Some people say that the only things we can know are what science and logic will tell us. That is a self-refuting statement. What God has revealed is all we can know. That is not a self-refuting statement.
Jesus Christ reveals directly. It is Christ Who reveals that the Bible is the Word of God without error. It is Jesus Christ Who speaks to us through the Bible, through creation, through the word spoken by the Holy Spirit in His people. Someone who doesn’t want to know God (though everyone does know–we know that they do because God reveals that to us.) will observe and then make up creative stories, make up assumptions, make up irrational thoughts, or make up outright lies to try to claim that they don’t know God exists. Unfortunately for them, God knows their innermost thoughts. He knows that they have heard His Voice through many means, but they would not listen to Him, nor would they come to Him in humility and submission.
Every evidence that is brought against God, His creation in 6 days, the catastrophic worldwide flood, or His Bible is based on using human imagination to add something to or to remove something from what God is saying either through His creation, His Bible, His history, or His logic. With some overlap, we can catagorize these additions into four types: made-up stories, arbitrary assumptions, irrational statements, or outright lies.
We might consider the idea that God knows more about the nature of reality than we do. He has revealed some things to us, but, in His Wisdom, He has revealed relatively little. Some people are very patient with the concept that science is incomplete but are very impatient with the concept that revelation is incomplete. Yet science, meaning real science, is one of the ways that God reveals things to people. The Heavens declare the glory of God and the Earth shows forth His handiwork. Of course we could easily look at many things that are called “science,” which, upon examination, would be shown to be really based on made-up stories, arbitrary assumptions, irrational statements, or outright lies. And these would make sense within the paradigm/fake-reality of the person putting a label of science on something that is obviously non-science.
Science and logic, while gifts from God, are very limited in their scope. Thinking that they are the ultimate way to know things would be a mistake. In fact, without revelation, logic can never be sound reasoning. You could observe things around you, but you could never make a statement about them without making up a story, making an arbitrary assumption, making an irrational statement, or telling an outright lie. Where do you start with your thought process about your empirical observation? If not by revelation, then what can you know? How valid is a made-up story? How valid is an arbitrary assumption? How valid is an irrational statement? How valid is an outright lie? Unless God reveals, you cannot know anything about anything. You can’t even prove that you or the world around you exists. Someone can make up an alternate story (and some people have) to even that. So the problem is really the problem of acknowledging God when He speaks to you, whether through the Bible, through what I am writing now, through creation, or some other means.