1

.

L. WITTGENSTEIN

1999

2

____________________________ 3

_______________________________________ 3

1.______________________________________________ 4

2. WITTGENSTEIN: _ 5

) ________ 10

) _________________________ 21

3. _______________________________________ 32

4. _________________________________________________ 35

_____________________________________________ 36

3

BGM: Bemerkungen uber die Grundlagen der Mathematik (Wittgenstein)

RFM

LFM: Lectures on the Foundations of Mathematics (Wittgenstein)

KB: (Wittgenstein)

MB: (Wittgenstein)

: (Wittgenstein)

: (Wittgenstein)

: (Wittgenstein)

RFM: Remarks on the Foundations of Mathematics (Wittgenstein)

Tr.: Tractatus Logico- Philosophicus (Wittgenstein)

: (Wittgenstein)

: (Wittgenstein)

: (Wittgenstein)

WL1: Wittgensteins Lectures: Cambridge 1930-1932

WL2: Wittgensteins Lectures: Cambridge 1932-1935

WWK: Wittgenstein und der Wiener Kreis (Waismann)

4

138-242

.

,

, 138-142

Wittgenstein ,

( ,

).

(1930, 25-27),

Wittgenstein,

.

:

,

.

5

1.

138-242, (

),

, (. 32-40, 56-57, 94-95, 133-

135, 173-174, 194-197 ), ,

( 26, 28-29, 44, 46, 61-62, 139-140),

( 75, 35, 98-99, 119, 121, 291, 302-303

, ), Remarks

on the Foundations of Mathematics (VI -12, VI-16, VI-22, VI-28, VI-29, VI-31, VI-38),

Zettel ( 296,430),

(.. 53-54, 80-86, 100-101,

108, 125, 126, 129, 497, 558,560, 567, 568, 653, 692, 693,

. . 280-281). L. Wittgenstein

Fr. Waismann , Ludwig Wittgenstein und

der Wiener Kreis, Blackwell, Oxford 1967 (121-123, 126, 133, 155).

, Wittgenstein

( , )

)

, (-)

(Tr. 4.112:

, 109:

, 128:

,

, , . 44:

), ) ,

(Sprachspiele, language-games) -

,

6

,

-

( )

, (

. . 44), ( .

122) ,

1 ( 7, 65, 133)

(

, 130)

,

, ,

, calculi ( 81,

136).

:

, - ,

,

2 ,

(Frege) (Russell) -

-

, ,

3 .

Wittgenstein , 4 .

,

Wittgenstein. Tractatus Logico -

Philosophicus G. Frege

1 . Rush Rees, , . 1984, . 13 ., .

, Tractatus 9, 1974, . 26-29 2 (Begriffsschrift) Frege . . ,

. , . 1998, . 71-77 ( ). 3 Tractatus

, (Tr. 5.47, 5.471) 4 . .. R. J. Fogelin, Wittgensteins critique of philosophy, in: The Cambridge companion to

Wittgenstein, by H. Sluga-D.G. Stern (eds.), Cambridge Univ. Press 1997, . 50-55 ( indeterminacy, underdeter mination, incoherence of rules)

7

B. Russell (Principles of Mathematics 1903, Principia Mathematica

1913), ,

( )

Fritz Mauthner5 , (

Tractatus ,

). Mauthner, ,

,

(

).

:

(RFM VI - 28).

,

( )

( , )6 .

,

, ,

( proposition sentence),

- .

( -7 ) :

( - .

120: (, .), ,

), ,

.

5 . H. Sluga, Ludwig Wittgenstein: Life and work. An introduction, in : The Cambridge companion to

Wittgenstein (. . 4), . 3, 13 . , , 17, 1977, . 4-5. 6 . . ,

L. Wittgenstein ( : 1989), . 24-27, , R. Monk, . . , 1999, . 568-569, 574-576 ( Defense of Common Sense 1925 G. E. Moore). 7 , . ,

(: - ) , , , . - -.

8

8 (

), (..

)

(), ,

,

. Wittgenstein

(

,

, 138: ),

(

9 )

( .. ,

23, 241).

, :

- ( ) -

, , ,

, . .. WL1 Cx/86:

, .

.

10 , 496: ( ) ,

, 497:

,

.

,

8 . . , , 1987, . 12, H. - J. Glock,

Necessity and normativity, in: The Cambridge companion to Wittgenstein (. . 4), . 201-202, Br.Bix, Law, language and legal determinacy, Clarendon Press Oxford, 1993, . 46-47 9 . . .. (. 8) P. Hacker (Insight and Illusion 1972, . 151):

, Br. Bix .. (.8), . 46. 10

Wittgensteins Lectures: Cambridge 1930-1932, Oxford 1980 : .... 1994, . 505 . 29 ( . ).

9

(.. ).

, ,

(

, ),

,

,

,

-

- , (

Wittgenstein ) ( 66, 67, 108)

(

).

. .. 133: .

( ).

.

.

.

,

, 137:

( 139), 140:

:

.

(

, )

Wittgenstein

( ,

), -

( 204, 625).

10

2. WITTGENSTEIN:

)

L. Wittgenstein

(

,

,

, .. , ): )

, )

calculi. ( 569)

( 7, 83), , ,

(

).

Tractatus,

()

.

( 53, 54)

, ( 83).

,

prima facie , Wittgenstein

(

): - make

up rules as we go along; - - as we

go along ( 83).

,

,

,

(

):

11

(RFM, VI - 28)11

.

12 ( 102,

20, 43), , ( 124:

),

- (

), (.

81). ;

, ,

(

132 ., ,

, ).

,

,

, ..

,

; (

, Wittgenstein,

) ,

,

,

( 39:

. (

)).

..

,

11

H.-J. Glock, Necessity and normativity, in: The Cambridge companion to Wittgenstein (. . 4), . 223. 12

Wittgenstein . . , . .... 1994, . 502, . 16.

12

( )13 ,

-

,

, ( )

, - . 187: ,

, ,

( )

.

,

, 14 ,

( ,

).

Wittgenstein

138-242,

, ,

. Wittgenstein

, ,

,

, :

, ,

,

13

( ) J.R. Searle ( ; . 17, 1977, . 73-90) J. Rawls ( . 12/3, 1994. . 313-340) : , .. , , . . 14

. . , Wittgenstein: , : Wittgenstein (.: . ), 1991, . 163

13

,

,

, (;) - .

,

( 98, 99, 101-106,

100: , . -

;). ,

( 107) (

)

Wittgenstein

, 116:

, (. 72:

, ,

- - .

, ,

15 ).

. ;

(..

);

Wittgenstein,

( 98:

,

) , , ,

, ( 91,

76).

( 77:

15

. 57: .

14

,

. , ).

, ,

, ,

(

) .. ,

, ( 154-155),

( 90),

,

, ,

( , ).

, ,

16 .

, ,

, :

,

,

. - (Zettel, 351)17 .

( )

,

, ,

( , 36). ,

, ,

Wittgenstein

( 81, 88, 100-107, 57:

16

. 464: : . L.W. . 17

Br. Bix. .., (. 8), . 43 (. 142)

15

. ,

, ).

Wittgenstein

,

,

,

:

, ,

.

(

hinc et nunc L.W.).

( )

18,

( 80).

Wittgenstein

, 19 ,

20 (

), . .. 54:

,

,

.

Wittgenstein ,

, ,

18

. . , , .. (. 14), . 163. 19

, R. Fogelin (Wittgensteins critique of philosophy, .. (.4), . 53), . 20

. 24-25: : , ( ).

16

21 .. ,

, .

, ,

(

Brouwer22 ),

,

. (

1932-1934) contradictio in

terminis 23 ,

, ,

, ( 320), ,

,

(WWK 208)24

( 320),

, ,

(WWK 125)25

, .

, , (

) ( 318).

, , -

(WWK 195)26. ,

21

55: , ; 22

. . , . , 1992, . 41-42 23

. R. Fogelin, Wittgensteins critique of philosophy, .. (.4), . 53-55, . , , .., (. 12), . 30-31. 24

. , .., .., (. 12), . 31. 25

(. 24), . 518. 26

(. 24), . 31

17

,

,

Wittgenstein :

: ()

: ( 319).

( ..

), 1939

(Lectures on the Foundations of Mathematics)

Alan Turing, ,

, Wittgenstein

. ,

,

: ..

,

.

, Wittgenstein, ,

:

. , ,

(LFM 217)27 . -

- ,

, ,

- , ,

,

( )

,

,

, .

27

. , , .. (.12), . 517. . R. Monk, . . , 1999, . 421-425.

18

( 320) 28

,

,

, ,

,

29 .

, .. ,

, .

, ,

( 264),

-

, ( 125).

, prima facie ,

, ,

, ,

. , (. . 28) Wittgenstein

28

Wittgenstein, , (. 125: : ) , , , : , ( 320), , , . Wittgenstein ( ), , . ( ) . , : [] , . , ( 26, ). 29

, Wittgenstein , (. , V. Kraft, , 1986, . 27 .)

19

,

.

:

, (BGM VII.16/378)30.

,

, ,

(

), ,

- (

.. ),

Wittgenstein

.

264, 125 ;

, ., , ,

.

:

. (

31), -

Russell

. (WL2I.11/13)32 . ,

: , ,

, .

,

33 ,

30

Bermerkungen uber die Grundlagen der Mathematik, : , .... 1994, ( . ), . 30 31

Wittgensteins Lectures: Cambridge 1932-1935, Oxford 1979, .., .. (. 30), . 516, 32

.., (.31), . 517 33

. R.Monk, . , .. (.27), . 311-313 WWK 123,126,133,156: ;

20

, ,

, ;

( 366)

; ,

; Wittgenstein

.. ,

- 34 -

, , ,

(

).

( )

. .

.

Wittgenstein (. . 34)

,

.

(

), :

,

( ) ( 225:

).

34

, (.. ) . , , , ( ) , , . , : Tractatus (Tr. 3: ) , L.W. - , : ( 580). ( ); . .

21

)

,

, , ,

(M. Dummett35),

(J.McDowell36) (S. Kripke Cr.

Wright37

).

:

) Wittgenstein (

213,486,551) ( 307-8, 498,550), ( 171-178,

232)

,

, ,

),

( ,

431: - , , -.,

71: ( )

. 432),

.

)

38 .. ( 143,

185-190) ( 206:

: ) +1

. (..

+2 +1) 1000,1001 1000,1002

1000

1001,

35

. . , Wittgenstein , 13/2-3,1995, . 139-142, . , , .. (. 14), . 180, . 46. 36

J.McDowell, o Wittgenstein (.: .), 13/2-3, 1995, . 175-214 37

Kripke , . . , .. (. 35), . 146-173, J.McDowell, . (. 36), passim. 38

. P. Strawson, Wittgenstein (. : . ), 27/28, 1979, . 297-303

22

, ;

Wittgenstein (

) ( 187)

.

( )

()

( 187: , ,

,

). ;

( 190),

. ; ,

( 193-194) :

, ,

( 193). Wittgenstein

; ,

( 193),

:

( 431). ;

) , (

) -, ,

( ).

i) ( ),

, , ,

, , -

! ( 195).

(

, ;). Wittgenstein

( 195) :

, .

23

,

, ,

, ,

(. 302) -

:

() - -

- -

( ,

-

). , ,

; -

, ,

( 197). , ,

, (,

) ( 199). (.

.

202).

, (

39 ) ()

, hinc

et nunc (

- Wittgenstein

).

,

, -

;

(..

) ; Wittgenstein

39

, (40).

24

, .

.

( 241).

:

(

; - regresus ad infinitum). ,

, Wittgenstein

40 ,

, (

). , , -

- ( . 281)41 .

, , ,

( ,

,

).

;

, -

, ( 204).

(

),

Wittgenstein (MB41-42) -

, (

)

.

, 42 .

,

, ,

40

. , .. (. 35), . 169 41

(S160,51) : Baker and Hacker, Wittgenstein: Rules, Grammar and Necessity, 258, Br. Bix, .. (. 8), . 44. 42

. , , 1989, . 30

25

.

( 199) - -

,

-

( 202, 380)

( , 243

.).

, ,

Wittgenstein ,

: ,

. : ! (

217), ,

.. 43 .

(

219): .

; 211:

. ,

, ,

-

( ). : )

( ) -

, )

, ( ,

,

Wittgenstein).

( ),

, , (

), )

) ,

43

. J.McDowell, .. (. 36), . 201-206.

26

. ( )

.

Wittgenstein

( ) ,

.

, ,

,

, ,

:

,

,

, ;.

,

, .

.

198: , , ,

- , .

.

, 201 ( :

Wittgenstein on Rules and Private Langauge (an elementary exposition), Blackwell

19892 Saul Kripke Wittgenstein

201, ):

,

,

.

27

, , ( 28)44 ,

Wittgenstein !

: ;

; ( 506), ,

, ; ,

,

( , ). ,

, 45

(

, :

, )46 .

;

-

- ,

( 41).

(

). ( )

(

: Wittgenstein

,

, , 224:

, ):

44

. 9: . , . ! ( , , ). 45

, ( ...) . 46

, . , ( 45).

28

: ,

, , ,

( 10).

:

( 11).

(10),

( () )

( ;

, ;

12) ,

(.. / ,

,

, ).

(

) ( 13) :

, (

, .)47 .

ii) ,

,

( 504);

,

,

;

, ,

, Wittgenstein

, .

, 48 ,

47

. , , .. (. 14), . 170-1 - . Wittgenstein ( ) ( ), , (). 48

. , .. (. 35), . 159, . , , .. (. 12), . 169-171.

29

Wittgenstein :

( 445),

,

( 112), (95)

. 50. ,

, ,

. (

), ( ,

)

, (

) ,

( ),

,

, ,

49 , (

) ,

.

;

(

),

,

,

, ( 55),

50 .

, -

! ( 437),

,

49

457: : . 50

: ; , 441 ( Tractatus, , ).

30

,

( ),

.

(:

,

453). , , ,

, ,

, (

): , -

- .

. . :

( 376-377

. 95). ( 461,

102-103, 112, 240),

, (.. 25 25) (625)

( 111),

, ( ):

,

.

() , ( 101-102 .

572, 574).

, 51 :

- -

()

( 240),

:

) ;

( 241) ..

51

- . 692-693.

31

( ,

) ,

, ( 242), ,

Wittgenstein, ,

, (

, ), 52,

,

( 234, 240), ( 381:

; - :

), , ( 242, 83),

,

, (

,

).

) .

Wittgenstein ,

(

), ,

, : ,

( ,

. ,

337,

, 3380),

,

( ,

).

52

. , .. (. 35), . 167-168.

32

3.

(

), Wittgenstein

:

)

,

Wittgenstein , -

,

, , -

,

(

,

, ,

,

). Wittgenstein

53

.

(

),

, , (

.. , ) ,

,

.

:

(

) Wittgenstein

(

53

Ludwig Wittgenstein: A Lecture on Ethics (. . ) : . , 1997.

33

, , ) :

(

.. ).

)

(..

) ,

( ),

, .

: ,

, -

()

(

, ,

). (

) Wittgenstein

.

) ,

Wittgenstein

( )

,

, .

,

( ) ,

(

), .

in claris non fit interpretatio

Wittgenstein,

(

,

, ; , ). Wittgenstein

( ),

34

( minimum),

in claris non fit interpretatio,

( ,

, , .,

).

Wittgenstein

( )

,

. ,

..

,

( clear cases) ,

(hard cases)54 55

, Wittgenstein

,

, .

,

Wittgenstein, (

, Wittgenstein, 56 -

).

H.L.A.

Hart :

Wittgenstein

Tractatus

(core)

(.. ) (penumbra),

54

Br Bix, .. (. 8), . 61-62 55

D. Patterson, Laws Pragmatism: Law as Practice and Narrative, 76 Virginia law Review (1990), . 937 ( Br. Bix, . (. 8), . 50) 56

Chatrapati Singh, Can Wittgensteins Philosophy Yield a Theory of Justice? Proceedings IWS 5 (1981), . 365-367 ( . - , Wittgenstein, : Wittgenstein (.: . ) 1991, . 108, . 22.

35

(.. ,

Hart : ). ,

(

)

(.. ...).

(

) ,

,

. Wittgenstein :

( ) (

);.

, Hart

J.L. Austin, .

, ,

Hart ,

(

) ,

57 . Wittgenstein

,

.

57

. . , , , : H.L.A. Hart, 1993, . 300-302.

36

4.

,

,

. ,

,

. Wittgenstein

, (

, ).

,

, . ,

( , ). Wittgenstein

, ,

, .

, (

) ,

(

). (

).

37

1. Wittgenstein L. , Tractatus Logico - Philosophicus (. : . ),

. 1978.

2. Wittgenstein L., (. - . - .: . ),

. .... 1994

3. Wittgenstein L., (.: . ), .

1977

4. Wittgenstein L., (.: .

), . . . , 2 1987

5. Wittgenstein L., (.: . ), .

1989

6. Wittgenstein L., (. : . ), .

, 1984.

7. Wittgenstein L., (.: . - . -

), . 1986

8. .,

: Wittgenstein (.: . ), .

1991, . 118-138.

9. Bix. Br., Law, Language and Legal determinacy, Clarendon Press Oxford

1993, . 36-62

10. ., , 1977, . 171-230.

11. ..

Ludwig Wittgenstein () : , .

1989, . 13-41.

12. - ., Wittgenstein,

: Wittgenstein (.: . ) .

1991, . 105-117

13. Fogelin R.J., Wittgensteins critique of philosophy, in: The Cambridge

companion to Wittgenstein, by H. Sluga - D. G. Stern (eds.), Cambridge

University Press 1997, p. 34-58

38

14. Glock H. - J., Necessity and normativity in: The Cambridge companion to

Wittgenstein, by H. Sluga - D. G. Stern (eds.), Cambridge University Press

1997, p. 198-225

15. ., , : Wittgenstein (.: .

), . 1991, . 157-199.

16. McDowell J., O Wittgenstein

(.: . ), 13/2-3, 1995, . 175-214.

17. Monk R., . (. : .

), . Scripta, 2 1999.

18. ., Brouwer

Wittgestein, : Wittgenstein (.: . ) .

1991, . 69-82

19. Strawson P.F.,

Wittgenstein (.: . ), 27-28 (

) 1979, . 287-322

20. Stroud B., Mind, meaning and practice, in: The Cambridge companion to

Wittgenstein, by H. Sluga - D. J. Stern (eds), Cambridge University Press

1997, . 296-319

21. , Wittgenstein

, 13/2-3, 1995, . 137-173

22. ., , 17,1977, . 3-18

23. ., Tractatus, 9,

1974, . 3-43

24. ., 1977,

. 3-15

25. ., 1987,

. 11-18

26. ., Wittgenstein :

Wittgenstein (.: . ), . 1991, . 51-68.