 A great deal of confusion comes from people misunderstanding the relationship between language and reality, between our words and the world. If we want to think clearly, we have to put up very clear boundaries between these three things, words, concepts, and their reference. What I mean by a word is a visual pattern. So a word could be ink on a piece of paper, so ink scratching is on a piece of paper. Or it could be if I'm communicating a word to you, it could be the actual talking about sound waves as they reach your ear, their sounds. Or if you're reading something on a screen, the actual assortment of pixels on a screen, that's what I'm talking about is a word. A word, when read or when experienced by a mind, will elicit a concept. The concept in your mind is different than the word on the piece of paper. So I'm in Auckland right now. If I were to write out the word Auckland or communicate the word Auckland and you hear those sounds, those sounds are different from the concept that arises in your mind when you think about what Auckland means. Which brings us to the third part, reference. Just like the word is not the concept, the concept in many cases is not the reference. So the concept of Auckland in your head is different from Auckland in the world. Another example I like to use is my dog named Goose. When I say the word Goose, there's a concept that comes in your mind. That's going to be a very different concept that comes in my mind because I know what type of dog Goose is. I know that Goose isn't actually an avian Goose. But those things are separate from Goose himself. If nobody were to conceive of my dog Goose, he would still exist. He has a mind independent existence. But here's where people get tripped up. It is not the case that every single concept has a mind independent existence. For example, if I'm talking about Pegasus, the mythical Pegasus, does Pegasus have some kind of external referent? When I say Pegasus, you've got a concept in your mind that comes up. But does that concept refer to anything that is physically or spatially extended in the world? I would say no. To the extent Pegasus references anything, it's actually referencing the entity in your mind. Pegasus is the concept of Pegasus. And this is true with all fictional objects. So when we're talking about Harry Potter, for example, we can still say true and false things about Harry Potter. But we're not talking about an actual person that exists separate of our conception of him. We're talking about a story in our head. Were there no minds, there would be no Harry Potter. Now, a stickler might say, but Harry Potter references Daniel Radcliffe. Well, no, that's just a case of ambiguity. If what you mean by Harry Potter is Daniel Radcliffe, then yes, Harry Potter would have an external reference. But what most people are talking about when they use those words, Harry Potter, is referencing a fictional story. Now, you might ask yourself, okay, so what? What does that have to do with anything? Well, first of all, we must maintain clarity when we're thinking about how our concepts relate to the world. But also, this comes up with huge implications when we're talking about mathematics. As I've said many times before, in my worldview, numbers are like fictional objects in the sense that they don't exist separate of our conception. The number four doesn't have some mind-independent reality. The number four is a concept we come up with in our head, just like Harry Potter. Now, that might sound esoteric and abstract, but as will be revealed over maybe the next year or so, it's actually a very radical idea. And if it's true, then we need to revise a great deal of modern mathematics, believe it or not. So as you think through philosophic concepts, keep very clear boundaries in your mind. The word is not the concept, concept is not the reference, and it is not the case that there's always some immediate external referent from the concept. That's all for today.