[wool_gather]

Let's clarify here: "Calculus"[0] and the lambda calculus have almost nothing to do with one another. They just share a word in their name, like the Department of Mathematics and the Fire Department. There are several different things called "the X calculus".

[0]:Could be called "numerical calculus" or "calculus of integration and differentiation", perhaps.

[JoelMcCracken]

A while back I was trying to under why some things are called algebras and others calculus. The answer I got is that the term calculus is related to the introduction/reduction of variables or symbols, whereas an algebra is manipulation of existing symbols.

[mruts]

I always thought it related to continuous variables and the highly useful concept of the infinitesimal. But maybe that definition works as well.

[User23]

I thought it was just yet another historical and linguistic oddity in English.

[mruts]

Calculus means "stone" in Latin. I suspect the relationship between stones and counting is why we use it so much (though I'm not an expert on how/why Romans used stones).

[User23]

Good clarification, but I wouldn't say almost nothing. All are formal symbolic reasoning techniques.

For example, The predicate calculus is invaluable for writing correct programs with mind-bogglingly large input domains, such as the set of all C++ programs.

[mlevental]

historically they were called the differential calculus and the integral calculus