Logic, Therefore God...

[Roy]

You are not making sense. If you have another option present it. The fact that you can't shows that the logic works for you too...

No it doesn't. I know that's a fallacy.

Nor is it the only flaw, merely the most obvious.

[seer]

No it doesn't. I know that's a fallacy.

Nor is it the only flaw, merely the most obvious.

I have no idea what you are talking about - do you? You have to show the actual mistake.

[Machinist]

I have refined my question:

Would you say that 1+1=2 is a law or a property of our world? If there is a difference, what is the relationship between laws and properties?

And when I say "our world", I mean 3D space. XYZ.

If a possible 4th could be added, would these laws and properties of 3D space mesh with, or interface with 4D space?

Would 1+1=2 in 4D?

The atheists are saying that a world exists other than our own where there may be different fundamentals of logic, and perhaps even properties. What are they talking about?

[Juvenal]

I have refined my question:

Would you say that 1+1=2 is a law or a property of our world? If there is a difference, what is the relationship between laws and properties?

And when I say "our world", I mean 3D space. XYZ.

If you go to the counter at the grocery store with two apples, and they charge you by the apple, then yeah, "1 + 1 = 2" is a property of our world, but most likely they'll charge you by the pound, and you're back in the "two apples equals one big apple equals three small ones" universe. Of course, if all apples weighed exactly the same, that wouldn't be an issue. Similarly, if we figure they all weigh pretty much the same, we can just say, or "assume," they're all equal, even though it's not actually true. And if we do that, we arrive at a simplification that makes "charging by the apple" arithmetic work in our world.

But you can't get there without assumptions. We talk about laws and properties when we're introducing a topic to beginners. Once students have advanced a bit, we change over to the language of axioms and theorems. In math, a collection of theorems is called a theory. Theories only exist in theoretical worlds. So the theoretical world where we do all the heavy lifting isn't real, it's abstract.

Now that's a good thing, because it allows us to look at the properties without being bound by what happens in the real world, and change the properties if it's convenient. And that opens the door to other real world applications, based on other assumptions. What do you assume when you see the symbol "+"? Understand, there's nothing wrong with assumptions in math, so long as you spell them out completely, and define your terms precisely.

Addition, or "+", is a binary operation that needs to be defined before we can talk about its laws or properties.

In the integers, Z, 1 + 1 = 2.
In Q/Z, 1 + 1 = 2, which is also to 3 or any other integer. This is arithmetic with fractions, where we're free to toss out the whole number part.
In boolean algebra, 1 + 1 = 1, because "+" stands for "or," and "1" stands for "true," which makes the calculation "true or true" — which equals "true."

The first "+" in that list is good for charging by the apple. The second "+" is good for knowing how long until the next class begins if classes start on the hour. The third "+" is good for setting up computer circuits to do arithmetic in the other two.

Sometimes, you want to use classical logics, especially if you're looking to make binary decisions, like whether you should grab that last dinner roll while no one's looking. But there are alternatives that work better than classical logics, depending on the application. For instance, most likely you've heard of fuzzy logics, like the one your phone's camera uses to focus, or your modern washing machine uses to figure if your clothes are clean yet. Fuzzy logics work by allowing for variables like "focused" or "clean" to be partly true and partly false. That's a non-starter in classical logics.

If a possible 4th could be added, would these laws and properties of 3D space mesh with, or interface with 4D space?

Would 1+1=2 in 4D?

The arithmetics we're talking about involve numbers we call "scalars" (short for "scale factors") when we use them in multiple dimensions. Scalars don't have any dimension themselves, and the number of dimensions in the space you're using them doesn't matter. I've done arithmetic in a 65,536-dimensional space to help out a grad student, and I've done serious calculations for myself in a bunch of 73-spaces I'd packed in tightly with a set of projective planes, so I could check their mirror planes. The prettiest one had billions of mirror planes.

The atheists are saying that a world exists other than our own where there may be different fundamentals of logic, and perhaps even properties. What are they talking about?

Existence is a question for ontologists, but we don't have to leave our own world to find applications for logics that take advantage of different fundamentals. Think cellphone cameras, or washing machines.

[seer]

Sometimes, you want to use classical logics, especially if you're looking to make binary decisions, like whether you should grab that last dinner roll while no one's looking. But there are alternatives that work better than classical logics, depending on the application. For instance, most likely you've heard of fuzzy logics, like the one your phone's camera uses to focus, or your modern washing machine uses to figure if your clothes are clean yet. Fuzzy logics work by allowing for variables like "focused" or "clean" to be partly true and partly false. That's a non-starter in classical logics.

Good grief! You rely on the law of non-contradiction to even make that statement. That the opposite of what you are saying is also not true. And you have yet to give a counter example to the law of identity - showing that it does not hold.

[Juvenal]

Good grief! You rely on the law of non-contradiction to even make that statement. That the opposite of what you are saying is also not true. And you have yet to give a counter example to the law of identity - showing that it does not hold.

When everyone else on your thread thinks you're not capable of understanding the examples you've been given, maybe the problem is you.

[seer]

When everyone else on your thread thinks you're not capable of understanding the examples you've been given, maybe the problem is you.

The fact is you rely on classic logic to make the very arguments that you are using. And I have asked you a number of times to show the law of identity being violated - YOU HAVE NOT. Nor can you and you know it...

[Machinist]

If you go to the counter at the grocery store with two apples, and they charge you by the apple, then yeah, "1 + 1 = 2" is a property of our world...

Could we just assume "charged by the apple" world for the sake of argument, and keep going...just see where it goes?

I understand that you can make relative logic and that there are many applications for it in our world, like programming and electronics. There are absolutes however, on which we begin to construct these relative logic systems, and these would be the fundamental laws of logic: law of non-contradiction, law of excluded middle and the Law of Identity.

These truths seem very very necessary. And with the law of identity, I get what you're saying about not being the same you you were ten minutes ago...

But again, for the sake of argument, the assumption that you would have to go along with is that you are the same you.

There are assumptions being made yes, and I think Seer would even agree with that. You have to assume some things in order to appreciate other view points.

If the law of identity were really shifty like that, I wouldn't feel good about it. I mean the philosophy and implications of that just give me a real nihilistic feeling. How do people deal with that feeling?

It just seems to me, or maybe I just want there to be, something very absolute and solid to stand on.

[Machinist]

The arithmetics we're talking about involve numbers we call "scalars" (short for "scale factors") when we use them in multiple dimensions. Scalars don't have any dimension themselves, and the number of dimensions in the space you're using them doesn't matter. I've done arithmetic in a 65,536-dimensional space to help out a grad student, and I've done serious calculations for myself in a bunch of 73-spaces I'd packed in tightly with a set of projective planes, so I could check their mirror planes. The prettiest one had billions of mirror planes.

That's really cool man.

[Juvenal]

If the law of identity were really shifty like that, I wouldn't feel good about it. I mean the philosophy and implications of that just give me a real nihilistic feeling. How do people deal with that feeling?

It just seems to me, or maybe I just want there to be, something very absolute and solid to stand on.

This is really the nub of it.

Comfort comes from familiarity, and so, naturally, the unfamiliar seems uncomfortable at first. At some point, none of us were familiar with addition, or multiplication, or non-classical logics. As we become more familiar with them, and especially as we find their applications, the discomfort fades away.

For some of us, that familiarity never happens, and the discomfort is forever. Every semester, I get a new batch of students coming in with math anxiety streaming out of every orifice like ectoplasm. When I succeed, the anxiety is put to rest, but I don't always succeed. Still, and at the same time, there are always successes.

Keep in mind that the classical logics themselves don't change as you become familiar with non-classical logics. What changes is the perception that they were absolute and universal. The discomfort of knowing you were once wrong comes with an immediate reward as you realize that now, you can get it right. Or more right, in any case. And the rewards keep on coming as you embrace the freedom to go beyond what you once knew, without giving up anything more than what you once knew that just wasn't so.

That's not nihilism, it's its polar opposite, an ever-expanding world of possibilities which you are now free to choose.

[Machinist]

Yes, there is the whole absoluteness in the relativity thing, and I guess it's possible to rest in that.

I can't. It's too eastern and i'm too western.

Can we assume the per the apple view?

I believe that belief in God is also an ever expanding world of possibilities in which we can freely choose.

[Machinist]

I want everybody to start with #1 : necessary truths exists.

[seer]

Keep in mind that the classical logics themselves don't change as you become familiar with non-classical logics. What changes is the perception that they were absolute and universal. The discomfort of knowing you were once wrong comes with an immediate reward as you realize that now, you can get it right. Or more right, in any case. And the rewards keep on coming as you embrace the freedom to go beyond what you once knew, without giving up anything more than what you once knew that just wasn't so.

So in theory or in reality what you just claimed is the case and not the case at the same time. There goes reason. And I will remind you that you have not shown an exception to the fundamental law of identity.

[seer]

I want everybody to start with #1 : necessary truths exists.

How could it be otherwise? Again I gave an example in my OP A=A. And no one has counter it. Even Juvenal is assuming the law of non-contradiction and the law of identity to be valid to make his arguments as he attacks the very foundations he stands.

[seer]

These truths seem very very necessary. And with the law of identity, I get what you're saying about not being the same you you were ten minutes ago...

Except that doesn't work - things change, that is accepted. He is identical to who he is now. There is no exception.