"I think we need to acknowledge that the aim of science is to discover facts, or particulars."
No. The purpose is to know and understand the world.
"That is, logic (reason) exists prior to facts"
No. reason is a process and facts are simply beliefs. There is no validity to any temporal ordering of reason and any set of beliefs.
"science... is used as a medium to obtain and to propagate those facts.
No. It's as I said, Science is a body of knowledge and understanding generated by reason; it is the whole thing that is science. You are thinking of the scientific method, which is not science itself. Science itself includes everything.
"Clearly, the analogy portraying science as the raft (particular, concrete, a posteriori facts) carried by the current of logic is more accurate."
No. That's not clear at all. Also, a current represents a flow of something in time and is represented by: things/t. Logic is a process, which is not similar in any way to a flow. A body of knowledge and understanding with a commonality of having the property of being validated by the scientific method does have a similarity to flow and can be modeled mathematically as a flow: things/t.
"It’s best not to try to hijack an analogy, because one’s familiarity with it is not likely to be as extensive as that of its author."
Logic, reason and science are independent of any author. Either the analogy is a true representation, or it's not.
Re: "Reason is a logical process that stands on it’s own. It is not dependent on any being, or any premise for validity."
"Any particular line of reasoning must have a premise.
No.
" ...particular reasoning does not give general validity to reason itself.
Yes it does. Example: A=A.
" As I have stated, reason can be considered valid ultimately through faith alone."
Faith is simply belief in what someone has said, regardless of one's justifications for doing so. Reason requires rational justifications for it's validity, and as I said, it is author independent.
The separation of science from philosophy was an academic separation, but it mirrors a conceptual separation which I’ve been trying to explain. I reject the notion that you don’t understand the difference between general reasoning and particular facts. As pointed out earlier, it’s like the difference between mathematical statements using the variable x and mathematical statements of particular values for x.
Of course a process is a kind of flow. (This is a bit silly, picking apart a perfectly good metaphor.)
A=A only validates its own particular reasoning. What I was trying to explain is that it does not validate reason in the abstract.
If you contemplate Descartes’ cogito proposition, you’ll see how faith is the groundwork for reason.
And the claim that the law of conservation of energy extends infinitely into the past has yet to be demonstrated.