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Theatetus describes a recent conversation with his teacher, Theodorus, on the nature of mathematical squares. Beginning with instances, Theodorus proceeded sequentially to work through the numbers, “the power of 3 square feet and the power of 5 square feet . . . and he went on in this way, taking each case in turn till he came to the power of 17 square feet; there for some reason he stopped. So the idea occurred to us that, since the powers were turning out to be unlimited in number, we might try to collect the powers in question under one term, which would apply to them all.”95 Lonergan provides a similar example in the following series, “1+1=2; 2+1=3; 3+1=4; etc., etc., etc. . . .” suggesting that the most important aspect in the example is “etc., etc., etc. . . .” for “. . .” indicates that the process can go on indefinitely under a rule or formula.96 Like Theatetus, one can stop, realize that the instances are potentially unlimited in number, and provide an explanatory formula rather than working through each and every instance. In so doing, one has grasped necessity in the relations, what must be present for the relations to be intelligible rather than accidental, and the “single term” or formula articulates what is necessarily present in the intelligibility of each instance covered by the formula, precisely the anticipation of the Socratic method’s search for a definition including each relevant instance while excluding each instance of a different kind.

      Theory and the Real

      Although articulated differently, both Plato and Aristotle consider the formal necessity grasped in theory to be real and objectively knowable, and thus metaphysics became the master science. In common sense, the real was envisioned as bodies, as the “already out there now real,” or presence, what could be seen or touched, because common sense begins with an anticipation of what exists in relation to me and my sensation. Since concern is for that which exists in relation to me, I expect that what exists is that which exists over and against me, and being is modeled after bodies. With theory, being is whatever is intended as meaningful, and only the invariant and necessary is fully meaningful:

Metaphysics is said to be the most abstract and the most universal of sciences. All science must have some universality and therefore must be to some extent abstract. If we consider things with all their individual differences, there is no general truth that will apply to them all and no general law or principle that can be derived from them. It is only by leaving out of sight the individual differences and taking what is common to many individuals that we can formulate a universal law or principle. This is what we do when we abstract. We leave out what is peculiar to the individual and take only what is common. To abstract, therefore, is to universalize what is abstracted. Now Metaphysics, having for its object to study being as such, abstracted from all conditions under which reality exists, and considers only the reality itself. Therefore the notions we derive from such consideration of reality will apply to all reality, and consequently the science of Metaphysics is most universal.97

      Metaphysics is a science, and thus will follow the rules of the other sciences, just having greater extension and thus abstraction, but metaphysics follows entirely the rules implicit in theory’s anticipation of meaning.

The shaping of metaphysics by our anticipations is true not only in the definition of metaphysics itself but also in its elements. For instance, in keeping with the notions of episteme found in classical theory, where demonstrative knowledge proceeds from necessary first principles, so metaphysics is “the science of first principles” providing those “things from which all reality derives,” or ontology, as well as those “truths on which all knowledge depends,” or epistemology.98 For both studies, since metaphysics deals with the most abstract and necessary aspects, it is from metaphysics that our knowledge of the principles of both reality and knowledge are derived, “on which the validity of all our knowledge depends.”99

      Theory as Law

Within classical theory, a law is “an unchanging correlation among changing quantities that supplies . . . a standard for measuring. . . . A classical norm was assumed to be a universal necessary standard for judging all cases without exception.”100 And in looking for this, one “is concerned with an immanent intelligibility in the thing, event of process,” meaning that one heuristically anticipates necessity to be discovered in the contingency and variability of the concrete, by abstracting from the contingency to discover intelligibility, which is necessary, unchanging, and explanatory.101 Abstracting from contingency means abstracting from the individual, even abstracting from the world of bodies to the non-imaginable world of definitions, as when in geometry reference is made to points (which are not dots and cannot be imagined) or when the formula for calculating velocity in a free fall assumes the ideal of a vacuum (which is not to be found in this or that actual instance of a falling ball). The necessity is an abstraction, albeit an anticipated one, from which to attain the status of law.

      Note the anticipation for data to “conform to some law.” The heuristic shapes what we anticipate, and thus how we interpret what we find, in an interesting pivoting of discovery and anticipation. We anticipate intelligibility under a certain heuristic, thereby discovering such intelligibility in the data given to us. For instance, Theatetus mentions that Theodorus began to teach about squares with the assistance of diagrams, namely, that which could be viewed and imagined, so to arrive at the formula after the intelligible principle was discovered through the use of the data supplied by the diagrams. But many people could look at the diagrams and find no intelligibility; only those anticipating finding something, only those looking for something, some unknown x of a certain type find x. Once found, the formula governs the anticipation of how additional instances will be understood, even before those instances are diagramed. So our anticipation allows for discovery which provides the basis for ongoing anticipation.

While common sense uses proverbs to articulate what wisdom has found to be true for the most part, helpful rules of thumb to get you through, more often than not, classical theories tend towards abstraction in “(1) their heuristic anticipation, (2) in the experimental techniques of their discovery, (3) in their formulations, and (4) in their verification.”102 In heuristic, classical theory looks to understand the intelligibility immanent to the data, expecting also that genuine understanding could be extended to all similar data, for the “nature to be known will be the same for all data that are not significantly different.”103 Further, concrete differences of time, place, or person, are to be ignored, and the techniques of experiment are to be applicable and repeatable for all. Consequently, the language with which intelligibility is formulated must not rely upon the vagaries of particular times or places, and thus a specialized and abstract language is required. Finally, a possible grasp of intelligibility is not verified with an isolated concrete instance but by a general and large number of instances; certainly the testimony of the wise person alone is not sufficient.

We see how the heuristic shapes conceptions of law, most obviously in the sense of a scientific law of nature: Law expresses a necessary principle based upon a grasp of the intelligibility within data, and which cannot be rationally denied. Of course, the question arises as to what allows such cognition to be moral law, as opposed to just a law of how intelligibility is anticipated. What makes law normative?104 For theory, natural law looks very much like a law of nature in its structure, for the forms of thought operate within the theoretical mode of meaning.

      Theoretical Natural Law—The Default

      Jacques Maritain summarizes much of the classical tradition of natural law when he writes:

I am taking it for granted that there is a human nature, and that this human nature is

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