Notes from the underground |
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Updated 1 August 2024 |
10. Truth-value gap
The reasoning below claims to show that no statement can be neither true nor false. (That is, every statement must be either true or false.)
Can you see its logic?
(S is an abritrary statement.)
Can you see its logic?
No statement can be neither true nor false because ‘S’ and ‘It is true that S’ must always have the same truth value, whereas if ‘S’ were neither true nor false, ‘It is true that S’ would be false.
(S is an abritrary statement.)
| If ‘S’ were neither true nor false, ‘It is true that S’ would be false |
↓ |
| If ‘S’ were neither true nor false, ‘S’ and ‘It is true that S’ would have different truth values | ‘S’ and ‘It is true that S’ must always have the same truth value |
↓ |
‘S’ cannot be neither true nor false |
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