To assume something exists without empirical evidence is purely illogical. If you could accept a belief in something without evidence, you could believe any possibility. You could assert that there is a large dog floating in the sky striking down those that displease it, and think it true. However, it could be said that just because you can't prove something doesn't mean it's been disproved. This being true, the converse is also true, you can't believe in something because of a lack of evidence. We know the wind is there because we feel it on our face as it blows into us, we know the ground exists because we feel it beneath our feet. We can assert these things exist because we can prove them by reviewing sensory perceptions, these being imprints of an interaction with our environment, a physical impression of some thing's existence imprinted in the neural connections of the brain. Without these, there is no proof that something exists.
Well, without "guessing" (no empirical evidence), somethings would have no other evidence. No, those things do not count as evidence. Let's take ancient animals for examples. The giant squid was believed to be extinct a long time ago. Pictures and paintings revealed that some people believed in them at that time. But science disagreed. And science is what takes us this far. Sure, the people who saw and painted the squid might of say, and empirically confirmed the existence of this creature, however scientists today are more successful. Yet, the empirical evidence came AFTER the beliefs. Based on reports from people, people simply drew the giant squid because they thought they existed. There weren't many eyewitness reports anyway. And of those, our great scientists denied.
Without direct empirical evidence, we can still make assumptions based on logic- as proved with the case above.
The Abstract idea category includes logic. How many ideas come from just theories? General "theory" of relativity? Ever heard of that? If needed empirical evidence for everything, our physicists would be of no use. And they ARE of use. How much have we learned about the world from them theoretical physicists?
Like my previous statement, you don't NEED empirical evidence to assume something exists. Black holes? Our friend Stephen Hawkings assumed these existed LONG before it was proven! How do you think that happened? It's because we have enough theoretical ideas to make an educated "guess."