I believe calculus also solves this problem.

It's linguistic evolution. How words are pronounced, spelled, and defined change over time. It's why we speak so many different languages. Words do not have intrinsic meaning.

I believe that the possibility of a creator agent is unfalsifiable. I don't have to label it, I can just state it. I don't care if people call my position atheistic or agnostic or agnostic atheist. I only care that I've communicated my position.

Would I like to see the language we use to be more rich and better defined? Sure. But it's not the case. So I just speak plainly.

I would say:

• We exist in some capacity
• Our experiences exist
• Things that aren't our personal experiences exist (e.g. whatever produces your experiences)

From your experience, you can know a lot of things. Thoughts exist. Symbolic thought exists. Language exists. Math exists. Logic exists.

Any deductive argument you know leads to a necessary truth.

You know that you come across characters (e.g. human beings). And that they can respond to you and can do things you cannot predict. You know they come from somewhere. You know they can have intellectual conversations with you, even if it's just a character in a dream. You know the world you explore appears to be full of characters and history that you have to discover to know. You experience complex interactions with the world you perceive.

If you define intelligence as your "capacity to acquire and utilize knowledge", then you would know very little inside an empty universe. You need to make observations to acquire knowledge.

When you are born as a baby, your brain requires certain things to develop. If you were born as a baby in an empty environment without needing food, your brain would not develop properly. This is true with other animals as well. Without a stimulating environment, your brain does not learn. Learning is a part of development, you start learning when your brain has very high plasticity and making many new connections.

You say born as an adult though, but consider what that means. An adult animal has a brain that has been stimulated during the crucial development of the brain. You learned a language for one. It took your brain a few years in a very stimulating world to learn basic things, by seeing, listening, touching, tasting and smelling the world.

"do we get born with some kind of basic information with which we could then derive some basic concepts and eventually geometry and math?"

I would say no. We're more of a blank slate. You may be interested in learning about feral children. There is at least a couple of good studies on it. There is Dina Sanichar, who was raised by wolves.

"What can logic do without information?"

Logic needs information. You need to make observations. That's why science was able to push into places that philosophers could not reach. They went out and made observations, and created experiments to make precise observations. How do you infer something, if you have no observations to infer with?