We have already said that the "and" is what makes possible the operations of addition and multiplication, while the "or" underlies subtraction and division.
Similarly, the "and" underlies all quantity, or all numbers greater than one. The number two would not be possible without the "and" conjoining separate units. While the "and" makes quantity possible, the "or" makes possible differences in quantity.
We can take that all of this a step further, and say that mathematics consists largely of equations. And equations, in their simplest form, consist of two sides, a left side and a right side separated by an "=" sign. Statements of equality essentially join together the two sides, saying their the same. Thus, we can say that the "and" makes possible all mathematical equations.
Now, there are different schools of thought concerning what mathematical equations really say. It has been said that they don't say anything about the world. Rather, they are entirely self referential, with the statement on one side simply being another way of expressing the statement on the other. And if the two sides of an equation are not really different but are really the same thing, then we are arguably not tying together two different things, and the "and" is not operative, for in order for the "and" to be operative, there must be at least two things.
While there may be some validity to this point of view, we cannot say the "and" is not present at all, as the "and" underlies all quantity. Moreover, while the quantity on each side of an equation maybe the same, we can't say that all ways of naming the same quantity have the same meaning. The quantity (4+2) may be the same as (5+1) but it is hard to argue that we mean the same thing when we say (4+2) as when we say (5+1). At the very least, it would seem, an equation would would tie together two putatively different quantities by showing that they are in fact the same. And once again, in this tying together of putatively different meanings, the "and" is present.
It can also be argued that an equation ties together two different sets, one on each side of the equation. This is a relatively dynamic picture of what happens in an equation. In the equation 4 plus two equals six, according to this school of thought, you have a set of six units on the right side of the equation, and two sets on the left side, one consisting of four units and the other of two. These two sets are joined together, and when you count the total number of units on the left side (6), you see that the quantity is the same as what is on the right side. The "and" is prominently featured in this conception, and as noted above, it is dynamic. Things are happening. Things are being joined together or, in the case of subtraction, wrenched apart.
While we usually think of mathematics consisting of statements of equality, it can also consist of statements of inequality, such as four plus two does not equal 7, or 4+2<7. The "or" would appear to be present in such statements, distinguishing between the different quantities.
We can attempt to compare the strength of the "and" and the "or" in the mathematical realm by asking whether there are more possible statements of equality or inequality. It would appear at first blush that there are more possible statements of inequality. Four plus two can only equal 6. It can't equal 7, 8, 9 etc. Thus, it may seem that for each statement of equality, the number of statements of inequality is infinite. However, there are an infinite number of numbers that add up to 6 (3 plus 3, 2 1/2 + 3 1/2, 2 1/3 + 3 2/3 etc.) And if we wished to compare the number of statements of inequality with the number of statements of equality by mapping each statement of inequality to a statement of equality, since the number of both is infinite, it is always possible to find a statement of equality to map against a statement of inequality.
Thus, we can say that the "and" and the "or" are equally strong in the mathematical realm. And there we have another statement of equality!!
Similarly, we can say that the "and" is always present in a statement of inequality. For even when we say that two numbers are different, we are linking them together when we compare them.
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