[quote]Dr.Matt581 wrote:
[quote]Tiribulus wrote:
[quote]OldManJoe wrote:<<< Yes and how do we know those are really the laws from God and not just made up by men?[/quote]The same way you know that a “scientist” with a 3 pound brain can tell you what happened billions of years ago in spite of the fact that he can’t even tell you how and why he knows that 2+2=4.
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In reference to the question of why 2 + 2 = 4, the answer is that it does not always do so. There are certain axioms that must be specified before the claim that 2 + 2 = 4 can be made. The first is that one is using modern Arabic numerals.
Next an actual counting system must be imposed, and numerals must be assigned to represent a number of objects. This will be completely arbitrary. The most common counting system these days is base 10. Other common number systems used in fields like computer science include base 2 and base 16. The ancient Sumerian civilization counted in base 60.
Base 10 means that using Arabic numerals, a single object is arbitrarily assigned a value of 1, and grouping another single object with that first object is assigned a value of 2, again arbitrarily since the symbols used do not really matter since it is just another way to represent real objects. A single object is 1, if another object added to the other one in some way, the group is arbitrarily assigned a symbol of 2, another object added to that group is assigned a value of 3 and so on up to 9 (zero is a number, and the only non-positive integer in modern set theory, as well as number theory, but instead of representing a number of objects, it represents an absence of whatever is being represented with numerals). It does not matter if you want to make up your own symbols to represent a group of objects, the symbol that you use to represent a single object will be equivalent to the value represented by the Arabic symbol 1.
This means that a single object in our counting system is one, another object added to that is 2 another object added to the group is 3 and another is 4. This can be represented symbolically, with the “+” symbol being used to represent objects being grouped together somehow (it doesn’t matter what is being grouped together or how in pure mathematics like this, all that matters is that that is happening. Imaging rocks being thrown into a bucket if it helps) and the “=” symbol meaning that the statements on both sides of the symbol mean the same thing. Now, the symbols used in the arbitrarily chosen number system must be defined based around the basic unit in the number system. For base 10 using Arabic numerals, that is 1, which represents a single object. It is really no different then using letters to represent sounds that a person is making. Without assigning arbitrary meaning to these sounds, by grouping them into words and assigning meaning to those words, they are meaningless. If you go up to a person who speaks only mandarin and speak English, they will not know what you are saying without some way of assigning meaning to those sounds since the sounds we make have no intrinsic meaning.
To symbolically define the symbol represents an absence of objects, one must state that adding that symbol to a single object, defined as 1, yields the same number of objects:
1 + 0 = 1
If, for instance, you wanted & to represent an absence of objects and * to represent a single object, you would state:
As long as you define those symbols as stated above along with the counting system used and what “+” and “=” represent, that is the same as saying that “1 + 0 = 1.”
Defining the rest of the numbers, we get the following:
1 + 1 = 2
1 + 1 + 1 = 3
1 + 1 + 1 + 1 = 4
1 + 1 + 1 + 1 + 1 = 5
1 + 1 + 1 + 1 + 1 + 1 = 6
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 9
Using the guidelines that I outlined above, 2 + 2 = 4 is a true statement, since you have defined 2 as 1 + 1, thus you can express the above operation as 1 + 1 + 1 + 1, which is defined as 4 and can never be anything else as long as the above axioms are being followed, and if you are using the modern day version of counting in base 10 using modern Arabic numerals then you are following these axioms
Now, we are not going to go around declaring what number system and what kind of numerals we are using. That would be a waste of time since almost everyone in the world is taught to count in base 10 using Arabic numerals, which I just defined above; it is so common place that it is just assumed that we are following the above definitions, which are taught in some way to most people in school, even if they do not realize it. It is much easier to require one to specify when one is not following these axioms.
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Nice Dr. Matt… Long time no speak, been doing ok?