>>11599955>However, the foundation of CS, lambda calculus,lambda calculus is a foundation of our conventional notion of computable and is equivalent to the Turing model.
>not a mathematical system per sayLMAO WHAT. Lambda calculus is nothing *but* mathematical logic. We can say logic underlying mathematics is on a 'deeper' level of meta theory, but in regards to CS and math, lambda calculus sits as a form of higher-order logic. These are well studied mathematics
>but computer science at its fundamental level is just formal logic. no, one of the objects is formalized by higher order logic, but computation, the central study of CS, has various modes of study. CS consists of the core study of many other objects, ideas, and with different tools - to suggest otherwise is in bad faith. It's like saying even though we work on top of first order logic with many mathematical structures, that mathematics is the act of studying first order logic...which it's clearly not, at least not in the majority of its study. The same can be said for CS, with activities like domain theory.
>CS is constructivelolno, we would like to be totally constructive since it usually admits algorithms, but there are quite a fuckton of nonconstructive proofs in complexity theory.
>CS necessarily hinges on finitismNo. It hinges on computation being 'nice' when we need to make a finite number of decisions on local information to perform a task. The objects we study don't have to be necessarily discrete as long as we can discretize the steps and actions. Realizability is important for practical purposes but is not an express requirement or even a goal in CS, and certainly not a lot of TCS.
