• Journal for History of Mathematics
• /
• v.22 no.3
• /
• pp.1-30
• /
• 2009

Frege's logicism has been frequently regarded as a development in number theory which succeeded to the so called arithmetization of analysis in the late 19th century. But it is not easy for us to accept this opinion if we carefully examine his actual works on real analysis. So it has been often argued that his logicism was just a philosophical program which had not contact with any contemporary mathematical practices. In this paper I will show that these two opinions are all ill-founded ones which are due to the misunderstanding of the theoretical place of Frege's logicism in the context of contemporary mathematical practices. Firstly, I will carefully examine Cantorian definition of real numbers and Frege's critiques of it. On the basis of this, I will show that Frege's aim was to produce the purely logical definition of ratios of quantities. Secondly, I will consider the mathematical background of Frege's logicism. On the basis of this, I will show that his standpoint in real analysis was much subtler than what we used to expect. On the one hand, unlike Weierstrass and Cantor, Frege wanted to get such real analysis that could be universally applicable. On the other hand, unlike most mathematicians who insisted on the traditional conceptions, he would not depend upon any geometrical considerations in establishing real analysis. Thirdly, I will argue that Frege regarded these two aspects - the independence from geometry and the universal applicability - as those which characterized logic itself and, by logicism, arithmetic itself. And I will show that his conception of real numbers as ratios of quantities stemmed from his methodological maxim according to which the nature of numbers should be explained by the common roles they played in various contexts to which they applied, and that he thought that the universal applicability of numbers could not be adequately explicated without such an explanation.

• The Journal of the Petrological Society of Korea
• /
• v.22 no.1
• /
• pp.19-34
• /
• 2013

The Ipcheon Subbasin is an isolated Miocene basin in SE Korea, which has the geometry of an asymmetric graben elongated in the NE-SW direction. It is in contact with basement rocks by faults and separated from adjacent Waup and Eoil basins by the basement. The strata of the basin fills have an overall homoclinal structure, dipping toward NW or WNW. The basin fills consist of Early Miocene sediments rich in dacitic volcanic and volcaniclastic deposits and Middle Miocene non-volcanic and nonmarine conglomerates intercalated with sand layers, which are distributed in the northeastern and southwestern parts of the basin, respectively. Kinematic analysis of syndepositional conjugate faults in the basin fills indicates WNW-ESE extension of the basin. These features are very similar to those of the adjacent Waup and Eoil basins, indicating that the basin extension was governed by the NE-trending northwestern border faults and that the basin experienced a propagating rifting from NE to SW. Basaltic materials, which occur abundantly in the Eoil Basin, are totally absent in the Ipcheon Subbasin. The observations of the dacitic tuff and tuffaceous mudstone in the subbasin, on slabs and under microscope, suggest that they have lithologies very similar to those of the Yondongri Tuff in the Waup Basin. The Middle Miocene non-volcanic sediments of the Waup and Eoil basins and the Ipcheon Subbasin are distributed consistently in the southwestern part of each basin. It is thus concluded that the extension of the Ipcheon Subbasin began at about 22 Ma together with the Waup Basin and was lulled during the main extension period of the Eoil Basin between 20-18 Ma. At about 17 Ma, the subbasin was re-extended due to the activation of the Yeonil Tectonic Line associated with the propagating rifting toward SW. This event is interpreted to have provided new sedimentation space for the Middle Miocene sediments in the southwestern parts of the Waup and Eoil basins and the Ipcheon Subbasin as well.

• Journal of the Korean Chemical Society
• /
• v.37 no.3
• /
• pp.344-350
• /
• 1993

25,26,27,28-Tetraacetoxycalix[4]arene·monohydrate is orthorhombic, space group Pbca with a = 14.979(4), b = 15.154(4), c = 27.890(3) ${\AA}$, Z = 8, V = 6330.6 ${\AA}^{-3}$, D$_c$ = 1.28 $g{\cdot}cm^{-3}$, (Mo K${\alpha}$) = 0.71069 ${\AA}$, ${\mu}$ = 0.86 cm$^{-1}$, F(000) = 2600, and R = 0.069 for 3376 unique observed reflections with I > 1.0 ${\sigma}$(I). The structure was solved by direct methods and refined by cascade diagonal least-squares refinement. All the C-H bond lengths(= 0.96 ${\AA}$), the methyl groups and the methylene groups are fixed and refined as the rigid groups with ideal geometry. The macrocycle exists in the 1,3 alternate conformation (by Conforth) making the angles of 110.7, 684, 113.7 and 68.8$^{\circ}$ between the benzene rings and the methylenic mean plane, and four each acetoxy groups are twisted away from their own benzene rings with the angles of 68.2, 97.6, 78.9 and 71.3$^{\circ}$, respectively. The relative dihedral angles between two opposite side of the benzene rings are 135.6$^{\circ}$ for the rings (1) and (3) and 135.2$^{\circ}$ for (2) and (4). A water molecule which has nearly the same height of the methylenic plane of the macrocycle in the c-axis, is located within the distances of 2.942(5) ${\AA}$ from the O(8) atom of the carbonyl group and 2.901 ${\AA}$ from, another O(2)(1/2-x, -1/2＋y, z). The shortest contact between the molecule is 3.193 ${\AA}$ from the O(4) to the C(3)(1/2＋x, 1/2-y,-z).

• The Journal of the Petrological Society of Korea
• /
• v.18 no.1
• /
• pp.19-30
• /
• 2009

The main fault of Yangsan Fault Zone (YFZ) and Quaternary fault were found in a trench section with NW-SE direction at an entrance of the Sinheung village in the northern Eonyang, Ulsan, Korea. We interpreted the movement history of the southern part of the YFZ from the geometric and kinematic characteristics of basement rock's fault of the YFZ (Sinheung Fault) and Quaternary fault (Quaternary Sinheung Fault) investigated at the trench section. The trench outcrop consists mainly of Cretaceous sedimentary rocks of Hayang Group and volcanic rocks of Yucheon Group which lie in fault contact and Quaternary deposits which unconformably overlie these basement rocks. This study suggests that the movement history of the southern part of the YFZ can be explained at least by two different strike-slip movements, named as D1 and D2 events, and then two different dip-slip movements, named as D3 and D4 events. (1) D1 event: a sinistral strike-slip movement which caused the bedding of sedimentary rocks to be high-angled toward the main fault of the YFZ. (2) D2 event: a dextral strike-slip movement slipped along the high-angled beddings as fault surfaces. The main characteristic structural elements are predominant sub-horizontal slickenlines and sub-vertical fault foliations which show a NNE trend. The event formed the main fault rocks of the YFZ. (3) D3 event: a conjugate reverse-slip movement slipped along fault surfaces which trend (E)NE and moderately dip (S)SE or (N)NW. The slickenlines, which plunge in the dip direction of fault surfaces, overprint the previous sub-horizontal slickenlines. The fault is characterized by S-C fabrics superimposed on the D2 fault gouges, fault surfaces showing ramp and flat geometry, asymmetric and drag folds and collapse structures accompanied with it. The event dispersed the orientation of the main fault surface of the YFZ. (4) D4 event: a Quaternary reverse-slip movement showing a displacement of several centimeters with S-C fabrics on the Quternary deposits. The D4 fault surfaces are developed along the extensions of the D3 fault surfaces of basement rocks, like the other Quaternary faults within the YFZ. This indicates that these faults were formed under the same compression of (N)NW-(S)SE direction.