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.