By David Fleischacker

Dedicated to Br. Dunstan Robidoux, OSB on his birthday

Lonergan does discuss statistics within this 1943 essay, however, it is clear that he has not developed the notion of statistics to the level one finds in Insight 14 years later.  But it is not as far as one might think. Yet, one wonders if this will undo much of what he says in this essay regarding the role of finality within marriage. The next few blogs will answer that query explanatorily. But, the short answer is that it does not. I would argue that his expansion of the notion of statistics in Insight reinforces his notion of finality, and hence a key piece of the argument based upon that notion in this 1943 essay.  For this blog, we will focus just on the six times that Lonergan uses the term statistics in Finality, Love, and Marriage, and in the next blog discuss its relationship to finality.

Use 1: Statistical Law

Lonergan’s first use of the term “statistics” (actually “statistical”) takes place within his development of vertical finality.

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.[1]

Notice the notion of “conjoined plurality” which reminds one both of coincidental manifolds or coincidental aggregates and its role in statistics in Insight, as well as the non-systematic convergence of conditions upon a conditioned.[2] Both the non-systematic convergence, and the coincidental aggregates are grounds for statistical probabilities. Both are based on acts of forms of potencies.  Every act can be examined in terms of its frequencies.  One could specify the frequency of some act within a particular spatial-temporal time frame, such as death rates within a particular region over a year. This is the absolute type of frequency.  There is as well a relative type which is discovered in terms of the alternative sets of conditioneds that can arise within a set of conditions.  In other words, the relative type of statistical probabilities are those based upon the possibilities of things and the realization of their conjugate forms in relation to the actualization of other things and the realization of their conjugates within a set of conditions.  This is how conjugates set boundary conditions for statistical probabilities.[4] In the absolute type of statistic, it is not the relative rates of alternative conjugates, but the rate of a conjugate within a particular spatial-temporal frame of reference. The relative rates are based upon possibilities that arise from converging conditions.  A simple illustration of the absolute rates are the standard birth rates which include boundaries set within space and time, and thus are not merely boundaries set by classical laws or systematic processes. Birth rates include the empirical residue (spatial-temporal given-ness) as part of what they mean.  In contrast, getting the genes for green or brown eyes (hence the proteins that give color to the eyes) is based upon the conjugates themselves (the alleles) and thus is based on the possibilities of conjugate forms (alleles) as setting the boundary conditions.

Use 2: Statistical Law

The second is found in a footnote to the first.

There is a noteworthy affinity between modern statistical law and the contingens ut in maiori parte, between modern ‘chance variation’ and the contingens ut in minori parte.[5]

This, I think, is getting at some of our common sense descriptive terms that refer to statistical frequencies. When we say it happens all the time, or it rarely happens, or it happens for the most part, or it happens once in a while… we are using statistically based descriptive terms. Descriptive because we do not have an insight into actual probabilities.   Lonergan is simply noting how the notion of “statistics” has its history within the tradition and was not entirely absent until it became popular in gambling and genetics.

Use 3: Statistical Infallibility

In the third use of statistics in the article, it falls within the hierarchies of the three ends of human existence which sets up the context for the three ends of marriage.  The three ends divide into three levels, and the first level is focused on “nature”—which he limits to “physical, vital, sensitive spontaneity” (a restricted sense of the term as Lonergan notes)—it is repetitive, spontaneous in its formation of community, and efficient in how it operates. At first glance, there does not seem to be any role of statistics, yet in his discussion on “efficiency” he mentions how it operates with “statistical infallibility.”

While nature with the ease of a superautomaton pursues with statistical infallibility and regularly attains through organistic harmonies its repetitive ends, the reason and rational appetite of fallen man limp in the disequilibrium of high aspiration and poor performance to make the progress of reason a dialectic of decline as well as of advance, and the rational community of men a divided unity of hatred and war as well as the indivisible unity of fraternity and peace.[6]

One can think of the simple example of a coin toss.[7]  As long as both sides of the coin have a negligible difference in mass distribution, then the fact of two sides sets the boundary conditions for the probability around which multiple random tosses will oscillate.  One can then specify the “likelihood” of getting heads or tails on any random toss.  The point is this that the more the tosses, the more it approaches the probability or ideal frequency. That increasing movement to the ideal frequency is likely the “statistical infallibility” that Lonergan has in mind when he uses this term.  And when organisms operate, they use this type of ideal frequency to live.  There are ideal frequencies of water supplies, food supplies, zones of protection, and many other needs of the organism for survival which are provided around a statistical probability upon which the organism depends for its existence. In evolutionary terms, one might say that a sequence of organisms adapted themselves to these ideal frequencies.  With the introduction of molecular biology, which really grew rapidly after Lonergan wrote this essay, one comes to a deeper sense of the role of ideal frequencies within the molecular and biochemical pathways of the organism. Everything makes use of these probabilities.  Most of us, for example, have heard of the Krebs cycle.  The cycle is not a physical machine, but it is a kind of chemical one, which operates not only using specific types of atoms and molecules within a controlled environment (mitochondria), but the statistical frequency of these molecules occurs in such a manner as to set the rates of ATP production.  ATP (adenosine tri-phosphate) is the energy molecule of every cell.   This production has to occur at certain rates which increase or decrease with the needs of the cell and cellular activities (it increases for example if we get up from sitting and go for a walk).  The point is this that if you have high enough frequencies of events (such as coin tosses) you will make the ideal rate that you want.  In an everyday way you can call that a kind of infallibility. The fewer the events, the further you might diverge from the ideal. Unlike the Krebs cycle, water and food supplies for most organisms are not always numerous events in a given spatial-temporal frame of reference, and hence there can be periods of draught or starvation. But over the long run, there is an ideal around which actual frequencies of such supplies oscillate unless the “boundary conditions” change – such as when an oasis becomes a desert.

So, in the points that Lonergan makes about nature – hence about physical, vital, and sensitive spontaneity, along with the actuation of the spontaneity, which has an end in the emergence and maintenance of life, one does find some hints of the statistical element.  It is repetitive and this includes a kind of statistical infallibility that makes it so.  This means that the link of the physical, vital, and sensitive spontaneity and its horizontal finality to its ends involves a statistical element.

Since fecundity is a particular feature of physical, vital, and sensitive spontaneity, one can assume that it too has a statistical infallibility, at least when one examines the entire human race as a whole.  There will be repetitive conceptions and births, and adult offspring because of this statistical probability.

Use 4: Statistical spontaneity

The fourth quote is found on the same page, and makes a similar point though he is using it to complete his contrast of the three ends of the human person.

It is not the statistical spontaneity of nature, nor the incoherent liberty of man, but the gratuitous action of God.[8]

Here the contrast is how the end that is natural has a statistical element to it that is not deliberate and rational nor is it the same as the operations of God.  This does not add anything significant to our discussion about statistics.

Use 5: Statistical laws and probabilities

In the fifth use, he is discussing the concrete plurality of a man and a woman who come together in union, and how this united concrete plurality is the point at which vertical finality resides that is then integrated into the higher levels and ends of the human person (I will treat of this in a latter blog).  He then goes on to illustrate this vertical finality within the non-human worlds of life – vegetative and sensate life.

Further, the actuation of sex involves the organistic union of a concrete plurality, and as such it has a vertical finality. Such an upward drive follows from our general theory. In the vegetal and animal kingdoms it has its verification in the measure of truth that may be attributed to theories of evolution in terms of statistical laws and probabilities regarding combinations of genes through random mating.[9]

The key here is that he is formulating a connection between statistical laws and probabilities with the emergence of new species and even new genii.  The concrete plurality refers to the plurality of genetic alleles and combinations.  In Insight, when Lonergan is linking the lower manifolds to vertical relationships, he calls the manifold a coincidental manifold. These operate in a statistical manner with regard to inheritance.  And in turn, this provides a finality.  He was obviously aware of what became known as the Modern synthesis in evolutionary theory, which linked Darwin and Mendel in the late 1930 and early 40s.

Use 6: Statistical Laws

The last quote actually raises some questions.  It focused upon the level of nature, but moves from the statistical relationship of nature to its end in the emergence and maintenance of life, and specifies this to the level of fecundity, organistic union, and adult offspring. It is found in a footnote.

… 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, because the ordination of inter­ course to conception is not a natural law, like ‘fire burns,’ but a statistical law which suffices for an objective ordination.[10]

What is the question that this raises?  Lonergan refers to natural law, and links fire and burning.  This account of fire and burning is a descriptive account, and he calls it a law.  But explanatorily, fire burning involves both conjugate forms and statistical realizations of those forms (in terms of chemical and physical changes), so that in the explanatory context, there is a statistical element to fire burning. Likewise, regarding the relationship between the conjugal act and conception, the relationship involves a set of correlations as well as statistical frequencies of those correlations. So, metaphysically, there is no different between the fire burning and conception.  Both involve conjugate forms with a certain frequency of actualization that diverges non-systematically from an ideal frequency.  I would argue that there is a bit of development at this point in Lonergan’s thought from the point of view of this essay to his writing of Insight. In Insight, I would argue that he linked together natural law and statistics more thoroughly, and instead of natural law as descriptively formulated, he differentiated classical laws and statistics. In chapter 10 of Insight, the “self-affirmation of the knower,” Lonergan reveals this development.

Cognitional process does not lie outside the realm of natural law. Not merely do I possess the power to elicit certain types of acts when certain conditions are fulfilled, but, also with statistical regularity, the conditions are fulfilled and the acts occur.[11]

Still, is there a truth in what he is saying?  Sure.  In this case, he seems to say that something that is natural has a relationship to its end that has a kind of determinate certainty to it that other types of events do not have. He might very well have in mind “statistical infallibility” with regard to “fire burns.” It is a bit like asking “What is the probability that the sun rises each day?”  Not everything however does have that kind of regularity, and when you limit the spatial-temporal boundary conditions sufficiently on certain types of events, then the regularity is not so regular.  This is what happens when one moves from a large population to individuals on just about any type of event, including the realization of the end of fecundity. So when one looks at a single couple, and asks about the probability of their being able to realize their fecundity, then one no longer speaks of statistical infallibility.   But this is not surprising.  When one looks at the thousands of conditions needed for fecundity to take place, and that each of those conditions requires a certain ideal frequency, then the regularity that one might call “statistical infallibility” belongs not to the individual, but to the species.

This particular sixth quote however reveals something crucial in Lonergan’s entire argument in the essay, namely the link of statistics and finality.  In the next blog, due to arrive on June 11th, I will explore the relationship of statistics to finality within Finality, Love, and Marriage.

[1] Finality, Love, Marriage, 22.

[2] In Insight, the phrase “coincidental manifold” gains significance as Lonergan develops his notion of a thing, and the higher and lower orders of conjugates, in which the lower provide a coincidental manifold that can be systematized by the higher (262-263). He develops it more precisely in chapter 15, “Elements of Metaphysics,” where he develops explanatory genera and species (437), finality (444), development (451-452).  Coincidental aggregates is used earlier in relationship to statistics as is the notion of the non-systematic.

[4] Insight, 103.

[5] Finality, Love, Marriage, 22 footnote 16.

[6] Ibid., 39.

[7] The understanding of a coin toss and its final outcome largely is descriptive for most people, but fortunately the descriptive and explanatory accounts of both a coin toss and its final resting place in being either heads up or down result in a similar result. In other words, the descriptive conjugates and explanatory conjugates for this sequence of events results in the same set of events.  Sometimes descriptive accounts are significantly differentiated by explanatory accounts, and hence the “statistical” accounts end up being different. This is true of human height for example, which is caused by a multiplicity of explanatory conjugates—many genes and environmental factors.

[8] Finality, Love, Marriage, 39.

[9] Finality, Love, Marriage, 43.

[10] Finality, Love, Marriage, 46, footnote 73.

[11] Insight, 330.