(2016 1 ) 111-150

30013 101 E-mail: dokkyrote2003@hotmail.com

(realism) (nominalism)

2015. 06. 302015. 11. 16

112

(1909-1995)1 1939-40 31-32 1941 9 2

(Bertrand Russell, 1872-1970) (Alfred North Whitehead, 1861-1947) Principia Mathematica, 1910-19133 (logicism)

1 2003

2 8-10

3 Principia Mathematica

Principia Mathematica The Principles of Mathematics(1903) Principia MathematicaThe Principles of Mathematics Principia Mathematica

113

theory of class4

(implication)

(axiom of reducibility) (axiom of infinity) (multiplicative axiom) (existence theorems)5

6

4 class theory of classes set, set theory class

5 551-608 6

1989 63-74

114

1949 1956-57 7

8

9

1955

10 107-1161995 53-57

7 23-24 8 1955 12-13

9 N. Serina Chan, The Thought of Mou Zongsan. (Leiden, Boston: Brill, 2011), pp.13-14.

1987 5

115

10 (1895-1984)

10 1941

1

116

11

12

13

11 2002

2002 6 208-209208 209

12 137-143 13 (Immanuel Kant,

1724-1804) (Otto Hlder, 1859-1937)

117

(realism) (nominalism)

(1937) Otto Hlder, Die Mathematische Methode. Logisch Erkenntnistheoretische Untersuchungen im Gebiete der Mathematik, Mechanik und Physik. (Berlin: Springer, 1924.)

118

John G. Slater Bertrand Russell

John Ongley Rosalind Carey Russell

1897 14

5+7=12

14 An Essay on the Foundations of Geometry

John G. Slater, Bertrand Russell (Bristol: Thoemmes Press, 1994), pp.15-16

119

(ontology)

(epistemology)

(reduce)

15

15

Michele Friend, Introducing Philosophy of Mathematics (Stocksfield: Acumen 2007), pp.49-50.

120

(rationalism)

(rational intuition) (innate idea)

16

(Aristotle) (valid) 17

(Euclid)(Elements)

16 Horsten, Leon, "Philosophy of Mathematics", The Stanford Encyclopedia of Philosophy

(Spring 2015 Edition), Edward N. Zalta (ed.), available from http://plato.stanford.edu/archives/spr2015/entries/philosophy-mathematics/ 2015 3 1

17 John G. Slater, Bertrand Russell, p.16.

121

18

1897 1900 (Giuseppe Peano, 1858-1932) 1890

19

10 20

2 (successor) 21

322

18 John Ongley and Rosalind Carey, Russell (New York: Bloomsbury Academic, 2013),

pp.3-5. 19

Richard Dedekind 1872

John Ongley and Rosalind Carey, Russell, p.4. 20 0 is a number. 1

1 0 0 John Ongley and Rosalind Carey, Russell, p.27.

21 The successor of any number is a number. 1

122

40 23

5 (property) 0 24

21 0 2 1 3 2

10 2

3

4 0 0 512 0 0

5 0

5

25

22 No two numbers have the same successor. 23 0 is not the successor of any number. 24 Any property which belongs to 0, and also to the successor of any number which has the

property, belongs to all numbers. 25 John G. Slater, Bertrand Russell, p.16-18. John

Ongley and Rosalind Carey, Russell, pp.26-27.

123

0

(truth) 19

0

26

27

4 2 (predicate)28 2 X,Y 29 2

26

John G. Slater, Bertrand Russell, p.17.

27 Gottlob Frege (1848-1925)

28 member

29 X,YX,Y (subject)

John Ongley and Rosalind Carey, Russell, p.2.

124

1 0 1, 2 0 0 1 X X X 2 X, Y X Y X Y 1 230

(1-to-1 correspondence) X Y X Y X Y Y

A B A(similar to) B

30 John G. Slater, Bertrand Russell, p.19.

125

(the number of a class)

31

0

032

31 John G. Slater, Bertrand Russell, pp.18-20.

(the theory of logical types) 1901

(paradox)1903 1910

John G. Slater, Bertrand Russell, pp.21-23John Ongley and Rosalind Carey, Russell, pp.12-14. Michele Friend, Introducing Philosophy of Mathematics, pp.66-69.

32 0 N N 1 N X X

126

0, 1, 2, 3

(infinity)

33

33

John Ongley and Rosalind Carey, Russell, p.184.

127

0, 1, 2 1010 1 11 11 11

11

11, 12, 13 11=12=13 10+1 11+1, 11+1 12+110, 11

34

34 John Ongley and Rosalind Carey, Russell, pp.184-187.

128

35

(m+n) A m B n A B m+n 36 (mn) A m B n A B (ordered pairs) AX1, X2Xm BY1, Y2YnX1,Y1, X1,Y2, X1,Yn, X2,Y1, X2,Y2, X2,Yn, Xm,Y1, Xm,Y2, Xm,Yn37

mn

mn A B

35 John Ongley and Rosalind Carey, Russell, p.184. 36 m+n A B m+n A

B 37 XY

Xm,YnYn, Xm

129

mn

38

(well-ordered)

38

0

1 John Ongley and Rosalind Carey, Russell, p.189.

130

39

40

X

X (attribute to) (substance)

39 John Ongley and Rosalind Carey, Russell, pp.187-192. 40 Michele Friend, Introducing Philosophy of Mathematics, p.70.

131

X

X

X X

X X

X X X X X (individuality)

(ontology)

X X X

(realism)

(nominalism)

132

41

2 3 (universal) 2 3 2 32+3=52 32 1 3 12 32 1 3 1

42

1(ideal objects) (perceptible) (intelligible)

41 David Bostock, Philosophy of

Mathematics: An Introduction (Malden, MA: Wiley-Blackwell, 2009), p.30, 262. 42 (Platonism)

David Bostock, Philosophy of Mathematics: An Introduction, pp.7-14.

133

2 3

43

2

(a priori knowledge) 2 3 2 32+3=5

1 2

43

Michele Friend, Introducing Philosophy of Mathematics, pp.28-29.

134

44

44

hypothesis

135

45

46

45 (theory

of form)

David Bostock, Philosophy of Mathematics: An Introduction, pp.10-11. David Bostock, Aristotles Philosophy of Mathematics, in Christopher Shields ed., The Oxford Handbook on Aristotle (Oxford; New York: Oxford University Press, 2012), pp.465-491.

46

136

(individuality)

47

47

infinity David Bostock, Philosophy of Mathematics: An Introduction, pp.23-28.

137

48

49

48 David Bostock, Philosophy of Mathematics: An

Introduction, pp.15-31. David Bostock, Empiricism in Philosophy of Mathematics, in A.D. Irvine ed., Handbook of the Philosophy of Mathematics (Amsterdam; Boston: North Holland / Elsevier, 2009), pp.157-229.

49

138

50

50

2 3

X X X X X (David Hume, 1711-1776) (empiricism) X

139

(entity) (fact)

51

51 137-143 636

140

7

52

1 (scheme) (category)

2(reason itself)

3

52 616-619

141

53

454

5

655

7(sign of position)56

8

53 8 619 54 55 145-151 56 7

634-638 169-181

142

9

57

12

3

123

4545

67

57

163-168

143

58 59

60

58 7

(demonstrate)

59 169 60 89

144

145

61

61

1955 9

1987 6

146

2003

147

62

63

64

65

62 72-73 63 64 74-75 65

148

MOU Zongshan1989 Wushi zishu [Taipei] [Ehu chubanshe]

2003 Renshishin zi pipan Mozongshan xiansheng quanji Vol.18 [Taipei] [Linking publishing]

2003Luoji dianfan Mozongshan xiansheng quanji Vol.11 [Taipei] [Linking publishing]

JIN Yuelin2002 Luoji dianfan pingshen shu 32 1 Tsing Hua Journal of Chinese Studies, Vol.32 no.1.

TSAI Renhou2003Mozongshab xianshen nianpu Mozongshan xiansheng quanji Vol.32 [Taipei] [Linking publishing]

YAN Binggang1995 Zhenghe yu chongzhu dangdai daru Mo Zhong-shan xianshen sixiang yanjiu [Taipei] [Taiwan Studentbook]

149

Bostock, David. 2009. Empiricism in Philosophy of Mathematics, in A.D. Irvine ed., Handbook of the Philosophy of Mathematics. Amsterdam; Boston: North Holland / Elsevier.

2009. Philosophy of Mathematics: An Introduction. Malden, MA: Wiley-Blackwell.

2012. Aristotles Philosophy of Mathematics, in Christopher Shields ed., The Oxford Handbook on Aristotle. New York: Oxford University Press.

Chan, N.Serina. 2011. The Thought of Mou Zongsan. Leiden, Boston: Brill.

Friend, Michele. 2007. Introducing Philosophy of Mathematics. Stocksfield: Acumen.

Horsten, Leon. Spring 2015 Edition. Philosophy of Mathematics , The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), available from:http://plato.stanford.edu/archives/spr2015/entries/philosophy-mathematics/. 2015 3 1

Ongley, John and Carey, Rosalind. 2013. Russell. New York: Bloomsbury Academic.

Slater, John G. 1994. Bertrand Russell. Bristol: Thoemmes Press.

150

Mou Zongsans Criticism of Russells Logicism

LIU Ying-Cheng Doctoral student of Department of Chinese Literature,

National Tsing Hua University

Address: No.101, Sec. 2, Guangfu Rd., East Dist., Hsinchu City 30013, Taiwan

E-mail: dokkyrote2003@hotmail.com

Abstract

The present essay examines Mou Zongsans criticism in his Luoji dianfan of Russells logicism. First, the author gives a sketch of how Russell reduces mathematics to logic on the base of the set theory and why he has to assume the axiom of infinity and the multiplicative axiom. Second, Russells position is traced to nominalism, one of the two main traditions in the philosophy of mathematics. Finally, I present Mous doctrine that logic (and mathematics) is the displaying of pure reason itself and give my reflection on the doctrine. I conclude that in spite of Mous disagreement with Russell, Luoji dianfan did play an indispensable role in the development of his thought.

Keywords: Mou Zongsan, Russell, mathematics, rationalism, Paradigm of Logic (Luoji dianfan)