My presentation focuses largely on materials I have covered in The Modeling of Nature (CUA Press 1996). [I] First, I give an overview of that work for those not familiar with it, and explain how Thomism is the basic philosophy behind it, although this is not made explicit in the text itself. [II] Then I elaborate on a few distinctively Thomistic themes that are latent within Modeling and that lend themselves to theological exploration. Among these are selected topics pertaining to prt hul or material prima, which I shall continue to call protomatter, namely, its dispositions and its appetite, and how these are related to the evolution of species, hominization, the resurrection of the body, and the Incarnation of the Word in human flesh. [III] Finally, I concentrate on the Thomistic concept of quantity to develop a few mathematical models that were not discussed in Modeling. These will enable me to address epistemological issues relating to non-Euclidean geometries and Hilbert spaces, and the bearing of these teachings on current interpretations of Einstein's theory of general relativity and the quantum theories of Schrödinger and Heisenberg.

Throughout I use transparencies to present some graphics that may prove helpful.

I. THE THOMISM IMPLICIT IN MODELING

Although I nowhere mention this in Modeling, what is implicit in my treatment is the following idea. Aquinas, having been taught by Albert the Great, had an excellent grasp of Aristotle's science of nature. He upgraded the knowledge this gave him to organize, as it were, a science of supernature (that of revealed theology), making use of analogy and the Aristotelian concept of a "mixed science," one combining propositions established by reason with propositions assented to by faith. My project was to do something similar: to take knowledge we possess by ordinary experience of nature to organize the special type of knowing we call modern science, making use of analogy or modeling techniques and the "mixed science" of mathematical physics, which combines propositions established through observation of nature with those of mathematics. Here I rely on a teaching that is distinctive of Thomism, in contrast to other Scholastic systems, namely, that analogical middle terms are sufficient for a valid demonstration, no less in mathematical physics than in the science of sacred theology. Such terms, and the models they frequently employ, can provide us with insights into the microworld and the megacosm that are not unlike those Aquinas offered his contemporaries into the spirit world of the immaterial and the incorporeal.

The path I used to develop this idea is traced in the following transparencies:

1. Stimulus-Response Models

2. A Schematic Robot Model & Animal Powers

3. Modeling the Soul as an Energizing Field

4. A Natural Body for Aristotle

5. Thomas Aquinas's Powers of the Human Soul

6. Natural Form as Energizing Protomatter

7. A Powers Model of Various Natures

8. Iconic Models

9. A Powers Model of an Inorganic Nature

10. A Powers Model of a Plant Nature

11. A Powers Model of an Animal Nature

12. A Powers Model of Human Nature

13. Human Perfectibility

14. An Overlay Model of Human Nature

II. TOPICS RELATING TO PROTOMATTER

In this section I plan to develop more fully points that were touched on in Modeling but not worked out there in any detail. In doing this I draw on materials developed in two previously published essays, "Nature and Human Nature as the Norm in Medical Ethics" and "St. Thomas on the Beginning and Ending of Human Life." The problems I address are grouped around various attributes of protomatter, how it functions in individuation, and its role in relation to quantity and quantitative dispositions in effecting substantial change. The following transparencies will be used to illustrate this development:

15. A Creation-Evolution Schematic

16. Protomatter as Concreated, and Its Appetite

17. The Principle of Individuation (Protomatter and Quantity)

18. Natural Radioactivity (The Eduction of Natural Forms)

19. Delayed Hominization

20. The Individuation of the Human Soul and the Resurrection

21. Immediate Hominization: The Conception of Christ

III. TOPICS RELATING TO QUANTITY

Most of the models that were presented in Modeling were either iconic models or powers models, the second of which I spoke of as epistemic (or ontic) models. I did not enter into the subject of mathematical models, mainly because I wanted to keep the mathematics simple and easy to visualize. That, of course, prevented me from discussing anomalies arising in twentieth-century physics, particularly in the general theory of relativity and quantum mechanics. In this section I draw on two books that discuss such anomalies from a philosophical point of view compatible by Thomism. The first is Philip Soccorsi's De Geometriis et Spatiis Neo-Euclideis (Rome: Gregorian U.P., 1960) and the second is Wolfgang Smith's The Quantum Enigma: Finding the Hidden Key (Peru, Ill.: Sherwood Sugden & Company, 1996). My review of Smith book is forthcoming in The Thomist for July 1997 entitled "Thomism and the Quantum Enigma," and it is this that supplies the proximate stimulus for what follows. I offer these reflections as explicating in fuller detail two theoretical entities mentioned in Modeling, namely, "space-time" and "wave-particle." The following transparencies should assist my development:

22. Types of Concepts II

23. Projective Geometry

24. Euclidean and Non-Euclidean Geometries

25. Beltrami's Pseudo-Spheres I

26. Beltrami's Pseudo-Spheres II

27. Number Systems (in Modern Mathematics)

28. The Continuum (Extensive Quantity)

29. The Individual Natural Body

30. Potentiality and Actuality in Mathematical Physics

31. Relativity and Quantum Theories