I'll summarizes some of the main points of the video here.  This is largely a question of if the authority of Scriptures, the reliability of the translation of  Scripture, the infallibility of Scripture (as communicated by God the Holy Spirit to the original authors) and the clarity with which God communicated His message to His intended audience.  I typically follow the Historical-Grammatical approach to Biblical Interpretation (see How to Interpret the Bible which speaks of the various approaches to biblical hermeneutics).  With that in mind, a key verse here would be Exodus 20:11 (the justification for the fourth commandment), "For in six days the Lord made the heavens and the earth, the sea, and all that is in them, and rested on the seventh day. Therefore the Lord blessed the Sabbath day and made it holy."  This leaves no room for Progressive Evolution, The Gap Theory, or any other Theistic Evolution model that tries to insert millions, billions, or even trillions of years into the Bible (what some people call "deep time").

Without the creation account of Genesis 1, the story of Adam and Eve which gives the foundation of law, government, family, and the good work that God calls us to to "keep" (protect and cultivate) His creation don't make sense.  We then also can't explain the existence of sin and death which are explained by Genesis 3, and then the whole gospel falls apart because if there is no First Adam, there is no need for a Second Adam. 

Also, the end of Revelation doesn't make much sense without a literal interpretation of Genesis as the end is a better version of the beginning.  We see the Tree of Life as bookends of the story--Adam and Eve are kept from the Garden so that they might not eat of the Tree of Life after they sinned, but the Tree of Life is available for all to eat freely in the New Heavens and New Earth.  The video makes other good points, but these were a few that I wanted to highlight.

Let's first start with why I'm so interested in all of these areas and how so many of the people involved in math and science were also involved in logic, theology, and philosophy.  Science at its core wants to understand the way things are around you and to understand the rules that nature plays by.  This naturally assumes though that there are rules and that they are consistent or at least predictable and knowable and that they can be found out empirically (through observation).  These assumptions come together in what we call "The Scientific Method" which is a way in which someone who is a "scientist" tests theories and "truth claims."  But can all truth be tested by way of The Scientific Method?  Certainly not, because, assuming The Scientific Method itself is true, it is not something that can be empirically tested.

So, there must be something bigger than The Scientific Method.  The same can be said for the laws of mathematics.  while these rules are more conceptual and reaching towards metaphysics instead of physics (thought instead of material), they are not yet sufficient in explaining the order that we see in the universe, but are simply just a language used to describe the patterns and nature of the universe that we see.

Philosophy is usually defined as the study of how to know that something is true.  There are many philosophies though that take the same facts and come up with drastically different conclusions.  For example Is the whole equal to the sum of its parts or is it greater than the sum of its parts?  Context may be necessary here, but it is going to require some more information that may not be a part of the problem itself--it may involve things from outside like presuppositions, axioms, undefined terms, postulates, and theorems.  These are all integrated deeply into the disciplines of math and science, but also other areas of our lives.  We just may not be as honest about how these things play a role in our view of things like economics, politics, law, or education.  What many people call a "philosophy" is actually a much larger topic called a "worldview."  It moves beyond simply how to know and identify truth and actually establishes a belief system and how you filter truth claims to decide if they are consistent or inconsistent with that system of beliefs and how you handle apparent inconsistencies.

All of these cases so far that we've been discussing--math, science, philosophy, and apologetics (as well as many other disciplines) first require us to have a common basis for forming and argument and knowing what the definitions of words like "true" and "false" are and under what circumstances are are statements going to take on a truth value of true or false.  If truth is relative and words can simultaneously mean different things to different people and there is no common "right" or "wrong" way to interpret the words that someone is saying, then communication is nearly impossible.  We therefore must establish some common ground rules which is where logic comes into play.  There are three main laws of logic which are assumed to be true for all future arguments and discussions (and have been assumed to be true up to this point as well):
1) The Law of Identity:  "If A, then A."  This may seem like a silly law but it necessary sometimes to make such a statement that something is itself.  This is not a statement of causality, but simply of identity.
2) The Law of Excluded Middle:  A "truth claim" (from hereon called a logical proposition) can have a truth value of "true" or "false" and nothing else.  If it has no truth value or you cannot say that it has a binary truth value of "true" or "false," then it is not a logical proposition.
3) The Law of Non-Contradiction:  A logical proposition cannot be both true and false (in the same way at the same time).

There are lots of materials on these laws, so I won't go into them very much, but this still leaves us at a place where we have something where we cannot use the laws of logic to explain themselves and there has to be something bigger than logic itself.  This drove many people in these fields to search for their answers in the disciplines of theology and religion, stemming from a belief that all law must come from a law-giver and that we best understand what is true and right when we understand the Creator as it is His nature and character that we see at work and things consistent with that nature and character are "true" or "right" and things inconsistent with that character are "false" or "wrong." Other words may also be used in other contexts such as "righteous" and "wicked."

It is here that we reach what appears to be the end result of our search.  God would seem to be the "Unmoved Mover" and the "Uncaused Cause."  While someone like Dawkins might sarcastically ask, "Who created God?" the simple answer is "No one, that is why He is God."  Genesis 1:1 tells us, "In the beginning God created the heavens and the earth."  This short verse contains many profound truths:
1) There was a beginning--therefore matter is not eternal
2) God existed outside of time and is eternal
3) God created everything (and is therefore sovereign over it)

However, even our understanding of God relies on some presuppositions.  For instance, I'll be honest with what I just did.  I didn't tell you that I believed that God exists, He's knowable, that at least some truth is absolute and knowable, and that I believed that God revealed truth about Himself in the Bible so that we could know it and know more about Him.  I just quoted the Bible as a source of truth and I assumed you figured all that out.  You may not agree with me on those points, but if you don't then our conversation probably won't go very far because we're going to have a very difficult time coming to the same conclusion on anything if we can't agree on some of these foundational issues.

These types of discussions are often not encouraged in today's culture and people are usually afraid to ask the deep, probing questions about what someone believes and why they believe it and what kinds of underlying assumptions may have played a role in their coming to their conclusion.  I hope to be open and honest about my views with you and that this will inspire you to not only ask me questions but possibly for you to ask these questions of yourselves and others.  I believe in a God big enough to deal with the questions we need answers to (though He is not required to give answers and doesn't always answer our questions want in the way we want or in the time frame we want).

That brings me to my last point here and that is that there are some things in life that we know are true, but we may not be able to explain them to anyone else.  Hebrews 11 talks much about the subject of faith and those who had great faith.  Here are just a few verses from that chapter:
"1 Now faith is confidence in what we hope for and assurance about what we do not see. 2 This is what the ancients were commended for.3 By faith we understand that the universe was formed at God’s command, so that what is seen was not made out of what was visible."

6 And without faith it is impossible to please God, because anyone who comes to him must believe that he exists and that he rewards those who earnestly seek him.

There will be some things that are bigger than science or even my personal observations which I know to be true.  I can tell you that for sure there a thing called a "point" in geometry even though I can't define for you what it is.  All of us have faith in order to build the foundation for our belief system because every belief system has to start with something that is not provable by any of the other items built on top of those foundational items (axioms and undefined terms).  It's okay to reach a point in your worldview where you can't dig any deeper and say "I just know this to be true," but even those statements should be consistent and coherent with the rest of your belief system.
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It may be surprising that I start here of all places, but this is often times where much of the conflict between where worldviews starts. Propositional logic starts with some fundamental assumptions that are often unable to be be proved. “Water is wet.” We know that’s true, but we can’t really define what “wet” means without using a synonym or coming back to “having a similar essence to that of water.” Its just a true statement that everyone agrees on without the ability to break to down anymore and people come to common agreement on what all the words in that sentence mean and the larger meaning of that sentence.

However, a problem occurs when people can no longer agree on such a consistent “language” to talk to each other with. What if I made a statement like “water is wet,” but we couldn’t agree on what the words “water” or “wet” were or what the essence of the verb “is” meant? We’d have a hard time communicating if even a few important words were up for grabs to mean different things. So what about words like “good” and “evil”? What about “love” and “hate”? How do we define the word “god” or “God”? You may notice that it’s capitalized sometimes and lower-case other times. Does that change its meaning?

Unless you can agree on such things, it’s nearly impossible to have a conversation about morality, ethics, philosophy and theology. It’s hard, but not impossible. It may be necessary sometimes to flesh out some definitions at the beginning of the conversation or to stop at certain points to ask, “When you use that word, what do you mean by that?” It shows that you are listening and that you care to understand the person, just let them finish their thought before you stop them when possible so it doesn’t appear that you are always interrupting them.

There will be some words that can’t be defined though and this creates a huge issue if we can’t agree on what those words are supposed to mean. So, when possible, I’ll try to explain what I mean when I use certain words where the meaning of what I’m saying could be interpreted differently to different worldviews. I can’t help using some undefined terms and that will mean that we have to have some common understanding of certain things for us to have some of these discussions. If you have questions, please ask and I’ll do my best to try to answer any honest questions that help move the conversation forward.