Logic does not rely on assumptions. It relies on making deductions about what is probable when faced with the current knowledge.

I see what you are meaning, but it's a misunderstanding of how the scientific method works. Base Assumptions never come into play.

The hypothesis comes from the existing evidence, not the other way around.

For example, Eratosthenes didn't have an "assumption" that the earth was round and then said, "hmmm...how shall we test this?" Rather, he had heard from someone or other that at noon is a certain city, there was no shadow. While in another city, there was a shadow being cast by objects. He started to logically deduce why that could be. He had his evidence, that in one city to the south, no shadow, and in another city, a shadow of 7 degrees at the same time of day. He knew the distance between the two cities and deduced not only that the earth was round, but it's size as well.

No gut assumptions necessary.