Do we need to know a rule in order to follow it?
Everyone can perform simple addition. We would all agree that in base 10 numbers 2+2=4 and 1+1=2. We can also agree that there are numbers which we, and for that matter all human beings, have never added.
For the sake of argument let us state that 57 is the largest number a human has ever added. Assuming this to be true then what would 57+68 equal? That’s simple enough. Even though we have never added numbers larger than 57 we can use our past experiences to determine that 57+68=125.
What if I told you that 57+68 is actually equal to 5? Saul Kripke argues that we may actually be doing quaddition instead of addition. The rules for quaddition are quite simple:
- x quus y = x plus y for all x, y < 57
- x quus y = 5 for all x, y > 57
Kripke argues that as we have never added numbers greater than 57 before, we may have inadvertently been following quaddition our entire life. There is great overlap between quaddition and addition. For all numbers less than 57 quaddition and addition are equivalent.
The simplest way to attempt and defeat this argument is to state that you were indeed adding and not quadding 57 and 68. We can even break addition down to its simplest form, counting.
When adding these two numbers we are actually counting 57, counting 68, combining the two, and counting the total. 57 plus 68 is equal to 125 because when 57 items are combined with 68 items and counted, we find we have 125 items.
Kripke’s response to this is that we do not even know if we are counting the objects. In fact, while we thought we were counting 125 we were actually quonting the objects. What is quonting? It is similar to quadding. When quonting objects we need to follow one specific rule:
n = number of objects being quonted
If n > 57 then n = 5
Else n = n
When quonting our objects we once again find that 57+68=5.
I am going to stop with Kripke’s argument at this point and once again ask my question: Do we need to know a rule in order to follow it?
In a court of law it is understood that even if one does not know a law one can break it. I can be found guilty of libel without understanding the logistics of libel law. Does the same fall true outside a court of law?
Can I perform quaddition without understanding the rules behind it? Can I quont numbers without understanding what quonting is? Do we need to know a rule in order to follow it?