Is There a Straight Line in Space between Two Thomists?

The following outlines an argument that I will develop in greater detail in a paper at the 41st American Maritain Association meeting. It concerns “the other debate” between Maritain and De Koninck.

The year is 1934. At the University of Louvain, the 28-year-old Charles De Koninck has just completed his doctoral dissertation, The Philosophy of Sir Arthur Eddington,a spirited defense of one of the earliest (and still one of the best) popularizers of the then cutting-edge theory of relativity. In his exposition of Eddingtons views, De Koninck notes summarily that relativity has shown us that we do not know as much of space as we think in philosophy.1 In his subsequent assessment, De Koninck devotes a lengthy passage to a vigorous critique of the philosophical understanding of real spacepresented by Jacques Maritain just two years earlier in The Degrees of Knowledge. The young Belgian Thomist declares that Maritain has not addressed the basic problem. His whole philosophy of science is thereby vitiated” (154). This “other” debate between De Koninck and Maritain—whose lines are much more clearly drawn than the controversy of the primacy of the common good—must be examined and adjudicated, for the importance of the topic extends beyond the abstruse nature of space-time ontology and involves the foundations of the Thomistic interpretation of modern science. It seems that each has something to learn from the other, and that they offer us important common ground.

First, let us consider Maritain’s main contentions about the reality of space.2 Maritains assessment hinges upon an analysis of the reality and truth of space from the perspectives of the geometrician, the physicist, and the philosopher. This approach allows Maritain to advance a dilemma: non-Euclidean space is real if and only if its concepts either do not imply a contradiction when claimed to exist outside the mind or if they can be constructed in intuition in a way that ensures its physical possibility. However, in neither way is non-Euclidean space real.Maritain concludes that In both ways we are thus led to admit that non-Euclidean spaces are beings of reason in spite of the use that astronomy makes of them,” and, “It is Euclidean space which appears to the philosopher to be an ens geometricum reale” (180; or here). Nonetheless, Maritain goes on to defend the idea that such a being of reason appears as a geometrical symbol of real physical space (understanding physicalspace in the sense given to this word by the philosopher of whom we were speaking above)” (184; or here).

Let us now turn to De Konincks criticisms of Maritain.3 De Koninck begins his treatment, as he says, at the end. M. Maritain affirms that real space is necessarily tridimensionally Euclidean(147). De Koninck then fixes his sights upon Maritains dilemma that was just outlined: It seems to me that this text refutes itself(148), De Koninck asserts. The heart of De Konincks critique points out two errors that he thinks Maritain commits. De Koninck claims that, first, Maritain confuses extension with quantity (which De Koninck also calls physical magnitude). Second, he says, Maritain does not grasp the importance of Eddington’s notion of philosophical relativity involved in physical measurement. The first confusion allows Maritain to import a Euclidean metric into his intuitions about space. This goes uncorrected, thinks De Koninck, because of Maritains second error. De Koninck claims that, to the contrary, As a philosopher, he can say nothing about the metric structure of space. That is for the physicist. And he replies that there is curved space(149). Because this claim about the actual metric of space is only justified by measurement (the nature of which helps to constitute the character of the formal object of physics), De Koninck considers himself justified in claiming that Maritains philosophy of science is vitiated. However, De Koninck later takes up the idea of symbols, and claims that physical symbols move against an obscure backdrop which is the order of non-intuited yet quite real essences . . . and it is indeed this background that gives a meaning to symbols(212). De Koninck gives to the symbolic constructs of mathematical physics a role similar to the one granted them by Maritain.

Note that both philosophers must deal with the nature and origin of our spatial concepts. Furthermore, they must contend with how measurement plays a role in claims regarding whether or not a given conception of space is physically real. These two stages provide them with grounds to claim to have eliminated what is primitive in our ideas about physical space and hold on to what is perennial. Yet Maritain sides with Euclid, De Koninck with Eddington and Einstein. Notably, however, both men give a significant role to the symbolic or representative character of the mathematics involved. This common ground is the key.

With this dialectical array in mind perhaps a resolution to the debate is possible. Three questions seem important. First, what is physical magnitude? Here, it seems one should side with De Koninck. The mathematical degree of abstraction effectively occludes our access to the metric structure that obtains in physical space. Second, how can we give an ontological sense to measurements that discover the metric structure of space? This question is again answered by De Koninck. The metric structure of physical space is determined through the formal object of mathematical physics, which is an object constructed in the act of physical measurement. This involves a crucial application of the Thomistic notion of sensible matter. Finally, does this ontological sense, given to general relativity, resolve to the notion of symbolic construction? Here, the answer would seem to be in the affirmative, but I would point out that the young De Koninck appears to miss the importance of Maritains notion of geometrical symbol. The importance of the symbolic concept was one with which De Koninck wrestled during his entire career. The nature of the symbolic concept and its role in mediating between the first two degrees of abstraction provide a common connection between these two Thomists, while their differences show up elsewhere. It seems we should conclude, by way of corollary, that the Thomistic philosophy of nature shows its perennial worth in its attentiveness to the human act of knowing through measurement and symbolization.

* * *

1 Charles De Koninck, The Philosophy of Sir Arthur Eddington,” in The Writings of Charles De Koninck: Volume One, ed. and trans. by R. McInerny (Notre Dame, IN: University of Notre Dame Press, 2008) 115.

2 See Jacques Maritain, Distinguish to Unite, Or, The Degrees of Knowledge, ed. by R. M. McInerny, trans. by G. B. Phelan, Vol. 7. The Collected Works of Jacques Maritain (Notre Dame, IN: University of Notre Dame Press, 1995) ch. 4, Knowledge of Sensible Nature,” 145–214. The section dealing specifically with the nature of physical space, A Digression on the Question of Real Space’,” occurs on 17584. Inline citations in this paragraph from this volume.

3 De Koninck, The Philosophy of Sir Arthur Eddington,” 147–54, 207–18, and 22425 n. 66. Inline citations in this paragraph are from this volume.

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