>>14218172Keep in mind that I am not that poster (I used third person pronouns), and I don't consider this to be arithmetic but rather a kind of crazy "logic" using the same symbols. Nevertheless, here is my interpretation.
Positive numbers represent classes of true statements while negative numbers represent classes of false statements. 1 represents ordinary true statements. If we apply + to two 1s, we get a positive result, truth. As will be evident later, however, we do have to ignore the magnitude of the result. This means that conjunction and disjunction applied to two true statements result in truth. -1 represents ordinary false statements. If we apply + to two -1s, we get a negative result, falsehood. This means that conjunction and disjunction applied to two false statements result in falsehood.
If we look into some cases resulting in 0, we encounter a problem (which we can pretend is the one he was describing). Since 0 = -0, we can't say that it's a positive or negative number. To interpret this, we can say that conjunction and disjunction have different results. For example -1 + 1 gives 0. This is what we expect, and it just means that the normal rules for conjunctions of true and false statements apply.
Now, there are many numbers other than -1, 0, and 1. Consider 2. If we take 2 + 1, we get 3, a positive number. So when taken in conjunction or disjunction with a 1 statement, a 2 statement behaves just the same. But consider 2 + -1. We end up with 1 as a result. This means that 2 statements are so strongly true that even in conjunction with ordinary false statements, the result is true! Likewise, -2 + 1 results in -1, so -2 statements are so strongly false that even in disjunction with true statements, the result is false! 2 + -2 is 0, implying that they behave the same way with each other as 1 and -1 do. This is the reason why we have to discard the magnitude of results, since we can't actually get a 2 statement just from two 1 statements.
