Practice question · Multiple choice
"This sentence is false." Why does the liar paradox matter to a subject that insists every statement is either true or false?
Hints
- Assume it is true and see what follows. Now assume it is false.
- Ask whether mathematics discovered that its sentences behave well, or arranged for them to.
Show the answer
C. Because it is a well-formed sentence that can be neither
Why
Suppose it true and it is false; suppose it false and it is true. Nothing is malformed, which is why mathematics restricts itself to a language where such self-reference cannot be built. Russell's paradox is the same shape in set theory, and it is why the axioms are written as carefully as they are.
Practise Mathematical Statements and Logic
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