First my logic studying was not done in English. So I'm sorry if I'm not very clear.
Formal logic is a scholarly reflection of how things do exist.
It is not an invention nor a thing that evolved.
It's like how all languages refer to the sun using different words in their own tongues.
Remove all languages and then the sun is actually still there.
Heck. Remove humans altogether and the sun is still there.
So basically logic, in the broad sense obviously, is merely a tool that is reflecting something true in itself.
"Of course, there’s no inherently logical reason to trust that future events will resemble past events at all. This is just an intuition most humans (and perhaps animals) have, presumably because we’ve evolved in an environment that behaves somewhat regularly and therefore rewards this kind of reasoning. But for all we know, the “laws” of physics could suddenly change at any moment.
This is not how logic works.
The core of logic is something like A can't be A at the very same time it is NOT A.
This does not refer to things like colors. A brick can be orange or white or blue...etc.
So a brick does not have to be either red or green. It can be any color. or not.
It also only applies to things that can apply to.
Formal logic is so stupid. A brick is neither alive or not alive. Hooray, we defeated logic.
No. A brick does not even accept the "value" of alive.
So again logic is how we think and can perceive the world.
I can't get into details without requiring you to study formal logic for sometime.
But it's just how things are. No science denies that.
In fact without constants there is NO science.
Here is a little experiment. Give drug A to the people in the test group and they are cured from disease B.
This is science as you gave them the medicine and then they show, in the lab, that they stopped the disease.
Now what tells you that your 100 or 1000 reflect all humans?
Yep. Why? Because humans is a logical, and biological and a lot of other but I'm doing classical logic here, construct and the "truth" of all human beings is the same.
So science creates the drug and logic says that it is probably going to work for the rest of the category of humans because they share a fundamental core or truth.
Remove that and tell what remains of science?
This thinking is not "scientific" as it is not done in a lab or with any experiment. It is logical.
Without logic you will have to try every single drug on every single human.
And the applications are endless.
So I'd say that no. You can't have thinking a form or another of logic.
And I'm sorry if I could not explain properly.