All Circular Reasoning is Linear

[Eodnhoj7]

All circular reasoning is linear




1) The observation of arguing an axiom requires an argument from a separate set of axioms which begins with a secondary axiom that exists through the first axiom and cycles back to it.




2) This set of axioms circularity through eachother exists as a third axiom which cycles through the prior two while progressing away from the original axiom(s). In these respects the axiom(s) as a premise point of order through which further axioms extend and are directed back towards. In these respects the axiom exists as limit which gives foundation to itself by progressing away from itself, negating itself through further axioms.




3) The original axiom, as a premise point of order for further axioms, exists through the other axioms as causal themselves; hence the circularity of the axiom "reflecting itself" results in a linear expansion of axioms as cause is directed away from itself through itself. In these respects all axioms linearly project through a self-sustain circularity.



A simpler example of this would a circle existing through PI as an infinitely progressive line with the line as PI being compose of infinite other PI's through as infinite circles linearly projecting away from there origins.

[Dalek Prime]

Yes, I was just thinking about recursive programming in Lisp whilst reading this.

[Eodnhoj7]

Yes, I was just thinking about recursive programming in Lisp whilst reading this.

Not familiar with what you are talking about...elaborate. Little experience, on my part, in programming.

[Dalek Prime]

Yes, I was just thinking about recursive programming in Lisp whilst reading this.

Not familiar with what you are talking about...elaborate. Little experience, on my part, in programming.

Functions calling and controlling themselves, in essence. Same concept as mirrors facing each other. Most Lisp programming is done naturally in the language. Actually, the lisp interpreter itself is one simple recursive program. It listens for instructions, completes them, and calls itself to listen yet again.

[Eodnhoj7]

Yes, I was just thinking about recursive programming in Lisp whilst reading this.

Not familiar with what you are talking about...elaborate. Little experience, on my part, in programming.

Functions calling and controlling themselves, in essence. Same concept as mirrors facing each other. Most Lisp programming is done naturally in the language. Actually, the lisp interpreter itself is one simple recursive program. It listens for instructions, completes them, and calls itself to listen yet again.

Reflection is the foundation of limit then?

[Dalek Prime]

Not familiar with what you are talking about...elaborate. Little experience, on my part, in programming.

Functions calling and controlling themselves, in essence. Same concept as mirrors facing each other. Most Lisp programming is done naturally in the language. Actually, the lisp interpreter itself is one simple recursive program. It listens for instructions, completes them, and calls itself to listen yet again.

Reflection is the foundation of limit then?

I'd have to think about that. There may be exceptions, at least in programming. A jump outside the recursive call could be made. But that is limited by the functional parameters itself.

[Eodnhoj7]

Functions calling and controlling themselves, in essence. Same concept as mirrors facing each other. Most Lisp programming is done naturally in the language. Actually, the lisp interpreter itself is one simple recursive program. It listens for instructions, completes them, and calls itself to listen yet again.

Reflection is the foundation of limit then?

I'd have to think about that. There may be exceptions, at least in programming. A jump outside the recursive call could be made. But that is limited by the functional parameters itself.

Hence the "jump" would be the functional parameter's mirroring themselves?

[Dalek Prime]

Reflection is the foundation of limit then?

I'd have to think about that. There may be exceptions, at least in programming. A jump outside the recursive call could be made. But that is limited by the functional parameters itself.

Hence the "jump" would be the functional parameter's mirroring themselves?

Yes, but Lisp includes macro facilities that could conceivably write other languages or new material as well. So I don't want to say in all cases, because i cant conceive them at the moment. So that is a guarded yes.

And actually, I just thought of a case where the exception may lie, and that is in the recursive Lisp interpreter itself, where everything happens under it. The interpreter is unchanging, but what happens with it is computationally possible. So, I guess I'm saying that recursion can build on itself.

[Eodnhoj7]

I'd have to think about that. There may be exceptions, at least in programming. A jump outside the recursive call could be made. But that is limited by the functional parameters itself.

Hence the "jump" would be the functional parameter's mirroring themselves?

Yes, but Lisp includes macro facilities that could conceivably write other languages or new material as well. So I don't want to say in all cases, because i cant conceive them at the moment. So that is a guarded yes.

And actually, I just thought of a case where the exception may lie, and that is in the recursive Lisp interpreter itself, where everything happens under it. The interpreter is unchanging, but what happens with it is computationally possible.

Bear with me, my programming knowledge is....ehh...non-existent.

You are talking about the recurvise Lisp interpreter being a "person" or synonymous to a "functional parameter"?

[Dalek Prime]

Hence the "jump" would be the functional parameter's mirroring themselves?

Yes, but Lisp includes macro facilities that could conceivably write other languages or new material as well. So I don't want to say in all cases, because i cant conceive them at the moment. So that is a guarded yes.

And actually, I just thought of a case where the exception may lie, and that is in the recursive Lisp interpreter itself, where everything happens under it. The interpreter is unchanging, but what happens with it is computationally possible.

Bear with me, my programming knowledge is....ehh...non-existent.

You are talking about the recurvise Lisp interpreter being a "person" or synonymous to a "functional parameter"?

The parameters of operation. And I realized I goofed in what I said about the jump. The jump is outside to another code section apart from the recursive call. But the recursive call has that jump in each iteration.

[Eodnhoj7]

Yes, but Lisp includes macro facilities that could conceivably write other languages or new material as well. So I don't want to say in all cases, because i cant conceive them at the moment. So that is a guarded yes.

And actually, I just thought of a case where the exception may lie, and that is in the recursive Lisp interpreter itself, where everything happens under it. The interpreter is unchanging, but what happens with it is computationally possible.

Bear with me, my programming knowledge is....ehh...non-existent.

You are talking about the recurvise Lisp interpreter being a "person" or synonymous to a "functional parameter"?

The parameters of operation.

It appears the most the program could do is replicate itself, but in replicating itself the replicated programs which have an inherent element of randomness to them as the replication of one program to another would have to take into account changing outside variables?

[Dalek Prime]

Bear with me, my programming knowledge is....ehh...non-existent.

You are talking about the recurvise Lisp interpreter being a "person" or synonymous to a "functional parameter"?

The parameters of operation.

It appears the most the program could do is replicate itself, but in replicating itself the replicated programs which have an inherent element of randomness to them as the replication of one program to another would have to take into account changing outside variables?

It's not the most it can do, in replicating itself, but it can be used easily in such a matter. In fact, Lisp is great at writing Lisp itself, or creating a new language as needed. Lisp was the first language used for web programming for two reasons. One, because it is highly flexible, and the other, because it doesn't have side effects in it's purely functional form ie. For each network call to the program, the state of variables will always be pristine. That is important because you don't want one user changing states on the second user.

[Eodnhoj7]

The parameters of operation.

It appears the most the program could do is replicate itself, but in replicating itself the replicated programs which have an inherent element of randomness to them as the replication of one program to another would have to take into account changing outside variables?

It's not the most it can do, in replicating itself, but it can be used easily in such a matter. In fact, Lisp is great at writing Lisp itself, or creating a new language as needed. Lisp was the first language used for web programming for two reasons. One, because it is highly flexible, and the other, because it doesn't have side effects in it's purely functional form ie. For each network call to the program, the state of variables will always be pristine. That is important because you don't want one user changing states on the second user.

How is the creation of a new language not a replication of a prior language?

[Dalek Prime]

It appears the most the program could do is replicate itself, but in replicating itself the replicated programs which have an inherent element of randomness to them as the replication of one program to another would have to take into account changing outside variables?

It's not the most it can do, in replicating itself, but it can be used easily in such a matter. In fact, Lisp is great at writing Lisp itself, or creating a new language as needed. Lisp was the first language used for web programming for two reasons. One, because it is highly flexible, and the other, because it doesn't have side effects in it's purely functional form ie. For each network call to the program, the state of variables will always be pristine. That is important because you don't want one user changing states on the second user.

How is the creation of a new language not a replication of a prior language?

Domain specific is useful in many situations. Besides, I've lived through the evolution of programming languages. It hasn't stopped yet.

Actually, I just remembered a geek joke pertaining to this... Someone once said about the Forth language, ''if you've seen one (implementation of) Forth, you've seen one (implementation of) Forth'. That's because every time you you write a program in it, you build a new language library.

[TimeSeeker]

It doesn't matter if your axioms are "true" as long as any particular language is consistently interpreted against them.

The taxonomy of languages as proposed by the Chomsky hierarchy is that any recursively-enumerable grammar is effectively parseable by a Turing machine e.g it solves the symbol-grounding problem. In English ALL regular languages are computation!

This ties into the Curry-Howard isomorphism, Lambda calculus and Type theory.