Jacob, an alethic thought is one that follows from reason and solid premises (axioms), while a non-alethic thought is an autistic notion, a result of day-dreaming or other non-linear thought processes?

Please allow me to analyze each one of the relevant words you use in your phrase, and also in my reply:

a) alethic: referring to a proposition that is fundamentally true, meaning not clearly untrue, i.e., not absurd.

b) proposition: a phrase that is offered without intending to assure its veracity. Compare with 'statement.'

c) statement: a phrase purported to communicate facts. (realities based on evidence.)

d) thought: a defined mental (of the mind) construct, which has not yet been communicated in speech or writing.

e) reason: the process of utilizing the elements of logical thinking, by the syllogistic Aristotelian method of specific premises leading to a specific conclusion.
Russell and Whitehead's symbolic method is not 'material' as Aristotle's is, but 'formal' ('ideal,' in the Platonic sense) being therefore 'universal'. The 'if' in the premises makes the conclusion entirely conditional, being therefore applicable to hypothetical situations. I believe that the 'if'...'then' allow for the rest of the Boolean process basic to computing in a strict sense.

f) premises: the 'material' (factual) or hypothetical conditions that permit the factual or hypothetical conclusions.

g) axioms: self-evident truths. Sciences start with them. In geometry, "A straight line is the shortest distance..." In biology: "Life is being born, growing, reproducing and dying." In physics: "An apple doesn't stay in the air nor moves up."

h) "non-alethic thought" is a 'non-alethic' expression, actually a faulty phrase, incapable of conveying information.
Only propositions can be non-alethic. You were probably meaning to say, "A non-alethic expression (phrase.)"

i) autistic: used to qualify one of the three ways of thinking. "Autistic thinking" is using the mind in the 'day-dreaming' manner.

j) "non-linear thought process": I propose the following: Thought processes are linear. When a person claims to be able to think about more than one subject at a time, his neurons are trained to use the same 'thinking line' alternatively. This is an analogy with the technique used by telephone communication.

Thus, DrZ, your phrase (a proposition presented as a question) might be edited as follows:

"An alethic proposition follows the rules of logical thinking. Not being based on facts, it is not a statement. Being alethic means being possibly true. A non-alethic proposition is clearly absurd, non-true. No facts can be found to substantiate it."