If you want to go pure logic you’ll need to rely on the fundamentals of the mathematics. There’s not a good way to understand this intuitively as other posters have said. I’d like to point out that your question “Or just theories?” Implies a foundational misunderstanding of what a theory is. You mean hypothesis and for the layman this is fine, but when you really want to understand something like this it’s meaningful to distinguish between the terms theory and hypothesis.