I come to praise the dead, or perhaps, to recognize their importance at the least. Actually a little of both. Last week the intellectual world lost two more giants. Perhaps I am getting old, but this seems to be happening with greater frequency. Michael Novak and Kenneth Arrow both died. Novak (1933-2017) and Arrow (1921-2017) were quite different in their outlooks and professions, though they shared some common interests (not however through mutual acquaintance).

Novak was a widely respected Roman Catholic public intellectual who experienced a not uncommon movement of the mind and affections from socialism to “democratic capitalism.” Though not an economist or political scientist, but rather a theologian, he came to write and think extensively on those subjects, often in tandem. Here is a list of some of his wide-ranging work:

*Social Justice Isn’t What You Think It Is*(2015)*Writing from Left to Right: My Journey From Liberal to Conservative*(2013)*The Myth of Romantic Love and Other Essays*(with Elizabeth Shaw) (2012)*Living the Call: An Introduction to the Lay Vocation*(with William E. Simon) (2011)*All Nature is a Sacramental Fire: Moments of Beauty, Sorrow, and Joy*(2011)*No One Sees God: The Dark Night of Atheists and Believers*(2008)*Washington’s God: Religion, Liberty, and the Father of Our Country*(with Jana Novak), 2006*Universal Hunger for Liberty: Why the Clash of Civilizations is Not Inevitable*(2004)*On Two Wings: Humble Faith and Common Sense at the American Founding*(2001)*Business as a Calling*(1996)*The Catholic Ethic and the Spirit of Capitalism*(1993).*Free Persons and the Common Good*(1988)*Tell Me Why*(1998)*The Open Church*(1964, 2002)*Joy of Sports*(1976, 1994)*Catholic Social Thought and Liberal Institutions*(1984, 1989)*This Hemisphere of Liberty*(1990, 1992)*Will it Liberate*(1986)*Toward the Future**Toward a theology of the corporation*, Lanham, MD : University Press of America, 1985*Confession of a Catholic*, Lanham, MD: University Press of America, 1985*Moral Clarity in a Nuclear Age*(1983)*Ascent of the Mountain, Flight of the Dove**Character and Crime*London: Brownson Institute, 1988.*On Cultivating Liberty**The Fire of Invention**The Guns of Lattimer**Choosing Presidents**A Free Society Reader**Three in One**The New Consensus on Family and Welfare: A Community of Self-Reliance*(Novak et al.) (1987).*The Spirit of Democratic Capitalism*(1982).*Rise of the Unmeltable Ethnics*(1972).*The Experience of Nothingness*(1970; revised and expanded 1998).*Naked I Leave*(novel, 1970).*Belief and Unbelief, a Philosophy of Self-Knowledge*(1965; 3rd ed. 1994).*The Tiber was Silver*(novel, 1962).

I admit I obtained this list from Wikipedia, but have indeed verified the data, and read some of these works. As you can see he was quite the polymath. But I did have the opportunity to meet and hear him once, about five years ago, and found him to be the model of a gentleman and a scholar. He was not just for Catholics. His work on Democratic Capitalism is still highly valued. And for me, his recent work on social justice–and its misuses–was something I prize in working through the historical issues of this concept. He also wrote on Liberation Theology and at times produced some deep philosophical reflections. At his death he was by all accounts a conservative in the Edmund Burke mold (by the way, if you want to find out what that means, you should read Yuval Levin’s 2014 book, * The Great Debate: Edmund Burke, Thomas Paine, and the Birth of Right and Left*). Novak was also an ambassador and won many prizes in his long and illustrious career.

Kenneth Arrow was a very different kind of person, foremost a scholar in a heavily mathematical tradition crossing between economics and political science. I first encountered his name and ideas about forty years ago and then read his actual work–which can be all but incomprehensible, though the conclusions are relatively commonsensical. In his book *Social Choice and Individual Values* (1951) he developed what is labeled the “General Impossibility Theorem,” otherwise known as Arrow’s Impossibility Theorem. There he stated:

it is impossible to formulate a social preference ordering that satisfies all of the following conditions:

**Nondictatorship**: The preferences of an individual should not become the group ranking without considering the preferences of others.**Individual Sovereignty**: each individual should be able to order the choices in any way and indicate ties**Unanimity**: If every individual prefers one choice to another, then the group ranking should do the same**Freedom From Irrelevant Alternatives**: If a choice is removed, then the others’ order should not change**Uniqueness of Group Rank**: The method should yield the same result whenever applied to a set of preferences. The group ranking should be transitive.

Obviously this theorem, if true, had significant implications in the sub-field of Public Choice, an offshoot of Rational Choice theory, itself related to both economics and political science. The idea had to do with voting in combinations and what would or would not result given rational individuals. He wrote earlier, “If we exclude the possibility of interpersonal comparisons of utility, then the only methods of passing from individual tastes to social preferences which will be satisfactory and which will be defined for a wide range of sets of individual orderings are either imposed or dictatorial.” (*A Difficulty in the Concept of Social Welfare*, 1950) All of this is ultimately about transforming individual preferences into a collective outcome. Arrow’s work stimulated much very crucial work on voting (James Buchanan and Gordon Tullock) as well as political decision-making more generally. This problem will continue to be both important and vexing for the foreseeable future, but has been made easier at least by Arrow’s path-breaking work.

Arrow also did important work in pure economic theory with his explorations in general equilibrium theory. But I will save that for now. I want to leave the reader with a taste for his kind of work–not for the faint of heart:

1.2.1. x > y means Xh _ Yh for each component h; x ) y means x ? y but not x = y; x > y means xh > Yh for each component h. R’ is the Euclidean space of 1 dimensions, i.e., the set of all vectors with 1 components. 0 is the vector all of whose components are 0. {x I}, where the blank is filled in by some statement involving x, means the set of all x’s for which that statement is true. Q = {x I x e R’, x > 0}. For any set of vectors A, let -A = {x I -x e A}. For any sets of vector A, (L 1, I , v), let EA,L x I x = E x, for some xi, * x, xv, where x, e A,. 9-1 .-1 1.2.2. For each production unit j, there is a set Y, of possible production plans. An element yj of Yj is a vector in R’, the hth component of which, yhi, designates the output of commodity h according to that plan. Inputs are treated as negative components. Let Y = SEJ Yj; then the elements of Y represent all possible input-output schedules for the production sector as a whole. The following assumptions about the sets Yj will be made: I.a. Yj is a closed convex subset of R’ containing 0 (j = 1, , n). I.b. Y nf = O. I.c. Yfn (-Y) =0. Assumption I.a. implies non-increasing returns to scale, for if yj E Yj and 0 < X _ 1, then Xyj = Xyj + (1-X)O e Yi, since O e Yj and Yj is convex. If we assumed in addition the additivity of production possibility vectors, Y, would be a convex cone, i.e., constant returns to scale would prevail. If, however, we assume that among the factors used by a firm are some which are not transferable in the market and so do not appear in the list of commodities, the production possibility vectors, if we consider only the components which correspond to marketable commodities, will not satisfy the additivity axiom.2 The closure of Yj merely says that if vectors arbitrarily close to yj are in Yi, then so is yj. Naturally, 0 e Yj, since a production unit can always go out of existence. It is to be noted that the list of production units should include not 2 The existence of factors private to the firm is the standard justification in economic theory for diminishing returns to scale. See, e.g., the discussion of “free rationed goods” by Professor Hart [91, pp. 4, 38; also, Hicks [10], pp. 82-83; Samuelson [18], pp. 84. This content downloaded from 163.11.75.215 on Sun, 26 Feb 2017 23:26:51 UTC All use subject to http://about.jstor.org/terms 268 KENNETH J. ARROW AND GERARD DEBREU only actually existing ones but those that might enter the market under suitable price conditions. I.b. says that one cannot have an aggregate production possibility vector with a positive component unless at least one component is negative. I.e., it is im- possible to have any output unless there is some input. I.c. asserts the impossibility of two production possibility vectors which exactly cancel each other, in the sense that the outputs of one are exactly the inputs of the other. The simplest justification for I.c. is to note that some type of labor is necessary for any production activity, while labor cannot be produced by production-units. If y e Y, and y # 0, then y, < 0 for some h corresponding to a type of labor, so that -Yh > 0, (here, Yh is the hth component of the vector y). Since labor cannot be produced, -y cannot belong to Y.3 Since commodities are differentiated according to time as well as physical characteristics, investment plans which involve future planned purchases and sales are included in the model of production used here. 1.2.3. The preceding assumptions have related to the technological aspects of production. Under the usual assumptions of perfect competition, the economic motivation for production is the maximization of profits taking prices as given. One property of the competitive equilibrium must certainly be 1. y* maximizes p*.yj over the set Yj , for each j. Here, the asterisks denote equilibrium values, and p* denotes the equilibrium price vector.4 The above condition is the first of a series which, taken together, define the notion of competitive equilibrium. 1.3.0. Analogously to production, we assume the existence of a number of consumption units, typically families or individuals but including also institutional consumers. The number of consumption units is m; different consumption units will be designated by the letter i. For any consumption unit i, the vector in R’ representing its consumption will be designated by xi. The hth component, Xhi, represents the quantity of the hth commodity consumed by the ith individual. For any commodity, other than a labor service supplied by the in- dividual, the rate of consumption is necessarily non-negative. For labor services, the amount supplied may be regarded as the negative of the rate of “consumption,” so that Xhi ? 0 if h denotes a labor service. Let ? denote the set of com- modities which are labor services. For any h e ?, we may suppose there is some upper limit to the amount supplied, i.e., a lower limit to Xhi, since, for example, he cannot supply more than 24 hours of labor in a day. II. The set of consumption vectors Xi available to individual i (= 1, *., m) is a closed convex subset of R’ which is bounded from below; i.e., there is a vector ti such that {i < xi for all xi e Xi . 3 The assumptions about production used here are a generalization of the “linear pro- gramming” assumptions. The present set is closely related to that given by Professor Koopmans [12]. In particular, I.b. is Koopmans’ “Impossibility of the Land of Cockaigne,” Ic. is “Irreversibility”; see [12], pp. 48-50. 4For any two vectors u, v, the notation u v denotes their inner product, i.e., UhV. Since yji is positive for outputs, negative for inputs, p*-y; denotes the profit from the production plan yi at prices p*. (Kenneth Arrow and Gerard Debreu, “Existence of an Equilibrium for a Competitive Economy,” *Econometrica*, Vol. 22, No. 3 (Jul., 1954), pp. 265-290).

As I said, not for the faint of heart. But important contributions to both economics and political science.

Of the two, it is hard to say which was the greater. I suspect the legacy of Michael Novak will last longer than that of Arrow, but I do not want to diminish Arrow’s foundational work.

Posted in: Obituaries

As I’ve grown older, I’ve been blessed to start encountering the geniuses of years past, but it’s comes with the downside that as soon as I’m discovering them, they are passing away. Both these men had incredible minds and were endowed with great sagacity (though Arrow may have been guilty of mathematicide in economics). Regardless, I’m thankful for both of their works. Hopefully, Thomas Sowell doesn’t have any plans of passing on anytime soon.

You made my day by talking about Kenneth Arrow. I introduced him to every one of my math students for 11 years.

Ha Ha Thanks.

I am familiar with the work of Michael Novak and am saddened to hear of his passing. Thank you for honoring the lives of these two men and giving them what their work deserves: access to the minds of the next generation of academics in and beyond their fields of study.

Very interesting list of works and ideas these individuals put forth. I’ll make sure to look into them.