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Indwelling

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.

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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.”

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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”).
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When Does the Human Being Begin to Exist? Special Question 1: Is There a Valid Argument to Say that Human Life Begins at Implantation?

By Dr. David Fleischacker

[This springs from a series of blogs titled “When does the human being begin to exist?” which I had written starting in December, 2007. I had drafted this piece in 2008, but just now finished it.]

Some will argue that an embryo becomes a human being at implantation in the uterine wall. In the business world, this became one of the arguments for those selling the contraceptive pill as well as the morning after pill. These companies could argue that their pill was not an abortifacient, because though it might prevent implantation (as one of the ways for preventing a pregnancy), this did not kill a human being because that “this” was not yet human.

To a philosopher who reads through a biology text on implantation, the argument may sound a bit arbitrary at first glance. Why is something different after implantation? However, there are some biological reasons for saying this. This becomes apparent if one examines the various developmental stages of the embryo.

Early Stages of Development

In any mammal, the first stage of development begins at the moment of fertilization. Sperm entered into an oocyte through a protective layer originally created by the mother called the zona pelucida (or the ZP as it is usually labeled). For many types of animals, the entry location of the sperm then determines a polarity to the cell. Polarity refers to different layouts of the biochemical schemes and constituents of the cell, such that as it begins to divide, these materials begin to cause differences in the way subsequent daughter cells function. Such differences in subsequent daughter cells that are created through mitosis are called cell differentiation. As the zygote begins to divide, the daughter cells form a mass of cells scattered within the housing of the ZP. This is called the morula stage. As cell division continues, some of the cells begin to form a ring called the trophoblast just on the inside of the ZP. Other cells come to fill the inner ring and a blastocoel forms pushing these inner cells to one half of the ring, leaving the fluid called the blastocoel on the other half. This is the beginning of the “blastocyst” stage.

Many texts will identify the “inner cell mass” as that which becomes the adult organism, because it is from this that the matured cell systems of the organism develop. The cells that form the trophoblast are not the source of cells that continue into adulthood. However, not all of this inner cell mass will become the adult either. Once the blastcyst bursts the ZP, it is now possible for the blastocyst to unite with the wall of the mother, which usually occurs in the uterus (though if it bursts from the ZP in the fallopian tube, it could bond at that location causing an ectopic pregnancy). Some of these cells will form part of the placenta with some of the cell schemes attaching to the uterine wall, others to form the amniotic cavity. In other words, only some of these cells of the inner cell mass will become the matured adult systems.

When implantation occurs, there is a further determination or differentiation of these cells such that one can then identify specific cells that will become the adult. This process leads to the gastrula stage where some of the cells then form into a primitive streak and into a node of cells that become important for the induction of further differentiation of cells. Because of this differentiation that determines cell fates, twinning is no longer possible, and hence, this is the reason that some will argue that life begins at this point of differentiation.

The basis for saying human life begins at implantation

The notion implicit in this search for the beginning of life is the search for the determined originating cells that will lead to the matured systems of the adult, such as the circulatory and immune systems. In the zygote, the cell is not yet determined, it could be split multiple times and thus form twins or triplets. Likewise for the morula and blastocyst stages. So in many standard textbooks, a particular life or thing does not yet exists at these earlier stages.

Hence in the language of many textbooks, the “real embryo” is that which arises from those cells which have reached a stage of determined fate.

Shifting the Basis to the beginning of the Unity-Identity-Whole (see Chapter 8 of INSIGHT for more on Unity-Idenity-Whole)

The argument needs to shift seeking the origin of human life from that of the “fate determined cells directly leading to the adult organism” to the origin of the “unity-identity-whole.” One way to think through this is in the following way: At different stages of existence, one and the same being has different relationships to its environment. This is rooted in Lonergan’s point that the unity is a unity in changes (INSIGHT, chapter 8). One sees this after birth. In early stages, young infants nurse from the mother’s milk which has nutrients suited to these first post-natal stages. As the infant grows into a child, a young calf, a kit, or some other pre-adult creature, its abilities to relate and interact with the environment expand in such activities as the food it eats and its mobility. This ongoing horizontal and vertical differentiation and expansion of the creature to the environment is no less true in human beings who have the lengthiest sequence of stages of growth from infancy through childhood, adolescence, and into various phases of adulthood. It is the same unity-identity-whole through all these developmental changes.

This is true as well for the unborn. A zygote is largely related to the zona pleucida, that protective coat of cells formed by the mother when the oocyte was first formed. As the zygote divides within the context of the ZP, it grows until the ZP bursts, at which stage (during the blastocyst stage) it has interiorly differentiated sufficiently to become related to the uterine lining and the environment of the uterus. Hence, differentiations of cells and cells systems at each stage are really part of one and the same being, but having different purposes. The embryonic stage, for example, includes the cell systems that form the trophoblasts, which will then form the amniotic cell system as well as the placenta cell system. These are not distinct from the being of the embryo, but rather “parts” of that whole, in the same way that the immune system and the circulatory system are “parts” of the whole adult organism. The functional meaning of these cell systems at this early stage are grounded upon unity with the entire growing embryo and fetus. Separate these from the whole, and these will loose their wholistic properties. The plancenta for example is not merely an aggregate of cells, but rather it is like the digestive and respiratory systems tied together. The cells of the digestive system and the cells of the respiratory system collaborate in a functional whole which is quite different from each of the properties of the individual cells composing these systems (no one cell digests and no one cell respires). Likewise for the placenta and its role in exchanging nutrients and respiration. Each cell has a function that is part of a whole order of cells. Disconnect the placenta from its relationships both to the mother and to the other cells in the embryo, and it looses this higher intelligible meaning. The cells may still survive for a time, but not in a united way that makes them part of a nutritive scheme. And this nutritive scheme is one that belongs to the unity called the embryo.  It is not a scheme of the mother even though it is related to the mother.  Again, this is much like the lungs which have a relationship to the atmosphere that is breathed. The lungs are schemes not of the atmosphere, but of the creature that breaths.

In contrast

Thus, though implantation does bring about some differentiating cell schemes, it is not the beginning of a new unity-identity-whole, but rather the continued differentiation of an already existing unity-identity-whole. The somewhat confusing language in the world of developmental biology and thus in many text books has led to these ideas that the embryo was distinct from some of these temporary “parts” of the embryo.  However upon closer examination, the “embryo” as a unity is not one distinct thing and the  trophoblastic set of cells another. Furthermore, though this confusion suggests that implantation might be a valid starting point for the organism, the argument here is to eliminate that confusion and shift to the origin of the unity-identity-whole that develops. [Note: Though this point is more or less correct, to be more precise, it is a shift that looks not merely at fated originating cells that will develop into adult schemes, but to a unity-identity-whole that is differentiated both by its current integration and unfolding through its operators into its next stages, and then asks, what is the first stage of “this thing”].  Hence one is moving away from defining this thing and its starting point in terms of a developmental stage, and shifting really to a search for the initial stage with its finality for all the subsequent stages. It does not mean that cell fate is not relevant, but it puts it within the different functions of the cells and cell systems that relate the intrinsic cell schemes to the chemical and cellular world of the creature. Hence, in this larger functional set of relationships in which the unity-identity-whole thrives, the cells that form the placenta and other support functions are just as much a part of the unity as are the cells that form the primitive ectoderm that come to constitute the systems of the adult creature. The fact that they “disappear” at latter stages does not change the central form to which they belong at these earlier stages.

This shift results in turning not to implantation as the starting point of a living thing, but the zygote, since the zygote has the real finality to develop into a mature adult organism (even if twinning occurs). This argument was made in an earlier blog with greater precision however and does not need to be made here.

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Lonergan and the Shift to Method

by David Fleischacker

 

Method can be looked at as technique. This of course entirely misses the meaning of method as Lonergan conceived of it. For Lonergan, method is a set of heuristic conceptions that morally guide human self-transcendence, and hence are based on the structure of self-transcendence.

Historically, the cultural need to articulate method arises from the breakthroughs of modern science. It is a great wonder how such a stream of breakthroughs was possible. The answer was the discovery of a fruitful method. To articulate this, even imperfectly as an inductive method (see Bacon for instance), has its fruits.

It is imperfect because it tends to attend only to a few elements of the human subject, most of which are organs that look out onto the world for sensory experiences.  A more comprehensive understanding of the human person will lead to a more profound method. Lonergan makes this shift from an account of the human subject as one of self-transcendence to a resulting transcendental method.  His comprehensive understanding of the human subject is the source of this shift.

Key in his understanding of the human subject are the transcendental notions and their unity. These notions articulate the heart and soul of human presence but we only begin to glimpse the scope of these through a long sequence of steps that Lonergan calls self-appropriation. It requires a heightening of attention to one’s own conscious operations, and when we begin to attend these operations, we begin to discover patterns and overarching structures that ultimately  1) spring from the transcendental notions, and 2)  unite to form a capacity for self-transcendence.  And unless you are going to live for 3000 years, I would suggest you need a guide, and INSIGHT is a good place to start.

If you start with INSIGHT, you should either have already been actively doing math and science, or you will need to do so. Also, you will need to exercise a great deal of common sense and if you have not really done so in life by building and using technologies, building and participating in family, civic, or ecclesiastical economies, or participating in civic or ecclesiastical polity, you should be prepared to do so or at least watch and explore others who do.  Likewise, you will need to study history, and even master one or two of its major trends.  The history of philosophy is a good one. In other words, you need to become more in order for the kind of self-appropriation to take place which is necessary to become an authentic philosopher in the vein called for by Lonergan.

If you do, then such things as a heuristic notion, implicit definition, inverse insight, the empirical residue, higher and lower genera of things, emergent probability, the integral heuristic structure of proportionate being, functional specialization, transcendental method, and dialectic will all come to make perfect sense.  So will notions like isomorphism.   These are explanatory articulations that arise through the kind of self-transcendence that happens when you do math, science, and common sense, then you attend to the interiority of these doings, discover that interiority, and formulate it, and affirm it.  Then, with this self-discovery in mind, you can develop precepts that guide you and others in your existential unfolding.

As you explore the interiority of a scientist, a philosopher, a theologian, an artist, a man or woman of common sense, and you discover how these are united, you will discover more and more the profundity of the transcendental notions and the capacity for self-transcendence.   As you discover the unity of correlations and probabilities into schemes of recurrence and schemes of development, you will discover more and more the profundity of the meaning of central and conjugate potency, form, and act, and the entire nature and character of metaphysics.  Furthermore, you will grasp with greater significance the relationship of interiority and the universe of being.  And as this opens up into human freedom and the free participation of the unfolding of this universe of being and of the unfolding of the human subject in that being, you will discover the existential isomorphism that exists between a self-transcending subject and the entire order of the universe.

Link this existential isomorphism to a divine entrance into the world mediated by meaning and regulated by value, by both unpacking the interiority of this entrance (sanctifying grace, the theological virtues) and the sublation of the world of proportionate being into a transcendent order, then one moves into a supernatural existential isomorphism.  Such individuals provide us with precepts for eternity.

Now that is the kind of method for which Lonergan would call. And it is not a technique, but really an attunement to mystery.

 

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Almost 50 Years Since Humanae Vitae: Statistics and Finality in Conception

[this was a piece drafted in 2008 when I had been publishing a series on Humanae Vitae.  I had not published this one yet–and now that we are heading toward 50 years since Humanae Vitae, I thought it might be good to get these going again.]

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There are a number of factors that effect the statistical probabilities for conception. Sometimes individuals have used statistics to undermine the Catholic teaching against contraception.  Usually the arguments claim that since there is not a direct causal relationship between the conjugal act and conception but rather only a “statistical” one, and contraception simply changes the statistical relationship, then in some circumstances contraception would be ok.  However, this is to fail to understand the nature of the statistical relationship of the conjugal act to conception along with the nature of the moral act involved in this relationship.  In this blog, I intend on developing the nature of statistics and its impact on understanding conception.

The Nature of Statistics

In general, the enriching intelligibility of statistics is centered upon ideal frequencies and rates. These ideal frequencies in turn are based upon the actualization of conjugate forms (events). In any given situation, events that take place do so with certain frequencies. One might say that every type of event has its ideal frequencies, and sometimes that ideal might be all but negligible, and other times it might be quite high. Part of what influences the particular ideal frequency depends upon the spatial and temporal framework, along with the particular ranges of events and their ideal frequencies that currently constitute that situation with its spatial-temporal boundaries. So, for example, one could ask what is the frequency of births. Now, that is meaningless until one starts to set spatial-temporal boundaries. For example, one could say births in a year, within the United States. In addition to the spatial-temporal boundaries, one should know something about the events within that spatial temporal boundary as well. If all that one wants is an actual frequency, then one would just need to count the actual births in a particular spatial-temporal set of boundaries, however, in order to get to ideal frequencies, more needs to be known.  There needs to be a move that grasps an intelligible rate that even abstracts from concrete space and time.

Lonergan notes that there are two ways to get to this ideal frequency (Chapter 2, INSIGHT);

  1. empirically from measure frequencies of events of certain types
  2. or from a knowledge of the given conjugate forms and their realization in events.

The first can be illustrated by the monk, Gregor Mendel, when he counted actual manifestations of traits in pea plants and their progeny. Notice that his starting point already set him in a direction that would allow him to abstract an ideal rate from mating events within concrete space and time (as a note, sometimes one does want to start with concrete space and time as part of the measure, but to reach full ideal frequencies, one needs to break from this so as to return to it with a concrete inference of statistical laws).  For example, he does not in the end ask “how often does one find rough or smooth seeds within a year in such and such a territory.”  Rather, he sets the boundary as another type of event rather than space and time, namely that boundary being the mating of pea plants.  The concrete location, such as Austria or Hungary, and the duration in the region is no longer of interest.  The parents of the seeds are the interest. And in the end, this leads him to some interesting correlations (namely genotype to phenotype–which is an explanatory definition–see ch. 1 of INSIGHT) The more actual frequencies he gathered, the more numbers began to converge on ideals (3:1, etc.).

The second is illustrated by flipping a coin. One knows ahead of time that in flipping a coin there are two outcomes, and unless one side is weighted more than the other, all things equal, the coin has a 50:50 chance of being heads or tails (notice that the concrete space and concrete time is present, but not part of the focus in this either).

One can make a similar move in genetics once the theory of dominant and recessive alleles developed. One can calculate the reason why their is a 3:1 ratio for certain traits when mating two heterozygote pea plants. Thus, if one knew the theory first, one could predict the ideal frequency prior to even counting frequencies. In the case of Mendel, it was the ideal frequencies which led to the theory, but the reverse can happen in science as well. One might just know that there are two possibilities when “something happens”, and thus be able to predict the statistical outcome.

However, our concern with statistics is not so much prediction, but its occurrence within concrete situations. When we ask, for example, what is the statistical probability for conception, one can specify any number of situations. In each case, knowing the statistics tells us something about the situation that we otherwise would not know. And the ideal frequency of various events within a situation is something objective about the situation (if a concrete inference of statistical laws is made, which is similar to a concrete inference of classical laws–see ch. 2 of INSIGHT for more). The situation, with all of its species of events, and with its non-systematically related sets of events, creates a situation in which coincidentality is part of the situation. Now, this is not the place to repeat all of Lonergan’s arguments on this, but his sections in chapters 2, 3, and 4 of Insight provide rather convincing pointers to the coincidental aggregation of events within a spatial-temporal manifold. This coincidentality has its roots in what Lonergan calls the empirical residue (Lonergan’s transposition of the traditional meaning of prime matter).

Statistics and Conception

Thus, the statistical probability of conception informs us of something objective about one facet of world process. Conception is the union of the oocyte and the spermatozoa. The formation of the zygote is the particular actualization of concern. The probability of its occurrence is the ideal frequency of its occurrence. Of course, to understand this probability, one needs to specify further factors. For example, one could be just asking this frequency in a given population in a particular region, during a particular time frame, say San Francisco over the course of a year. At the same time, one might be narrowing this a bit, let us say to individuals in the world who are married, or individuals who are not married. Or one might compare various religious groups in the world, and their conception rates. One might have political agenda, or perhaps they might be interested in sorting out various biological difference between ethnic groups (always a dangerous subject!), for good or bad purposes. Notice as well that as one learns more and more factors that might shift the rates, one can further specify these factors, and study sub-groups. So, let us say, that one wants to study the rates of conception for males who have had measles during their life, or perhaps who have been promiscuous during their teenage years. Likewise, one could examine women, and sort them out according to smoking or dietary habits, or perhaps look at certain psychological dispositions. Notice, that the list of sub-factors seems limitless, and this is because there are so many factors that condition conception.

To give a sense of this, let’s name a few more factors:: the rates of production of spermatozoa, the days on which an oocyte is released into the fallopian tubes, the general state and health of the woman’s and man’s bodies, the character of the relationship between the man and the woman (and various psychological states as well), the work habits and home life of the man and woman which influence their marital activities. Many of us recognize for example, that a couple who hate each other and never stay together in the same home will find themselves living in a situation with virtually no possiblity of conception. On the other hand, a young couple, celebrating the honeymoon of their marriage, and seriously desiring to be part of the creation of new life together, and who possess healthy bodies, have a significantly better probability of conceiving.

[I do want to note that many of the factors effecting the probability for conception are identified in a descriptive manner, and thus to become more precise, a shift to theoretically differentiation is needed (which would also significantly multiply the number of factors actually involved). This theoretical differentiation using explanatory conjugates is the level  of probability of which I am concerned in the end.]

Now, one of the points that I would like to highlight is that at any given context of conditions, a couple has a particular statistical probability for conception. This probability however does shift because of numerous factors each day, some of which might be based on regular schemes of recurrence (such as the woman’s fertility cycle), and other on non-systematic components relative to their own organic schemes of recurrence, say certain bacteria or viruses that the man or woman might have contracted that might reduce the production of spermatozoa or perhaps harm the ability to complete the maturation of the oocyte before it is released into the fallopian tube. Regarding the regular cycles in the life of the man and the woman, the statistical probabilities for conception probably hover around certain sets of ideal frequencies during the fertile stages of their adult lives. When the occyte has been released, and the woman’s body prepares itself for the possibility of conception and implantation, which then changes her psyche in relation to the man (yes, this really does happen), and in turn, changes the man’s psyche in relation to her, along with the moral and religious contexts that impact the relationship on a regular basis as well, then one could probably formulate the ideal frequencies of conception. Changes in the lifestyle, in the physical well-being, also change this, as does age, but in the end, there are given objective probabilities for conception between the couple during the course of their lives together and at each stage of their lives together.

Finality and Statistics: The real heart of the matter in conception

If statistics deals with ideal frequencies of the actuation of conjugate forms and of the emergence and existence of things, finality introduces development of those conjugate forms, their ideal frequencies, and of things. Now, let us begin to examine some of the different ways that statistics impacts and relates to finality. Finality deals with a direction of development. Earlier stages possess a set of conjugate forms and their distribution and integration that results in an unfolding sequence of stages of development. The zygote possesses within it a variety of elements that, given the right environment, will unfold into a multi-cellular being, with a variety of higher or vertical intelligible orders of being. So, what starts as a zygote with largely undifferentiated organic schemes that operate within a narrow range of conditions unfolds first in a series of horizontal developments of differentiated organic schemes (eg. new functioning systems such as circulation, digestion, endocrine, exocrine, immunological, etc, systems). Then as the neural system advances, it makes a first vertical leap into motor-sensory operations, with affective re-sponses and pro-sponses through a growing sensory apprehension while in the womb.  As imagination and memory grow and develop, this then prepares the stage for another vertical leap, one into the world of understanding, judgment, and decision (see the blog on the “beginning of the human person” for more precise treatments of this leap as well as challenges to it, since it involves the capacity to transcend the empirical residue).

In each of the horizontal and vertical developments, each stage has a statistical probability for emergence and survival. Earlier stages had made the probability of the current stage likely, but not absolute. The operators (for more on operators, see chapter 15 in INSIGHT) in the earlier stages for these later stages are what shift the entire likelihood of emergence. So, though the emergence of something with a neural structure is very unlikely in this universe, in the zygote of a frog or a cat or a human being, this likelihood is significantly increased, almost systematically. Now, this is not technically a system, because it really is a set of developmental operators. Hence, it is not a scheme of recurrence that brings about these developments. Operators are different than schemes. But they are similar in that these bring about the same kind of development if other events are equal, just as the scheme brings about the same sets of events if other events are equal. Hence, in a development, just as with a scheme, the regular frequencies of various types of events are needed. For example, in order for Kreb’s cycle (a scheme of recurrence) to operate, various proteins, glucose, and other molecules need to be supplied in a statistically regular manner. If the rate of glucose declines, then the rate of kreb’s cycle will decline. If certain proteins are not made regularly, likewise, the cycle will not work regularly. Likewise for development. If the probabilities of events in certain schemes are not maintained, development will cease. If certain proteins are missing, adolescent changes will not take place.

One thing to note however, is that even if later stages do not in fact emerge, the finality of the earlier is not changed. Proper development requires “other events being equal” and just because development fails because other events are not equal does not change the finality. A zygote for example, may fail to continue its development because it fails to implant in the wall of the womb, a failure which may have been made likely because of some chemical deformation of the wall of the womb. This does not change the finality of the zygote however. Or to take another example, human intelligence has a finality for understanding and truth. That finality is manifested in the question for understanding (at the level of understanding) and the question for reflection (at the level of judgment), and just because a person fails to ask these questions, or perhaps undergoes a severe debilitation later in life (perhaps brain damage) that makes it impossible to ask the questions, does not change the finality. Hence, though finality unfolds in and through statistical probabilities of events, schemes, and things, it does not necessarily change in and through those things. Really, in the end, it only changes when the base conditions that essentially constituted the finality in the first place change. Hence the zygote has that finality, unless one removes the genes, destroys the cellular plasma, or some other detrimental effects that essentially kill the zygote. Then this little being has been destroyed, and his or her finality is gone as well. Likewise, one could substantially change the biochemistry, and thus destroy the direction of development (the finality). To take one last example, one could destroy the finality by replacing the genetics in a substantial manner, so that instead of a cow, one gets a cat (though one would have to change other components of the cell along with the genetics). Then the finality has changed.

How to change the finality of procreative fecundity….

Procreative (or sexual) fecundity also has a finality.  And to destroy this finality would require the destruction of the embodied human person. Descriptively, the sexual makeup of the human person permeates his or her whole being. Explanatorily, nearly every system of the body is impacted by it, especially the neural patterns that are formed. Sterilization, contraception, and other non-substantial changes to the human body simply do not change the sexual finality. Earlier in development, arguably, it is easier to make changes in the finality of sexual fecundity, and thus to change a boy into a girl or vice versa (though having the power to do so would not be right because there is a finality within each person linked to the finality of the entire species and to the generalized emergence of the universe). I suppose, if we were creative enough, and had the right technologies, we would be able to even create an androgenous creature, though I am not sure what that would mean because it would require a much different body and brain than men and women currently possess because of how much each of these are tied into the sexual elements of our beings (and I mean all the way down to the cellular and biochemical layouts). As a note, there are no large, multi-cellular organism that possess such androgeny because it would have detrimental effects on the species as whole.  Pick up a textbook on the importance of bi-sexual procreativity in organisms if you want to read about the “advantages” of this kind of setup. We need the pluralism of the genetics and the diversity of roles in order to flourish.

So what does this mean for conception?

Statistics in short is integral to finality.  One stage of development is constituted by various ideal probabilities of events that in various ways condition each other, sometimes in schemes of recurrence, sometimes in a manner that brings about shifts of schemes, and when these shifts involve changes in the kinds of operations possible, a development has occurred.

When understanding the body of a man and the body of a woman, specifically the procreative schemes that are operative after procreative activation has taken place in adolescence, one discovers a finality that is built upon the ideal frequencies of a variety of events leading up to and including the procreative conjugal act.  Finality is not built upon a mechanistic view of the human body, but upon the potentialities that constitute probabilities of emergence.  Human freedom is involved in shifting these probabilities of emergence.  It is from this point, that one can begin to examine the moral relevance of shifting these probabilities with human decisions.

For those who say that “nature” shifts the probabilities for conception–and therefore it is not wrong for human beings to do the same–have failed to investigate the situation thoroughly and make distinctions.  If one wants to appeal to nature, nature as Lonergan argues is for increasing not decreasing intelligibility.  In other words, the concrete intelligibility of this universe is generalize emergent probability, and once one gets that argument, then one begins to see how central the creation of more human beings is to this universe and this unfolding emergent probability. Then one sees that even nature is striving for more beings that can help increase the generic and specific intelligibilities of the universe.  Conception is key in this.  And thus, “nature” is not disconnected statistically from conception, but rather uses statistical probabilities for emergence to increase conception and the fruits of conception (namely matured adult men and women to use a phrase from Lonergan’s essay on Love and Finality–though Lonergan had not integrated statistics into this piece yet).    Thus, human freedom is a freedom to enhance this probability for emergence and its fruits (unfolding horizontal and vertical developments that arise from this emergence of a human being).   One can continue to examine all of the horizontal and vertical developments that spring from conception, and this will differentiate all of the ways that human understanding, judgment, and decision cooperate with this in the right acts that lead to conception.

As a note, what I have put forth, is not an argument that results in complete support for all the Catholic teachings on marriage and family in relation to the conjugal act, but it does I think eliminate a particular challenge to those teachings, especially as one looks at the challenge of contraception.  One of the arguments in favor of contraception (a deliberate intention to attempt to eliminate the probability of conception through deliberate acts to eliminate one or more of the conditions required for conception while taking place after a decision has been made to engage in the sexual act between a man and a woman) was based upon the statistical elements of conception, but the argument that nature already builds in contraception into the system is not adequate to say therefore human beings can use the same no matter what or how.  Even the unconscious elements of the organism discriminate because of “nature” on what or how the body is prevented from conceiving, simply because emergent probability is part of the intelligibility of this order.  Understanding, judgment, and decision likewise discriminate, not because they have to, but because they should.  The transcendental notions that are intrinsic operators of each of these levels of consciousness constitute exigences of this discrimination.  And when these transcendental operators are operative within the lower manifolds which are intrinsically conditioned by the empirical residue, they do so with a statistical reality that is intrinsic to the finality of this universe, or at least they should do so to be authentic.

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Gender Ideology, Evolution, and Finality

I just returned from a fantastic conference on gender ideology in Denver. I use ideology in the Voegelinian sense, as a deformation of the metaxy or the in-between. Eric Voegelin formulated the in-between as an account of the human subject and community. Our conscious existence is a tension between the beginning and the beyond, the immanent and the transcendent. For those familiar with Lonergan, it has a kind of symbolic appeal to the nature of the human subject, though it lacks the precision found in Lonergan, namely that of formulating the human subject as one who is a capacity for self-transcendence and the different levels of this capacity. Yet, it captures a basic truth, a truth which helps to articulate the character of the modern ideology surrounding gender identity and freedom.

I recall reading somewhere in Voegelin that modern ideology tends toward the transcendent or the beyond, and then naively thinks itself to be beyond the beginning or the immanent. What this means is that in modern ideologies, the beginning and the immanent are evils. In gender ideology, the limits of the body are an evil to be transcended. Evil of course is not a word that most gender ideologists would accept as a description of what they are doing to the body. But in my claiming this of the ideology, I would appeal to the ideology’s mode of operation. To start, something that causes unhappiness or a kind of privation in one’s soul is an evil. And according to gender ideology, being born with the “wrong body” is seen as privating one of happiness. Thus, it is an evil.

Now let’s translate this into Voegelin. The body is part of what Voegelin would call the beginning or the immanent. It has its roots back into the foundations of the world and it ties us to that foundation. It also is that reality in and through which we transcend and have our conscious existence, and so when it limits the kind of conscious existence that we want, gender ideology would proclaim that the  immanent reality of the body must be sublated in the Hegelian sense and discarded as the rubbish of an enslaved past. That would be the mode of operation in someone fully habituated to the life lived in the atmosphere of gender ideology.

The ideology also suffers what Voegelin calls the immanentization of the Transcendent. The Transcendent is the source of true and authentic happiness. Only in the Transcendent exists beatitude. To attempt to establish ultimate and everlasting beatitude in the immanent is the kind of deformation that takes what belongs to the Transcendent by storm. This violence is the only mode of operation available to the modern ideologues. Natural emergence would never be allowed because what is natural would be seen as hindering our freedom and hence our happiness. This violence has been the tactic of all modern ideologies such as the French and Communist Revolutionaries, the Nazi fascist movement, and the assortment of totalitarian uprisings whether in Asia, Africa, Europe, or the Americas. Gender ideology really is no different. It cannot use the art of authentic persuasion to reach its ends. It has to mutilate the body and use the power of civil law to totalize it goals.

Though I do enjoy Voegelin, I think one can arrive at a deeper explanatory account of the modern ideologies, including that of gender ideology, using Lonergan. His discovery of the levels of conscious intentionality, the nature of the capacity for self-transcendence and its actuation, and how this participates in the finality of the unfolding universe of being as one of generalized emergent probability provides a heuristic, and hence a horizon, that opens the doors and windows for a comprehensive account of ideology and its modern sexual manifestation.

What I am saying here is really more of a project to be completed. Some years ago, I had worked through the coming-to-be of the human person (see blogs back in 2008). One of the things that I began to think through was a transposition of evolutionary biology’s account of sexual differentiation into Lonergan’s notion of finality. The modern evolutionary theorist has noticed for example the emergence of bi-sexual differentiation within higher level species of plants and animals. This differentiation provides selective advantages (to use evolutionary terms) – advantages which include more adequate diversity in genetic alleles that allow for greater adaptabilities of the species to environmental needs and changes. More precisely, I think the right range of probabilities in the mixing and remixing of alleles that takes place through sexual reproduction provides for the right kind of plasticity needed for higher orders of intelligibility to have adequate probabilities for emergence and fitting probabilities of survival (much like carbon and some other atoms have the right statistical distributions of electrons to allow for the adequate emergence and survival of molecules that can interact to form organic systems–where as atoms such as the inert gases do not). Using Lonergan, one can dramatically expand the meaning of species and of the nature of evolutionary causality. The conjugate forms for example that constitute the things as a species within an explanatory genera (see chapter 8 of INSIGHT) are necessary to account for the developmental sequences one finds within evolutionary trees. One can also turn to the reality of finality within potencies to help further expand the developmental operators and trends that arise within evolution. And these are just a couple of the examples of how one can expand the heuristics found in most evolutionary theories using Lonergan’s account of both proportionate being (being that can be known by the human mind) and the nature of the human subject within that world of being.

With regard to gender ideology, an explanatory account of sexual differentiation and its sublation (Lonergan’s notion not Hegel’s) into higher levels of conscious intentionality would provide a first set of clarifications of the relationship of organic sexual schemes of development with motor-sensory, intellectual, rational, and volitional operators and operations.

The finality that leads to and springs from sexual differentiation would provide a further set of clarifications, and I think it would also be the key to revealing the magnitude of the deformation of gender ideology. Sexual differentiation in the human species is for the individuals, but it also regards the entire species. Its intelligibility requires that one introduce the operators that link generations of parents and grandparents to children. Concretely coming into existence as a male or a female takes place within a set of probabilities that is sequentially linked into a finality that springs from the entire order of the universe, an order that includes its concrete spatial and temporal residues (see chapter 4 of INSIGHT to glimpse more of this). When one decides to “change out” one’s concrete sexual differentiation through gender re-assignment, one is actually privating oneself and others of the finality in which one came to be. I am not proving this point right now, but giving you some conclusions that I had discovered some years ago.

To point you toward the evidence that led me down this trail, let me mention a notion developed by evolutionary theorists. The emergence of a new trait is followed up by a rapid perfection of that trait over relatively few generations. In evolution, few can mean thousands of years rather than millions depending on the complexity of the organism – the more complex multi-cellular organisms require longer periods of time to evolve. Something like a virus or bacteria however evolves in much shorter periods of time. This rapid perfection of a mode of operation within its operator means that certain kinds of operations in the human body reached a type of perfection long ago (even before the emergence of the human species). Sexual union based on sexual differentiation is one of those. If you look at plant sexual differentiation, it is a bit undifferentiated with many plants having both male and female components (and the number of chromosomes is a bit loose as well). As one moves to higher and higher animals, there is a set of clarifications of the male and female differentiations. One can describe these perfections or clarifications as a refinement of the nurturing operators and schemes on the one side of the differentiation (which we call female), and the refinement of protective operators and schemes on the other (which we call male). This gives all kinds of selective advantage to a community of the species (to use evolutionary terms again).

What this means is that human sexual differentiation arises from within an evolutionary series of developments as a perfection upon which then builds the higher levels of being in the human subject. For the human subject to then “decide” that this differentiation is a false limitation, and is really an evil and something hindering one, is to fail to realize the kind of perfection that sexual differentiation has become within the order of the entire finality of the universe. Again, this has to be argued more thoroughly, and so I give to you simply a project to consider. Sexual differentiation is a fundamental differentiation upon which the emergence of conscious intentionality within the finality of the entire generalize emergent structure of the universe is taking place. Treating it as something that can be changed or even discarded at will is to join the Hegelian and Marxian revolutionaries, which when you look at history has a deeply disturbing root in hatred born of an even deeper root of despair and darkness.

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Insight into Chemistry: Introduction

by David Fleischacker

In Insight, Lonergan makes use of chemistry as one of the examples of higher and lower genii of things in this universe.  Biology is a higher integration of a coincidental manifold of chemical occurrences and schemes.  What I would like to do is to examine the history of chemistry to catch glimpse of the breakthroughs that led to its discovery.  The periodic table is a brilliant construct.  Before Mendeleev provided us with this final version, there were precursors, and before these precursors, there were a series of breakthroughs both in the way that sense data was gathered and in the way that the upper blade heuristics operated, upper blades of both classical and statistical heuristic structures, the former being formulated in terms of the relationships of matter and the latter being formulated in terms of reaction rates.  Even earlier, there was a series of descriptive breakthroughs with developing explanatory postulates that painted a complex path to modern chemistry.

Here are a few areas that I would like to explore.

  1. Whether there exist deductive and homogeneous expansions in chemistry.
  2. The role of inverse insights in chemistry.
  3. The degree to which classical and statistical heuristic structures developed in chemistry.
  4. The relationship of chemistry 1) to physics, 2) to biology (and on up).
  5. The explanatory conjugates in Chemistry.
  6. Schemes of recurrence in Chemistry.
  7. The nature of judgements in chemistry (eg. Provisional analytical principles)
  8. Epistemology in chemistry, especially in terms of the principle notion of objectivity.
  9. Vertical developments that emerged following the breakthroughs into modern chemistry, both heading down into quarks and heading up into DNA and replication.
  10. Chemistry and metaphysics – potencies, forms, and acts, along with generalized emergent probability.
    1. In this context, I would like to explore energy in chemistry (and whether Lonergan is right in suggesting a link between energy and finality.

Chemistry: A Deductive Expansion

I will begin by saying something about the first half of #1 above.

Lonergan introduces deductive expansion in chapter one of Insight to illustrate a particular type of development within mathematics.  It is deductive when the same operation is used over and over again.  Hence, when one adds over and over again:  1 + 1 = 2, 2 + 1 = 3, 3 + 1 = 4. Etc., etc., etc..  This type of deduction using addition can lead one to a viewpoint that is symbolized by addition tables. The key is that the mode of the expansion is entirely limited to a single operation, addition.

In Chemistry similar types of development take place.  Descriptively, one finds the growth of qualitative measures, that then became the “operation” used to investigate certain types of materials or substances. Examples include solubility in water and related to this, the formation of precipitates.  Salt and sugar dissolve in water for example. Wood and iron do not, at least in any rapid time frame.  One can take known substances, and see if these are soluble. Of course, one could switch water with acids, bases, or alcohols.  One could go on to mixing liquids or gases or gases with liquids, as well as liquids with solids.  Now, at first, it was not clear that solids, gases, and liquids are different forms of certain elements and molecules, but seeing the qualitative (descriptive) outcomes of such interactions is a general mode of operation that one finds in early chemistry (eg. Alchemy and medical chemistry).

Another kind of deductive expansion arose with the development of quantitative analysis in chemistry.  Basically, these sprung from long known units of measure, such as weight, volume, temperature, and to a lesser degree pressure.  One sees Boyle for example introducing the relationship of volume and pressure of gases.  You see a number of individuals introducing various means for measuring weight.  So a general operation was to quantify something.  I suppose one could argue that the real operation was a particular mode of quantifying, such as weight or volume.  One can repeat such an operation upon a number of different substances – gold, wood, water, etc., etc., etc..  This gets to be a bit more difficult with gases, but with some creativity it is not impossible with a bit of creativity. How does one weigh smoke for example? And is smoke a gas?

The point thus far is to show how there are developments like deductive expansions even in the early stages of chemistry.  Explanatorily, one also sees similar expansions.  In Dalton, one finds a proportionality of mass combinations. There are basic elements that combine in specific and definite ways with each other such that a particular substance is always composed of the same set(s) of elements, and hence have the same based masses.  Water is always formed of two hydrogens and one oxygen.  This is a deductive expansion that is even closer to math, because it says that adding particular elements in a certain manner always results in a particular compound of those elements that has specific properties because of how these elements are combined.

As a result, one can see how elements can be combined in twos or threes or fours.  And the masses of these compounds always equal the sum of the masses of the elements.  Of course, there is more to be discovered, because not just any element can be combined with any other element. Hence, this is where chemistry diverges from math.  In math, any number can be added to any number.

 

This is just a first set of observations about chemistry and its development, both descriptively and explanatorily.  I will return to this every so often and hopefully have something to say.

John Dalton’s Table of Elements and Compounds