Question.... (Processes of Logic)

In some radically different mathematics, sure. In the general mathematics that people refer to when they use numbers, no.If I sit down at a Monopoly board and start handing out the money, it's assumed that I'm following the rules of Monopoly, and am bound by them. But if I never sit down to play, I'm not bound by the rules. Similarly if I never use numbers to describe apples, I don't have to follow those rules.I know you're a platonist, but I'm not. It may be that we can't see eye to eye on this issue. Would a red object still be red if everyone had always been color-blind? Would the word have meaning? Right - an apple loses it's red color when you peel it. to remove that property you have to alter the object.But to go from two apples to one apple and one apple, I don't have to do anything to the apples except stop considering them as elements in the same set. The red is on the apple. The number is in my mind. Well, you know I disagree. Why are you arguing about this, then?You argue that math has an existence beyond our use of it. Is this true for everything? If I invent a new axiomatic system, did I actually just discover it? Did Tolkien discover elvish, or invent it?If not, what's so special about math? These are honest questions. I don't personally know any Platonists so I'd like to explore this with you, if that's ok. That isn't at all implied by what I said. I'm not sure you understand my point. Objects have an existence beyond my conception of them. Symbols don't. How so? What's physically different about an apple when I have one, two or three of them? What about that apple changes when I add two more? Nothing, as far as I can tell.The set of apples changes, to be sure. Whether or not that set exists in anything but our minds is the question at hand. Color is a physical property of that apple. Number is a property of the set of apples. This is the distintion that you don't appear to make but seems obvious to me. I just don't see how you can say that. Color is a unitary property of an individual object. Number describes a relationship between objects. Tastes like a pomegranate to me.But you see how you can only refute my explanations with more evidence that you hadn't introduced at the beginning. You hadn't mentioned that you had cut open the apple, or tasted it or anything. Prior to that, my ninja-supplied fake fruit totally explained your evidence. But only because you assumed one apple and one apple. It's your set-up and your mind, so of course you have perfect knowledge. We're talking about hypothetical apples. In the real world, apples might not act like you expect them to. There's a difference between reality and your mental model. Which can't exist in the real world. It can exist in whatever mental model you think describes reality, but you confuse the model and the reality if you think your absolute knowledge about your model has anything to do with your knowledge in reality. And it's reality we're talking about, not models. Real apples, like the ones in my fridge right now, not hypothetical ones.

"Jesus Would Read The F***in' Manual." If I'm not mistaken. I prefer "WWJDFAKB": "What Would Jesus Do For A Klondike Bar?"

Not to mention useless.I'm curious, it's been a while since I read Godel - could you give an example of a system that's sufficiently simple as to be both complete and consistent? You don't have to, I was just wondering. I think we're making that claim, yes. I am, anyway. Then you've forgotten the context. The original claim was in the context of a person asking for evidence that something doesn't exist. Evidence implies induction.In the broadest possible sense, yes you can prove negatives. In the context that we were talking about (using evidence to support inductive statements), you can't. Funny, all I see are fingers.

But if it can model arithmetic, isn't it sufficiently complex as to be incomplete? And how could you have addition without multiplication? And what would prevent the insertion of a self-contradicting statement into that algorithm?Perhaps it's best to open a new thread. Why? To determine their color, all I have to do is look at them. As a non-color blind person their color is immediately apparent. But to know how many there are I have to count them. Are you really saying that color and number are this related? That's a bold statement.Anyway, you said that I would see "five". Not five fingers, just five. Five in it's unitary nature apart from describing the set of my fingers.All I see are fingers. Explain to me how I'm supposed to just see "five".

And why is math "discovered", while baseball and Monopoly were "invented"? (To bring in Schraf's point again.) What's the difference? How do we tell?

Sorry, I'm not trying to argue these points. I really just don't understand. I was just curious. To look, all I have to do is point my eyes.To count, I have to go "One, two, three, four, five."Seems fundamentally different to me. But then: So, it's sets that have number, not objects. That's what I've been arguing all along.They why: No, like you said, it's not my individual fingers that have five-ness. It's the set of my fingers that has the quantity "five".This distinction between objects and sets containing objects seems to be a tough one for you. Why is that? The teapot is not the water it contains.

So is Monopoly. Prove me wrong. Does the mortgage value of Boardwalk change when we're not playing?Just because the rules don't change each time you play the game doesn't mean the game itself wasn't made up. Constancy is no argument, in this case, for independant existence.

I don't think it is. It has no physical existence. It's simply the expression of a relationship between objects. No, I'm saying there's nothing about any of my fingers that contains "five-ness". That's a property of the set of my fingers (on one hand) that isn't inherited by the objects in that set. If I'm not around - in which case I certainly wouldn't have fingers, nor be able to count them - how could I even asnwer that question? It's meaningless.Sets aren't objects because they have no independant existence. If you take the objects out of a set the set no longer exists (or becomes the null set, which is no difference.)If I have a relationship between two objects, but those two objects cease to exist, so does the relationship. it has no independant existence. It's just a concept we create in our heads, based on certain rules we all agree to.

Here's two apples. Point to their relationship. Better yet - here's two apples, only one of them is here and the other is in Sweden. Now point to their relationship. The set of fingers has five. The fingers themselves don't. How many times do I have to say it? No, I'm saying that when I count them, there's five. When I'm not counting them it's meaningless to say how many fingers there are. You're really putting words in my mouth, here, and it's starting to seem like you're playing games instead of supporting the assumptions that allow you to assume that numbers have an existence beyond our conception of them. I want to know what's so special about numbers that doesn't apply to Monopoly.

No, I'm not saying that. It really looks like you aren't paying attention to what I'm saying because you keep asking that. Is this your argument style? Ask the same inane question over and over again? Just curious. How could you possibly make an observation that would support the statement "numbers exist beyond our conception of them?" Any such observation you make only supports the proposition "numbers exist when I count things." Sure, your opinion. That's fine. My opinion is that your opinion is wrong. See where that gets us? How does one do math with no mathematicians? Anyway, the rules of Monopoly come with the box. I don't understand your objection. They're that way because we invented a number five to come between number four and number six, which we also invented. I'm not really impressed.

For no other reason than off-topic pique I thought I'd point out the condition "synthenesia" where people do experience the smells of colors, the sounds of numbers, and all kinds of sensory input that appears nonsensical to us.There's some thought that such a condition could be technologically induced in a brain so that sensory data like smell or touch could be transmitted through conventional means (ala television), encoded into auditory or visual data.I find it fascinating, personally.

Because there's a difference between counting something and arriving at the number five, and those objects themselves posessing any kind of self-sufficient "five-ness" that exists beyond socially agreed-upon models of mathematics. Because I'm not "seeing" five, I'm assigning five, based upon rules that I agreed to when I decided to use numbers. The rules themselves are simply convention, not some inherent property of the universe. Granted, but that's something that must be assumed, not proven. Any statements about inherent properties of the universe or objects are assumptions inferred by generalizing from specific cases. As of yet, you have not demonstrated why it is fruitful or logical to assume that objects have an inherent property of "number". At least, you haven't done so with any rationale that couldn't also be applied to Monopoly. See, that's your assumption again. The universe exists. We both assume that. But why assume the same is true for numbers but not for Monopoly? I don't even begin to see how that answers my questions, much less makes any kind of sense. You have to know math before you can do math. So what? You have to know the numbers before you can count with them. Or your society has to invent them. Not every society invents numbers. Cheapass Games. I'm a fan. But that doesn't have anything to do with Monopoly. When you play Monopoly, you're using the Monopoly rules. It doesn't matter what physical objects you use to keep track of the game state. (That's the point of the Cheapass Games concept.) But the fact that the game state may be independant of the physical objects you use to keep track of it doesn't mean that the game Monopoly has some existence beyond the rules we agree on as a society. It's still just a made-up conceptual frame, like mathematics. Nowhere near as useful (personally I hate playing Monopoly), I'll grant you that. But no more made-up, either. This is again your basic assumption. I'm not trying to do that. I'm trying to separate numberness from fingers (or any objects) in general. There's just no reason to assume that numberness is an inherent property of objects. It is a property of sets or groups of objects, but there's no real reason to grant that set or group independant existence either.At the end of the day, objects are objects. They have inherent properties, but numberness isn't one of them. That's a property of relationships between objects, but relationships aren't really real.

Because when I decide to use numbers, I agree to use the same numbers as everybody else. Just like, when you sit down to play Monopoly, you agree to play by the rules your group decides. It's just an arbitrary thing.If numbers are universal, why don't all cultures use numbers? How come the Arabs had to invent zero? If zero is a universal, why isn't it more... universal? I assume the universe exists simply because it's far more useful to do so. Not everybody feels that way - are Zen Buddists wrong? If so, how can you know? All you just demonstrated was that you have five fingers when you're paying attention. You assume, then, that means there's five even when you're not paying attention, but that's not something you just proved.Is the light on in the fridge when you close the door? By this logic, you must conclude that it is. Existence and occurance are different. Absent the players, Monopoly still exists. Absent mathematicians no math occurs. Your argument is a non-sequitor. It's these continued, nonsensical statements that make it hard to argue with you. How does five "happen"? Five is not an event, it's an abstraction. Yeah, it does. "Abstract" is the opposite of "Concrete". Concrete things exist, they have physical reality. Abstract things don't. That's what those words mean. Great, tautology. You're really reaching, aren't you? You've used numbers to prove that there's numbers. Great. I need something better. I need independant evidence that numbers exist beyond their use in describing relationships between objects. Yeah, there is a reason - there's no reason to assume there is. Therefore that's a reason to assume there isn't. A set is a concept. An object has physical existence. A concept does not. Concepts are not objects. That's confusing the model with reality. Only if an observer is there to observe the relationship. That's because relationships are concepts. Concepts don't exist outside of our heads because they're not objects.

I guess so. (Thanks for the spelling tip, though. I'll try to watch out for that.)

Interesting - how would such a machine operate? What physical properties of an object would it measure to determine how many of them there were? Except, obviously, in those cultures that don't develop mathematics. But if you don't develop language, you'll never develop math. That should be telling to you. That's not even true for things that actually are social, mental constructs. For instance, no matter how hard I think, the meaning of the words I'm using doesn't change - they have an agreed-upon social definition. That can change when we all decide it does.What we've tried to argue, and what you don't apparently understand, is that the numbers we use are social mental constructs - so, if you use numbers, you have to use the same numbers everyone else does.So, no, you can't make there be six fingers on your hand by thinking about it - but you can make there be an unnumbered amount of fingers on your hand by not thinking about it. I think what he's saying is that he can't answer questions about his hand without paying attention to it, so it's pointless to ask questions about his hand when he's not paying attention. Anything we think we know about his hand when he's not looking is just assumption on our part.You can think you know what happens to the light in the fridge when the door is closed - you can even test your theory by pushing the little doo-dad in the door frame - but even so, you still don't really know. You can only infer that the light goes off based on what it does when the door is open, but that's no proof of what happens when the foor is closed. Anything you think you know about your fridge when you can't observe it is simply assumption.