By David Fleischacker
In part two of this series, I mentioned that the “repetitive” element of the physical, vital, and sensitive spontaneity is differentiated into schemes of recurrence based on classical laws and statistical probabilities, and then schemes of development with one stage being not only an integrator but also an operator, hence possessing a finality, for later stages.
Concrete plurality and statistics
One element that does seem to stay the same between 1943 and 1957, though is explored more fully in Insight, is the relationship between the concrete plurality and its statistical possibilities that constitutes the potentiality that is horizontal and vertical finality.
As to the difficulty that frequently procreation is objectively impossible and may be known to be so, distinguish motives and ends; as to motives, the difficulty is solved only by multiple motive and ends; as to ends, there is no difficulty, for the ordination of intercourse to conception is not a natural law, like ‘fire burns,’ but a statistic laws which suffices for an objective ordination.
It is important to note that even though the relationship of the conjugal act to conception is statistical, it has an objective ordination to the end of adult offspring. If one backs up in the article a bit, this statistical element is linked to a concrete plurality.
This we term vertical finality. It has four manifestations: instrumental, dispositive, material, obediential. First, a concrete plurality of lower activities may be instrumental to a higher end in another subject: the many movements of the chisel give the beauty of the statue. Second, a concrete plurality of lower activities may be dispositive to a higher end in the same subject: the many sensitive experiences of research lead to the act of understanding that is scientific discovery. Third, a concrete plurality of lower entities may be the material cause from which a higher form is educed or into which a subsistent form is infused: examples are familiar. Fourth, a concrete plurality of rational beings have the obediential potency to receive the communication of God himself.
Notice the use of “concrete plurality.” From my reading, it has the same meaning as coincidental manifold in Insight. When a coincidental aggregate is understood in its finality, both horizontal and vertical, then that aggregate is a coincidental manifold. In each case, an aggregate of activities or materials have the potency to be formed into some higher order. In the types mentioned in the quote above, the second, third, and fourth are of particular interest in this essay. The parental contributions to the generation of an adult offspring provide a material that causes the vegetative and even motor-sensory levels in their child. But the motor-sensory level provides but a dispositive cause for the emergence and activation of intellectual, rational, and moral consciousness. This is because intellectual, rational, and moral consciousness is “headed toward the systematization, not of the particular animal that I am, but of the whole universe of being.” These higher levels of consciousness cannot be caused by the lower sensitive manifold because these are intrinsically independent of the empirical residue. In other words, these are spiritual and thus the lower sensitive level is incapable of being a “material cause.” But the sensitive level is still a manifold, and needs to be for the higher levels of consciousness to operate (insight is into phantasm, for example, and cannot take place without phantasm). In other words, the higher orders of spiritual consciousness are extrinsically dependent upon the empirical residue, and thus the lower has a dispositive causal relationship to the higher.  Then, finally, in the reception of divine revelation, a concrete plurality of human beings as a community form the recipient of that gift, hence the relationship of that concretely plurality to the gift is a vertical finality of obediential potency.
Conjoined plurality and emergence
In every case, the concrete plurality must form a set of conditions for the emergence of a conditioned, whether on the same horizontal order or of a higher vertical order. So, there is a need for some kind of unification of the concrete plurality in order for the conditioned to emerge. A bit later in the essay, Lonergan will call this unity a conjoined plurality.
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.
This quote was discussed in the last blog with regard to “statistical law.” But now I want to draw attention to the conjoined plurality. Notice how the isolated instance is not the point of potentiality for vertical finality, but rather it is the conjoined plurality that forms that locus. This is ABSULUTELY key. There needs to be a coming together of the right conditions for vertical finality to become a real potentiality. These conditions and their convergence each have a frequency, and thus as well, an ideal frequency rooted in the ranges of possibilities. As organisms become more complex, this range increases just as there is an increasing flexible circle of ranges of schemes of recurrence, and one might add, of development. 
The conjoined plurality arises in a statistical manner, with actual frequencies converging on an ideal. And it is true whether one speaks of instrumental, dispositive, material, or obediential potency. All involve frequencies of conditions and the conditioned. If one does not have the right distribution of molecules within a tree, then carving it into a canoe will result in failure. There has to be an ideal distribution of the molecules that allow for what descriptively we would call a “straight tree with its grains running evenly. Or there has to be the right distribution of molecules in a bio-soup if there is to be the likelihood of the emergence of a self-replicating molecule. Or sensitive images need to be in the right disposition if there is to emerge an insight. Or the individual receptive of divine revelation need to have the right disposition and sets of relationships to receive a public, communal divine revelation.
The statistics is a necessary element in finality. In Insight, Lonergan works this out metaphysically.
Finally, the foregoing account of potency, form, and act will cover any possible scientific explanation. For a scientific explanation is a theory verified in instances; as verified, it refers to act; as theory, it refers to form; as in instances, it refers to potency. Again, as a theory of the classical type, it refers to forms as forms; as a theory of the statistical type, it refers to forms as setting ideal frequencies from which acts do not diverge systematically; as a theory of the genetic type, it refers to the conditions of the emergence of form from potency.
Notice here that he is saying in an extremely succinct manner how correlations that define conjugate forms, along with statistical ideals frequencies and finality (as well as development) are linked in terms of the basic metaphysical elements (potency, form, and act). This could be further unpacked into his theory of generalized emergent probability. Concrete plurality is naming a situation in which frequencies that converge on an ideal frequency provide the potentiality for the emergence of forms from potencies, hence new acts, with their frequencies. This is all articulated in general metaphysical terms and relations which reveals with precision a close unity between statistics and finality. That close relationship, as the quotes above indicate, already existed in Finality, Love, and Marriage, and Insight. Obviously, Insight has unpacked and expanded upon all the elements involved in this relationship, but fundamentally, the link seems the same. A statistically distributed plurality provides a probability for emergence, and the potency of this plurality for emergence is finality.
Fecundity, statistics, and finality
Now let us turn to fecundity and its realization.
….the actuation of sex involves the organistic union of a concrete plurality, and as such it has a vertical finality.
Fecundity that is differentiated into two sexual genders is actuated through the “organistic union” of these genders. In other words, it is in this union that vertical finality of fecundity emerges. In a later blog, I will discuss the range of this vertical finality, because it includes both an intrinsic self-transcendence within the subjects who are sublating this finality into higher levels and ends of the human subject (notice how easy this will be to translate into the higher orders of conscious intentionality), as well as a vertical finality within their “adult offspring.” At the moment however, I want to highlight that the statistical features of this organistic union require that these be a union of two semi-fecundities. It is the actualization of fecundity that is under consideration, and for that to take place within a plurality of semi-fecundities means that a unification has to take place for the actualization to be initiated.
In short, the fact of a statistical, conjoined plurality or coincidental manifold is neither an elimination of the finality to an adult offspring nor to the finality to higher orders within the man and the woman and the child, but rather, it is the central locus of that finality. It is the potentiality that is that finality. It is that conjoined plurality (the conjugal act itself) that is integrated into the higher levels and ends of marriage. Understanding this locus that is elevated is what would lead one to say as Lonergan did in Finality, Love, and Marriage that the “statistical law” that is found in the relationship of the conjoined plurality to concenption
…suffices for an objective ordination.
 Finality, Love, Marriage, 46 footnote 73.
 Finality, Love, Marriage, 20.
 Insight, 515.
 Insight, 516.
 Finality, Love, Marriage, 22.
 Insight, 459.
 This is just one theory of the emergence of life, life being anything that can “reproduce” itself.
 Insight, 432 – 433.
 Finality, Love, Marriage, 43.
 There are other ways of course, given modern technologies, to actuate the adult offspring, but these usually involve by-passing and hence failing to actuate one or the other, or both of the semi-fecundities as such. More on that later – once I finish exploring the meaning of this essay, I will then turn to some of its ramification in lights of current questions and debates. And of course, there are ways to eliminate the finality to an adult offspring by through hindering the actuation of one or the other or both of the semi-fecundities. Both by-passing and hindering involve a loss of the conjoined plurality within the man and the woman as subjects.
 Lonergan links potency and finality in Insight, 444-451.
 Finality, Love, Marriage, 46 foot 73.