of man and the city of God.

In terms of intentionality analysis, a few notes are in order.

  1. Through the operators of the transcendental notions, intellectual operations (insight), rational operations (reflective insight and judgment), and moral operations (apprehension of value, judgments of value, and decisions) emerge within the subject.  Though these are intrinsically independent of the empirical residue, they are extrinsically dependent in and through motor-sensory conscious intentionality, which in turn operates within a neural matrix all the way down to quarks and primitive forms of energy.  Memory at these higher spiritual levels has a dependence upon these material levels, and so it can be disrupted by damages or disruptions of these lower levels. Destroy the neural matrices and the ability to re-enact intellectual, rational, and moral operations is lost.  In other words, these intellectual and moral habits are lost. To state this another way, images, phantasms, and certain types of symbols are necessary for the emergence in human subjects of insights, reflective  insight, and evaluative insights.  Memories always include this embodied element in the human subject. Once embodied, the transcendental notions are able to generate with greater ease those spiritual operations.
  2. In the human subject, there are not from what I can discern any memories that are purely spiritual and completely independent from the neural and motor-sensory levels.  This simply follows from Lonergan’s point about the relationship of spiritual operations upon the lower sensate operations in all human subjects.  Insight is always into image/phantasm. We need our bodies to have insights, to affirm judgments, and to make decisions.  Likewise, our memories require a re-enactment of our neural matrices involved in phantasms.
  3. Memory is not merely a material act however.  Once one has an insight, “recalling” that insight, and becoming intelligibly present to the object of the insight again is simply to have the same exact insight as the original.  There is no difference.  However, the recollected insight does emerge “easily” or habitually because a change has taken place in the neural matrix (though there is much work to be done, many studies of the biochemistry of memory have been conducted, and reveal some interesting and fascinating processes).
  4. Having the freedom to recall insights, judgments, and decisions, or in more comprehensive ways, systems of thought and scales of value, itself includes a neural matrix of embodied connections. From what I can tell from neurological studies, key parts of the forebrain (or what some call the executive brain) are involved in this liberty.
  5. True direct insights are isomorphorphic with the form that is known by these insights. This allows for an indwelling of the known in the knower, and the beloved in the love.  Thus when mutual intellectual subjects know and love each other, then there arises a mutual indwelling.  This provides the basis and possibility of commemoratio.  When that mutual indwelling is rooted upon the indwelling of the Holy Trinity, along with the entire City of God, then one begins to get a sense of the more comprehensive character of commemoratio.
  6. The transcendental notions are likewise a key in recalling memories as well.  A mere forebrain neural structure is not going to be able to pull forward the proper images needed for insight because it is not capable of seeking a spiritual operation, such as an insight.  The forebrain needs to be sublated within the spiritual operators that we call the transcendental notions (of intelligibility, of being, and of value) which form the comprehensive capacity for self-transcendence.
  7. One final note, from what I have seen in the biochemical studies on neurons, “memory” is not stored in one location while the image/phantasm is located in another. Rather, once one has an insight, the recollection of that insight is simply an enactment of the same neural streams that led to the original insight.  (the same is true when one remembers a sense operation — seeing is not one operation and the memory of seeing another, rather, remembering a seen object is simply activating the neural patterns involved in first seeing the object.


By David Fleischacker

I am aware of at least two theological teachings that make significant use of the notion of indwelling. The first deals with the indwelling of God in the soul, and most would think of the indwelling of the Holy Spirit.  The second deals with the mutual indwelling of the Father, Son, and Holy Spirit.  To indwell is a profound notion, and I think Lonergan can help us unpack it.

In volume 2 of the Triune God–the one on systematics–and in a number of other places, Lonergan writes about how the known is in the knower, and the beloved in the lover.  It is this type of presence and consciousness that articulates what happens to us when we know and love God, and each other.

To grasp the full scope of this, one must fully break with the extroverted notion of knowing. In the extroverted notion, the object remains “outside” of the knower, and hence love of the object also is perceived as a love of that which is outside of one.  But once one shifts to the interior nature of the act of understanding that has been affirmed true in judgment, then that which is understood indwells in the human subject.  This indwelling takes place because understanding and knowing (Judgment) is isomorphic with the form and act of the reality understood and known.  When the judgment is not merely a judgment on the correctness of understanding (eg. understanding the nature of democracy), but rather is a judgment of fact (eg. this is a democracy), then the reality thus known as fact indwells in the knowing of the knower. It is a presence of the reality that constitutes the realization of the subject.  The “other” really is in one, and even more precisely, constitutive of one.

Then, with this cognitive indwelling, there arises the possibility that the reality can dwell within the very orientation of one’s capacity for self-transcendence. This is what it means for something known to dwell in one’s heart. This is the more complete realization of indwelling.

Existentially we have all experienced this indwelling at some point in our lives.  When we have first fallen in love, witnessed the birth of one of our children, or said yes at one’s wedding, one has experienced an indwelling.  The same experience happens when a loved one dies.  We feel like we have died.  The basis of these experiences is the nature of how realities come to dwell in each of us.  This is a profound reality.

When we turn to faith, and to a Transcendent being, we then begin to realize the greatest meaning and character of indwelling. The mystics are some of the most articulate, but because few have glimpsed such a level of indwelling, few have any insight into what they mean.  Individuals like Saint Theresa of Avila, Saint John of the Cross, or more recently, Saint Theresa Benedicta (Edith Stein) give us glimpses into the way that God lives at the center of the human soul (this by the way is explained in understanding the transcendental notions and how these notions are created participations in unrestricted intelligibility and intelligence, being and rationality, goodness and responsibility), and that our journey to God is simultaneously a journey into the authentic self.  But to travel this route, much has to be purified and opened up, something which the mystics can teach us far beyond what one finds in Lonergan. But using Lonergan’s call for interiority analysis can help to further clarify this journey within an explanatory context.  One can link the Christian mystics to Lonergan’s way of self-appropriating our cognition, our volition, and most profoundly our capacity for self-transcendence as it culminates in a state of being in love with God. This would allow one to develop an explanatory account of indwelling.  Here, all that I have done is given a few clues.

Conscience, Saint Thomas More, and Dr. Peter Kreeft

Sorry this is late. I try to get these out as near to 3 pm on Fridays as possible, however yesterday, I was busy with a guest we had the last few days at the University of Mary — Dr. Peter Kreeft.  What a joy he was for all the students and faculty, and me.

On Thursday evening, Dr. Kreeft spoke about Conscience on the Feast of Saint Thomas More and Saint John Fischer.  It was a fantastic talk that linked together conscience, the heart of the human person, and then painted the landscape of the state of conscience today.  This talk pairs well with a book I have been re-reading lately, The Science of the Cross by Saint Theresa Benedicta (Edith Stein).  I am nearing the end of the book, and there are a series of sections that link well with Lonergan’s work on the human person, and also with conscience as Dr. Kreeft presented it the other night.

Saint Theresa Benedicta speaks about the inner self where God resides. When one reads through how she relates it to the various operations and powers of the human soul, one begins to see the mystics grasp of the capacity for self-transcendence as constituted by the union of the transcendental notions in their full potency.  That full potency is as a created participation in the divine light.  Saint Theresa identifies this as the real inner self of the human person that we do not “see” entirely. The more exteriorized we are from this center, the less we know of our selves.  The more we move toward it, the more we move toward authentic subjectivity, and the more we encounter God. This links to Lonergan and the explanatory manner that he articulates the capacity for self-transcendence and acts of self-transcendence (and Aquinas and Aristotle’s notion of Agent Intellect, and Plato’s and Saint Augustine’s notion of the Light of Being).  Saint Theresa will discuss as well how when we move more fully into the interior regions of the self, the more authentically we grasp others and the world around us.

The same was true with the notion of conscience as Dr. Kreeft discussed it. He linked it not only with Saint Thomas More, the man for all seasons (the title of his talk was A Conscience for All Seasons), but with others such as C.S. Lewis and his book on the Abolition of Man.  Conscience gets to the very heart and essence of the human person.  We can easily become lost into the exterior world, to the world of pleasure and pain, to a thousand things that take us away from an attunement to our conscience.  And our conscience is us as the mirror of God.  When you proclaim the death of God, especially in the violence of ideology and hatred, the reality in the mirror disappears – and that is the disappearance of the real self.  We were made in the image of God.  And the only way to lose the self then is to head into the life of a beast who has no such image.  We then become a civilization of beasts, or as Dr. Kreeft was saying trousered apes.

Conscience for Lonergan is similar.  Descriptively, it is the interior voice of God.  Explanatorily, it is the transcendental notion of the good as the measure and call to responsibility, a life that names sin as sin and the good as good.  It calls us to repent of our moral inauthenticity.  And it calls us to move horizontally and vertically into the farthest reaches of the horizon of the good (I am deliberately using good instead of value).

A Conscious for All Seasons was a beautiful and moving talk. Thank you Dr. Kreeft for visiting us. He is a man who really has moved into those regions of wisdom that spring from a life liberated into thanksgiving and joy, a joy that is the fruit of living in contrition, truth, and love.  To enter even in small ways into the Kingdom of Wisdom makes any man  or woman into a “man for all seasons.”

From Newton to Dalton: Physics to Chemistry

David Fleischacker, Ph.D.

[May 26, 2009]

If Newton’s physics and Dalton’s chemistry are related as a lower to a higher viewpoint, there must be some point of contact, just as numbers and operations were the points of contact between arithmetic and algebra. It seems that this point is mass. Newton and Dalton dealt with masses within the context of “relative weight.” Newton related objects in terms of masses, distances, accelerations, and forces, especially his well-known discovery of the law of gravitation. Dalton discovered patterns in the “relative weights” that lead him to some postulates about atoms and compounds. A significant difference arises though. Newton studied large objects, large meaning what can be seen such as marbles and planets. Dalton studied gases and mixtures of solids and liquids (especially gases), and then made postulates about objects that cannot be seen. The objects that they studied seem very different, so how can they be related as lower and higher viewpoints?

Before drawing some conclusions, a closer examination of Newton and Dalton is in order.


1. Isaac Newton: The Law of Gravitation

Newton studied the relation of objects in terms of mass, distances, accelerations, forces, and the gravitational constant. If we specifically examine his equation for universal gravitation, his focus will become clear. The equation requires little space to write,

F = (Gm1m2)/d2

Explanation of this formula requires far more than writing it out, and though a full explanation will not be given here (any physics text book will give an explanation and some examples, along with some problems to solve), some identification of each of the terms is in order.  In brief, “F” stands for force. “G” for a gravitational constant that is relevant for any mass. “m1” stands for a mass. “m2” stands for a second mass. “d2” is the square of the distance between the masses. The equation relates only two masses. Relating more would be far more complicated. It says nothing about what kind of masses are used, whether they are planets or marbles. Furthermore, it is supposed to be true of any masses whatsoever, hence it received the title of the universal law of gravitation. But, in the concrete, rarely, if ever, are only two masses involved. This law presupposed something similar to the “vacuum” that is presumed in Galileo’s law of falling bodies In that law, without friction a feather and a marble would fall to the earth in the same amount of time. In Newton’s law, without any other masses, presumably, the equation would hold true. However, just as with object falling on earth are effect by friction, so planets are affected by a number of other masses in addition to the earth or sun. So, this law really does not fully explain the motions of any particular planet (In fact, Newton realized it did not explain the data better than Ptolemy’s circular theories, though it was a simpler explanation). Yet, it is an important first step, just as distinguishing acceleration from velocity was an important step toward the law of inertia, the notion of mass, and the law of gravitation.

2. John Dalton: The Atomic Theory and Relative Weights

Dalton developed a new atomic theory of mass from their weight relationships. He writes “In all chemical investigations, it has justly been considered an important object to ascertain the relative weights of the “simples” which constitute a compound.”(1) He goes on “Now it is one great object of this work, to show the importance and advantage of ascertaining the relative weights of the ultimate particles, both of simple and compound bodies, the number of simple elementary particles which constitute one compound particle, and the number of less compound particles which enter into the formation of one or more compound particle. Dalton, like Newton, speaks of “two bodies,” but unlike Newton, Dalton adds the concern with their combination, not their gravitational relation.

“If there are two bodies, A and B, which are disposed to combine, the following is the order in which the combinations may take place, beginning with the most simple:

1 atom of A + 1 atom of B = 1 atom of C, binary.

1 atom of A + 2 atoms of B = 1 atom of D, ternary.

2 atoms of A + 1 atom of B = 1 atom of E, ternary.

1 atom of A + 3 atoms of B = 1 atom of F, quaternary.

3 atoms of A + 1 atom of B = 1 atom of G, quaternary.” (Page 112)

Then he adds, “etc., etc.”

This is rather similar to what happens when one is discovering algebraic patterns within arithmetic.

Dalton then proceeds to discuss the actual relative weights of different substances that were known. Hydrogen was given a base weight of 1, and to this all the other “simples” or “ultimate particles” can be determined. Carbon is five times the weight of hydrogen, hence it has a relative mass weight of 5. Oxygen is seven times hydrogen, so it has a relative weight of 7. Water is a binary combination of hydrogen and oxygen, so it has a relative mass weight of 8. From this, he then unites the rules for combining bodies with their discovered relative weights to formulate another law which presupposes the law of the conservation of mass. The weights of binary, ternary, and quaternary compounds should be equal to the combined weights of the “simples” that constitute the compounds. Still, analyzing and synthesizing these “simples” and compounds is not an easy matter, and Dalton develops some rules of thumb.(2)

After developing these rules of thumb, Dalton then proceeds to explain which actual weights are combinations of simples, binaries, ternary, etc., and what those simples, binaries, ternaries, etc., might be. For example, he then discussed how one might reason that water is a binary of hydrogen and oxygen.


3. The Higher Viewpoint

So, what is the link between Dalton and Newton? The link can be grasped by paying closer attention to the experiments and theories each relied upon and developed. Newton’s law of gravitation applied not only to planets but to any mass object. The gases, solids, and liquids of the chemist are some of those objects. Gases, liquids, and solids have weight, and weight is a combination of a mass and gravitation. Newton was concerned with relationships between any masses, relationships which were defined in terms of their respective distances, and the changes in their velocities (or lack of such changes). So, he described force as a product of mass times acceleration, or force as a product of a gravitational constant multiplied by the two masses, then divided by the distance between them. Dalton does not use Newton’s law of universal gravitation as the lower viewpoint in which he discovers patterns and laws of a higher viewpoint.  He only uses the notion of weight, but because he refines it in terms of relative weights, the real difference is due to a difference of mass.  When developing “relative weights” what really distinguishes the objects is the mass, because the “gravitational component” is equal.(3) So, what distinguishes Newton’s concern from Dalton’s is that Dalton wanted to discover patterns of different mass relations, Newton wanted an explanation of weight itself.  It would be many centuries before the actual formulas of physics could be utilized in the lower viewpoint as a phantasm or image for the higher viewpoint of chemistry.(4) At this point, problems in the combining of weight was the starting point for chemistry just as negative numbers, fractions, and other arithmetic problems were the starting points for algebraic rules.

Dalton’s concerns or horizon form a higher viewpoint because he is developing new principles and laws regarding weights and the combining of weights into compounds.(5) He is not developing a fully elaborate higher viewpoint of all aspects of Newton’s theories and formula’s, but it is a higher viewpoint with regard to one dimension, and that is weight, and implicit in weight, mass. (I will continue to articulate this point in further revisions of these notes because the point of “physics” at which Dalton’s viewpoint arises is much like the initial development of the higher viewpoint of algebra from the problems of negative numbers or of calculus from the power rule, and ignoring all the other areas of arithmetic from which algebra can formulate its new rules, or the other areas of algebra, from which calculus can build its rules).

A further inquiry would bring us to grasp the relationship of Dalton and Mendeleev. Is Mendeleev’s periodic table a higher viewpoint to Dalton’s atomic theory, or is it a homogeneous expansion? That is a further question, which would be worthwhile to investigate.

  1. John Dalton, “A New System of Chemical Philosophy,” in Breakthroughs in Chemistry, ed. Peter Wolff (New York: A Signet Science Library Book, 1967), 111.
  2. Dalton lists seven rules. “1st. When only one combination of two bodies can be obtained, it must be presumed to be a binary one, unless some cause appears to the contrary. 2nd. When two combinations are observed, they must be presumed to be a binary and a ternary. 3rd. When three combinations are obtained, we should expect one binary and the other two ternary. 4th. When four combinations are observed, we should expect one binary, two ternary, and one quaternary, etc. 5th. A binary compound should always be specifically heavier than the mere mixture of its two ingredients. 6th. A ternary compound should be specifically heavier than the mixture of a binary and a simple, which would, if combined, constitute it; etc. 7th. The above rules and observations equally apply, when two bodies, such as C and D, D and E, etc. are combined” (115).    As a note, Dalton was also one of the first to develop symbols of these “simples” and compounds (recall the need for phantasm to obtain insight).
  3. If the masses of the objects were greater, then they would affect the overall gravitational force, but like most of the objects that Galileo studied, there mass is insignificant (which is why “light” and “heavy” object fall to the earth with the same acceleration, baring any significant friction). These relative masses would hold even if the gases, liquids, and solids were on a different planet, or on the moon, hence the real term that distinguishes is the difference of the masses between the gases, liquids, and solids.
  4. Gases became important because they, as a matter of fact, were able to be produced from mixing substances, and these gases tended to be divided into what we now call elements. Dalton was one of the first to postulate that these were elements, or as he named them, “simples.”
  5. Also, notice the similarities to arithmetic and algebra. Arithmetic wanted to get numbers through the operations of addition, subtraction, multiplication, division, powers, and roots. Algebra discovered patterns in adding, subtracting, multiplying, dividing, powering, rooting. Similarly, Newton wanted to related masses through distances, accelerations, gravitational constants, and forces. Dalton discovered some patterns in a particular range of these related weights (that range being limited to the weights of gases, solids, and liquids on earth that can “combine”).