Philosophers are concerned with two points: soundness and validity. A valid argument is one where the conclusion follows from the premises. The way to think abo

Philosophers are concerned with two points: soundness and validity. A valid argument is one where the conclusion follows from the premises. The way to think about this is 'If I assume the premises are true, is my conclusion likely to be true'. A sound argument is a valid argument with true premises. Now valid arguments can be interesting in their own right even if their premises aren't true. Given this, the proper way to read Lucas's opinion is: I am taking it as given that the computational theory of mind requires a consistent system of inference rules + math; if that isn't true, my argument might be unsound but not invalid (and its validity is interesting); but I also think it is true for x,y,z reasons (though these additional reasons do not constitute a proof). In other words, the Lucas-Penrose argument is interesting from both a truth-of-premises and validity perspective which is far from dead in the water.