Draft Excerpts

Check out a draft section at my other page.

So, you're not supposed to write the introduction first. Yeah, right. A twofold purpose is what I can see: 1) help me to focus my thoughts, and 2) help you all focus yours so that I can benefit from such helpful, sharp thoughts.

The title (evidently a record): "Mobiles, Bodies, and the Science of Quantified Motion: Corpus in Aquinas's Exposition of Physics VI.4 and in Early Modern Mathematical Physics"

John of St. Thomas, Cursus Theologicus, q.10, d.9, distinguishes two types of measurement:

EXTRINSECA est, quae mensurat aliquid extra se, et ideo per applicationem, vel continentiam illius dicitur mensura, sicut duratio, et motus coeli mensurat motus inferiores tam quam extrinseca mensura illorum, et ulna mensura pannum, et libra pondus. Unde talis mensura terminat relationem realem sui mensurati. INTRINSECA mensura est illa, quae inest rei mensuratae, et ita non mensurat per applicationem, sed per informationem, unde habet perfectionem mensurae, licet non relationem realem et imperfectionem dependentiae, qua mensuratum dependet a mensura, sicut tempus licet sit mensura extrinseca respectu nostri, intrinsece tamen mensurat ipsum motum coeli, neque enim habet aliud tempus superius, quo mensuretur, et in unoquoque genere perfectissimum est mensura sui, et caeterorum, sui quidem intrinseca, aliorum vero extrinseca.

EXTRINSIC [measurement] is what measures something outside itself, and thus through application or the containment of that which it is said to measure, as duration and the motion of the heaven measures the inferior motions just as their extrinsic measure, and the forearm the measure cloth, and the pound, weight. Whence such a measure determines a real relation of itself [and] of the measured. INTRINSIC measurement is that which is in the measured thing, and thus it does not measure through application, but through information, when it has the perfection of [being] a measure, granting that it does not have a real relation and the imperfection of dependence by which the measured depends upon the measure: just as time, while it is an extrinsic measure with respect to us, it yet measures intrinsically the motion of the heaven itself, for there is not time superior to it by which it would be measured; and in what genus soever the most perfect is measure of itself and of the rest, of itself intrinsically, but of the other extrinsically.

Extrinsic and intrinsic measures thus exclude each other on three counts: relation to another vs. relation to itself, which relation is borne out in a measurement by application or containment (e.g., meter-sticks or place) vs. measurement by forming or informing something (as a body's quantity measures it), and such relations in measuring or making known the quantity of a thing give rise to real or rational relations. An intrinsic measure thus bears the mark of being a perfect measure (requiring no dependence upon another) while an extrinsic measure imports a relationship of dependence of the measured upon the measure.

Some extrinsic measurements, such as the motion of the heavens measuring an inferior motions as to their time, require for their completion as measures a mind to which their 'measuring' is revealed. That is, the past and the future have a real order, but they bear no real relation to each other since they have no real simultaneous existence. These parts of the measurement have a relation "secundum esse" but not a real relation, for a real relation requires that both related things obtain in reality. Thus John of St. Thomas recognizes that: "In ipsa autem perfectione mensurae advertendum est, quod aliquae mensurae sunt, quae in ipsa sunt constitutione, et perfectione requirunt aliquid rationis tamquam conditionem, et complementum." The mind makes time one through enumeration, and makes meter-stick measurements one through a like operation. The measure, however, still bears a real relation to the measured insofar as the basis for the enumeration obtains simultaneously (the motion of the heavens is related causally to the motions of the inferior spheres). The oneness of the units of measurement are what required the enumeration of mind (for the now is not a per se part of time).

Scientia Media

In his preface to Newton's Principia, Cotes igives a syllogistic argument for the attraction of all planetary bodies towards the sun that could be construed as a syllogism in “scientia media” form (the major term is more mathematical, Prop.2 of Principia; and the minor term seems more physical, Kepler’s second law). (From Cohen’s edition, p.387-88, with my [additions]/italics):

“Now, it is reasonable to accept something that can be found by mathematics and proved with the greatest certainty: namely, that:
[M:] all bodies moving in some curved line described in a plane, which by a radius drawn to a point (either at rest or moving in any way) describe areas about that point proportional to the times, are urged by forces that tend toward that same point.
Therefore, since it is agreed among astronomers that
[m:] the primary planets describe areas around the sun proportional to the times, as to the secondary planets around their own primary planets,
[C:] it follows that [etc.] ...  This force can, appropriately, be called centripetal ... From whatever cause it may in the end be imagined to arise."

I understand the last phrase to be Cotes’ recognition that mathematical physics as a scientia media abstracts from considering physical causes as such.

Newer Posts Older Posts Home