If you really 'knew' what you were writing about you wouldn't have to hide behind 'logic'.
Well, that's the first clue.
I am clearly not a scientist and neither are you
That's the second clue, because the definition used the phrase 'the science', not 'a scientist'. Science follows a set of investigative principle, which a scientist is trained in, but which anyone can follow.
'Reason'? What is reason, where is reason? I've surely never come across it in my travels
That's the next clue - because all up you are trying to establish reasons not to answer the question
'System' - what system? Where is this 'system'? Is there a place you can go to view this 'system'?
That's the fourth clue, said despite the fact that we have to use a system of language to communicate
What 'principles'? Have you in your life ever come across any 'principles'? I surely have not, and 'correct'?
The fifth clue, because you have principles that help guide your life, help determine the style of your writing etc.
'Persuasiveness' is another hint in the direction of these words giving you a certain conceptualization attached with them.
That's the sixth clue - All words have conceptual attachments. That's just a given. Trying to use a given for all words as grounds to argue away the usefulness of a single word is silly, considering you find many other words useful to establish your 'logic'. Now if you wanted to argue that a word doesn't quite encompass what you are trying to convey - that would be wonderful...but in this case you are just trying to avoid answering a question, or giving a sensible answer....hence it being the sixth clue.
Don't 'you' have to be there for 'logic' to even be an option?
And despite your objections to you, you now admit the concept exists. And were you to use logic, and I to read it then we would both have used logic. Two 'you' (s) if you prefer, were there for logic to be an option.