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1. If you haven't studied formal logic, then I'm not sure if I can explain it to you in a way that you will accept. This is my simplest attempt: There is more than one way to reason. Formal logic is one way to do so. When using any type of reasoning we assume that our method is valid in reaching useful or meaningful conclusions.
I am currently in the process of studying formal logic (see "Elementary Symbolic Logic" by William Gustason and Dolphe E. Ulrich for an excellent introduction), and the terms you use are unrecognisable to me. Once again:
"I've no idea what a "property of formal logic" is, or what is meant by "reach conclusions in a meaningful way". I am requesting, implicitly, that you explain what is meant by these statements".
Furthermore, I would now like it to be explained what it is to "reach useful conclusions" and explicate what is meant by "a way to reason". I am asking you to explain what you mean. A failure to do this will be considered a form of obfuscation, and lead to the termination of our exchange.

2. Originally Posted by The_Liquid_Laser
No we cannot be sure that "2+2=4" is true. It only seems this way. In fact "2+2=4" is based upon assumptions and in fact it can be shown that 2+2 does not always equal 4. For example in mod 3 arithmetic 2+2=1 and in mod 4 arithmetic 2+2=0.
It is certainly possible to conceive of and develop elaborate systems wherein adding two things to another two things does not result in four things. However, in this universe, where adding two things to another two things results in four things, such systems fail to tell us anything real about the universe we inhabit.

Just because you can think a thing does not make it real.

If you haven't studied formal logic, then I'm not sure if I can explain it to you in a way that you will accept. This is my simplest attempt: There is more than one way to reason. Formal logic is one way to do so. When using any type of reasoning we assume that our method is valid in reaching useful or meaningful conclusions.
Spoken like a proper shaman.

3. Originally Posted by Mycroft
It is certainly possible to conceive of and develop elaborate systems wherein adding two things to another two things does not result in four things. However, in this universe, where adding two things to another two things results in four things, such systems fail to tell us anything real about the universe we inhabit.

Just because you can think a thing does not make it real.
Modulus arithmetic does exist in the real world although the most common example is modulus 12. Hours on the clock use numbers 1 through 12 and then start over again. When talking about hours 7 + 7 = 2.

4. Originally Posted by The_Liquid_Laser
Modulus arithmetic does exist in the real world although the most common example is modulus 12. Hours on the clock use numbers 1 through 12 and then start over again. When talking about hours 7 + 7 = 2.
You're confusing mathematics with a unit of measurement. Mathematics is a representation of observed, real-world phenomenon. (e.g. if I have two objects and I add another object I will have three objects; if I divide these four objects into two separate groups, each group will contain two objects; etc.) Units of measurement, while useful, are, indeed, quite arbitrary and made-up.

5. Originally Posted by Mycroft
You're confusing mathematics with a unit of measurement. Mathematics is a representation of observed, real-world phenomenon. (e.g. if I have two objects and I add another object I will have three objects; if I divide these four objects into two separate groups, each group will contain two objects; etc.) Units of measurement, while useful, are, indeed, quite arbitrary and made-up.
I'm not confusing the two. Units of measurement are a part of mathematics, and they also have obvious application to reality. Science would fall apart pretty quickly without units of measurement.

6. Originally Posted by The_Liquid_Laser
I'm not confusing the two. Units of measurement are a part of mathematics, and they also have obvious application to reality. Science would fall apart pretty quickly without units of measurement.
Yes, you are. In pure mathematics, units of measurement do not come into play.

Units of measurement are certainly useful. As you state, attempting science without them, while possible, would be a severe headache. You would have the metrics-versus-American issues that mechanics bemoan on an even greater scale. However, units of measurement are used simply to aid man in his endeavors; no scientist would claim that units of measurement, in and of themselves, tell us anything about the universe.

7. Originally Posted by Mycroft
Yes, you are. In pure mathematics, units of measurement do not come into play.

Units of measurement are certainly useful. As you state, attempting science without them, while possible, would be a severe headache. You would have the metrics-versus-American issues that mechanics bemoan on an even greater scale. However, units of measurement are used simply to aid man in his endeavors; no scientist would claim that units of measurement, in and of themselves, tell us anything about the universe.
I believe that you are saying that pure mathematics represents reality while units of measurement are disconnected. I would say the opposite is true. Units of measurement exist solely to describe reality. Pure mathematics does not have to represent reality at all. Units of measurement are what make mathematics concrete rather than abstract. The number "2" when used as a noun is abstract, but the words "two meters" are concrete. Units of measurement may be man made, but they are created specfically with the purpose of connecting mathematics to reality.

8. Originally Posted by mibnelius
Here's why God must exist: We live in a vastly complex system that has endured for eons. Perhaps there was some progenitor race that constructed this all from nothing or nearly nothing, but then where did they come from? The big bang theory currently maintains that the universe as we experience it resulted from the collision of two massive 9-dimensional objects. I wish I more completely understood this, but so do most theoretical physicists. Anyway, those must have come from somewhere, and following this recursion back far enough, something must have come from nothing. Therefore, something which transcends our knowledge and understanding must have created the energy that coalesced into the universe as we know it today.
Originally Posted by mibnelius
I agree with your position on the definitive origin of the Universe. Despite my belief in God, that still leaves me in a position where I want to see how everything happened. Perhaps a part of my mental block is caused by my inability to create a mental picture of what the Universe would be like in true nothingness. If it were just a vacuum, then it would still have volume and is therefore easy to imagine, but if it were truly nothing, then the weirdness of null space eludes me. Is it possible for anything to exist in the absence of matter/energy/time? Are these the universal constants which are the underpinnings of our existence? Can even God exist without these things?
What you're describing is string theory, as articulated in works such as Kaku's Hyperspace and Brian Greene's Elegant Universe. In the latter, he actually mentions a supposed "primal realm" that the strings making up the "fabric of space" lie in, in which the notions of time and space break down and ordinary geometry is replaced by something known as non-commutative geometry. [such as matrices, as opposed to normal Cartesian coordinates]. That to me showed that spacetime as we know it is not the ultimate reality.
Unfortunately, they seemed to have moved away from discussing this, for so-called "Membrane theory" where the collision of "branes" or 4D spacetimes in an 11 D space collide and spawn "big bangs". As was pointed out, this just pushes the question back further.

Originally Posted by simulatedworld
What you've just described is commonly referred to as the problem of causation. It does necessitate that some kind of greater force, some first cause, independent of the known universe must have existed in order for the universe to exist at all.

This is a good argument, actually. I agree that we can't really account for this, and so therefore some kind of something must have existed before or independently of the known universe.

The problem with theology is that right here is where the reasoning stops. We have no idea if this unknown force is a conscious entity, or just the sum of all natural forces, or any number of other things--in fact, we don't know anything about it, and therefore can't possibly attempt to assign any specific properties to it.

You are correct that anyone who claims he knows for certain that no such greater force of any kind exists or ever existed is fooling himself--it's obvious that he has no answer to the problem of causation.

But anyone who claims that he knows any specific properties of this vague greater force is also fooling himself, because there is no evidence for any of them and no way to obtain any. Whatever this vague greater force is--call it "God" if you really want to--it's a far a cry from most modern theistic conceptions of God, and that's why many people identify as atheists. Intelligent atheists don't claim to have any real knowledge about the origin of the universe or any solution to the problem of causation--they identify as atheists simply to signify that they don't buy into any of the specific theistic conceptions of "God" that are abundant in popular religion today.

I think it's quite possible to be an atheist and still not claim any answer to the problem of causation, because this "vague greater force" that we know nothing about and can't possibly hope to comprehend is not necessarily "God"--what are the properties of God? Most people who believe in God try to claim that they know specific properties about him, but that's clearly impossible.

Who says this vague greater force is actually God, anyway? It may not be omnipotent or omniscient or any of that stuff, but theists think that they know all about it. "God" by most people's definitions has all kinds of specific properties, and atheists identify ourselves in this way simply as a method of dismissing any conceptions of God as a conscious entity, or as something about which we can really know anything. We don't claim to know how the universe was created, and we don't have a good answer to the problem of causation--but these things don't necessitate the existence of so-called "God" by any modern popular definition.
There is actually a point to this, for Isaiah 40:25 does say "To whom then will all of you liken me, or shall I be equal? says the Holy One". There is nothing we can liken Him to. So a lot of the "properties" we have come up are either our own fabrication, or at least shorthand for things we cannot comprehend. The raw concept of God is some kind of reality who caused this to be, and in the case of revealed religion, communicated through creation. Hence, this debate is just the dispute with those who don't trust their fellow creatures to have perceived or relayed the information right (whether the inspiration of the texts to begin with, or on the next level, the interpretation of them), and want to test things for themselves.

For this reason, I have come to find trying to convince anyone to be futile.

9. Originally Posted by The_Liquid_Laser
I believe that you are saying that pure mathematics represents reality while units of measurement are disconnected. I would say the opposite is true. Units of measurement exist solely to describe reality. Pure mathematics does not have to represent reality at all. Units of measurement are what make mathematics concrete rather than abstract. The number "2" when used as a noun is abstract, but the words "two meters" are concrete. Units of measurement may be man made, but they are created specfically with the purpose of connecting mathematics to reality.
What exists is a length; we may express this length as, say, x, in which case x becomes a representation of the existent length. We can apply units of measurement, say centimeters or inches, but these serve only to simplify the proceedings and allow different human beings discussing this length to share a frame of reference. The important distinction is that x is a representation of an existent, while the units of measurement are merely a tool -- they represent only themselves.

I believe that you are, again, placing the cart before the horse.

10. Originally Posted by Mycroft
What exists is a length; we may express this length as, say, x, in which case x becomes a representation of the existent length. We can apply units of measurement, say centimeters or inches, but these serve only to simplify the proceedings and allow different human beings discussing this length to share a frame of reference. The important distinction is that x is a representation of an existent, while the units of measurement are merely a tool -- they represent only themselves.

I believe that you are, again, placing the cart before the horse.
I can't believe that you are making a distinction on this minor level of abstraction, and yet at the same time think that numbers are real entities. If you consider measurement abstract, then numbers are much much more abstract, lol.

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