:hmmm...I always thought of it as universal. Whoa! not so fast. You thought you caught me, but you're wrong! I think that even God wants us to use + to mean plus. In fact, I think She demands it.:
That is the problem. We have been taught that + "means" plus for so long, we have come to believe that it is "universal" or God-given. But one cannot prove irrefutably that + = plus. Frank Tipler rightly notes:
"For example, if I ask you, 'What do you get if you multiply 52 times 27?" an 'algorithm' you can use to get the correct answer 1,404 is just the procedure you were taught to use as a child to multiply two numbers together. A problem for which there exist an algorithm to solve it is said to be solvable" (Frank J. Tipler, The Physics of Immortality, 25).
quote:But the + sign is purely arbitrary. It only possesses the value that a certain community imputes to it.
six :I hope my daughter doesn't get ahold of that argument. Btw, isn't that "community" pretty much the whole of mankind?:
At this point in time, it is most likely is. But such was not the case from the beginning. :-)
quote:IT does not inherently mean "plus."
six: I'm sure that using rigid logic definitions, a case can be made for that statement. Perhaps I'm being arbitrary and dogmatic, but I can't help but believe that to do so would be apodieticly worthless. If you see some value in that argument, please reveal it. I suspect I'm being neither arbitrary or dogmatic, just practical.:
Maybe an illustration from language will help. Linguists say that language is arbitrary. Signifiers point to or mean what a specific language community says a word means. There is evidently no metaphysical reason why we could not use the term "heat" to describe H20 or the word "water" to signify molecules in motion. The terms are putatively arbitrary. I submit that mathematics can be viewed in the same light. Signs such as + or - are arbitrary symbols that allow us to manipulate concepts (numbers) in a supposedly precise and practical fashion. But we need not think these signs essentially "mean" anything.
One web site discusses the problem set out in Kripke's work in some detail. Here is the address for this site.
http://csmaclab-www.cs.uchicago.edu/philosophyProject/chomsky/Kripke1.html
Note what Kripke himself writes:
"First, consider what is true of one person considered in isolation. The most obvious fact is that . . . [a]lmost all of us unhesitatingly produce the answer '125' when asked for the sum of 68 +57, without any thought to the theoretical possibility that a quus-like rule might have been appropriate! And we do so without justification. Of course, if asked why we said '125', most of us will say that we added 8 and 7 to get 15, that we put down 5 and carried 1 and so on. But then, what will we say if asked why we 'carried' as we do? Might our past intention not have been that 'carry' meant quarry; where to 'quarry' is . . . ? The entire point of the sceptical argument is that ultimately we reach a level where we act without any reason in terms of which we can justify our action. We act unhesitatingly but blindly (Saul Kripke, Wittgenstein on Rules and Private Language, 87).
Sincerely,
Dan
Duns the Scot
