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That difficulty is not accidental. It is the whole problem.
The obvious move: define what thinking actually is, then check whether a machine does it. Turing tried. Every definition fell apart.
Thinking means processing information. Fine. Now a thermostat thinks. It senses temperature, compares it to a target, and acts. That is not what we meant.
Thinking means being conscious. Fine. Now you cannot prove anyone else thinks. You only know you are conscious. Everyone else might be a very convincing machine. That is also not what we meant.
No definition worked. Every one either let in too much, or demanded something you cannot actually measure.
So Turing stopped trying to define thinking. He asked a different question instead.