-
(2016 1 ) 111-150
30013 101 E-mail: [email protected]
(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
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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.
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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: [email protected]
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)