Finally, we have the individual by supposition (ex suppositione) or by circumlocution (circumlocutione), represented by the phrase 'son of Sophroniscus'.
Things seen as actual are necessary by supposition (i. e., with respect to God's knowledge and providence), but many of them are contingent with respect to their proximate causes (Sent. I.38.1.5, Summa contra gentiles I.67, Summa theologiae I, 14.13, De veritate 2.12).
If this psychology of belief were true, then the second principle of Bayle's doctrine would destroy belief in monotheism because, by supposition, it would be impossible to believe in the unity of God after acknowledging the irresistible force of the Manicheans' objections.
end{aligned} (9)The matrix B in Eq. (6) includes n linearly independent column vectors over (Z_{varphi ( N )} ) by supposition, it follows that the matrix ({B}^{prime }) is non-singular over (Z_{varphi ( N )} ) [i.e., det ((B^{{prime }})ne 0]) with overwhelming probability, and thus, we have (v_i^{prime } ne 0( {hbox {mod},varphi ( N )} )).
By supposition, we can replace x by u and y by v in (4.1), and by the lower semi-continuity of ψ, we obtain d ( v, u ) = d ( T v, S u ) ≤ ψ ( d ( R v, R u ), d ( R v, T v ), d ( R u, S u ), d ( R v, S u ), d ( u, T v ) ) ≤ ψ ( d ( v, u ), 0, 0, d ( v, u ), d ( u, v ) ) < d ( u, v ), a contradiction.
By supposition, we can replace (x) by (u) and (y) by (v) in (4.1) to obtain begin{aligned}&T(d(mathcal F u,mathcal G v),d(mathcal R u,mathcal R v),d(mathcal R u,mathcal F u),d(mathcal R v,mathcal G v),d(mathcal R u,mathcal G v),d(mathcal R v,mathcal F u))le 0&text{ or}&T(d u,v),d u,v),0,0,d u,v),d v,u))le 0 end{aligned}which is a contradiction to ((mathfrak T ^{prime }_2) ).
The last inequality follows as and by suppositions in the lemma.
Nevertheless, the various regulations and limitations of the use of PPD in personal care products are not substantiated by the intrinsic toxicity of PPD only but by suppositions regarding harmful reaction products also.
But the result of supposing an item presupposes that the information in question is indeed part of the suppositional scenario created by the supposition of the said item.
Nor that it can be explained by the supposition that, philosophy being concerned above all with arguments, women are naturally less adept in the field.
Students will understand that appropriate referral for radiological investigation is justified by a supposition of change in clinical management.
