Materialism Vs. Mathematics: Why Math Needs God!

Revealed Apologetics

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Welcome back to Revealed Apologetics. I'm your host Eli Ayala, and today we're gonna be diving into a topic that is both fascinating and foundational.

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So get your floaties ready because we're gonna be heading straight into the deep end of the philosophical pool.

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We're gonna be exploring some big ideas that might sound intimidating at first if you're not familiar with things like philosophy, but we're gonna be discussing the topic of what is known as universals and particulars, okay, in philosophy.

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And we'll talk about why this is relevant here, but I'm gonna walk you through this step by step, and my goal here is not just to explain these concepts, but also show you how they connect to something practical— defending the

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Christian faith, okay? So these philosophical concepts are gonna be very important for you to become familiar with, especially when you're talking with atheists and materialistic naturalists, if you're with those, you know, that terminology, okay?

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And this isn't, again, this isn't just philosophy for the sake of philosophy, okay? I think understanding these ideas are gonna help you see why the

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Christian worldview makes sense of even the most basic truths, like how we know, I don't know, how do we know two plus two equals four?

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We'll explore that and why other worldviews, especially materialistic atheism, cannot. So buckle up and let's get started, okay?

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The first things first is to define our terms, okay? But before we get into that question of why atheists cannot count for something like mathematics, two plus two equals four, we're gonna need to take a step back and define some of the big ideas that affect this question, okay?

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So these ideas are called universals and particulars, and they play a huge role in how we understand the world, including math.

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So very, very important. So these are deep philosophical concepts. I'm gonna try my best to walk slowly through them, take you by the hand if you're not familiar with philosophy, and hopefully help you understand what these concepts are and why they are important, how they can be useful in conversation, okay?

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So let's start with the concept known as universals, okay? Universals are abstract concepts or ideas that don't change and can apply to many specific things.

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So they're the big picture ideas that help us make sense of reality, okay?

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Example would be the concept of numbers. If you think about, for example, the number two, it's not tied to any specific object, like a physical object.

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The number two applies to two apples, it applies to two chairs, or it applies to two books, but it's always the same idea, no matter what you're counting, okay?

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Does that make sense? Another concept of universal would be something like shapes or colors.

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So take a triangle, okay? A triangle can be small or large.

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It can be red or blue, but it's still a triangle because it has three sides. And so the idea of a triangle is universal, even though the specific ones you see, like a road sign or even a slice of pizza, even though those things are different, the idea of, you know, triangle is not limited to those specific instances of triangular objects, okay?

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You can think of universals as kind of like a blueprint or a pattern. Every time you see something that fits the pattern of two or it fits the pattern of triangularity or it fits the pattern of red, you're seeing a particular example of a universal idea, okay?

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Now you want to be very careful. We're speaking of abstractions, like ideas, but these are real.

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So even though you can't hold two, the number two, in your hand, it's real.

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Universals help us organize and understand the particulars that we experience in the actual world.

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If you think about it, without these universal ideas, we couldn't share ideas or make sense of the world in a consistent way.

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And so the concept of universal, I think, is very, very important to get a grasp on.

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So those are some examples of what a universal is, all right? So for example, a red barn, which often uses an example.

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We can say that a barn is red, okay, but that redness, okay, can be in other things, like a red apple, the red barn, the red car, okay?

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The physical objects that possess the universal can change, but the universal category itself doesn't change, and it can be in multiple places at once, which is very different than what we might call in philosophy particulars, okay?

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Particulars are the specific individual things that exist in the actual material world, okay?

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These are the objects or instances you can see, you can touch, you could interact with, okay?

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An example of a particular could be something like an apple or a pair of apples, okay?

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If you have two apples on the table, for example, if you're sitting next to fruit or something like that, you could take two apples, put it on the table.

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Those apples are what we would call particulars, okay? They're individual examples of the universal idea of two.

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You can take, for example, a red balloon. And so a red balloon at a party, you know, wherever you might find a red balloon or a clown is holding a red balloon or something creepy like that, okay?

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A red balloon at a party, we'll go with a party since clowns are super scary, you take a red balloon at a party, we can call that red balloon a particular.

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It is a specific example of the universal idea of redness.

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A red balloon is a specific example of the universal idea of redness, okay?

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And so particulars are what we experience in the physical world. They're specific and they're tied to time and place.

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And particulars, in differentiation from universals, particulars don't last forever.

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For example, if you take apples, apples can go rotten, you can pop a balloon, but the universal ideas behind them, like two or redness or things like that, remain the same.

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And so those are the differences between universals and particulars, okay?

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Now, the next question we could ask is, how do universals and particulars relate to each other?

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How are they connected? Okay, this is so important. And this is a big question in philosophy, in essence, how do abstract universals connect to specific particulars in the real world?

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For example, how does the universal truth of 2 plus 2 equals 4 apply to actual apples or chairs or any other particular, okay?

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Here's why this matters. Universals apply to particulars. When we say 2 plus 2 equals 4, we're using universals.

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The abstract ideas of 2, addition, right? 2 plus 2, addition, and 4, okay?

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But we're also applying those ideas to particulars like apples or chairs or cherries or any material, particular object that we can point to, okay?

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Now, for 2 plus 2 to equal 4 to make sense, there has to be a connection between the universal ideas of math and the specific things we count in the real world.

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So, without this connection, universals would just float around as meaningless ideas, and particulars would be random and chaotic objects that don't hold any specific relationship to each other, okay?

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This is so important. Now, throughout the history of philosophy, these concepts have—people have grappled with these concepts.

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People have tried to provide different explanations as to how universal concepts relate and connect to particular things in our experience, okay?

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So, let's look at—I mean, this is a broad category of the history of philosophy, which

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I'm not going to bore you with the details of the history of it all, but these—there have been many attempts to bring these categories together, and so we're going to be going through some of those, and hopefully that will give you some context in how and why this is important, okay?

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So, let's look at four main approaches, and what these approaches get right in their attempt, and what they get wrong, okay?

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And so we have to dig back deep. A long time ago, in a galaxy far, far away, there is this philosopher named

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Plato, okay? Plato. Not to be confused with Play -Doh, the wonderful, fun, child -sculpting clay, okay?

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It's Play -Toh, not Play -Doh. By the way, if philosophy interests you—I mean, these are—they're known as the big three.

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You want to be familiar with Plato, or rather Socrates, Plato, and Aristotle.

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Those are the three big names in Greek philosophy, and, of course, the first attempt to explain the connection here is in a view known as Platonic—after Plato—Platonic realism, okay?

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And this view holds that universals are in a separate realm than the particulars, okay?

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So, Plato believed that the universals exist—these universal concepts exist—in a perfect, eternal realm that's separate from the physical world.

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Particulars, for Plato, like apples and chairs, are just reflections of these perfect universals, okay?

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So, Plato would say that the number two exists as a perfect idea in a realm of forms, and when you see two apples, you're seeing an imperfect reflection of this perfect two, okay?

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He also said that he compared—Plato compared the physical world of particulars to shadows on a wall, if you're familiar with his famous cave analogy, right?

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The things we experience are just blurry copies of the real, perfect universals.

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You know, to put this idea across to my students, I'll often ask the students, you know, what is a chair?

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You know, what is a chair? Can someone define for me a chair? And so, you know, one of my students might say something like, well, a chair is something you can sit on.

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I say, okay, a chair is something you can sit on. Well, I can sit on the floor. Is the floor a chair?

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Well, I mean, the floor is not a chair. I was like, oh, so then what is a chair? And so they begin to have difficulty defining what a chair is without having a conception of a chair.

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How do we know what a particular instance or particular exemplifies the concept, okay?

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These are some deep questions, okay? So for Plato, we can define the physical chair, but it's always imperfect.

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It doesn't capture the essence or the ideal of what a chair really is, okay?

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That's why Plato would say that these are shadows. They're not the perfect. They reflect in an imperfect way the perfect, okay?

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Now, platonic realism does, I think, a good job explaining why universals don't change.

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They exist in this changeless realm of ideas. The number two is the same for everyone, everywhere, because it's part of this eternal realm.

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However, the problem for Plato and platonic realism, from a philosophical perspective, is that if universals are stuck in another realm we call the realm of ideas or the realm of forms, how do they reflect the real world?

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How does the number two in this perfect realm actually connect to two apples, say, in your kitchen, okay?

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It's one thing to posit this immaterial realm of ideals and this realm of particulars that are filled with physical objects that are constantly undergoing change, but how do you connect them, okay?

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And what relationship does this immaterial realm have with the physical realm of particulars?

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And I don't think that Plato's philosophy could account for that in a meaningful fashion, and therefore there are problems in accounting for both universals and particulars in their relationship, okay?

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Because if you think about it, in order for you to have an intelligible experience of a duck, for example, you have to have a concept of what it means to be a duck.

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The nature of a duck, the concept, then is imposed upon the particular instance of a duck, say, in a pond somewhere, and then the concept there has meaning, but why are they related?

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The immaterial realm and the physical realm, these conceptual realms and the particular realm, how are they connected to one another, okay?

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Important question. And so the Platonic realism perspective is one way that people try to kind of express these ideas of universals and particulars.

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Then along comes Aristotle. Aristotle was Plato's student, okay, and he kind of had a different take on it.

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If you want to know what this position is, it's often referred to as Aristotelian, after Aristotle.

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Aristotelian realism. So the universals for Aristotle are not in this realm out there somewhere, but they actually are in the things.

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They're in the particulars, okay? So Aristotle thought universals, again, weren't in a separate realm, but were actually part of the particulars.

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Universals only exist within the things that they describe. So for example, two, the universal two exists in the apples that we are looking at.

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So the concept two is in the two apples that you're holding. You don't need a separate realm,

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Aristotle believed. You don't need a separate realm of forms to explain it, okay? Aristotle thought that universals were the shared features of things.

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Every triangle has three sides, and every two, every number two involves a pair of objects, okay?

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Now again, Aristotle's approach ties universals closely to the observable reality, and this explains why we can count objects and recognize patterns in the world and so forth.

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And so in that sense, someone might favor Aristotle's view because it is not as far and lofty as Plato's view of a realm out there, but rather it's rooted—what we can know about objects, the universals, and the particulars—it's rooted in the material world that we could observe, okay?

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And so that's why Aristotle is typically associated with kind of like empirical considerations, you know, the observation, the eyeball experience sort of thing, okay?

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However, I think Aristotle's explanation and people who owe to Aristotelian realism kind of run into some problems.

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Think about it. If universals only exist in the things that we see, how can we think about them as abstract ideas?

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I mean, how do we know two is true, even when we're not looking at two apples, right?

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Seems like they're not necessarily instantiated in the specific physical things. Does the concept have meaningfulness when we're not holding two apples in our hands or something along those lines, okay?

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So that's another way that people have tried to understand the relationship between universals and particulars.

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Nominalism, okay? And nominalism will reject the reality of universal categories altogether.

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Universals on nominalism are just labels, okay? They say universals are, you know, anomalists will say that universals are just names or labels we use to group things that seem similar.

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So, nominalists would say that, number two, it isn't a real thing. It's just a label we use to group pairs of objects, like two apples or two chairs or something along those lines.

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And I think the positive aspect of this view, at least I can see as to why someone might want to hold to it, is that it keeps things rather simple, right?

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It says, you know, listen, let's not overcomplicate things. Universals are just ways we talk about patterns that we see, okay?

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And so I can see the kind of the simplicity in that view might be attractive to some people who are trying to work through this concept philosophically and come to conclusions.

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But I think there's something missing here. Think about it. If universals are just labels we made up, there's a question.

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It's just a question. Why do they work so consistently? Why does 2 plus 2 equal 4 hold true for apples, for chairs, stars, even in places we've never been, right?

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Why the consistency? If these are just labels, are they just labels or are they telling us something about the nature of reality itself?

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I think that's an important question to consider. Again, we're not offering a full frontal refutation to all of this right here, but these are some of the ways that people have understood these concepts.

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Then along comes Christian theism, okay? And we ground universals and particulars in the very nature of God.

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And I think this often is overlooked by people who are not familiar with these categories. It's one of the reasons why the

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Christian worldview—when we say, for example, only the Christian worldview provides the foundation for intelligible experience, knowledge, science, logic, mathematics—I mean, the answer to those philosophical puzzles is rooted in the very nature of God and His revelation.

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I mean, think about this. Christianity offers a unique solution to this very deep philosophical issue.

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Universals and particulars exist and connect because they are rooted and grounded in God Himself.

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You see, in Christianity, universals like numbers, logic, and shapes exist because they reflect the nature of God.

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Not that God is a shape, but that the universal concepts are grounded in His being.

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They're part of His nature, right? God is unchanging, He's eternal, and the ground of all truth. Now, God also created the physical world, and the spiritual world for that matter, but in terms of the physical world, every apple, every chair, you know, the star that exists out there exists because God created all things.

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He created the material out of which we make things, right? God is the source and fount of all of the physical world.

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And the immaterial world, that does not include Him. Obviously, we don't believe God created Himself, right? That's an incoherent concept, okay?

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And it is within the Christian worldview that you have the important bridging of the gap between abstract realities and particular things, right?

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The connection between universals and particulars exist because God designed it that way, okay?

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Numbers apply to apples because God created a world where they fit together, okay?

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God does not only create the physical world, He defines the facts of the physical world and establishes the relationship between particular things, okay?

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And so He's established those things. They are grounded in Him, they find their connection in God, and we know about these connections through His revelation, okay?

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Now, think in terms of God's nature, though, and this is, I think, super helpful here. Within the Christian worldview,

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God is a Trinity. God is a triunity of persons. God is one being who exists as three persons—Father,

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Son, and Holy Spirit. Now, this is not the episode where we're gonna be defending the Trinity, per se. I obviously believe that it is the

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Christian position that God exists as a Trinity. Working with students, sometimes, you know, the kids would ask, well, why?

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Why does God—why is God a Trinity, you know? And I've had—I've heard some people try to answer this question, they're all confused.

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I don't think it's a hard question. It's like saying, why is God God? Well, that's the nature of God.

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That's who He is. God didn't make Himself a Trinity. God is a triune being by nature, okay?

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So I want you to think in terms of the nature of the triune God, okay? Even God's nature as Father, Son, and Holy Spirit helps us understand this connection between abstractions and particulars, the realm of individual objects, okay?

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In the Trinity, we see both unity and diversity, right?

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One God in three persons. And again, if you think about it, this reflects how universals—unity—those concepts that unify the particular individual things, this explains why they work together in the world.

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I want you to think about this, okay? I want to slow down here, okay? God is one being who exists as three persons.

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So in God, both unity and plurality are equally ultimate.

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So the plurality of God does not begin or derive from something more ultimate, the unity.

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Both the unity and the plurality are equally ultimate in God, and creation reflects that unity and plurality.

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Why? Do we have a plurality of things? And why are the plurality of things meaningful, okay, is because they are unified by universal concepts.

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They reflect the Creator. This makes perfect sense within a

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Christian worldview. However, it does not make sense in an atheistic worldview, a materialistic atheistic worldview specifically, okay?

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So, how does Christianity make sense out of, say, 2 plus 2 equals 4? Let's explore that. Let's bring this back to math, right?

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Christianity explains 2 plus 2 equals 4, okay? I would argue in a way that no other worldview can.

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Universals like 2, okay, exist because of God. God, in the Christian worldview, is the source of eternal, unchanging truths.

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They exist because they reflect His rational, consistent nature, okay?

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The physical world exists because God made it. It's orderly and countable, okay, because He designed the world that way, okay?

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Universals and particulars connect because God created both and designed them to work together.

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Numbers apply to objects because God built that order into creation.

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Now, again, you might be listening and saying, well, wait a minute. Well, I don't believe in the God of the Bible, so on and so forth, okay?

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That's not what I'm talking about. You can reject the Christian worldview. The question then is, how do you make sense out of the things you take for granted?

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For example, 2 plus 2 equals 4. It's a fair question, okay? From a biblical perspective, it is obvious that the unbeliever is borrowing from the

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Christian worldview when they are arguing against the Christian worldview. And again, this is not just a bare claim.

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We're not just claiming that they're doing that. Of course, when you're interacting with an unbeliever, you're gonna have to actually, in some cases, explain what you mean by that.

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Again, I have a whole video where I explain how this is actually the case. I have a whole video where we talk about, where I talk about the specific ways in which the unbeliever borrows from the

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Christian worldview. But nevertheless, when an atheist says 2 plus 2 equals 4, okay?

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The materialistic atheist, he's doing math, right? What they're doing is they're using a truth that makes sense in Christianity, but I would argue doesn't fit in their worldview.

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They can account, I'm sorry, they can count, as Van Til said, they can count, they can do math, but they cannot explain why counting works.

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They can count, but they cannot account for the counting that they engage in, okay?

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Now when I say account, they cannot account for something, I'm not simply saying they can't come up with a story. This is, you know, this is how math works, so on and so forth.

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No, I'm saying, in a philosophical sense, they cannot provide an adequate justification for why numbers are what they are and how, why immaterial abstract universals apply in a meaningful way and relate in a meaningful way to the particulars, the individual things of experience, okay?

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They cannot bring together both unity and diversity within a worldview that is not grounded in something that is both ultimately unity and diversity, like the

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Christian worldview can, all right? So that's very, very important. So the atheist cannot account for these things, and any worldview that is self -vitiating, any worldview that is contradictory at its core at a fundamental level is not able to give an accounting for these things as well, okay?

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Now we're not talking about other worldview perspectives at this moment, I'm just kind of using materialistic atheism as an example here.

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But why is this all important? Well, to express kind of the practical apologetic application of these things, let's kind of go through some questions, and I'll kind of provide, you know, my views here in terms of how

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I would address some of these questions. And these questions here, they're pretty practical for, you know, if you're a

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Christian and you're having a conversation with, you know, an atheist who is somewhat knowledgeable about philosophy and things like this, and they might hear you say some of the things that we've just expressed here, you know, how might we respond and explain some of these questions, okay?

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So let's take some time to do that, okay? So here's the first question here. How does this idea of universals and particulars even come up in conversations with atheists?

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Aren't we just talking about math, okay? This is the pragmatist, right? It's like, what's going on here?

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Why are we talking about philosophy? We just brought up numbers and things like this. That's a great question, okay? And I think at first glance it might seem like we're simply talking about numbers and math, but the discussion about universals and particulars

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I think really gets to the heart of how we explain reality itself. Okay, so for example, the atheist might say something like, we don't need

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God to know that 2 plus 2 equals 4. It's just basic math, okay? And then someone might say that, and you might even be thinking, why would

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I even be bringing this up? But by the way, when I talk to atheists, it doesn't come up all the time, but it does come up, right?

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When I talk about how the unbelieving worldview, specifically the atheist that I'm talking about, he does not have unity in his worldview.

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He cannot account for the basic things he takes for granted when he says, but how? I don't need God to know 2 plus 2 equals 4, okay?

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And then of course it's at this point where we're going to have to strategically press in a little deeper to get to the heart of the issue, right?

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If you press the atheist, the materialistic atheist, to explain why math works, you'll see very quickly that they will run into some problems.

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Math involves universals, like we've been discussing, abstract concepts like numbers and addition, okay?

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Math involves particulars, real world objects, objects we actually count.

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You see, atheism doesn't have a foundation for why universals exist or why they connect to particulars in a consistent way.

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You see, they're left borrowing from the Christian worldview, which does provide a foundation in God's rational and orderly nature.

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It's the teaching of scripture, okay? This isn't just about numbers. It's about the consistency of the entire universe.

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Without God, you can't account for why math, logic, or science even work, okay?

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Now, of course some might say, well, I don't need to account for those things. Well, of course, you could say that. You're free to say that. But at that point, the person is just being arbitrary.

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Anything they assert, any fact that they state or assert is going to, by necessity, presuppose these categories of unity and diversity, universals and particulars, okay?

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And so they're gonna argue all day long and ask you not to look behind the curtain to show that actually the things that they are asserting, the things that they're presupposing, when they assert a fact, okay, they cannot give an account for the very foundation upon which those things issue forth from.

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And so your job is to pull away the curtain and show, actually, I agree, Mr. Atheist, you're very good at math, you're better at math than I am, but here's the kicker.

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Your world, you cannot account for math. Your world, you cannot account for universals and particular things in the relationship between individual things and how they relate to each other with these overarching universal categories.

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The unbeliever cannot account for those things. They cannot provide a rational justification for them, okay?

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All right. Well, what if, you know, your atheist friend comes along and says that math is just a human invention, okay?

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It's something we made up to describe the world, right? And I've heard this in various capacities, okay? Now, if the atheist says that math is just a human invention, you could ask, if math is something we made up, here's a question, okay?

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Why does it work so perfectly in describing the universe, right? For example, why do the laws of physics rely on mathematical principles?

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Why can we use math to make accurate predictions about things we've never seen before, like distant planets and things like that?

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It's a question. It's a good question to ask. You see, the Bible explains this.

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God created the universe with order and structure, reflecting His rational nature, right?

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In the beginning, God created the heavens and the earth, okay? He created all things seen and unseen, right? He holds all things together by the power of His Word.

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You see, humans didn't invent math. Humans discovered order. They discovered the order that God built into His creation.

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If math were just a human invention, it would be arbitrary, right?

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And it wouldn't consistently apply to reality. But because God governs all things, math and everything else works universally, from counting apples to calculating the orbits of the planets, okay?

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There's an order to it. And again, that is sufficiently accounted for within the Christian worldview.

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Now, if someone were to say, how do I explain to an atheist that they're borrowing from the Christian worldview, isn't that just an assumption, okay?

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Now, that's a fair question, okay? And this is important because a lot of, especially presuppositionalists, you know, out there on the street, they'll say, hey, you're borrowing from the

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Christian worldview, or they'll say, by what standard, or they'll say, Christianity is true by the impossibility of the contrary.

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All of those things have their place, but you need to learn to go beyond simply asserting those facts.

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You need to be able to explain, you know, what you mean by that and demonstrate that, because that's what apologetics requires.

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We're giving an answer, we're not just making assertions, right? We need to defend and get into some of the details.

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And sometimes it's gonna require us to go a little deeper than simply making those assertions, which are popular presuppositional talking points, but we want to go deeper than that.

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So when we say that atheists are—they are borrowing, okay, one second here—that they are borrowing from the

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Christian worldview, we mean they're relying on concepts that only make sense if God exists.

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So even though they deny him, right, they're borrowing concepts that only make sense if God exists, the

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God that we're talking about exists. For example, atheists trust in universal consistency of math and logic, right?

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They might say in their explanation, well, you know, it's a human invention, it's a language game. They might say those things, but they don't live consistently with that, right?

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They rely on their minds to reason accurately about the world, right? They think that that helps them reason accurately about the world.

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They assume the physical universe operates in an orderly and predictable way. They might give lip service to, well, you know, you never know, right?

33:19

But really, they assume these things in every—in their everyday experience. But if you think about it, none of these things fit with a worldview that says the universe came from random chance processes.

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You see, the Bible tells us that God is the source of all truth. He upholds the universe by his power,

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Hebrews 1 .3, and humans are made in his image with the ability to think rationally. God created us in his image,

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Genesis 1 .27. And so when an atheist says 2 plus 2 equals 4 is just true, you could ask the question.

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It's a fair question. Why? Where does that truth come from? How do you know it will always be true?

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And their answers ultimately rely on assumptions about order, truth, reason, that are themselves grounded in the nature of God, and they are unable to account for those things, okay?

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And so again, you want to press, you want to ask questions. There's nothing wrong with asking questions. People, you know, presuppositionalists specifically will get a bad rabble.

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There you go, they're playing the skeptic game, how do you know, how do you know, how do you know? But those are fair questions, are they not?

34:23

When we're debating worldviews, are we not supposed to ask for justifications for your assertions, right?

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If you want to reject God, then make sense out of the world without him. We don't just—we're not just gonna grant you the things that you want, right, and then just let you argue from there.

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If you reject the Christian worldview and you think you can get along fine without the truth of the Christian worldview, then yes, account for numbers, account for mathematics, account for the things that we take for granted.

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You see, a lot of people just think that we should give them those things, and we shouldn't, because when we're dealing with the existence of God, we're dealing with fundamental foundational issues.

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And so in a debate on worldviews, there are no free lunches, all right?

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We need to get into those details, okay? The unbeliever is always looking for that little thing that you'll give them.

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Well, let's just grant this, and then I'll show you—no, no, no, no. If you reject the God of the Scriptures, if you reject the

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God who says that all men have a knowledge of him and they are without excuse, then you're gonna have to construct your worldview and provide explanations that are native to your unbelief, not things that you have to borrow from a

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Christian perspective, okay? We want to be able to point those things out. Very, very important.

35:42

All right, so, how does—you know, if someone were to ask, how does the Trinity, specifically the Triune God, explain the relationship between universals and particulars?

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Can you give an example? Yeah, so we can, all right? Again, these are deep issues, you're not gonna always get into the conversations like this, but this is important.

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Lest you think a nuanced and philosophically heavy discussion is irrelevant to practical apologetics.

36:07

Even if it's true that you might not use the terminology that I'm using—universals, particulars, abstractions, these sorts of things—it is so important that you are at least familiar with the concepts, because everything that someone says are gonna assume those categories.

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So even though you're not using these concepts, you want to be able to take what we're learning here and make application to the specific context in which you're speaking.

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Does that make sense? So even though we don't use this language, the concepts are important. You want to have these concepts playing as kind of the background music of your mind, and be able to make practical application when you are talking with the atheist or whoever you might be engaging with, okay?

36:52

So nevertheless, the question, how does the Trinity explain the relationship between universals and particulars? Can The doctrine of the

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Trinity helps us understand, I think, the balance between universals, or the unity, right, and the particulars, the diversity, the one and the many, right?

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There are many things we see in the world—rocks, plants, you know, animals, humans—and then there are things that unify and relate those concepts, the universals.

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Logic, right? Without logic, how do we even make sense and differentiate between individual things, right?

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In the Trinity, we see one God—there's the unity—in three distinct persons, there's the diversity.

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Father, Son, and Holy Spirit. Both unity, the oneness of God, and diversity, the manyness of God, are equally ultimate in God.

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And this reflects the way universals and particulars work in the world. So, for example, universals.

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The concept of two is universal. It applies everywhere, whether you're counting apples or stars or whatever.

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Particulars, okay? You got two apples. Two apples are specific objects. They're individual objects in the real world.

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And so just as the Trinity brings harmony between unity and diversity, God's creation brings harmony between universals and particulars.

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Without the triune God, there's no reason to expect this balance to exist at all. Okay? Hope that's helpful to that specific question.

38:28

Now, someone might say—someone might walk up and say, well, doesn't evolution explain how humans developed the ability to reason and use math?

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And the straightforward answer to that is, no, not at all. Evolution can't explain the human ability to reason or the existence of math at all.

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And here's why. Think about it. Reason requires order, right? Evolution is typically associated with random mutations, natural selection, and other considerations.

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But reason requires consistent universal principles like logic, math, which don't come from random processes.

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Okay? You don't get order from disorder. You don't get rational from irrational. These sorts of things.

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Okay? Another thing is that math isn't something physical that evolves. It's not part of the biological realm.

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The truth of 2 plus 2 equaling 4 existed before humans were—humans ever discovered it.

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If math were a product of evolution, it wouldn't apply universally. It would just be a useful tool for survival, which evolution is concerned about.

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It's an issue of, you know, adopting survival traits, these sorts of things. Okay? Now, Scripture says that humans are made in God's image, which means that we reflect

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God's nature in some capacity. And one capacity is that we reflect His rational nature.

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Our ability to reason, think logically, and use math is part of how God designed us to understand and steward

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His creation. And so evolution can't account for the universal, unchanging nature of math, or the rational minds needed to understand it.

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Okay? Evolution cannot account for truth, and evolution's geared towards survival. You don't even, you know, believing true things is not necessary for survival.

40:16

Isn't that right? You could have false beliefs, and those false beliefs can help you survive. That's why evolution is not concerned with truth, it's concerned with survival.

40:25

I mean, what do I mean by this? You know, suppose, you know, in the early evolutionary development of man, you know, the caveman

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Ooga Booga, we'll call him, okay, develops the false belief that humanity is engaged, or his kind is engaged, in a game of tag with tigers.

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Okay? And so he believes that all of his relatives, okay, the people part of his tribe, are in a game of tag with the tigers running around out there.

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And so based upon that false belief, every time he sees a tiger, our caveman

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Ooga Booga begins to run as fast as he can, and he escapes, for the most part, the tiger.

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Every time he encounters the tiger, you see? And so his false belief that humanity is in a game of tag with the tiger has allowed him to survive, since he tries very hard to run away from the tigers when he sees them.

41:24

Okay? And so false beliefs can sometimes cater to survival, and so evolution is not concerned with truth.

41:31

We evolve to survive. We do not evolve to learn truth. Okay? So kind of just a little example there.

41:39

Hopefully that's helpful with respect to evolution. All right. Someone might ask, how would you respond if an atheist says,

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I don't need God to believe math works, I just trust it does? Okay? And of course, people have said that in various and sundry contexts, but again, if an atheist says,

41:56

I just trust math works, you could ask, okay, this is a fair question. Why do you trust it? Where does that trust come from?

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You see, the person says, well, I just trust that it does. Okay, now let's think about this. If the Christian were to do this, this would not be acceptable at all.

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I believe in God, and I believe the Bible is his word. Well, why do you believe that?

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Well, because I just do. You see? We call that arbitrariness, right?

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You believe something literally without a justification. You just, it is that way because that's just the way that it is.

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Okay? Now, this is not at all what the Christian is called to do. We are called to offer an apologia, okay?

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Or if you want to say it incorrectly, apologia. Okay? So we offer an apologia, we offer an irrational defense, a vindication, and that does not permit us to simply assert things with arbitrariness.

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Okay? In the Christian worldview, we trust math because God is faithful and unchanging. God does not change,

42:56

Malachi 3 .6. He created the universe with order and logic, and he sustains it consistently,

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Colossians 1, 16 through 17. Okay? Now, logic reflects his mind. I don't think God created logic in that sense, you know,

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I think it is a reflection of his thinking. I know there are different views with respect to that. Without God, there's no guarantee that the universe will continue to follow mathematical laws.

43:20

The atheists' trust in math, I would argue, is a blind faith that doesn't fit in their worldview.

43:25

They're assuming the universe is orderly and consistent without being able to explain why and provide a rational justification for that.

43:33

I'm not saying that atheists can't explain why they believe certain things and they can give the inner workings.

43:38

We're talking about at the worldview level. Can their worldview, their philosophy of life, provide a sufficient justification for why these things are the case?

43:49

Right? Nevertheless, someone might ask, doesn't science explain why math works?

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Again, I've heard this before. Now, science uses math, okay, but it doesn't explain why math works, right?

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In fact, science depends on math to even get started, okay? Science doesn't prove mathematics or anything like that or prove logic or anything like that.

44:14

Science presupposes both logic and math, okay? Scientists use equations to describe the laws of physics.

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They rely on logic to interpret their experiments, etc., etc., but why do these tools work?

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Science doesn't answer that question. You see, the Christian worldview explains it. God created both the universe and the human mind, so there's a harmony between the physical world and the abstract principles we use to describe it.

44:37

That's it. Without God, science has no foundation for the mathematical and logical principles it depends on, right?

44:44

People might not like that answer, oh, well, you're invoking God. Yeah, I'm invoking God. I'm invoking

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God in his word because God is the necessary precondition for intelligible experience, which includes the intelligibility of science, math, logic, and all the rest, okay?

44:59

So it's not a fault when someone says, oh, you can't invoke God. Why? Why can't

45:05

I invoke God, right? I love that why question. It's a very good question to ask when someone makes an assertion.

45:12

You got to be ready to answer it when someone asks you why as well, so there's two sides to that coin. Someone might ask, well, what

45:17

Bible verses support the idea that math reflects God's nature? Now, again, the Bible doesn't teach in any explicit way, like, you know, math relates to God, right?

45:28

You know, but here are a couple of verses to chew on, okay? So, in the beginning, God created the heavens and the earth. You see, think about that.

45:34

God created the universe with structure and order. The Bible does teach that, which includes mathematical principles, so it's assumed in those concepts.

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Colossians 1, 16 through 17, for by him all things were created, and in him all things hold together, okay? And so this shows that Christ sustains the universe, ensuring its consistency, which is related to logic, truth, and the consistency and consistent relationship between things within the created order, connecting universals and particulars, things like this, okay?

46:00

Hebrews 1, 3 says that Christ upholds the universe by the word of his power, okay? God's power ensures the reliability of the physical world and the principles that govern it, okay?

46:10

Also promises that seed, time, and harvest, right, will remain the same, that passage in Genesis 8, 22,

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I think, okay? In Proverbs 3, 19, we're told that the Lord, by wisdom, founded the earth.

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By understanding, he established the heavens. God's wisdom, God's understanding, are the sources of all order in creation, including math, which is a reflection of his creation, his nature, okay?

46:33

Very, very important. Now someone might say, can't we just say that 2 plus 2 equals 4, it's true, because it's obvious, why bring

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God into it at all? Again, people ask these sorts of questions, maybe you might be asking this question yourself.

46:44

It might feel obvious that 2 plus 2 equals 4, but the question still is there. Why is it true?

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And why, why can we trust it, okay? Something being obvious, this is a key part here,

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I want you to pay attention to this, something being obvious doesn't explain its foundation.

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You'll have some atheists and unbelievers that, well, why do we need to find the foundation? Why do we need a foundation, okay?

47:10

Well, without a foundation, then there's nothing for which the ideas you are asserting and taking for granted rests on, okay?

47:17

That's important, all right? Someone's like, well, I don't need a foundation. Well, you could say that, but then you're going to lend yourself to arbitrariness and not being able to provide a justification for the very things you simply take for granted.

47:29

Again, the Christian's not allowed to do this, right? The unbeliever will point that out very quickly when we say, well, it's just that way, right?

47:36

They need to be able to take the same thing when we assert, well, wait a minute. You say, well, why do I need a foundation, right? It's just obvious.

47:42

I really be very careful with words like obvious and, well, it's just common sense. You see, common sense is worldview dependent, isn't that right?

47:51

What's common sense to one person might not be common sense to another person. It's common sense for me to look all around and say, look,

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God, this is the handiwork of God. The atheist is going to come along and say, well, that's not common sense. It's common sense to believe there is no

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God, because look at all the evil and suffering in the world. Someone, you might get different explanations there, okay?

48:09

What we think about what is obvious or what is common sense is going to be based upon our worldviews, be based upon our presuppositions.

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You see, in the Christian worldview, it's obvious because God created a rational universe and gave us rational minds to understand it.

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That's the Christian worldview. Without God, there's no foundation for universal, unchanging truths that make something like math work.

48:33

So if an atheist says, you know, it's just obvious, you want to ask them, why is it obvious?

48:40

Why do numbers exist? Well, they don't exist. Maybe he's anomalous. You give your response to that, right?

48:46

Why do they always work the same way? These questions point to God, or they require God as the ultimate explanation, we would argue, okay?

48:54

Now, to end things here with a final question, again, we can ask this question just generally, how does this entire discussion, this entire video, kind of just wrapping it up, how does this entire discussion about math, particularly, help me in apologetic conversations, all right?

49:10

That's a fair question. We want to make some practical application. Maybe by the time you've gotten to this part of the video, you'd be like, man,

49:15

Eli talks really fast. He promised he was going to walk us through this, and instead he took our hand and ran through everything, and I don't remember anything he said.

49:23

That might be possible. I'm sorry if that was your experience, okay? But if we're going to ask the question, in other words, if nothing that I've said helps you, then we can jump right to the end of the video, and maybe this part will help you, okay?

49:38

How does this discussion about math help in terms of apologetic conversations? Okay, now, think about it.

49:45

This discussion about math and universals, we've been talking about universal and particulars, I think is a great way to show that even the simplest truths, like 2 plus 2 equals 4, requires

49:57

God. That's it. Many atheists think they don't need God to explain the world, but when you ask them to account for things like math, logic, science, they quickly run out of answers, and so by pointing to the

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Christian worldview, you can show that God is the foundation for all truth, including math, right?

50:18

You can show that without God, even basic truths like 2 plus 2 equals 4 becomes meaningless, right?

50:24

And you can show that atheists must use concepts like math, but they're borrowing from the

50:29

Christian worldview to do so. And so to make all of this in a short and crystallized way for you to see the of it, understanding these ideas will prepare us to better identify instances where the unbeliever has to assume categories that only make sense if the

50:50

Christian worldview is true. Now, with respect to presuppositional apologetics and transcendental reasoning, right, trying to demonstrate something by the impossibility of the contrary and so forth, understanding these categories, pardon, will help to that end.

51:07

And so that's why it's important. Ultimately, it shows that God is needed to even understand basic truths, even though the basic truth of 2 plus 2 equals 4 has a whole host of things related to it that are not as basic, right?

51:20

You got the debate between mathematical realism, numbers are a real thing, and like mathematical nominalism, math is, you know, there's no universals out there, math are just symbols that we apply to the you know, you know, there are different views out there, okay?

51:36

We can get into the deep stuff, but ultimately, for those who don't want to get into the deep stuff, that's basically what we're talking about.

51:42

God is needed to explain even things that appear to be very, very simple and mundane.

51:48

And this is the value, I think, of reasoning in a presuppositional way.

51:53

It is often done in traditional apologetics that we appeal to the miraculous, you know, the evidences for the resurrection and the evidence for miracles.

52:02

By the way, I think all of those are appropriate to refer to and talk about within the context of apologetic interaction, right?

52:13

I'm not demeaning those things at all. I'm very grateful for people like Dr. Gary Habermas, who wrote two monstrous volumes on the resurrection of Jesus.

52:23

I don't hold to Dr. Gary Habermas's apologetic methodology, but the information in his work is very, very helpful.

52:32

I'm not, you know, I'm not Frank Turek, who is a classical apologist and follows along the lines of Norman Geisler.

52:41

I greatly appreciate the work of those men. I differ greatly in methodology, but that doesn't mean that they haven't provided useful and helpful, you know, things with respect to the specifics of evidence and things like that, you see, right?

52:58

But we can point to those things, we know miracles and all that kind of stuff, but because God is the creator and definer of all things, and that he's left his imprint on all of creation such that everything in the created order is evidence of him, that means as Christians, the connecting point, the point of contact between the believer and unbeliever is great.

53:22

For not only can we appeal to the resurrection in apologetics, but we could appeal also as evidence of the triune

53:31

God of Scripture, the mundane facts of human experience, like 2 plus 2 equals 4.

53:37

We can talk about nature, animals, what is a cow? A cow is, you know, again you could define a cow in the biological sense, but ultimately the understanding of how we might define something like a cow assumes other beliefs.

53:53

It assumes a worldview. So do you have a worldview that can make sense out of something we call a cow? You know, even talking about cows and planets and nature and all that kind of stuff, mundane things, art, okay, concepts of beauty, these sorts of things, everything points to God.

54:10

And so we can use the wide range of creation as talking points, not talking points, points of contact when we are interacting with the unbeliever.

54:20

You want to talk about logic? Let's talk about logic. You want to talk about universals and particulars? Let's talk about universals and particulars.

54:27

You want to talk about art? Let's talk about art. Let's talk about whether there is something like objective beauty. You want to talk about morality?

54:33

Let's do it. You want to talk about nature? Let's do it. You want to talk about science, history, philosophy?

54:39

The Christian worldview provides the context in which all of those categories are meaningful, not so for the unbelieving worldview.

54:47

And so in order to meaningfully interact with the unbelievers, we do need to know and listen to them. You know, hey, this is what

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I believe and why. We want to have that open and, you know, conversation with the unbeliever.

55:00

We want to listen. This is so important because when we're equipped with apologetics and we're getting excited to share the faith and to share it with others and things like this, it's very easy to come at that from a very aggressive perspective, and we're kind of just talking and talking and talking.

55:14

This doesn't count, by the way. This is my YouTube channel. I have to talk, so I'm talking, right? It's just me, okay?

55:21

But it's important that we let the person with whom we are sharing the gospel with and having these conversations, it's important that we let them share their views and let them define their own categories, and then from there we interact presuppositionally, biblically, using scripture.

55:39

In this case, we're using some philosophy. There's nothing wrong with that as well. You see, that's very interesting too, because philosophy is not off -limits to the

55:47

Christian. You see, the Bible says that we must be aware of a philosophy that is not according to Christ, okay?

55:56

Philosophy is a very useful tool for the Christian apologist, okay? I think it's vital.

56:01

But of course, the boundaries of what we assert and assume and speculate with respect to philosophy, the boundaries must be bordered in by scripture, okay?

56:14

And so that's very, very important. Our philosophy is going to be governed by principles that are grounded in scripture itself, alright?

56:22

Alright, well, you had your floaties. I threw you into the deep side of the pool. Hopefully this is a little helpful.

56:29

I mean, it really just depends. There are people who are engaged in a apologetics, and the conversations you have with skeptics and atheists and things like this might involve these sorts of topics, and you might be talking to your atheist neighbor who doesn't know anything about philosophy or anything along those lines, and your conversation might look different.

56:48

Perhaps in a different video, we'll talk a little bit more about apologetics in that context, as opposed to, say, this context.

56:55

This is the beauty of having a channel that focuses on apologetic methodology. I can cover the wide range. So today we talked about something super heavy, and then maybe in a future video, we'll talk about what happens when

57:06

I talk to my atheist friend, he doesn't care about philosophy. He just says, hey, I don't believe in God.

57:11

I can't, you know, I can't see him. I only believe things that are scientifically, empirically verified, or, you know, if God exists, you know, why did my uncle die of cancer?

57:21

These sorts of, like, real, tangible, you know, situations that people deal with, we'll do a whole show addressing those as well.

57:29

So I want to provide a wide range of apologetic material for my listeners, guys.

57:34

Thank you so much for listening. I hope your ears are not leaking after hearing—I hope

57:40

I haven't melted your brain, okay? That's a big topic, but super important. So thank you so much for listening in, guys.