Counting and Adding
Curator’s note: This was probably copied from the defunct Autonomist forum.
The following was originally posted in response to the following:
And when I say this is “basically the same issue” you declare this idea to be “absurd!”
My response is to the above statement, as well as a suggestion that addition does not always result in true sums, and addresses some of the questions of the nature and epistemology of mathematics:
Because it is [absurd]. You ignored the simple observation that not all people who can count can add. If they were, “basically the same thing,” anyone who learned one should be able to do the other.
Addition is hugely more sophisticated than counting, which is really quite limited. We can count units, entities, or discrete existents (and only units, entities and discrete existents). But one cannot add units, or entities, or discrete existents, because we can only add numbers. Counting deals directly with existents, addition is an abstract function that deals with those abstractions we call numbers. Numbers are invented to make counting possible. Actually counting results in specific numbers. Those numbers are abstracts that can be added (subtracted, multiplied, divided, etc.). What those numbers represent are not subject to any of those functions.
We speak of adding sugar to our recipe and adding this group to that group, but addition, in those cases, is not a mathematical term. Interestingly enough, it is an analogy borrowed from mathematics, but, in those cases, “add to,” only means, “combine with.” It is misunderstanding this, and dropping the context of how the word add is used, that is behind stupid statements like, “if you add a liter of alcohol to a liter of water, you do not get two liters of water/alcohol mixture, but something less than two liters, proving that one plus one does not always equal two.” Of course when you “add” alcohol to water, you are not performing a mathematical function, you are performing the physical act of combining substances. This error also confuses counting and measurement, a disaster in science which you apparently advocate.
Because addition is not restricted to actual existents and is abstract, addition is not restricted to the cardinal (counting) numbers as counting is. Fractions, decimals, imaginaries, even unknowns can be added, none of which can be counted.
Counting and addition are anything but, “basically the same issue.”
Regi