Presupposition/Axiom is an arbitrary assumption (all assumptions are arbitrary) that is treated as if it were a fact. (read) Naturalism/Atheism (read) Materialism/Atheism (read) Uniformitarianism (read) and Atheism/Humanism/Secularism (read) are very common. Axioms are often said to be self-evident, but there is not too much that actually is self-evident. In informal speech, self-evident often merely means obvious, but the definition is more strict for determining what is true and what is not.

There is quite a difference between an axiom and something that is true by definition.

"For the purposes of this discussion, evolution will mean molecules-to-man development according to neo-darwinism. When speaking of the small changes within kinds of living things that take place from generation to generation, we will use the word, adaptations."

These are not really assumptions. They are word definitions that could be changed for a future discussion.

To make a hypothetical statement, it may be necessary to make an assumption momentarily, but it is important to remember that the assumption is a vapor, a nothing.

"Let's just assume for the sake of this discussion, that we don't actually exist. If we don't actually exist, then what is the explanation for all of our thoughts and all of our experiences?"

Here is a typical thing that is said about assumptions/presuppositions/axioms:

"Everyone works within certain axioms or assumptions; ideas that are just accepted, believed to be true without the need to be proven—and often incapable of proof anyway. These assumptions can be based on experience; or cultural, educational and religious conditioning. We interpret the world around us, and often take actions, too, based on assumptions."

The hidden assumption in such a statement is that there is no alternative. But there is an alternative. The alternative clashes with the assumption/axiom of Naturalism, however. Naturalism rules out God and also rules out revelation.

God speaks to us through the Bible. Is this saying that God is an assumption? Through the Bible, God also also says that He brings His Word to our remembrance. Is that an assumption when He speaks to us in that way? Through the Bible, God also says that people can speak by the Holy Spirit and gives examples of those who spoke, but it was God speaking, not the person. We may live in a naturalistic/atheistic world where even members of the Body of Christ are swayed along with naturalism/atheism, but the Holy Spirit is real and He is hear to renew our minds to be able to deal with real Reality/Truth rather than paradigms/fake-realities and assumptions/presuppositions. Jesus is the Truth, not a theory, theology, or assumption. The only way given in Scripture to have faith is by hearing God's word, which is the Greek word, rhema, which means Utterance. Jesus is the Logos, which also means Utterance. (some caveats about hearing God's Voice)

While revelation is very much partial, it is also very real. (read) If someone thinks this is impossible, they are flying in the face of every person who has ever followed Jesus in truth. And, what do they think would prevent the Almighty God from having fellowship with those who love Him and who seek Him? What would make it impossible for God to lead them and fulfill His promises?

Some of these statements are true. It is probably true that everyone works within certain axioms or assumptions. There is a real problem with, ". . . without the need to be proven." If there are things upon which we are basing our thoughts that don't need to be proven, and we are just claiming them to be true, then where do we draw the line on that, and how dependable are those things that we think are true as compared with the dependability of the conflicting things that others think are true? If we say, we simply assume that the Bible is God's Word, without error, we have no basis to say to an Atheist, "Your assumption that the Bible is not God's Word, without error, is not valid."

If we believe the Bible, then we believe what Jesus says through the Bible, "My sheep hear My Voice," and "Whoever is on the side of truth listens to Me," and "Today, if you hear His Voice . . ." and many other such verses.

You believe that your friend exists because of your interaction with your friend. But do you trust your friend? Anyone who follows Christ is led by Christ and interacts with Christ. Faith comes by hearing and hearing by the word (Greek: rhema = utterance) of God. God speaks. We are to speak as the oracles of God, the very mouthpiece of God. We are not supposed to be speaking our own words but those words that come from God.