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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
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Judgment and the Recovery of Being

by Dr. David Fleischacker

Lonergan’s explanatory formulation of the interior structure of judgment dismantles one of the great culprits of the modern world that has left vast reaches of the Western world in a dark age. It is dark because it thwarts self-transcendence precisely in one of the great powers of the human mind.  Judgement makes possible a real presence of a person to that which is.  It mediates a true encounter with intelligible being. In other words, authentic judgment allows being to dwell within one.  This darkness is the real forgetfulness of being.  Heidegger was only partially right. He did recognize something that was true about the fallen state of us.  But he still left one with out the ability to enjoy and rejoice in the goodness of even the littlest beings in the world.  Those little, finite beings–trees, rocks, the human body, stars, planets–were merely ontic things.  For him Being– the Ontological–was all that mattered, and even that notion lacks in Heidegger the liberty that Lonergan comes to discover. It is after all a transcendental notion.

When one proclaims that all is mere perspective, or one announces that one can never be sure of what truly is, or one thinks of reality as out there but not in here (in my head), then one is proclaiming that being is fundamentally unknown.  It is as Kant said, in the noumena.  This is the darkness in which today we are chained and enslaved.  It is a self-inflicted cave of own’s own mind, and if one is completely honest, then Derrida is right, even that cave is a mere trace. It too resides in the darkness.  Even my own thoughts flow in the differance of lost presence.

For most, I think the world of entertainment and work keeps them from facing this haunting darkness which they have absorbed since their day of birth.  Many do escape into a world of common sense and do not bother with these questions.  But if pushed in a direction they do not like, then as an instinctual mechanism of self-defense, they pull out the darkness of the no-nothings.

I remember one day saying to a friend, “don’t you know that you can’t find happiness in hockey — he loved hockey to the neglect of nearly everything. He was able to deconstruct my simple quest with one stutter of his vocal cords and a brush of air sent my way in the wave of a hand.  I knew what he meant.  He meant you can’t really know the answer to what you are asking.  Don’t bother me with it.

Lonergan does not answer this deconstructive shallowness with the same brush of air and grunt.  No such simplicity can be found with his response.  Yet, amazingly, in one book he sends to the grave this particular darkness for any who want freedom from these chains that have been growing and entangling the Western world for 500 or more years.  I suppose one could argue that it has been longer and started with the nominalists, but the other day, someone I know — Dr. Chris Blum — pointed out rightly that without the founders of modernity (Descartes, Hume, Kant, etc.), these nominalists would have been forgotten.

Lonergan in one book opens the doors to the cave. That book is Insight. He let’s in some light. We can discover that the shadows and traces of being are not our genie lamp. With the great skill of a gifted surgeon, Lonergan, at the beginning of the book, asks the reader to examine in themselves the act of understanding. It begins a journey into a massive world of interiority and self-appropriation.  The attentive and careful reader who takes this journey is not asked to trust the writer in the end, though one must trust along the way.  He leads the reader from insight in math and science to that of common sense and things, all before he turns to the excavating work of exploring judgment.

It is a brilliant plan as anyone knows who has seriously read the text.  His first eight chapters remove the rocks that block the path to light and freedom, and then finally he removes the hinges of the locked doors of the cave.

Starting in chapter 9, he then begins to open the door.  In chapter 11, the reader gets asked to walk out of the cave unless he or she is too afraid to do so and simply refuses to see the beauty and the landscape of being.

In the next couple of chapters, through the notion of being and then of objectivity, Lonergan provides an explanatory account of why we can be present to being, and why being can dwell within us.  It gives the subject who has dwelt in the cave of the modern world a new wineskin and a new garment.  More technically, it is a new heuristic foundation to taste the beauty and glory of the real universe of being.

I could repeat Lonergan’s answer with regard to the conditions required for true judgments and the principle notion of objectivity, and why these happen in us all the time.  But for the full meaning of these explanatory formulations to burst forth and make sense, one really does need to travel down all of those earlier chapters of Insight first.

Hence, this blog you are reading is merely an invitation to those who have some inkling that perspectivalism and relativism are unhappy conclusions, and that traces of others are not so joyful as their real presence in filial and agapic bonds of love.

By the way, for those who are not able for various reasons to move into the explanatory account of the freedom and light of true judgment, do not worry.  Lonergan’s account reveals that good sound judgment gives you that liberty even when you are unable to explain why.  You really can love–in a mutual indwelling presence–your friend, your spouse, your child….and God, even if the how remains a mystery.

 

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From David Fleischacker

Just a quick note.  I will be publishing a reflection every Friday at 3 pm. Most of these will be short pointers and thoughts about the writings of Bernard Lonergan.

Kindly,

David Fleischacker

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Trinitarian Reflections: The Transcentdental Notions and God, blog 1

by David Fleischacker

About two years ago, I started a new notebook on linking together the University and its life with that of the Holy Trinity.  One of the areas that I wondered about was whether the Transcendental Notions (TN) could provide any type of analogy for understanding the three persons of the Holy Trinity.  There are after all, three transcendental notions that Lonergan develops which are spiritual in nature, hence intrinsically independent of the empirical residue.  These spiritual transcendental notions are Lonergan’s transposition of the agent intellect found in Aristotle and St. Thomas, and of the Light of Being (conscience, mind, etc) as found in the Platonists and St. Augustine (as a note, Augustine was clearly not a Platonist once you get into his head more thoroughly even if he learned much from them and borrowed some notions from them).

One of the immediate difficulties of course which one finds noted in Lonergan is that in finding an analogy for the Holy Trinity, we need to deal with acts or operations, not with anything in potency.  The TN are a kind of potency, but much different than normal.  These actually have the power or capacity to bring about self-transcendence.  In St. Thomas (and Aristotle), these “lights” of the mind have the power to illumine, hence they act as agent causes.  Most potencies do not have such capabilities.  Hence the reason these lights are in a kind of actuality as well.  Notice how some of the metaphysical terms and relations get stretched (but not violated! or confused).  The TN are in a potency in relationship to the operations that arise, but in relationship to the potencies in the human subject to receive these operations they are in act.  Many would say that this imprecision of the metaphysical terms and relations is why one needs to leave out the metaphysical, and turn to intentionality analysis. That is true in part, but if one does so, one as Lonergan notes in Insight, needs to run the full circuit, and return to metaphysics, both to refine the metaphysics, but also to articulate the intelligibilities discovered as belonging to being.  To stay merely with a cognitive apprehension of conscious and intentional life leaves one ignorant of its “reality.”  So the circuit does need to be run.

The reason I mention the circuit is because if one is to transpose the analogies for the Holy Trinity found in St. Thomas, then one needs to deal with some of the metaphysical points that he makes, such as God is pure act, and hence we need to find analogies in act that help us, and this is true of the Persons as well as of God.  The Father is pure act, as is the Son, and the Holy Spirit.

Hence, are the TN in act enough for them to be used as analogies?

The TNs, though in a kind of potency, are also the “light” that makes possible the conscious and intentional operations.  This means that in some manner, they are more in act than the operations.  They underpin, penetrate, and transcend all operations.  Still, there must be a reason that Lonergan did not turn toward these as analogies. He stuck with operations (eg. apprehension of the good, judgment of value of the good, love/decision of/for the good). I suppose one could argue that these operations are in part constituted by the TN, as the TN penetrate them.  We could look at what that “penetration” means.  It of course is not physical, but spiritual.  Descriptively, it “illumines” the operation.  It is what “receives” the operation.  It is what “beholds” the operation.  The TN is not only light, but also an intentional focus, hence can be described as the “eye” of the mind as well.  I am tending to think that the TN is both light and eye (hence not distinct as these are physically in us — but I could be wrong).  I suppose one could say the “eye” is the conscious subject as awakened in a TN and thus seeking an answer, hence waiting for an operation that mediates the answer.  Then once the operation emerges, the subject as beholding the operation in the TN is an eye that beholds.  The subject is however conscious through the TN, and thus the TN constitutes both the horizon and the subject as a gazing subject.

One of the areas that I explored a couple years ago in my notebook was whether there was a sufficient distinction and set of relations between the TN to result in some kind of analogy that sheds light upon the Father, Son, and Holy Spirit.  Thus, does the TN of intelligibility have a kind of relationship to that of being/truth such that the former begets that latter.  Of course, this does not happen without an operation. And it does not happen without the subject moving (raising the question for reflection).  Likewise does the TN of goodness spirate from the TN of being?  I cannot repeat all of the reflections here, but I can say that my reflections were not conclusive.  I do intend however to start publishing these reflections in this particular sequence of blogs.

Even if I discover that those reflections do provide an interesting analogy, there is still the further question about whether the analogy is an improvement upon that of the operations as such.  I have a suspicion that they do not, but they might help to deepen my understanding of the operational based analogy (apprehension of the good, judgement of value of the good, decision for the good).  Part of my reason for this suspicion is that God as pure act is the cause of the light that is in us, which we call the TNs.  The TNs do allow us to grasp the unrestricted nature of the operations in God, but those are operations in God, not TNs.   Just a few thoughts.

More later.

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Feeding the thirst of Jesus Christ

Why does Jesus need or want us to feed him? It would seem that the only appropriate relation to him is to allow him to feed us. Very true of course. At the same time, from the Cross, he cries out that he thirsts.  He thirsts as St. Mother Theresa tells us.  Jesus is in those whom we meet, especially the poor and the destitute.  All of those who fall under the beatitudes.  He thirsts in and through them for us to give him a bit of drink and food.  It is part of the immense mystery of being a member of the body of our Lord.  He knows us.  He knows us in his divinity and he knows us in his humanity.  As he hung on the Cross, he proclaimed the thirst of his entire body, as it exists in his mind and heart.  This is the meaning of the unity of Christ and his body.  In fact, it is a unity that each of us has with each other.  When anyone thirsts, and it comes to dwell in us, it then comes to inform us as a constitutive act of meaning.  Hence another’s thirst becomes our own.  Likewise with Jesus Christ. We are his.  And we are in him.  He thirsts because we thirst.  He thirsts because he became one of us.  And as he fills that thirst, so we as part of him are to fill that thirst as well. This is the meaning of to abide and to mutually indwell.

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Part 8:  Love in Finality, Love, and Marriage

by David Fleischacker

Further, love is the act of a subject (principium quod), and as such it is the principle of union between different subjects. Such union is of two kinds, according as it emerges in love as process to an end or in love in the consummation of the end attained. The former may be illustrated by the love of friends pursuing in common a common goal. The latter has its simplest illustration in the ultimate end of the beatific vision, which at once is the term of process, of amor concupiscentiae , and  the fulfilment of union  with God,  of amor amicitiae (“Finality, Love, Marriage,” 24)

Though there is more to say on finality, I am now turning attention to the meaning of love within the 1943 essay “Finality, Love, and Marriage.” On an initial review, and I think final as well, Lonergan was only beginning to move into a deeper explanatory account of love in 1943.  His use of terms derived from faculty psychology and his notion of appetite illustrate this beginning. We must remember however that the use of faculty psychology does not make something false.  What happens once one shifts into intentionality analysis is a transposition which sometimes results in a translation of a term into the intentional framework and, at others, an elimination of a term.  For example, I would argue that the potential intellect gets translated into the capacity for self-transcendence, and hence expanded and united within the light of all the transcendental notions.  Likewise, the agent intellect becomes translated into the transcendental notions, and thus more adequately expanded as well.  Thus, Lonergan’s formulation of love in 1943, even if in faculty psychology, can be transposed, something which Lonergan had done by the time he wrote Method in Theology.

First, let’s look carefully at the 1943 text.  This section is titled “The Concept of Love.”  Notice Lonergan is using the term concept. However, in his opening line, he identifies love as utterly concrete.

The difficulty of conceiving love adequately arises from  its essential concreteness and  from  the  complexity of the concrete.(23)

Love is neither a concept or an abstraction, but of course in talking about it, one does have to conceive it.

In conceiving of love, Lonergan develops four aspects, the first two dealing with the nature and act of love itself, and the second dealing with the subject who loves.  The first two clearly are formulated within faculty psychology.  Love is an act of a faculty.  A faculty is a kind of power that is constitutive of what a living thing is.  It gives the living thing the ability to carry out certain type of operations.  To get an insight into a faculty, one has to carefully analyze a whole landscape of operations and then in  examining the operations, discover fundamental characteristics that unite those operations.  So, seeing, hearing, tasting, touching, and smelling all have a material element to them, such that the very operation itself regards a spatial-temporal element.  As well, these sensate operations allow one to be present and conscious of sense objects.  And hence recognizing that all of these sense activities both have a conscious element and a material element would allow one to then formulate a common power or capacity that one has in these types of activities.  This becomes the source of the insight into a particular faculty or power.  Other operations transcend certain material limitations, and the principle examples of this are the activities of understanding and knowledge.  One can posit a common power or faculty to these spiritual (non-material activities), such as the faculty if the intellect. Now on to each of the four aspects.

First Aspect: Love as an actuation of a faculty

Lonergan formulates love as a realization or actuation of faculty.  Specifically, it is a faculty of appetite, and love is the central appetite – “it is the pure response of appetite to the good” (23)  Other responses are derivative – desire, hope, joy, hatred, aversion, fear, and sadness.  Hope is the expectation to become present to that which is love. Hatred is toward that which has harmed the good that is loved.  Fear arises in response to the possible loss of the good that is loved.  Sadness is the response to that good as lost. Joy is the enjoyment of the good as present.  Love is key.  It is central.  There is nothing false in formulating love in this manner.  Identifying it with a faculty, and a fundamental appetite is to recognize that it is a real power or capacity of the human person.

Second Aspect: Love of a beloved as first principle

The second aspect is that it is the principle – “the first in an ordered series” – that initiates a process to its end, which is that which is loved. One can think of simple vital desires for example.  The desire for food is not only the “form” of the end process by which one goes out to find, hunt, or grow food, but it is the first principle of that entire process, and it has as its object the end, the food itself.  In the case of love it is the beloved.  The beloved becomes the first principle that moves the person in love to the beloved.

Third Aspect: Unification of subjects toward an end

The third aspect highlights that the act of love, the act of this fundamental appetite, this first principle of movement to the beloved as term, bonds the subjects who are in love based upon their common pursuit of an end.  Those who have not yet reached the end, and rather are still in pursuit of it, become bound when pursing that end collaboratively.  Lonergan draws this out further through Aristotle’s notion of friendship in a later section of his essay.  Notice that here, Lonergan does not specify the end that is pursued, because any good ends pursued can unite individuals to each other.  This pursuit also perfects the human subjects as such, and thus bonds them to each other for each other, but that is the point of the next aspect.

Fourth Aspect:  Love of Beloved as United, as Consummated

The fourth aspect highlights that love as realized unites subjects as mutual persons who enjoy the good that each is, a mutual unity that is based upon the good that each person is and has become.  The ultimate example of this aspect that Lonergan identifies is the beatific vision, “which at once is the term of process… and the fulfillment of union with God” (24).

 

It is important to note that Lonergan says these are simultaneous aspects (23). The differences between each is a different focus upon what is “utterly concrete.”  By simultaneous he means that one does not happen without the other, even if the individuals involved may be focusing in upon one of the aspects and not the others.

Contrast to love in Method in Theology

There is not only a clear difference of words between 1943 and 1972, but a clear difference in scope.  Lonergan by 1972, was able to formulate love in terms of insights that he had into the structure of consciousness, specifically in terms of the capacity for self-transcendence, and the different states of being of that capacity.  One not only has the notion of potency in a capacity, but it is a potency that has a directly relationship to states (which is derived from statistical notions – the difference between actual frequencies from ideal frequencies gives one an understanding of the state of something), and it includes a clear differentiation of the notions that constitute the capacity as a whole – the transcendental notions.  Lonergan thus could formulate love not as merely an actualization of a faculty, but one might say the actualization of the faculty of all faculties, the base of all bases.  Love is basic because it orientes all levels of consciousness.  All the questions that one pursues are guided by that which one loves.  In other words, the state of being orients all the operators of human development at all levels of conscious intentionality.  Love is the actuation of the capacity for self-transcendence, and the more profound it is, the more it underpins, penetrates, and transforms all of one’s horizon.

This does not negate the insights Lonergan had in 1943, but it does formulate these insights more clearly, and it expands upon what he understood of love.  It is still utterly concrete, and so concrete that nothing that human beings do escape it, because even getting up in the morning means there is some basic actuation of the capacity, some basic state of one’s being.  It is an actuation of a kind of faculty, but not just among others. Rather, it regards the capacity for any human intentional operator and operation. It is a central appetite, but it is also a the central finality of all human activities.  The transposition of faculty psychology into intentionality analysis reinforces what Lonergan says about love in 1943 and expands it.  Furthermore, the last two aspects can be understood more deeply.  When one understands that love is a realization of the capacity for self-transcendence, and that all other operators and operations thus emanate from this realization, then one comes to understand the more comprehensive scope upon which subjects can be bound to each other both as they self-transcend, and as they reach the fulfillment of their self-transcendence. This is especially true when one transposes the beatific vision into a perfection of the human capacity for self-transcendence by the gift  that is the Transcendent, the ultimate meaning and ultimate value because the Transcendent is the only true realization of the capacity.  Lonergan’s reflections upon Christology and Trinitarian theology draw this out even more (and one might add his work on grace).

Just a few things to think about as we start this exploration on Lonergan’s notion of love in “Finality, Love, and Marriage.”

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Higher Viewpoints: Part One, from arithmetic to algebra, the transition

This is a repost of a 1997 essay written for a seminar on Insight.

Higher Viewpoints: Part One

From Arithmetic to Algebra: the transition

by David Fleischacker
Draft Version 1

Copyright © 1997. All rights reserved

(This is a reflective commentary on one facet of sections 1 – 3 of chapter one in Insight.)

 

I. The Viewpoint of Arithmetic:

In Insight, Lonergan builds to the notion of a higher viewpoint after he has developed an understanding of clues, insight, concepts, questions, images, and definitions. A viewpoint is not merely a definition, but a set of systematically related definitions (and of the operations that underpin both the definitions and their systematic relations). It is not a single definition. Defining a circle, for example, is not a viewpoint, but it does arise out of a geometrical viewpoint, and contributes to it. The same is true of the distributive or commutative properties of algebra, or the power rule of calculus. They do not constitute an entire viewpoint, but they are components.

Lonergan illustrates lower and higher viewpoints with arithmetic and algebra. A mathematical viewpoint is constituted by rules, operations, and symbols (or numbers). The rules implicitly define the operations, and the operations implicitly define the symbols. What does he mean by this?

 

A. The Deductive Expansion of Arithmetic (the first horizontal development in mathematics):

Lonergan begins with arithmetic, more specifically with addition. One may count sheep or goats or troops in an army or persons inhabiting a town. The counting involves the operation of addition– one plus one plus one, and so forth. It is an activity relating quantities and defining them in terms of each other. The basic unit of this quantity can be symbolized, let us say with a “1” or “I”. Other symbols can be used to represent what one is doing when adding, such as “+” or “plus.”

Any number of symbols can be invented to represent operations (addition, subtraction, etc..) and numbers (some of which, Lonergan notes, are better conducive to the future development of mathematics than others because of their potential for leading to further insights). In order to simplify the ongoing definitions of numbers most cultures that developed mathematics introduced repeating schemes. Some introduced repetitions based on 30 or 60 (think of our clocks and watches). Our present system is based on repetitions of 10, so we developed a symbol for zero through nine, and then, once ten is reached, we add a place to the left indicating the number of “tens.” Then once the tens reaches beyond the ninth position, we add the hundreds, then thousands, and so on (Computers, you may have heard, are based on a binary, with ones and zeros).

From adding numbers we can develop, as Lonergan notes, a definition of the positive integers.

So,

1 + 1 = 2
2 + 1 = 3
3 + 1 = 4
etc., etc., etc..

Once the insight is gained, or in other words, when one understands what is meant by “etc., etc., etc.” then one can continue to indefinitely define any positive number. From this, one can create an entire deductive expansion of a viewpoint or horizon in arithmetic, and continue indefinitely to define the whole range of positive integers. One can also construct mathematical tables using 2s, 3s, 4s, etc..

2 + 2 = 4
4 + 2 = 6
6 + 2 = 8
Etc., etc., etc.. (“2” is added in a repeating fashion)

3 + 3 = 6
6 + 3 = 9
9 + 3 = 12
Etc., etc., etc.. (“3” is added in a repeating fashion)

4 + 4 = 8
8 + 4 = 12
12 + 4 = 16
Etc., etc., etc.. (“4” is added in a repeating fashion)

 

Then,

ETC., ETC., ETC. (For the entire process above)

Notice how all of the numbers are defined in terms of the operation of addition. It is the basic insight that grounds this operation which allows for the construction of an entire deductive expansion which creates a “world” or viewpoint, even if rather limited. It is a first, horizontal development of a horizon in mathematics.

 

B. The Homogeneous Expansion (the second horizontal development in mathematics)

One can become more creative, and begin to add a number to itself say three or four or five times.

So,

1 + 1 + 1 = 3
1 + 1 + 1 + 1 = 4
2 + 2 + 2 = 6
3 + 3 + 3 + 3 = 12
Etc., etc., etc..

 

And, instead of writing this with three 1’s or four 1’s or three 2’s or four 3’s, shorthand notation can be developed.

1 x 3 = 3
1 x 4 = 4
2 x 3 = 6
3 x 4 = 12

So, one introduces a different symbol, namely an “x” to indicate the number of times one is added to itself. Notice how this new symbol is still defined in terms of the old operation of addition. It means “adding” a number to itself so many times.

Creativity does not have to stop. If we can add one to another, then what happens if we take something away. We had three sheep, sold one, and now are left with two. This is the opposite of addition, and we can give it the symbolization of “-“(1) and call it subtraction. Again, one can develop charts of subtraction, just as with addition and multiplication. Likewise, just as one can reverse addition by removing something, so one can reverse multiplication by removing a number so many number of times. So, just as one can add 2 to itself four times to get 8, so one can remove 2 from 8 four times. This of course, is division.

Creatively constructing a viewpoint by introducing new symbols such as subtraction, multiplication and division, is what Lonergan calls a homogenous expansion. One has introduced new symbols relating numbers, but notice how everything is still thought of in terms of addition. Subtraction is the reverse of addition. Multiplication is the addition of a number to itself so many number of times. Division is the reverse of that. And if one wishes to add powers and roots, they likewise can be defined in terms of addition. A power is the multiplication of number by itself so many number of times.  Thus to define this in terms of addition, let the number that is powered equal y, and the power equal z.    Thus, the answer is defined as the number, y,  which has been added to itself y number of times, thus forming a group, a group which in turn is added to itself again y number of times, and repeating this formation of groups  z-1 number of times. This can be illustrated with 3 to the power of 4.  3 to the power of 4 is the same as 3 x 3 x 3 x 3.  The first group arises by converting 3 x 3 into 3 + 3 + 3. This group is then added to itself 3 times in order to get the equivalent of 3 x 3 x 3.  This results in a second group that can be written as [(3 + 3 + 3) + (3 + 3 + 3) + (3 + 3 + 3)].  Finally, take this second group and add it three times to itself.  The final answer comprises this third group, which can be written as

[(3+3+3) + (3+3+3) + (3+3+3)] + [(3+3+3) + (3+3+3) + (3+3+3)] + [(3+3+3) + (3+3+3) + (3+3+3)] = 81

A “root” is the reverse of this procedure. So, the 4th root of 81 requires breaking down the 81 into three groups, where the basic group, which when discussing powers was called the first group, is comprised of a number that has been added to itself its own number of times.  This number is the answer. So, even powers and roots can be thought of in terms of addition.

II. Algebra: The Higher Viewpoint ( a vertical expansion in mathematics)

The homogeneous expansion of arithmetic has not introduced any new rules. One can define each of the new operations in terms of addition (or the reverse of addition). New rules are only introduced when one starts “observing” patterns in arithmetic, and doing this initiates algebra (Lonergan notes that the image which leads to algebra is the doing of arithmetic). What does this mean? Lonergan notes that this “turn of question” that lead to the discovery of patterns in arithmetic occurred because of questions such as;

What happens when one subtracts more than one had?
Or what happens when division leads to fractions?
Or roots to surds?

Each of these refers to various problems that emerge in the homogenous expansion. Their answer lies in grasping patterns. Questions emerge which ask, what, in general, happens when one subtracts numbers, or adds numbers, or divides numbers, or adds powered numbers, etc.? Today, these initial patterns are given such names as commutative, distributive, and associative properties. Let us illustrate these laws.

A simple pattern is adding a number to zero.

1 + 0 = 1
2 + 0 = 2
3 + 0 = 3
4 + 0 = 4
5 + 0 = 5
6 + 0 = 6
etc., etc., etc..

The etc., etc., etc., again is introduced to gain the insight. A number added to zero results in an answer that is that number. This can be symbolized by creating a symbol that represents a number (or in other words, a variable).  Let that symbol be “A.” Below is the formulation of this pattern,

A + 0 = A

Another example is the multiplication of a number by 1.

1 x 1 = 1
2 x 1 = 2
3 x 1 = 3
4 x 1 = 4
5 x 1 = 5
etc., etc., etc..

If one recognizes the pattern, then one notices that a number multiplied by one, gives the number. Hence, this insight can be symbolized.

A x 1 = A

The same is true with the various laws or properties (as they are actually called) mentioned earlier. The commutative property of addition states that A + B = B + A. The commutative property of multiplication states that A x B = B x A. The associative property states that (A + B) + C = A + (B + C). The parenthesis means add these numbers first. The associative property of multiplication states that (A x B) x C = A x (B x C). As an exercise right now, try expressing these patterns using actual numbers and the “etc., etc., etc.” as I did above.

You can practice this further by opening any algebraic text, and examining the numerous rules about addition, multiplication, division, powers, roots, addition of powers, multiplication of powers, multiplication of roots, and the inverses of each of these formulas (subtraction of powers and roots, division of powers and roots, etc..)

Notice how one is understanding the operations in a manner beyond that of addition. One begins to grasp, for example, that multiplying two negatives leads to a positive, that dividing a negative into a negative also leads to a positive and many other characteristics. These recognized patterns then begin to form new rules, which constitute the higher viewpoint called algebra. These rules guide one in solving problems, since they implicitly define how one is to carry out operations and define the new symbols of A’s, B’s, and C’s, which represent variable numbers (this will be discussed with more precision and examples in a later commentary). The rules constitute a vertical expansion of the mathematical horizon.

Like arithmetic, algebra also has a deductive and homogeneous expansion, or, at least something analogous. This is for a later section.

 

David Fleischacker

Copyright © 1997. All rights reserved

1. For a history of mathematics that discusses these symbols, see a book that is frequently recommended in Lonergan circles, Carl Boyer, A History of Mathematics (New York: John Wiley & Sons, Inc., 1991).

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Part 7: Finality, Final Cause, and the Good in “Finality, Love, and Marriage”

by David Fleischacker

“For the final cause is the cuius gratia, and its specific or formal constituent is the good as cause.” (Finality, Love, Marriage, 19)

This quote” falls within the section on vertical finality in “Finality, Love, and Marriage.” In the paragraph before this quote, Lonergan was introducing the difficulties in apprehending finality. It is something that can be easily overlooked by the positivist because “quite coherently, any positivist will deny final causality.”  Instead, the positivist will only admit efficient causality.  Lonergan in short, defines finality in terms of final causality.  One wonders if he had yet broken from Aristotelian science sufficiently to provide an adequate account, even heuristically, of marriage and the marital acts.  I suspect many would say no.

To restate this difficulty, if vertical finality is defined in terms of final cause, it would seem that Lonergan has not adequately defined finality yet.  There is some truth in this as I stated in the last blog — since it seems that in light of Lonergan’s formulation of horizontal finality, he had not yet reached his more general formulation of finality that one finds in Insight, where it is isomorphic with the notion of being, and not related to essence alone (though it is related since essence or form is a component of being).  Just as one can expand on the notion of horizontal finality, so one can do the same with vertical. Let us push this a bit in this blog to see where it goes.

As the quote up top indicates, Lonergan is defining final cause in terms of the good.  In this section on vertical finality where he criticizes the positivist, Lonergan notes that the positivist can acknowledge  motives and terms, but only as efficient causes. The blindspot of the positivist is the denial of these motives as good and these terms as good.  In short, Lonergan is saying that in the potency, there is an orientation to the good that he calls finality.

One can find this orientation to the good throughout Lonergan’s later writings. In fact, it becomes more prominent, not less, as he formulates in a clear fashion the fourth level of consciousness and delineates the capacity for self-transcendence not in terms of one notion (being) as he does in Insight, but in terms of three transcendental notions — intelligibility, being, and the good (Method in Theology, 34 – 35 or 104- 105). As well, one can think of his formulation of the human good in chapter 2 of Method in Theology, especially the notion of the “terminal good” (Method in Theology, 51). In both cases, whether one thinks of the transcendental notion of the good/value or in terms of terminal value, these operate in the same manner as Lonergan’s formulation of a final cause in 1943.  In other words, the transcendental notion of value operates like the notion of being, and hence it is isomorphic with the good. And terminal value is the good as a term that is truly good.

Though their is a similar heuristic element to final cause in 1943 and Lonergan’s formulation of the notion of value later, there is an expansion.  Just as an expansion occurs in relating finality (whether horizontal or vertical) to the notion of being in Insight, so now one can isomorphically relate finality to the entire capacity for self-transcendence, which is constituted by the three transcendental notions–intelligibility, being, and the good.  To do this is not to say that what Lonergan defined as finality in 1943 is wrong, but rather it is to open up its meaning to the entire nature of the universe of intelligible and existing goodness.

Think about how Lonergan’s development of the capacity for self-transcendence actually points out a limitation in Insight.  Lonergan would have formulated the good in Insight in a manner similar to Aquinas, as convertible with being.  This point would be true later as well, but it receives some nuances.  The good  as a distinct transcendental notion in later writings, hence distinct in the human subject’s apprehension of the good, especially the hierarchy of the good/value, indicates the differential of something as existing (or some occurrence of a conjugate form as occurring) versus something as good.  In 1943, Lonergan introduced this goodness to being in terms of a final cause.  In other words, being and the good are more explanatorily developed in later writings but still operative in earlier writings. Final cause is not eliminated so much as explanatorily developed.  The manner that he used it in 1943 is still valid within its frame work.

Why was it and is it still valid? This validity is similar to how the Newtonian formulation of gravitation is valid within general relativity, but it is a more limited account. One can transpose the 1943 Lonergan into 1983 by formulating finality as the metaphysical and meta-ethical isomorphism with the capacity for self-transcendence.  This would further open the heuristic exploration of marriage and love that he formulated in 1943, and place his insights within a larger framework.  Already in the last blog, I have started to do this by uniting horizontal and vertical finality in terms of potency as one finds in Insight.   One can do more by relating finality to emergent probability as the emergent good.  The upwardly directed dynamism of finality for intelligibility, being, and the good/value (I have been using good partially because I do get tired of the relativistic overtones of the term “value” in modern culture).  Such a finality would apprehend the universe in its proportionate existence as an emerging good.  This recognizes the universe as an ultimate friendly universe in its very nature.  This also means that the entire intelligibility and being of marriage is not only real but good — and so getting that meaning right is crucial if the historical and traditional breakthrough into marriage is not to fade into the shadowland of scotosis or individual bias or group bias or the general bias (on the notion of scotosis and bias, see Insight, chapters 6 and 7).

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Part 6: Horizontal and Vertical Finality in Marriage, Love, and Finality

By David Fleischacker

Four ideas about the generic relationship of horizontal and vertical finality stand out in Lonergan’s 1943 essay – “Finality, Love, and Marriage.” It is important to note that I have not passed much beyond exploring the first section of the 1943 essay, which makes general statements about finality.  In his later sections, he treats of love and the personalist elements of marriage within the framework of finality, and so these later elements will be crucial to comprehend what he contributed with this essay.  That will be for future blogs.

 

First Idea: Horizontal as Essential, Vertical as Excellent

The first deals with linking horizontal to what is essential, and then vertical to what is excellent.  This is mentioned a number of times (see for instance pages 18, 22-23, and 48).  Essence refers to what something is (Lonergan uses nearly the same formulations of horizontal, vertical, and absolute finality in his 1976 essay, Mission and Spirit, but instead of essence he just writes that the proportionate end “results from what a thing is” — A Third Collection, page 24).  Essence constitutes a kind of limit to the types of activities or operations that a thing can engage upon or into which it can develop.  The excellent refers to a higher level perfection that can emerge from the lower.  Lonergan’s use of essential and excellent is directly linked to the course he was teaching on marriage at the time,  and to Casti Cannubii, in which the essential and excellent ends of marriage were distinguished.  I find it interesting that he defines horizontal in terms of essence, but he does not define vertical in terms of excellence.  Rather, he defines vertical finality in terms of a dynamic emergence of properties that arise from a conjoined plurality.

This distinction between horizontal and vertical finality seems to be lost by the time of Insight where the terms are not used at all. I would argue that this is a result of a broader, more general formulation of finality in which it is understood as proportionate or isomorphic with the notion of being (and hence the desire to know).  Finality is the “upwardly but indeterminately directed dynamism towards ever fuller realization of being” (Insight, chapter 15, section 6). As such, it is simply the potency of the universe for the emergence and maintenance of each and all intelligible being.  However, Lonergan does use the term “vertical” in a similar fashion to its use in 1943, though only once, when discussing the relations of a lower manifold to a higher order (Insight, chapter 15, section 7.3).  Hence he is not speaking of finality but of developmental relations. And instead of horizontal, he speaks of lateral developments.  In Insight, the only kind of distinction he makes regarding finality is in terms of minor and major flexibility (hence not horizontal and vertical), but explanatorily these are not different, especially in terms of the meaning of finality as a potency that is a directed dynamism (Insight, chapter 15, section 5). In Insight, finality as such is not merely within an individual, or species, or genus, but it is the potency for fuller being in each and all individuals, species, and genii.

There is one key notion that links the 1943 essay and Insight.  It is the notion of a concrete plurality which becomes formulated into terms of both the non-systematic and statistic residues in Insight.  The potency of a plurality of acts ends up being central to understanding the open ended dynamism of each individual, species, and genus. Take for instance a carbon atom.  The carbon atom itself is a chemical conjugate, and if in act, it is an existing chemical atom.  Within an existing atom of carbon, the concrete plurality that is a potency for other chemical forms is the sub-atomic elements which are either quarks or compounds of quarks.  These quarks and compounds of quarks are the lower manifold pluralities that have the potentiality for being informed as other chemical elements or compounds.   In carbon, there are sufficient materials to form other elements or compounds through atomic or nuclear changes–as long as the total masses of these elements and compounds does not exceed that of carbon.  One could theoretically form hydrogen or helium, or any other elements up to carbon from a carbon atom. Hence this concrete plurality of sub-atomic elements is the location of the potency for dynamic change.

In 1943, Lonergan tended to limit this dynamic notion of finality to vertical finality, since such finality is based in the “fertility of a concrete plurality” (and this is equal to an indeterminate but directed dynamism to his use of vertical finality).  However, one finds this concrete plurality to some degree in his use of horizontal as well.  There are a few points in his 1943 essay where Lonergan identifies a statistical relationship between two events on the same horizontal level (namely the conjugal act and conception—see page 46, footnote 73), but he tends to identify horizontal as rooted in essence still, rather than the potency of a non-systematically related set of aggregates that can become “conjoined” into an order whether on the same plane of being or a higher plane.

As mentioned, later in his life, Lonergan does reintroduce vertical and horizontal finality in his third collection that reprints a 1976 paper titled “Mission and Spirit.” He more or less repeats the same definitions as given in 1943 but without the link of horizontal to essence/natural law and vertical to concrete plurality and statistical law. Hence has a similar meaning as in 1943, but he has the developments of Insight in the background, along with the question of evolution.  It is almost if he had re-read the 1943 piece, and decided to bring the notions of horizontal, vertical, and absolute finality to attention.  Just a few years earlier, in Method in Theology published in 1972, he introduces horizontal and vertical liberty (not finality) taken from Joseph de Finance (Method, pages 40, 122, 237-8, 269) but there is no clear indications of any connections to finality and the 1943 essay (one can make connections however).

Second Idea: Horizontal within the field of natural law and vertical within the field of statistical law

Horizontal finality  results  from  abstract  essence;  it holds  even when  the  object  is in isolation;  it is to a motive  or  term  that  is proportionate to essence.  But vertical  finality is in the concrete; in point  of fact it is not from  the isolated  instance but from  the conjoined plurality; and it is in the  field  not of natural but  of statistical  law, not  of the  abstract per se but  of  the  concrete  per accidens. (22)

Tied to linking horizontal to “abstract essence” is the idea that it is in the field of natural law (I am presuming this is what he is implying above, but I could be wrong) rather than in the field of statistical law. The notion of natural law as well as the location of horizontal finality are modified by the time of Insight.  “Nature” in Insight is formulated in terms of a heuristic notion that is like naming an unknown “X” that needs to be understood (Insight, chapter 2, section 2.2).  In this context, nature, and one could argue natural laws, and statistical fields are not distinct, but rather closely linked. Nature as transposed into correlations identify the conjugate forms, and statistics deals with ideal frequencies of the actuation of those forms.  Hence, in Insight, Lonergan differentiates nature (and natural laws) into correlations (or functional relationships) and their statistical ideal realizations.  I would argue as well that developmental operators also belong to the realm of “nature” for Lonergan.  Hence, in Insight, Lonergan will shift finality not only to potency, but to a potency that is an indeterminate but directed dynamism to fuller being. Lonergan was moving in this direction with vertical finality in 1943, but had not worked it out in terms of horizontal yet.

 

Third Idea: Horizontal is not dynamic, the Vertical is the source of dynamism.

The claim that horizontal finality is not dynamic on the one hand and that vertical is dynamic on the other is closely related to the above two ideas.   Because Lonergan was conceiving of horizontal finality in terms of essence and a type of static natural law, he had not thought through the dynamism for fuller being that actually takes place due to horizontal finality.  Since in Insight, he works out his notion of finality in terms of potency and then how this notion fits in with his general theory of development (Insight, chapter 15, sections 5 – 6), even what he is getting at with horizontal finality will turn out to be dynamic as well, because there can be fuller realization of being on the same genus of conjugates.  Think for example about the illustration of arithmetic development in chapter 1.  Arithmetic is presented the first of three levels in math, and there are both deductive and homogeneous expansions at this level.  These expansions are developmental in nature, and they arise in the potency of operating with numbers from the moment one “combines” or adds numbers.  Or look at Lonergan’s formulation of minor and major flexibilities of development. Both illustrate these same points since both “rest on an initial manifold” and thus are rooted in a kind of potentiality that Lonergan would have a called a plurality in 1943 (Insight, chapter 15, section 6).  Minor flexibility refers to something that can have some variation while it unfolds into its mature state, but it still reaches the same mature state.  In major flexibility, a thing can unfold in a new and surprising manner which results in a shift in its mature state (Insight, chapter 15, section 6).  This shift could be a different species but on the same genus, hence horizontal, or it could be to a new genus, hence vertical. An example would be if a grass became a shrub (I am presuming these are different species, and the complexity of the change from one into another may be extremely difficulty or unlikely—I do not want to enter into the explanatory challenges to this within the realm of biochemistry, genetics, and molecular biology, though I acknowledge the challenge) (If you would like to see a bit into my understanding of explanation within biology, take a look at my blog on Behe’s book Darwin’s Black Box).  In this case, the relationship of the initial potency to this new species is a horizontal finality.  However, the major shift could be a shift from a lower to a higher genus, in which case then a vertical development has taken place, and the relationship of the initial potency to this vertical realization is one of vertical finality. Such an example would be the shift from a vegetative form of life into something that is sensate.  This is perhaps best illustrated by the development of an animal (dog, cat, etc.) from a single zygote that starts with cellular operations (or what was traditional called the vegetative level–a lower genus) and then adds sensitive operations (a higher genus).

In 1943, Lonergan tended to see horizontal finality in a static manner because of his formulation of it in terms of a kind of an essence (interestingly, he defines it similarly in his 1976 essay, so one wonders a) whether I am right in thinking that he had a more static notion of essence in 1943, or b) whether Lonergan had thought through the notion in light of Insight when he reintroduced it in 1976).  However, his illustrations show that there are dynamic elements to this as well.  I already mentioned the statistical link between the conjugal act and conception.  Another example is the link between fecundity, the conjugal act, and the adult offspring (41).  Adult offspring require development of course.  And Lonergan is thinking of adult offspring in terms of the matured and differentiated organic operations, not in terms of how these are then sublated into educated adult offspring, or religiously educated adult offspring.  And so, when he uses the phrase “adult offspring” alone, he identifies it as having a horizontal relationship to fecundity and the conjugal act (which is the actualization of fecundity in the union of two semi-fecundities).  Yet, there is clearly a developmental relationship, similar to what he later calls a homogeneous expansion or development.  Perhaps a more significant example is when he talks about the two levels above the organic, namely the life of reason and the life of grace.  With the life of reason, he talks about how the potency for a life of reason in both the man and the woman at this civil level is horizontally related to the historically unfolding good life (42).  This clearly recognizes a developmental unfolding which is not fully determinate, yet  dynamically directed by the desire to be intelligent and reasonable.

Fourth Idea: The vertical emerges all the more strongly as the horizontal is realized the more fully

If, then,  reason  incorporates sex as sex  is in itself,  It will incorporate it as subordinate to its horizontal end , and  so marriage will be an incorporation of the  horizontal finality of sex  much more  than of sex itself;  nor is this to forget vertical finality, for vertical and  horizontal finalities  are  not alternatives, but  the vertical emerges all the more strongly as the horizontal is realized  the more fully. (46)

Notice here that there is a kind of dynamic element implied in the horizontal.  Again, if we grasp that horizontal finality is a potency for dynamic realization of being (development), and it is distinct from mere flexible ranges of operations that are already in place, then such development is from an initial potency, and it is the dynamism in that potency that gives rise to it.  And this dynamism can be more fully or less fully realized.  If one turns to Lonergan’s arithmetic illustration in Insight, one can see this point right away.  Arithmetic provides the “image” for algebra.  The more arithmetic one does, the more one will apprehend general intelligible patterns in arithmetic. These patterns are algebraic. Adding A to B results in the same answer as adding B to A.  This results in the rule that states A + B = B + A, an algebraic rule.  And this is just one rule. If one has engaged in a number of operations over and over again not only with addition, but with subtraction, multiplication, division, powers, and roots, then one will begin to grasp all kinds of other patterns.  One will see that multiplying A to B results in the same answer as B to A.  In contrast, one will notice that one cannot do the same for subtraction or division (A-B does not equal B-A, nor does A divide by B equal B divided by A — unless A and B are the same).  Algebra emerges all the more strongly as arithmetic is realized the more fully.  The same is true in chemistry and biology.  The more that one carries out rightly designed experiments on matter, the more fully insights arise into patterns of elements and compounds.  And the more these are unfolded within living organisms, the more one understands higher order organic properties.  Through DNA and biochemical processes, one grasps more fully the organic operations of the cell. And as one unpacks these cellular operations within multicellular organisms, the more one grasps the operations of those multicellular organisms (eg. respiration, immunity, digestion, etc.). These cognitive expansions horizontally and vertically have ontological parallels within all developmental entities.

It is important to note that the vertical cannot emerge and be sustained without the proper operations of the horizontal.  If you eliminate the realization of the finality of stem cells which maintain and perfect cellular systems, then the systems will cease to function (respiration, immunity, etc).  And if these organic events and schemes cease, then sensitive operations and schemes will cease, along with the potential for deductive and homogeneous expansions of sensitive operations.  And if sensitive operations and their development fail, then there will be no insight into images, or judgment based on insights and evidence, or decisions based on judgments of fact and value, or the development of viewpoints.  The lower has to flourish for every higher order to flourish that is dependent upon the lower.

In terms of finality, this means that the more vibrantly that the horizontal finality is realized, the more fully the vertical can be realized.   Both the horizontal and vertical are rooted in potency, and the fact that the same potency is for both, and that the realization of higher is dependent on the lower, means that the two finalities are always necessarily dependent upon each other.  The ability to see is rooted in the neural networks that are tied to sight.  This potency to see is realized horizontally when the eyes are opened, the optical neurons are activated by light waves, and the associate and sensory cortices are integrating the neural activities initiated by the light waves.  It is realized vertically when these lower activities arise into a conscious sensory percept.  A similar relationship accrues to the development of sensory operations in relationship to the development of neural patterns, and these developments are actualizations of the finality, or potentiality, of each of these levels.

And interestingly, the higher can come to assist in the greater realization of the lower.  Problems, needs, and wants that arise with regard to higher level operations require a type of expansion–sometimes a shift, and even potentially a conversion–of the lower orders such that these can then bear fruit for the higher.  Lonergan in his later life sometimes called this the top down element, or the gift element, that allowed for the flourishing the lower.  This does not mean that the higher is free or independent of the lower.  Rather the fulfillment or realization of the higher still depends upon the lower, even if the higher is self-assembling, and acts as a mediator of the perfection of that lower. So to continue the illustration of an animal, associations of the percepts can take place through a kind of willful use of the sensory organs (cortices, etc.).  An animal can “pay attention” to this or that, it can shift its body or head to see or hear or taste or touch or smell something.  This higher order guidance and activation of the lower level neural manifolds allows for the further unfolding of those lower manifolds so that they can contribute to the construction of associative memories, imaginative constructs, and even feelings.

This point about the dependence of the vertical upon the horizontal–the dependence of the dynamic unfolding of the higher upon the lower–is expressed in a mulitude of ways in Lonergan’s later writings. In Insight, examine chapter 8 on things, or chapter 15 on explanatory genera and species.  In Method in Theology, see his formulation of the levels of consciousness and the levels of the functional specialities.  In 1943, the fecundity that is actualized through a union of two semi-fecundities has a horizontal relationship to adult offspring.  The more fully this fecundity is realized at the horizontal level, the more fully it provides for a realization at the higher vertical levels and ends (good life and eternal life).  One could differentiate these ends and levels in light of Lonergan’s later writings both within the parents (the four/five levels of consciousness) and the levels of the child.  One could as well, place these within the unfolding of all levels of being from quarks to the actuation of the capacity for self-transcendence in a state of being in love with God.

I intend on saying more about these higher levels in later blogs. At this point, I wanted to just comment on a basic metaphysical principle regarding the relationship of the lower to a higher level of being, whether that being is conscious or not.  If one eliminates the finality at a lower level, one destroys the possibility of the emergence of the higher.  And the more that the lower flowers, the more that the higher can flourish.

Grasping this finality within marriage sets up a heuristic that allows one to explore marriage in a differentiated and integrated way.  The differentiation is over the different generic levels of reality as sublated within human historical process.  As integrated, these provide the mode of inquiry into the relations of higher and lower orders of intelligibility as well as the potency for new types of operations and new levels of conscious life.   In this 1943 essay, Lonergan  introduced this heuristic first so that he could then suggest specific ways to explore the meaning of marriage.

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Book Review: Michael Behe’s Darwin’s Black Box

by David Fleischacker

I have been enjoying Michael Behe’s book Darwin’s Black Box (first published in 1996, with an update in 2006).  It brings out a significant challenge in thinking through evolution and so it is worth reading. However, I do not agree with his ultimate conclusion or even his explicit criterion for validating his argument.  The central point of his argument is that once one turns to the molecular and biochemical understanding of organisms, one finds systems with an irreducible complexity that could not result from the gradual steps of evolutionary development. In addition to his presentations of specific biochemical systems that are irreducibly complex, Behe supports his position with the lack of any serious biological arguments that explain such gradual steps that construct these complex biochemical systems.

The merit of his book is that it does raise the validity of evolutionary theory in light of the developments taking place within biology due to studies in biochemistry.  Behe does recognize the provisionality of his argument at times though at other times he presents his conclusions with complete certitude. As well, he recognizes that his insights regard only some biochemical systems, and not all. He does acknowledge that some systems at the molecular level can be explained by evolution so he does not consider his focus to be a comprehensive theory of organic life, but rather a focused inquiry that has ramifications for both intelligent design and for the explanatory scope of evolutionary theory (which he thinks is more limited than the field of biology recognizes)

At the same time, I would argue that the argument suffers a bit. Behe argues that a number of complex biochemical schemes are irreducibly complex.  Irreducibly complex means that key parts of a system contribute to the whole system and that removing any of the parts results in the loss of the function of the system as a whole. This functional whole seems to refer to two possibilities. In one case it is like a scheme of recurrence in which the main focus is upon one of the events in the scheme that is crucial for organic function, such as is the case of ATP in Kreb’s cycle within mitochondria.  ATP is one of the molecules constructed in the scheme of recurrence that we call Kreb’s cycle, and because it is a central energy molecule, it is crucial for many processes in the cell, and thus is sometimes referred to as the functional reason for the whole of the cycle.  Another meaning to functional whole however is what Lonergan would call the higher conjugate form that is built upon a lower matrix of conjugate forms (see explanatory genus and species in Insight – chapters 8 and 15).  So, something like an immune response is a conjugate form that exists within an aggregate of genetic/biochemical events.  In both cases take away one of the “parts” — which could be an event within a scheme or an event within an aggregate that constitutes a lower level matrix for a higher conjugate form–and the “functional whole” is lost.

Irreducible complexity alone is not an argument against evolution.  Part of the suffering is that it lacks an adequate account of the heuristic structures operative in biology and the isomorphic metaphysics that is implicit in those structures.  Key that is missing is the shift from descriptive definitions to implicit definitions, and then how this shift moves into an explanatory horizon that then begins to move into an explanatory account of development, whether of single organisms or organisms within ecological relationships.

Why is the shift from description to explanation such a key piece that is missing in his arguments? Because evolutionary theory was initiated from a series of descriptive traits that had been observed by Darwin and Wallace (and earlier folks who developed different explanations).  Descriptive knowledge identifies characteristics and activities of things through conjugates that are derived from the senses.  So, the blue bird has certain colors and shapes that are used to describe its bodily features, colors and shapes that derive their meaning from a relationship between the bird and our senses.  Our senses are attuned to a rather large range of objects in our spatial-temporal world.  We can see shifts in light patterns with our eyes (and of course the associative cortices and the sensory cortex involved in constructing the input that comes through the eyes), which we can articulate as colors or shapes or sizes.  We can hear shifts in auditory sound waves with our ears. We can smell patterns and changes of the chemicals that are found within our atmosphere through our noses and the chemical make-up of solids, liquids, and even gases that touch the sensory neurons of our taste buds.  Through touch we can feel textures and contours and temperatures.  All material objects that have a certain mass size can be detected by our senses.  Many physical objects in our world fall within our sensory capabilities.   So, when we talk about descriptive knowledge, one of the elements that Lonergan recovers against modernity is the degradation of such knowledge.  It is not imaginary.  It has a validity to it and a crucial place in our lives.

Behe does seem to suffer a bit from this modern mistake.  Descriptive knowledge is not false or misleading.  It is incomplete of course, but it is true as far as it goes.  This happened in physics. Copernicus argued that the sun no longer goes around the earth. But, now one can admit that because of relativity Copernicus was not right, at least entirely.  The sun does rise and set when one sets the frame of reference (the X, Y, and Z of a three dimensional manifold — and one must also include t as a fourth dimension) as one’s own sensory framework, or even the earth.  It is not that Copernicus was entirely wrong. One can set the sun as the center of that frame of reference.  Or one can set the center of the Milky Way galaxy (presumably a black hole).  Behe seems to want to say that in this more primitive descriptive world, one might come up with the idea of evolution, however, when you move to the “black box” of molecular and biochemical explanation, then one moves to reality and away from myth.  I say “seem” simply because of his phrase “black box” though he does not explicitly say that the data of Darwin was unreal.  One correction here is to suggest that discoveries made through descriptive knowledge do have their relevance when put within the right frame of reference. Behe does not adequately deal with the kind of descriptive knowledge that is involved in validating evolution (or the modern synthesis that integrated Mendel and Darwin, since it falls within the realm of explanation constituted by explanatory rather than implicit definitions — see chapter 1 of Insight).

Furthermore, scientific description is not merely another frame of reference based on the relations of things to us, but it is the way that science both collects its data and verifies its theories.  Concrete inferences of laws–whether classical or statistical or developmental–all require implementing and verifying those laws through descriptively articulated data. Ultimately, scientific description and scientific explanation are complementary to each other.  What is discovered and proposed in one cannot ultimately conflict with the other if they are both true (or converging provisionally upon what is true).

With regard to biology, I would argue that many do not adequately understand the stage of development in which it currently resides.  This is largely due to the complexity of the field.  Organisms as Lonergan outlines in Insight, chapter 15, require that one shift into a grasp of operators and development.  And these only arise after one has introduced correlations and statistics.  Furthermore, there are preliminary stages within the descriptive world.  There are descriptive conjugates that are preparatory for explanatory conjugates.  Describing what happens when liquids are mixed or when objects are projected or when the planets move in their orbits prepares the way for the world of correlations. Describing whether something happens for the most part, or infrequently, or all the time prepares the way for ideal frequencies whether these are based on descriptive, explanatory, or implicitly defined conjugates.  And with regard to development, one gets a sense that things grow and change in their descriptive conjugates before one discovers the operators that transform one system of conjugates into another.

At this stage in the development of biology, at least over the last century, I would say it largely resided within the world of explanatory definitions.  In an explanatory definition, one of the terms is descriptive, the other is explanatory.   One good example of this is Mendel. Notice that his theory of genetics incorporated one descriptive term, and one explanatory term.  Phenotype is descriptive. Genotype is explanatory (he use the term hereditary unit).  However, later in the century, genetics moved to implicit definition through Watson and Crick, who related genes to proteins (three nucleotide sequences are paired to an amino acid — the building blocks of proteins). Since their introduction of this implicit definition, there has been a vast expansion taking place.

Evolutionary theory when it was first introduced was like the explanatory definition.  All of the traits mentioned by Darwin are descriptively understood.   As such, they had not reached the level of explanatory definitions, let alone the level of implicit definitions. So what makes it like explanatory? Well, he identified a number of descriptive conjugates that seemed to be related across species through some kind of parental origin.  Notice, this springs from a recognition that organisms do come from other organisms (progeny come from parents), and that progeny are never exactly the same as the parental organism (s).  It is important to note that there is not a clear sense that evolution results or can result in development. Rather, it is the emergence of an adaptive, and advantageous, change.

In the early 20th century, Evolution moved into another explanatory level with the modern synthesis. Once Mendel was discovered, Evolutionary theorists went to work to integrate Mendel’s breakthroughs.  That synthesis was largely generic and heuristic because now biological explanation had to incorporate genetics.  This synthesis took another leap once one introduces molecular and biochemical analysis into the science. I would argue that this latest synthesis shifted the images in which biology operates, and this shift has allowed for recognizing new patterns that constitute organic life, and these patterns are defined implicitly.  Watson and Crick provide only one example.

What Behe catches upon is that the theories that had largely been developed from descriptive understandings of traits seem rather shaky in light of the shifts to molecular/biochemical accounts of the organism. He is right in a certain manner. The complexity of biochemical pathways involved in a number of organic activities are mind boggling.  It is hard to fathom how these could have developed. Behe argues that these are impossible to account for in some kind of evolutionary development.

Where I think he has been mistaken is thinking that one should be able to develop an evolutionary theory of a biochemical process at this stage in the history of the field of biology.  In the transition from explanatory to implicit definitions, it is natural that one first has to development a viewpoint that is constituted by implicit definitions which is adequate before one could then begin grasping the operators that unfold a deductive or homogeneous expansion, or a vertical expansion.

Another element that is missing from Behe, and nearly all other biologists or chemists, is the shift from lower levels of organic life to higher genera of sensate and rational life. This shift is far more difficult than from simple to complex organic processes (a horizontal shift). These are shifts from a lower to a higher level genus. These vertical developments add a new meaning to the complexity of evolutionary development.  If Behe understood Lonegan’s articulation of higher and lower genus and species, he could strengthen his argument more. But then he might also have the breakthrough into generalized emergent probability as well, which would, at minimum, severely modify his view of biochemistry and the basis of his entire argument. I say at minimum because the argument of evolution is still an argument based on evidence, hence one of fact, even if it never rises beyond a provisional analytical principle.

So, what would the shift to biochemical images and implicitly defined organic conjugates do to the validity of evolution?  I think it does weaken it a bit in terms of the degree of certainty that many hold evolution today.  Largely, it still is at the stage of an explanatory definition.  Its terms and its evidence are descriptive conjugates.  We are a long way from reaching the periodic table of organic life.  The traditional set of organic charts (kingdom, phylum, class, order, family, genus, species) are based on descriptive traits, though these are being modified daily as a result of biochemistry, molecular biology, cellular biology, and genetics into “evolutionary trees.”  We are even further from developing an adequate set of developmental operators of individuals, species, and genii. In reality, biologists really do not have an explanatory or an implicit definition of species (notice that saying something is reproductively compatible is not saying “what” it is, hence they have not articulated the key explanatory conjugates the form a species within the genera of organic/vegetative/cellular life).

However, just because the development of the discipline of biology is not yet beyond the explanatory definitions in the field of evolution (it has begun to move to implicit definitions in genetics and some other conjugates of biology), does not mean that the explanatory definitions are wrong.  They are based on evidence.   And hence, just because there seems to be some irreducible difficulties when one begins to examine biochemistry and molecular biology, that alone is not sufficient to reject evolution as a theory.  One still has to explain heredity, the differences of progeny from parents, and the ramifications of these differences over time. Evolution is one way to do that.

As Pat Byrne in his essay on “Lonergan, Evolutionary Science, and Intelligent Design,” argues, one of the things that Behe is missing is a grasp of emergent probability [Patrick Byrne, Revista Portuguesa de Filosofia T. 63, Fasc. 4, Os Domínios da Inteligência: Bernard Lonergan e a Filosofia. / The Realms of Insight: Bernard Lonergan and Philosophy (Oct. – Dec., 2007), pp. 893-918]. Emergent Probability, as Byrne notes is ultimately derived from Lonergan’s cognitional theory, not from empirical theories in the sciences and hence it is relatively independent from the development of specific scientific theories. Relatively independent because it is developed from the actual methodological operations involved in the sciences.  Cognitively and metaphysically, the classical and statistical heuristic structures point to the potential of a dynamically oriented developmental universe.  Still, as Lonergan notes, one has to argue what in fact the universe is about.  It does not need to be developmental or evolutionary.  Darwin’s theory has gained much weight through evidence that supports a matrix of descriptive conjugates that relate parents to progeny through generations in an environment where adaptation is possible and probable.  Molecular biology, genetics, biochemistry, and cellular biology are moving biology into the realm of a fully explanatory discipline that is built upon provisionally verified implicit definitions.  This shift is and will continue to bring with it challenges to the old explanatory definitions that had emerged in the field, including that of Darwin and those who advanced his theory in the modern synthesis (note that this synthesis relied on Mendel, not Watson and Crick).  A yet even newer synthesis is arising and Behe’s book highlights the challenges to evolution of this shift even if, in the end, Behe turns out to be wrong and that evolution will rise even stronger once the new explanatory biology matures. But then again, he could be right. Maybe evolution is not right.  I tend to think the evidence supporting the explanatory definitions of evolution theory have a significant weight that is left untouched by Behe’s arguments, and thus provide a valid way of proceeding in biology as it unfolds its new image (symbolic constructs from biochemistry) that is underlying its shift to implicit definitions. I suspect evolution will rise more nuanced in the end, and more like emergent probability, and hence stronger in the end. There many reasons for this beyond biology as well. There is evidence for emergent probability, quite a bit.  There are analogous types of developments in almost all other realms of being (human history, social development, dogmatic development, etc.)

As a note, I have not addressed Behe’s views on intelligent design. That is another discussion and has some serious defects I would argue.  I just wanted to discuss his views of evolution at this point.