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My comment was talking about a stronger kind of consistency, maybe "inevitability" would be a better word for it. You could make many different tiny changes to

My comment was talking about a stronger kind of consistency, maybe "inevitability" would be a better word for it. You could make many different tiny changes to the rules of C and still end up with a workable programming language. (Many people have done that, there are tons of languages derived from C.) You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. So learning the rules of C is more about memorization than logic. Math is different: when you learn a piece of math, you know exactly how it follows logically from the pieces you learned before, and you know it couldn't be any other way. That's why it feels more reasonable to me to inquire about math, rather than the details of C. Lawrence Kesteloot said it well at http://www.teamten.com/lawrence/writings/what_interests_me.html http://www.teamten.com/lawrence/writings/what_interests_me.h...: On a planet far away they have universities. In those universities they have many of the same subjects we teach here, such as math, biology, philosophy, history, computer science, psychology, and literature. But although the subjects of the classes are the same, the contents are different. They teach a history class, but their history is different from ours. So are their biology and literature. I’m not interested in subjects where their content is different from ours. In some classes, though, the content is the same. They’re teaching the same physics class (assuming they’re at the same level of understanding we’re at) and the same math classes (with a different base). In computer science most of what they teach is different, but their theory of computation is surely the same. Their biology is different, but their teaching of evolution is the same. Their philosophy is vastly different (think how different Eastern and Western philosophies are on earth), but their philosophy of science is probably very similar. Even if this point of view doesn't make sense to some people, I subscribe to it because it's very inspiring to me. YMMV.

ksk 13y ago
>You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. You're mis-applying things here. The language is not something to be theorized by itself. Like any (edit:spell) other body of knowledge, it has its own set of initial axioms and the 'C standard' which defines the language is simply a collection of rules other meta-knowledge which are based on those. In that sense it is internally consistent. Thats what I meant.
- patrickmclaren 13y ago
  Can you deduce the majority of the C language from these initial axioms? You misunderstand the usage of consistency regarding mathematics. It is not the same. These rules which compose C are design decisions, and whether they are entirely artificial. Mathematical consistency arises from imposing axioms, following which there are no decisions to be made.
  - ksk 13y ago
    >Can you deduce the majority of the C language from these initial axioms? Well, no. You can deduce A language but it might not be C. I sense we're going down a fruitless path here. In my first post I was only giving an analogy of someone understanding math at a fundamental level to someone understanding a programming language at a fundamental level and how they could inform similar abilities/prowess in people when it comes to dealing with complex problems/etc.
- cousin_it 13y ago
  Yes, you could say that the C standard is a formal theory. It won't be a very interesting one to a mathematician though, because it's huge and describes only one thing, C. There are no special considerations to single out that theory from a huge pool of similar ones. It's like devoting your life to the study of one particular differential equation with a thousand terms, which was written by a committee. Why not the other equation which has a minus instead of a plus over there? Why not study differential equations in general? Compare with a formal theory like PA, which fits on a page and describes the natural numbers. Proving a theorem about PA has implications everywhere, because natural numbers are everywhere. Or if we want to talk about computation, there are many formal theories with short descriptions that have much more to say about computation in general.
  - ksk 13y ago
    I am not against your POV ! I think we largely agree on most things here. I wanted to correct what I perceived to be a mischaracterization of my 'off the cuff' analogy.
pandaman 13y ago
My guess you apply your experience with some bizarre language (PHP?) to C, which you never learned. C and C++ are internally consistent in the same way a math theory is. Many programming languages are not, indeed. > You could make many different tiny changes to the rules of C and still end up with a workable programming language. (Many people have done that, there are tons of languages derived from C.) Coincidentally, same is Math. I give you Euclid's Fifth postulate as an example. >You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. This depends on how do you enumerate these rules. If you learn that auto variables are allocated on the stack it's easy to predict that you cannot return their addresses and there are not going to be default initializes for them.
- mden 13y ago
  I think the point was that mathematics relies on a small set of postulates from which you can derive everything else. Changing a postulate results in a separate system. The same is true in programming languages, but the number of postulates is very large compared to mathematics to the point that their utility is greatly reduced. And also there are so many languages each with its own postulate set that it's really inelegant when compared to mathematics. Another way to put it is, learning the postulates for langx doesn't provide enough value for many to be worth doing.
  - pandaman 13y ago
    >I think the point was that mathematics relies on a small set of postulates from which you can derive everything else. And I agree, this is one of the assertions my opponent has made. I did not go to refute it because, if not outright false, it's disingenuous. >Another way to put it is, learning the postulates for langx doesn't provide enough value for many to be worth doing. This is also true, same goes for everything else. I make money using C - I learn C's postulates. If somebody paid me to use topology - I'd learned topology postulates. What would be stupid if I were paid to use topology but said: "it's hard to learn and it makes no sense for me because I don't like mathematics and don't know any other math discipline so why would I all of sudden learn topology's postulate when I can copy formulas from the net and ask questions on manifoldoverflow.com?"

ksk 13y ago

>You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. You're mis-applying things here. The language is not something to be theorized by itself. Like any (edit:spell) other body of knowledge, it has its own set of initial axioms and the 'C standard' which defines the language is simply a collection of rules other meta-knowledge which are based on those. In that sense it is internally consistent. Thats what I meant.

patrickmclaren 13y ago
Can you deduce the majority of the C language from these initial axioms? You misunderstand the usage of consistency regarding mathematics. It is not the same. These rules which compose C are design decisions, and whether they are entirely artificial. Mathematical consistency arises from imposing axioms, following which there are no decisions to be made.
- ksk 13y ago
  >Can you deduce the majority of the C language from these initial axioms? Well, no. You can deduce A language but it might not be C. I sense we're going down a fruitless path here. In my first post I was only giving an analogy of someone understanding math at a fundamental level to someone understanding a programming language at a fundamental level and how they could inform similar abilities/prowess in people when it comes to dealing with complex problems/etc.
cousin_it 13y ago
Yes, you could say that the C standard is a formal theory. It won't be a very interesting one to a mathematician though, because it's huge and describes only one thing, C. There are no special considerations to single out that theory from a huge pool of similar ones. It's like devoting your life to the study of one particular differential equation with a thousand terms, which was written by a committee. Why not the other equation which has a minus instead of a plus over there? Why not study differential equations in general? Compare with a formal theory like PA, which fits on a page and describes the natural numbers. Proving a theorem about PA has implications everywhere, because natural numbers are everywhere. Or if we want to talk about computation, there are many formal theories with short descriptions that have much more to say about computation in general.
- ksk 13y ago
  I am not against your POV ! I think we largely agree on most things here. I wanted to correct what I perceived to be a mischaracterization of my 'off the cuff' analogy.

pandaman 13y ago

My guess you apply your experience with some bizarre language (PHP?) to C, which you never learned. C and C++ are internally consistent in the same way a math theory is. Many programming languages are not, indeed. > You could make many different tiny changes to the rules of C and still end up with a workable programming language. (Many people have done that, there are tons of languages derived from C.) Coincidentally, same is Math. I give you Euclid's Fifth postulate as an example. >You could say that the rules of C are "random" - after learning the first n rules, you cannot use logic to predict the n+1st. This depends on how do you enumerate these rules. If you learn that auto variables are allocated on the stack it's easy to predict that you cannot return their addresses and there are not going to be default initializes for them.

mden 13y ago
I think the point was that mathematics relies on a small set of postulates from which you can derive everything else. Changing a postulate results in a separate system. The same is true in programming languages, but the number of postulates is very large compared to mathematics to the point that their utility is greatly reduced. And also there are so many languages each with its own postulate set that it's really inelegant when compared to mathematics. Another way to put it is, learning the postulates for langx doesn't provide enough value for many to be worth doing.
- pandaman 13y ago
  >I think the point was that mathematics relies on a small set of postulates from which you can derive everything else. And I agree, this is one of the assertions my opponent has made. I did not go to refute it because, if not outright false, it's disingenuous. >Another way to put it is, learning the postulates for langx doesn't provide enough value for many to be worth doing. This is also true, same goes for everything else. I make money using C - I learn C's postulates. If somebody paid me to use topology - I'd learned topology postulates. What would be stupid if I were paid to use topology but said: "it's hard to learn and it makes no sense for me because I don't like mathematics and don't know any other math discipline so why would I all of sudden learn topology's postulate when I can copy formulas from the net and ask questions on manifoldoverflow.com?"