Is randomness anti-logical? I came across a comment recently "reads like sentences strung together with no logic."  But is this even possible?

Sentences can be strung together randomly if the selection process is random. (Random sentences in a random sequence.) Stochasticity does not seem logical&mdash;it's a probability distribution, not based on sequence or causality.

but

That stochastic process is part of an algorithm, which is a set of instructions that must be valid for the program to compute.   

So which is it?


Is randomness anti-logical?  






Some definitions of computational logic:

The arrangement of circuit elements (as in a computer) needed for computation
also: the circuits themselves Merriam Websters  A system or set of principles underlying the arrangements of elements in a computer or electronic device so as to perform a specified task. Logical operations collectively. Google Dictionary
The system or principles underlying the representation of logical operations. Logical operations collectively, as performed by electronic or other devices.
Oxford English Dictionary

Some definitions of randomness

Being or relating to a set or to an element of a set each of whose elements has equal probability of occurrence. Lacking a definite plan, purpose, or pattern.
Merriam Websters. Made, done, happening, or chosen without method or conscious decision. Google Dictionary Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method.  Seeming to be without purpose or direct relationship to a stimulus. Oxford English Dictionary
I think the answer here lies in that the dictionary definition of randomness you have is not the one used in statistics, ML, or mathematics. We define randomness to mean there exists a distribution with generally greater than 0 uncertainty.  

Depending on who you talk to, we live in a random universe (the way we define quantum mechanics depends on a wave function (essentially a probability distribution)  

So why if a sequence is drawn from a distribution is it illogical? First, even as humans we can make a strong argument that what we say is random. I mean we speak to convey some form of message or context, but there exists multiple ways to deliver this, but we choose a single one. Our brains inherently model $p(\vec w|c)$ where $\vec w$ is the sequence and $c$ is our context or message we want to convey.  

Takeaway: Generating a sequence in an ergodic or uniform manner would be illogical, but that is not what is being modeled or done in practice. Normally its drawn from some complex distribution. 

Sidenote: My above claim could make it seem that being uniformly random implicates something illogical, and I want to emphasize that is not the case. It is domain to domain, sometimes that is the most logical solution, just in the case of sentence generation it normally isnt. I would define a logical algorithm as one that given the information at hand acts in a sensible manner towards achieving some goal, and so if something purely random does that, I don't see the problem.