By D. M. Armstrong
It is a examine, in volumes, of 1 of the longest-standing philosophical difficulties: the matter of universals. In quantity I David Armstrong surveys and criticizes the most methods and ideas to the issues which have been canvassed, rejecting many of the different types of nominalism and 'Platonic' realism. In quantity II he develops a tremendous conception of his personal, an aim concept of universals established now not on linguistic conventions, yet at the genuine and capability findings of common technology. He therefore reconciles a realism approximately features and kinfolk with an empiricist epistemology. the idea permits, too, for a resounding rationalization of traditional legislation as relatives among those universals.
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Additional info for A Theory of Universals: Volume 2: Universals and Scientific Realism (v. 2)
Since the form of the integral curves depends essentially on their curvature, and since this curvature depends on the second diﬀerential quotient, we are led to study the right-hand side of (11) in more detail. And, in particular, we will ﬁrst determine where the right-hand side changes in sign. For this purpose, we consider the equation (12) (n − uN )(N − un) − AP (1 − u2 )2 = 0. It is convenient here to divide by the square of the impulse constant n and to introduce the abbreviations (13) v= N , n ±m2 = AP .
Sliding and boring friction for the top. 551 We can speak of the quantity a, which in the previous section signiﬁed the mean radius of the contact surface, as the radius of the original contact circle from which our contact point P was formed. The quantity tg α, on the other hand, signiﬁes (cf. Fig. 75) the distance of the contact point P from the intersection point Q of the instantaneous rotation axis with the horizontal plane. Our preceding proportion thus states that the work of the sliding friction is smaller or larger than that of the boring friction according to whether the instantaneous rotation axis passes through the contact circle or not.
We will substitute for the curvature the approximate expression b) d2 u , dv 2 whose instantaneous magnitude can be taken directly from the diﬀerential equation (19). This value is indeed somewhat too large, and coincides suﬃciently well with the exact value of the curvature only if the inclination of the tangent to the curve with respect to the axis of the abscissa is small. We cannot claim with certainty that this occurs in our case; it is only clear from a remark on the previous page that the inclination of the tangent to the curve never becomes inﬁnitely large, for then the projection of the integral curve onto the axis of the abscissa would not cover this axis in a single-valued manner.
A Theory of Universals: Volume 2: Universals and Scientific Realism (v. 2) by D. M. Armstrong