The Turing machine is a realisation of what a computing machine could be in a logical sense. It’s not so much constructed to be easy to reason about as to be the simplest form of what such a machine could be.
The fact that functions computable with such a machine is equivalent to functions computable in the lambda calculus and Herbrand general recursive functions is the remarkable results.
The fact that it can somehow be linked to an actual computing machines outside of logic is merely a happy accident.
Having said that you could think I disagree with Vardi but the truth is: I think the point he brings is just void of substance. That’s only of interest to people who like university politics and how departments hire. It’s of no impact to the field whatsoever. Why does it matter what is or isn’t semantically TCS and if it is or not mathematics? The problems will still be there the same.
Not a Turing Machine, but with a Lisp interpreter and few atoms (Lambda Calculus in the end) you can state the peano axioms, then a basic arithmetic calculator, and after that, a basic algebra solver in minutes.
The fact that functions computable with such a machine is equivalent to functions computable in the lambda calculus and Herbrand general recursive functions is the remarkable results.
The fact that it can somehow be linked to an actual computing machines outside of logic is merely a happy accident.
Having said that you could think I disagree with Vardi but the truth is: I think the point he brings is just void of substance. That’s only of interest to people who like university politics and how departments hire. It’s of no impact to the field whatsoever. Why does it matter what is or isn’t semantically TCS and if it is or not mathematics? The problems will still be there the same.