Here I want to explain why I think our logic is based on empirical observation, and therefore, our brain is not equipped to understand concepts that do not exist in this world, like "nothingness" or "infinity".
Humans are the result of a evolution in this very unique world. Our way of thinking comes with the physical environment around us. For example, "(P or Not P) is a tautology" is taken for granted because in our universe, black can not be white, and white can not be black. Our logical thinking is based on such crude observation.
But the Wave-Particle Duality challenges our fundamental assumption. A thing can be both wave and particle. So is "(P or Not P) is a tautology" still true? Or another example: scientist found that certain particles behave differently depending on whether or not there's people around. Another example: in our comprehension, there is always an end to a physical space, and beyond that end, there's something else bigger. Outside my house is the earth; outside the earth is galaxy. So what is outside the universe? Is there an end to our universe? If there is an end, then what is on the other side of that end?
These problems require us to rethink our fundamental assumptions. Our existing assumptions are made in a world of Newton physics. Our logic is then built on those assumptions. This logic is very powerful in dealing with questions in our layer of existence. But new scientific discoveries has revealed that when we go into other layers of existence (like quantum physics or astronomy), our old assumptions do not hold anymore.
This leads to my point: our logic belongs to our universe. With such logic, we can not imagine or understand things beyond our universe. We can not understand infinity or nothingness because they are not apart of our layer of existence.
"But", someone says, "of course we understand infinity. When I say the word 'infinity', you know what I am talking about, right?" Yes. I've heard the word "infinity". But that's far from understanding what infinity is. I tried hard, but there is no way that I can imagine infinity, or find a convincing explanation. Our definition of infinity is a compromise. We accept this compromise because it seems to be working pretty well in solving many problems, like in calculus. But this does not mean that we've really got it right.
I am fully aware that I am new to the field of logic and philosophy; I am not the first to ask certain questions; answers to my questions might have existed for thousands of years. I love to learn about my ignorance. Please let me know if there's a book that I should read, or some great minds that I should pay attention to. I'd love to hear your view points!