It is the proclamation of the Gospel, not argumentation, that transforms minds. See Give Them the Gospel.

How Can We Know Which Assumptions Are Valid?

There is no such thing as a valid assumption. Assumptions prove nothing, not even the assumptions made by a famous evolutionist. Not even if they call those assumptions, axioms. Not even if they claim that their assumptions are the correct assumptions. Evolution isn't science.

Detailed Answer

One of the reasons that many intelligent people have trouble making good, solid decisions is that they have been educated into a mindset that believes that assumptions are some part of logic or science. Universities are teaching things like evolution and socialism that can only be supported by many assumptions and a great deal of ignoring of facts. False logic is taught in classes that claim to be teaching logic. Most of this educating into ignorance has a single focus: to try to diminish God.

Here is a conversation that illustrates this point:

Evolutionist: "The trouble with the creationists is that they make the wrong assumptions."

Student: "What makes their assumptions wrong?"

Evolutionist: "The evolutionists make valid assumptions. The creationists' assumptions are not valid."

Student: "How can an assumption be valid? I thought that an assumption was just something you make up."

Evolutionist: "Well, the evolutionists' assumptions are based on observations of science."

Student: "If it's based on observation, why would you need to make an assumption? You could just state the observation, couldn't you."

Evolutionist: "Well, we haven't been able to observe the things that we need to assume, but none of our other observations contradict the things that we have assumed."

Student: "So you are saying that you are looking for an uncheckable lie?"

Evolutionist: "No! Our assumptions are not lies! The creationists assumptions are lies! Our assumptions are, in themselves, proof of evolution."

Student: "How can an assumption prove anything?"

Evolutionist: "Stop asking me all these nasty questions! You must be some kind of religious fanatic! I can see now that you aren't intelligent enough to understand the really deep things of science and logic!"

Student: "I wish we could have a mutually respectful conversation."

(This is taken from an actual conversation)

Evolutionists are forced to hold on tightly to some basic presuppositions. These presuppositions are just simple-minded assumptions. They are filters and a way to censor out any information that supports the existence of God. They set up a web of rules to filter out God. They will only accept those things that conform to Naturalism, Materialism, and Uniformitarianism. Naturalism claims that God does nothing. Materialism claims that there is no God or spiritual realm. Uniformitarianism claims that there was not creation and that there was no violent worldwide flood, as the Bible and numerous other historical accounts record. Whatever they observe that does not conform to this complex filter is censored. The way that it is censored can take several forms. Evolutionists may boldly proclaim that, though the data appears to support design and refute Evolution, yet it still must be interpreted to mean just the opposite of what it does mean. A backup method that Evolutionists use is to prophecy that in the future, science will be able to explain what they see as an anomaly. If that fails, they will hide the data, set it aside, or lie to keep the public from knowing the truth. The data clearly demolishes the story of Evolution and clearly supports the reality of the Creator God and His creation of the Universe and everything in it in a relatively short period of time. When confronted with the obvious, a closed-minded Evolutionists says, "Show me the design--I can't see it." They are willingly ignorant because they refuse to hold God in their knowledge. The reality is that these people, for whatever reason, don't what to know the Creator. They don't want to truly know Jesus, their Creator.

Numbers 15:39... and that ye seek not after your own mind and your own ability to observe, with which you used to commit fornication:

Romans 8:7 because the carnal mind is enmity against God, for it is not subject to the Law of God, neither indeed can it be.

Psalm 53:1 The fool hath said in his heart, There is no God.

Jeremiah 17:9 The heart is deceitful above all things, and desperately wicked: who can know it?

1 Corinthians 2:14 But the natural man does not receive the things of the Spirit of God: for they are foolishness to him: neither can he know them, because they are spiritually discerned.

Proverbs 28:26 He that trusteth in his own heart is a fool: but whoso walks wisely, he shall be delivered.

Jeremiah 23:16 Thus says the LORD of hosts, Hearken not to the words of the prophets that prophesy to you: they make you vain: they speak a vision of their own heart, and not out of the mouth of the LORD. They say still to them that despise me, The LORD hath said, Ye shall have peace; and they say to every one that walks after the imagination of his own heart, No evil shall come upon you.

James 1:17 Every good gift and every perfect gift is from above, and cometh down from the Father of lights, with whom is no variableness, neither shadow of turning.

Summary

There is no such thing as a valid assumption despite the efforts of so-called educators who teach many ideas that actually are simply extensions of assumptions. One example is the teaching of evolution. Evolution isn't science.

A little science on the human mind