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『論理哲学論考』の電気回路モデル : 真理表の哲

学(八)

著者

橋本 康二

雑誌名

哲学・思想論集

43

ページ

23( 154) - 62( 115)

発行年

2018- 03- 28

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八 

一 

((

一 

3

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二 

1

4

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1

W1

W2

W3

2 1 W1 W2 W3 W4

5

a1 a2 a3 a4 b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12 b13 b14 b15 b16 b1 a1 b1 a2 b1 a3 b1 a4 b2 a2 b2 a3 b2 a4 b3 a1 b3 a3 b3 a4 q T T F F p T F T F T T T F

T−F図式1

q T T F F p T F T F T T T F

p q

W1

q

W2

p

W3 W4

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b4 a1 b4 a2 b4 a4 b5 a1 b5 a2 b5 a3 b6 a3 b6 a4 b7 a2 b7 a4 b8 a2 b8 a3 b9 a1 b9 a4 b10 a1 b10 a3 b11 a1 b11 a2 b12 a4 b13 a3 b14 a2 b15 a1 a1 a2 a3 a4

a1 ・ ・ ・ a4 b1 ・ ・ ・ b16 b1 ・ ・ ・ b16

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b10

b11

a1

a2

a3

a1

a2

a3

三 

2

3 16

2 8

16 図3

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8 8

4

4 5

2

2 4

16

6 6

2

1 1

8

図4

図4

図5

図5

① ② ③ ④ ⑤ ⑥ ⑦ ⑧ ⑨ ⑩ ⑪ ⑫ ⑬ ⑭ ⑮ ⑯ A

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8

2

a1

a4

b1

b16

6

a1

a4

4 a1

a4

2 2

2 4

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W3

W4

4

a1

W1

a2

a3

W3

a4

W4

a1

a2

a3

a4

4

4

5 4

b1

b16

0 4

0

4

24

16 b16

7 6

b1

b16

b1

b16

b1

b2

b3

b4

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b6

b7

b8

b9

b10

b11

b12

b13

b14

b15

b16

7

8

W1

W2

W3

W4

4 7

b1

T−F図式7

T T F F p

T F T F

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b1

b16

9

10

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論 11

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12

b1

b16

b1

8

13 真理表8

q pまたはq

T T F F p

T F T F

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9

10

真理表9

pならばp、かつ、 qならばq

T T F F q p

T F T F

T T T T

p、かつ、pということはなく、 また、

q、かつ、qということもない

T T F F q p

T F T F

F F F F

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14

R* b2

a1

b3

a2

b4

a3

b5

a4

b6

a1

b6

a2

b7

a1

b7

a3

b8

a1

b8

a4

b9

a2

b9

a3

b10

a2

b10

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b11 a3 b11 a4 b12 a1 b12 a2 b12 a3 b13 a1 b13 a2 b13 a4 b14 a1 b14 a3 b14 a4 b15 a2 b15 a3 b15 a4 b16 a1 b16 a2 b16 a3 b16 a4 ψ* ψ* R* ψ* a1 a4 R* a1 a4 R* 2 11 16 8

図11

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12

R*

ψ* 図12

⑩ A

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13

⑯ A

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15

16

4

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4

4

4

4

4

4

4

4

14

15 図14

図14

リレー

図15

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16 17

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15

(23)

(24)

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18 2

16 16

17

18 19

21

17 19

10

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3

20 21

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四 

2 1

1

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b4

a1

b4

a2

a1

a2

ψ*

R*

ψ* ψ*

ψ*

2 8 22

23

26

b1

b2

b3

b4

図22 ①

④ A

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写真23 写真25

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b1

b2

b3

b4

23 20

24 27

25

26

25

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W1

W2

真理表27

pという ことはない

F T p

T F

p、かつ、pと いうことはない

F F pならばp

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2

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26

29 30 25

26

表28

N 現実世界

φ

pならばp いうことはないp、かつ、pと

N N

pという ことはない

N

TF 現実世界

W1,W2

pならばp いうことはないp、かつ、pと

T F

pという ことはない

TF

表29

TF T F N 現実世界

W1,W2

W1

W2

φ

pならばp いうことはないp、かつ、pと

T T T N F F F N pという

ことはない TF

F T N

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25

26 23

24

30

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W1

W2

W1

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1

2

q p> q

T T F F p

T F T F

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3 4

1

1

W ittgenstein 1922, pr op. 4.442 1 5

6

7

x’ y’ x’ y’ 8

9

10

11

12

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15

16

17

18

19

20 21 30 4 2 4 16 16 4

W

ittgenstein, L. 1922.

T

ractatus Logico-Philosophicus

. Routledge and Kegan Paul.

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In this electrical circuit, the switches are models of the possible worlds, and the pair of electric

light bulbs is the model of the truth-table-like sign for the sentence “if p, then q”. A switch

being on represents that the possible world modeled by the switch is the actual world. The

left electric light bulb glowing represents that the sentence modeled by the pair of electric

light bulbs is true, and the right electric light bulb glowing represents that the sentence is

false. Now if the switch 1, 2, or 4 is on (which represents that the possible world W1, W2, or

W4 is the actual world), then the left electric light bulb glows (which represents that the

truth-table-like sign for the sentence “if p, then q” is true). On the other hand, if the switch 3 is on

(which represents that the possible world W3 is the actual world), then the right electric light

bulb glows (which represents that the sign is false). I think that the simulation makes it clear

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A Philosophical Examination of Truth-Tables (VIII)

Kouji HASHIMOTO

 Wittgenstein’s Tractatus Logico-Philosophicus uses a sign like truth-table as a sentence. In

my previous paper “A Philosophical Examination of Truth-Tables (V)”, I argued that a

truth-table-like sign should be considered as a picture of some possible worlds, as shown in the

figure below.

Here the possible world W1 consists of both the fact p and the fact q, W2 consists of the fact

q, W3 consists of the fact p, and W4 contains no facts. This truth-table-like sign, which is

intended to be for the sentence “if p, then q”, is a picture of W1, W2, and W4. Then I pointed

out that the sign is true if and only if there exists the actual world among those possible

worlds of which the sign is a picture. In this case, the truth-table-like sign is not true if and

only if W3 is the actual world.

 In this paper, I show that an electrical circuit can simulate the relation between a

truth-table-like sign and possible worlds. For example, the electrical circuit represented by the circuit

diagram below simulates the relation shown in the figure above.

switch 3 switch 2 switch 1

T F F p

F T F

T F T

p q W1

q W2

Figure

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