11. A science can be subalternated to another on account of its end, its principles (only), or its subject (and its principles). Insofar as the first of these three modes of subalternation admitted by the Schoolmen does not coincide with the second or third, it is improper, and does not concern us here.{35}
In the second mode of subalternation (as to principles), a science is purely and simply (simpliciter) subalternated to another when it derives its principles from this other science, which discloses them to it. So that the subalternate science does not resolve its conclusions by itself (ex se) in naturally known or self-evident principles. Should a science perchance resolve its conclusions in principles naturally known, and yet occasionally borrow some principles from another science, it is said to be subalternate in a certain respect (secundum quid) to this science.
In the third mode of subalternation (as to subject) the subject or object of the subalternate science adds a difference that is accidental relative to the subject or object of the subalternate science. Thus, acoustics, a subalternate science to arithmetic, has for its subject sounding number; optics, a subalternate science to geometry, the visual line.{36}
Whenever there is subalternation as to subject there is always subalternation as to principles; but it is possible to have subalternation as to principles without subalternation as to subject. And as Cajetan (and the whole Thomistic School with him) has so forcefully pointed out, that which comprises the essential in subalternation consists in this: that a science receives its principles from another science without making them evident by its own powers: "The conclusions of a subalternating science are evident in and through their principles immediately and without the intermediary of another habitus; those of the subalternated science are evident in and through principles mediately, or through the intermediary of the subalternating scientific habitus. Herein resides the essential and natural (per se) difference between the subalternating and the subalternated science. Other conditions follow which cause a science to be subalternated in a particular way, not purely and simply. We may say, for example, that one science presents 'the fact that' (quia), another 'the reason why' (propter quid); or that the object of one adds an accidental and extrinsic difference to that of the other. This latter, in fact, is the condition of subalternation as to object; the former is the true condition of subalternation as to principles because of subject matter.
"By its nature, the habitus of the first principles of the subalternate science is the scientific habitus of the subalternant. The subalternate and the subalternant sciences are not necessarily distinct from the angle of the object or subject, but rather from that of the conditions of their light. This is so because the light in the subalternant science is immediately linked with self-evident principles, whereas that of the subalternate is linked thereto mediately, that is, through the intermediary of a habitus of another species.{37}
Thus, theology which has the same object as the intuitive science of the blessed is nonetheless subalternate to it as to its principles, which it receives from this superior science through the intermediary of faith.
We may remark that the examples which St. Thomas gives of sciences subalternated to mathematics as to subject (or object) -- musica, perspectiva, astrologia, that is to say, acoustics, geometrical optics, and astronomy -- he gives on other occasions as examples of scientiae mediae, formally mathematical and materially physical.{38} It is plain, as a matter of fact, that a science subalternated to another as to object is by this very fact an "intermediary science:" materially it pertains to the order or grade of the object in which it terminates (and whose proper structure requires that an accidental difference be added to the object of the subalternant science); formally it pertains to the order or grade of this subalternant science, since it considers and knows this very object which is proper to it only in so far as it connotes the object of the subalternating science, and thus is capable of falling within the formal perspective of this latter. Thus, geometrical optics, for example, is not only subalternated to geometry, but again it is itself a formally geometrical, though materially physical, science, and (by reason of the terminus of its operations) more physical than geometrical.{39}
It is not the same with sciences subalternated only as to principles. Such a subalternation is possible only where the subalternate science attains the same object as the subalternant science in a diminished light, and consequently in a different ratio formalis sub qua than the subalternant science. Thus the subalternate science cannot be a scientia media belonging formally to the same degree as the subalternant science and materially to a lower degree: of strict necessity it belongs, as to its formal reason itself, to a degree inferior to that of the subalternant science.
{35} This first mode of subalternation may imply subalternation by reason of principles or of subject, in which case it merges with the second or third modes; (thus we say -- p. 86 f. -- that moral philosophy adequately considered is subalternated to theology by reason of principles, because in fact the last end of man is supernatural, and in the order of practical knowledge ends play the role of principles). Or again, it may simply mean a dependence as to use (ministerium et imperium), -- for example, the art of bridlemaking is subordinated to the equestrian art, this latter to the military art, and this latter to the political art, -- without any concern about a dependence as to the manifestation of truth; wherefore the subalternation (which involves the subordination of one science to another) is improper. Cf. John of St. Thomas, Log. II. P., q. 26, a. 2.
{36} John of St. Thomas, Log., II. P., q. 26, a. 2.
{37} "Subalternantis scientiae conclusiones visibiles sunt ex et in principiis immediate, absque alio medio habitu; subalternatae vero conclusiones visibiles sunt ex et in principiis per se notis mediate, mediante scilicet habitu scientifico subalternante; et haec est essentialis et per se differentia inter subalternantem et subalternatam scientiam. Caeterae autem conditiones sunt consequentes, aut sunt talis subalternatae, non subalternatae ut sic. Puta, quod una dicat quia, et altera propter quid; aut quod objectum addat differentiam accidentalem et extraneam. Haec namque est conditio subalternationis quoad objectum, illa vera subalternationis quoad principia gratia materiae. Per se habitus principiorum proximorum scientiae subalternatae est habitus scientificus subalternans. Scientia subalternans et subalternata non necessario opponuntur ex parte objecti nec ex parte subjecti, sed potius ex parte conditionum medii: quia scilicet medium in subalternante immediate jungitur principiis per se notis, subalternatae vero mediate, mediante scilicet habitu alterius speciei." (CAJETAN, in I, 1, 2.) Cf. JOHN OF SAINT THOMAS, Curs. Theol. I. P., q. 1, disp. 2, a. 5.
{38} Cf. Saint Thomas, Sum. Theol., I, 1, 2; II-II, 9, 2, ad 3; in Phys., lib. II, 1, 3; in Boet. de Trin., 5, 1, ad 5; 5, 3, ad 6. See also my Réflexions sur l'Intelligence, p. 286 and Les Degrés du Savoir, p. 84.
{39} Cf. Les Degrés du Savoir, pp. 84-85 and 120-125.