1 Intelligible Matter in Aristotle, Aquinas, and Lonergan by Br. Dunstan Robidoux OSB In his In librum Boethii de Trinitate, q. 5, a. 3 [see The Division and Methods of the Sciences: Questions V and VI of his Commentary on the De Trinitate of Boethius translated with Introduction and Notes, 4 th rev. ed., trans. Armand Maurer (Toronto: Pontifical Institute of Mediaeval Studies, 1985), p. 38], with Aristotle, Aquinas distinguishes between sensible matter and intelligible matter and about how, through our acts of abstractive understanding (our acts of direct understanding), we can move, respectively, from what exists for us as a first kind of matter to what would exist for us as a second kind of matter. Cf. Lonergan, Verbum, p. 55, n In the context of the kind of scientific inquiry which we find in Aristotle, common matter (or, in other words, common potency) exists in a manner, however, which differs from the kind of common matter or common potency which we find within the praxis of modern empirical science when, within this new context, a transformation occurs or perhaps we say that a transposition occurs as we move from specifications of common matter in Aristotelian science that are known through the articulation of concepts and definitions toward new specifications of common matter in modern empirical science that are known in a mathematical way through the construction (the formalism) of mathematical symbols and the employment of operations which join mathematical symbols to each other in a manner that can lead to the construction of new mathematical symbols. On the one hand admittedly, apart from any differences which distinguish Aristotelian science from modern empirical science, in our acts of conceptualization we participate in a form of abstraction which differs from the kind of abstraction what properly occurs in our prior, direct acts of understanding. Cf. Verbum, 2 nd ed., p In direct understanding, an intelligible structure or an intelligible order is grasped (it is distinguished); it is detached from a set of material conditions. An intelligible order is extracted or it is set apart from material conditions which we have experienced through our different acts of sense and, by means of this extraction or abstraction, an intelligible form is freed from its connection with matter and the particularity which belongs to material conditions as these continually shift and vary (as we move from one spatial temporal context to a second spatial temporal context, ad infinitum). What emerges now, in this new context, is the ideational being of an abstracted universal. Its universal intelligibility is known by us through the self-experience which we have of our intellectual consciousness. We notice a difference as our sensible consciousness is superseded, as it shifts into experiences of intellectual consciousness and, later on, a second difference which is noticed when our intellectual consciousness shifts into the kind of consciousness which we have when, from our direct acts of understanding, we move into acts of reflective understanding which are proper to acts of judgment. In the acts of conceptualization which follow from our first acts of understanding, material components are taken from the data of our sensible experience and they are combined together in a way which detracts from the individuality of distinct material components. Or, in other words, the particularity which exists when we move from one spatial temporal context to another spatial temporal context is transcended (it is removed) in a manner which points to a second species of abstractive apprehension: one which refers to apprehensions of common matter and the kind of specification which occurs within the context of these apprehensions within our acts of conceptualization. In the context of Aristotelian science, essences are defined by words that are used and adapted in a manner which constructs technical definitions in order to provide new meanings for the words that we are using. Essential definitions which exist as concepts join a universally understood conceptualized form with a universalized conception of matter which, as common matter, differs from
2 instances of particular matter. No essence is to be simply identified with the being of a form nor are essences to be identified with apprehensions of common matter. As a component, common matter is quite other than the being of an essence. Cf. Lonergan, A Note on Geometrical Possibility, Collection, pp Through the ordering which accordingly exists in a definition, words (as concepts) come to have only one meaning and these meanings can only be changed if, through the ordering which exists within a new definition, we amend or we reject the order of words which has existed in the rendering of a given definition. We recall how, in the context of his day, Socrates had looked for definitions of moral virtues which would always hold amid the praxis of our human lives (despite all the vicissitudes that are commonly found within the context of our erratic moral behavior). However, as we move into the context of modern empirical science, we find a manner of abstraction which differs from what we find in Aristotelian science: an order which transcends the kind of abstraction which we had found when we had attended to what was given to us in the meaning of conceptualized definitions. In the abstraction which had been operative in Aristotelian science, sensible matter is transcended by acts of direct understanding which immediately lead to acts of conceptualization: an experience of inner words and concepts which can then be turned into definitions that can be expressed through the mediation and the possible construction of new outer, external words. In this way, sensible particularities are left behind and what is abandoned or what is left behind is turned into a species of remainder: an empirical residue which can only be sensed and which can never be understood by us. It exists apart from the presence of any kind of intelligibility. We opt for a designation which Lonergan employs in the context of his conceptuality. While this residue can never be understood by us, it can be known in an indirect way through our acts of understanding and conceptualization and a later reflection which knows that a real distinction exists between our acts of sense and our acts of understanding (hence, a real distinction between what sense knows and what understanding knows). With respect to this indeterminate, unintelligible, formless residue, nothing exists within it as a unifying principle which could bring together or which could unite anything which would exist at a lower level. In another way of speaking which joins a cognitional way of speaking with a metaphysical way of speaking, we can say, in general, that empirical residue (as a cognitionally defined concept) is to be regarded as a new species or a new specification of common matter (amid other possible specifications of common matter). Cf. Lonergan, A Note on Geometrical Possibility, Collection, p. 95. As mere common matter or as prime matter or prime potency: or, in other words, as a kind of inchoate mass, or as an amorphous collectivity, or as a material substratum (as the common matter of all higher unifications where the higher unifications refer to presences of form or essence), the empirical residue is to be understood as that which is known by us only by way of our acts of sense. It is that which is always given to us prior to the presence of any direct acts of understanding that we could have and it is that which is always left behind whenever, exhaustively, we have had our direct acts of understanding as these exist for us within our acts of human cognition. The peculiarity that is left behind refers to specific sensible qualities as we find these, for instance, in the color of this color or in the sound of this sound which we experience in this or that act of sense. Between the empirical residue of introspective cognitional analysis and the common matter of a metaphysical analysis, a parity of significance is to be admitted even if we realize and admit that cognitional analysis and metaphysical analysis begin from different points of departure: cognitional analysis, from the data of our human inquiry and an ordering of acts which inclines us toward acts of conceptualization by way of prior acts of direct understanding; and metaphysical analysis which moves us from judgments which know about the existence of objects or things which exist within nature toward a possible knowledge of the forms which exist within these naturally existing things or objects. Please distinguish between the existence of an intelligible form as
3 this exists within our minds (within the data of our understanding) and the existence of a natural form as this exists within an existing thing (something which is often other than ourselves) even as we admit that we do not speak about the presence of a real distinction. Cf. Collection, p. 97. Mere common matter is to be identified with what we mean when we speak about prime matter or prime potency since, in both cases, whether we speak about mere common matter or about prime matter or prime potency, we refer to a species of given that is totally lacking in any kind of specificity or differentiation. These things being said however, before we attend to the kind of abstraction which exists within the practice of modern empirical science, we should also speak about the second kind of matter (or the second kind of potency) which exists as intelligible matter or as intelligible potency within the practice of Aristotelian science as this kind of matter (or this kind of potency) exists as the term of our intellectual, mental acts. Within this context, we do not refer to our operative acts of human sense nor to any terms or data which properly belong to our acts of human sense. Cf. Aquinas, Super Boethium De Trinitate, q. 5, a. 3. In order the better to understand the kind of difference which we should notice here, please distinguish between sensibilia propria and sensibilia communia (things that can be sensed by the acts of sense which are proper to them and things which can be sensed in common by a number of different acts of sense). Cf. Lonergan, Verbum, p. 54, n. 196; p It is easy for us to imagine what a thing is or what an object is if it is the term of a specific act of sense. With a given act of seeing, something concrete is immediately seen. A given color is perceived or several colors are perceived at the same time. Act and object go together. Specific act goes with specific object. But, when we refer to acts of sensing which do not differ from each other, when we refer to acts of sensing which are lacking in any kind of discrimination which could exist among them as different kinds of act, when we refer to acts of sense which are only possible and not actual, we encounter difficulties if we should then try to imagine how our acts of sensing can exist and operate in a way which is entirely lacking in the specificity which is proper to our individual acts of sense whenever they exist (whenever they are operative or in a condition of act) in the context of our lives as sensing human subjects. In this next context, we try to imagine a type of matter or a type of potency which, for instance, indifferently refers to any kind of color which could be seen or any kind of sound which could be heard and we are not able to imagine what we would like to imagine because, simply put, what exists as the term of a suppositional or conceptualizing act is not something which can ever be the term of a sensing act. In working from our acts of sense and from a perspective which is determined by our acts of sense, we can never imagine anything which is lacking in size, magnitude, or dimension. However, or on the other hand, through our acts of supposition and conceptualization which occur in language (our inner or outer language), we can always speak about something which is lacking in size, magnitude, or dimension. Cf. Lonergan, Collection, p. 95. A real distinction exists, for instance, between a point which exists within mathematics and a dot which is drawn or inscribed on a surface of some kind and which always has some kind of magnitude or size (despite the smallness of its possible dimensions). A given dot also has a specific color although, if, in an incarnate sensible way, we should use lines and dots to construct images in mathematics in order to solve problems within the practice of algebra and geometry, we should also notice that the specific colors and the sizes of diagrams are of no relevance to the possible solution of any given mathematical problem. Any color or contrast will suffice and, in the same way, any term which could belong to other acts of sense. Cf. Lonergan, Verbum, pp The absence of specific sense data accordingly explains why, as a result, we are now left with a continuum of space and time which appears to be somewhat void or empty. This new continuum is constituted by images which do not representatively come to us directly from our acts of sense. We refer, instead, to images which come to us principally from what we suppose or what we freely create
4 and define within the context of the kinds of inquiries that we could be engaged in, using our imagination to fabricate connotative, symbolic images which do not sensibly resemble any objects which they are meant to signify or, in some way, to represent. Cf. Collection, p. 96. Denotative, representative images that are taken from our acts of sense and which are used to elicit acts of direct understanding within the common praxis of empirical science differ from connotative, symbolic images which we imaginatively construct and suppose and which we commonly use to elicit the acts of direct understanding which we desire within the practice of mathematics. Cf. Collection, p Within this context, in a manner which alludes to the presence of a new real distinction that exists between one kind of image and another kind of image, we find that Aquinas refers to some images which exist as perfect representations. These are drawn from our acts of sense. Cf. In librum Boethii de Trinitate, q. 6, a. 2, ad 5. However, at some level in our self-understanding and self-inquiry, whether we work from representative images that are drawn from our acts of sense or whether we work with symbolic images that are largely drawn from our acts of imagining and supposition (virtual images existing as a third species of image), we should know that always, through apt suggestive images (whether in science or in mathematics), we best create conditions that could lead us toward new acts of understanding (the possible reception of new acts of direct understanding). We understand something that we would like to understand or we solve problems which have been eliciting our attention and interest. Specifically, within mathematics, in the kind of symbolic imagining which occurs within the praxis of mathematics, we determine a possible value for x if we know about values which respectively belong to y and z. To some extent, whenever in the context of our anticipatory understanding we move from our acts of sense to our acts of imagining, we always work with images which function as symbolic representations. They move us away from what we directly experience in sense and they orient us or they point us toward a possible experience of new objects that we can begin to know: new acts and terms of understanding (insights) which will satisfactorily answer our questions or solve our problems. However, as we move from the praxis of Aristotelian science and as we shift into the ways and means of modern empirical science, a common mathematization of images should reveal or point to degrees of abstraction which exist within modern empirical science but which are not found within the common practice of Aristotelian science. We know of course that, in the early developments of Greek science and philosophy, in the 5 th Century BC, the Pythagoreans discovered that a natural affinity exists between mathematics and natural science. Cf. Patrick A. Heelan, S.J., A Realist Theory of Physical Science, Spirit as Inquiry, p. 34. Between number (geometry) and certain sensible qualities, a correlation can be observed. A correlation can be posited. From numbers which measure determinable quantities, we can move toward new sensible qualities which we would like to experience through new acts of sense. Tones or pitches of sound can be predictably determined if we work with number ratios which indicate differing comparisons of measure. The numbered length of one extension is lesser or greater than the numbered length of a second extension. But, if this type of insight comes to us from an early date in the history of science and philosophy, the common practice of representing apprehensions of sensible data in a manner which works with mathematical symbols is a much later development. In a new context, we think about the scientific inquiries of Galileo Galilei (d. 1642) who constructed number ratios which joined measurements of quantity with each other, lapses of time with changes in the physical location of moving bodies. Instead of moving directly from sensible experiences of data toward questions which ask for possible reasons or explanations, we work from abstracted specifications of data which exclude any correlatives or contents of sense that cannot be specified through any measurements or determinations of quantity (as we would have these determinations through the kinds of measuring which we are using in a given context). From
5 measurements of quantity that are given to us or which we obtain, we can then turn toward possible acts of direct understanding and then, if and when these acts of understanding are given to us, we can turn toward a mode of expression as this is given to us through the symbols of a mathematical equation. Instead of a specification of common matter (or a specification of common potency) which refers to technical definitions that can be given for the possible meaning of words, a new species or a new specification of common matter (or a new specification of common potency) presents itself to us when we turn to the kind of formalism which exists within mathematics and the construction of mathematical equations. In an applied use of mathematics, through our direct acts of understanding, we move from mathematicized abstractions of sense data toward mathematicized abstractions of conceptual meaning which now totally exclude words and phrases that are normally a part of our ordinary human speech. In the construction and formulation of mathematical equations, we work with images that are merely or solely visible or, in a more general sense, we work with images that are minimally detectable. The shapes or contours of mathematical symbols have only to be perceived by us in a minimal way if, as mathematical symbols, we are to employ them in contexts which exist or which we create through the mathematical operations which we engage in (this operation combined with this other operation). Hence, with respect to the data of sense, whatever exists within this data as a kind of extra is to be put aside and ignored. Expendable apprehensions of data are to be bracketed and not attended to. Hence, with respect now to our acts of sense, a new species of abstraction can be noticed: a species which differs from other kinds of abstraction. We refer to a species of abstraction which is defined by how our acts of sense function as potencies in relation to the kind of activity which exists when, through our acts of imagining and the kind of supposition which occurs in our acts of imagining (seemingly at will), we can construct new mathematical symbols for the purpose of a kind of play which belongs to mathematical operations and the ministrations of mathematics when the context is the inquiry, the methodology, and the understanding of modern empirical science. We construct images which, yes, minimally, we can perceive through our acts of sensing although the meaning of these images is something which we determine according to the kind of supposition and hypothesis which we are using and which exists within our varying acts of imagining. Cf. Lonergan, Collection, p. 96. For the sake of a possible growth in the extent of our understanding, we imagine this or we imagine that through mathematical forms of expression and image which appear to be most apt for us or which are most congenial for the kind of work that, now, we are doing or that, now, we would like to do in the inquiries which we are undertaking. The imagining which we do is not lacking in whatever degrees of reasonableness should properly belong to it. Moving on however, while we find mathematical kinds of abstraction within the practice of modern science and while we accordingly find a new species of common matter or a new species of common potency which exists as a new specification of intelligible matter (or as a new specification of intelligible potency within the practice of modern science), differing from the kind of intelligible matter which exists within Aristotelian science, it is to be admitted also that, in pure mathematics, we work with new specifications of intelligible matter or new specifications of intelligible potency which differ from what we had experienced when we had worked with the kind of significance which exists within the praxis of applied mathematics. Where, in modern empirical science, determinations of number refer to measurements of size as this exists within measured apprehensions of sense data, in pure mathematics, a complete separation exists between numbers which exist within the play and practice of mathematics and any numbers which refer to measurements of size as these would exist within our apprehensions of sense data. If, with applied mathematics as this exists within the praxis of the natural empirical sciences, we move from sensible, individual apprehensions of data toward acts of understanding which know about the possible presence of universal laws that allegedly exist within the sense data which we have experienced, in the praxis of pure mathematics, we work with species or
6 specifications of intelligible matter which consist of imaginary, imagined numbers. These numbers refer to imaginary quantities. A first major specification of abstraction which had moved from apprehensions of sense data toward new possible acts of direct understanding is replaced or, better still, it is transcended by a second major species of abstraction which moves from imagined apprehensions of multiplicity toward new possible acts of direct understanding as these acts can exist within the practice of a rarified form of mathematics. Cf. Verbum, pp As we have noted, these imagined apprehensions of multiplicity in data are not lacking in a primitive degree of sensibility. They can be encountered by us in a minimal way through our acts of sensing although, in this context, they exist for us primarily as terms which belong to our acts of supposition and hypothesis which exist for us as acts of inquiry within an order of acts which is constitutive of our human cognition. Beyond the subcategories of abstraction which we have found to exist within the first order or the first degree of abstraction, subcategories of abstraction also present themselves to us, however, within the practice of pure mathematics when we attend to how, in the progress of the development of mathematics, we can move from arithmetical operations to algebraic operations and then, from there, to the practice of calculus. Differing orders of intelligible matter succeed each other in a manner which leads to higher levels of abstraction which exist when we think about how, in a transition which moves from potency to act, we move from arithmetic to algebra and how, similarly, we can then move from algebra to calculus. Within pure mathematics (as also in applied mathematics), numerical multiplicities exist as a fundamental supposition (as a basic point of departure) since, in the practice of pure mathematics (as in applied mathematics), numerical multiplicities must exist. In the case of pure mathematics, they must be supposed or they must be postulated if, in any given mathematical exercise, we are to go from a number which refers to a hypothetical quantity to another number which refers to another hypothetical quantity. Cf. Verbum, p. 55. If we want to speak about the kind of diversity or the kind of multiplicity which exists for us within the practice of pure mathematics (to distinguish this diversity or multiplicity in a manner which can set it apart from other kinds of diversity or multiplicity), with Aquinas, we can refer to presences of individual intelligible matter. Cf. Summa Theologiae, 1a. q. 85, a. 1, ad 2. The individuality points to the kind of diversity or multiplicity which we must have if we are to move from the abstractions of science to the abstractions of mathematics. In general, with respect to the nature of our acts of understanding qua acts of understanding we refer to our acts of direct understanding these acts all work with diversities or multiplicities of one kind or another. They exist in order to reduce a multiplicity to unity or to convert a multiplicity into a unity that is grasped and which is introduced into an experience or a condition of disorder. Our acts of understanding always transcend what we had previously known or what had been given to us by our prior acts of sensing and by our prior acts of understanding. If then, however, through a later kind of inquiry, we would want to ask questions about being in general (as in what is being? or what is the nature of being? ), whether we refer to the unity or the being of things within empirical science or the unity or the being of things within mathematics) or, in other words, if we want to ask questions about what could be the beingness or the existence of every kind of thing which exists, if we want to ask questions about what could be constitutive of the beingness or the existence of every kind of thing (the givenness of being or the existence of all things functioning as a fundamental point of departure), we find a change of context in this new species of inquiry. We no longer work with quantities or multiplicities of one kind or another that, through our understanding, we would want to reduce to some kind of intelligible unity (an understood that would exist as the term of a new act of direct understanding). We would be working, instead, from a unity which is somehow already given to us as an a priori. This unity is not sensed through any of our acts
7 of sensing nor is it a unity which we could suppose or construct. This unity is not imagined. Instead, we would refer to a unity which we experience as an inner datum of our intellectual consciousness. We advert to a unity which is already currently operative within our consciousness of self in the inquiries which we make: a unity which points to a conscious joining or a constant unifying which intelligently occurs or which exists as we move from one act or datum of consciousness toward another act or datum of consciousness. In the context of our inquiries (whether about ourselves or about objects which are other than ourselves), a given, initial act or datum of consciousness elicits or it directs us to the necessity of a second act or datum of consciousness and then, from there, to other acts and data of consciousness which, together, reveal a pattern or a progress in the dynamic of our human cognition (a pattern which is self-constitutive). To a certain extent, we already know about a unity which we have yet to understand, a unity which we would like to understand (a unity which already exists as a given within our consciousness of self): a unity which functions as an anticipation of being (an anticipation of being which is specifically heuristic). An order of parts within the functioning of our cognition points to an order of parts or elements which exists within the being of the known and the ordering of parts or elements which exists within our cognition also points to a desire which shapes and governs how all our acts of inquiry should all fit together into a whole which determines how, through our cognitive acts, we are to respond to the different kinds of questions which we pose in the context of our different inquiries. From an a priori awareness of being as a comprehensive unity, in a new species of inquiry which points to a third degree of abstraction, we work toward a possible understanding and knowledge of being that would exist for us as a species of a posteriori knowledge. Being as intended could possibly turn into Being as it is understood and known. Through a species of unity which is cognitive and not metaphysical (we know that things exist independently of whether or not we might know anything about them), Being (as knowable) exists in a manner which accords with the nature and the order of our human cognition. Our questions about Being take us beyond what we can sense and what we have sensed through our various acts of sensing and these same questions also take us beyond what we can imagine or we have already imagined through our various acts of imagination, supposition, and hypothesis. They work with a new set of data which refers to a new specification of intelligible matter (a new specification of intelligible potency): a new specification which differs from the individual kind of intelligible matter (or the designated kind of intelligible matter) which Aquinas had spoken about about when speaking about the kind of abstraction which occurs in mathematics. In order to speak about this other, new kind of intelligible matter, Aquinas had distinguished between what he refers to as individual intelligible matter and what he refers to as common intelligible matter. Lack of plurality or diversity in intelligible matter is signified if we can speak about common intelligible matter. Through a kind of abstraction, we subtract individuality from intelligible matter and we get common intelligible matter as a result. Cf. Summa Theologiae, 1a. q. 85, a. 1, ad 2. However, if we would prefer to work with a terminology that largely derives from a study of human cognition, we can speak in a different way about conceptualized apprehensions of data or conceptualized postulations of data that have been imagined and how or why we should distinguish between individual conceptions of data which exist as intelligible data and a conception of data which transcends any specifications. We can think about a unity which already exists within the data of our cognitive consciousness (a unity that we directly experience and which we can advert to) although, admittedly, we refer to a unity which we have yet to understand. In our analysis, we break this unity into parts or elements to determine how this unity is constituted and then, from there, we go to the parts or the elements which are constitutive of the being of all things. We move from our self-understanding into an indirect form of inquiry which is determinative of the study and the science of metaphysics. The being which is to be known by us is to be viewed as a transcendental because a real distinction
8 distinguishes between being or existence per se and the kind of being which exists when we refer to categories (or predicaments) which are specific to the being or the existence of particular things. While Being or the being of all things cannot be known by us through a direct act of understanding, a heuristic knowledge of being serves as a species of first principle when it exists for us as a principle of order. We are ordered, we are guided in the manner of our questioning and understanding when we need to determine how the kind of being which is known by one discipline is to be related to the kind of being which is known by another discipline.