At 11:01 28/07/04 -0700, Hal Finney wrote:
This is confusing because "I believe p" has two different meanings. One is that I have written down "p" with a number in front of it, as one of my theorems.
OK. Let us call it the *intended meaning* of "I believe p" or of "Bp".
The other meaning is the string "Bp".
Well, *this* is confusing! I would prefer to avoid such move. You could
have said that the meaning of "I believe p" is the string contitutes by "I", "blank",
"b", "e", ... In which case "je crois p" (I believe p, in french) has not the same
meaning as "I believe p". But it is preferable that "meaning" is defined
in a way which makes it independent of the chosen language.
But that string only has meaning from the perspective of an outside observer. To me, as the machine, it is just a pair of letters. B doesn't have to mean "believe". It could mean "Belachen", which is German for "believe".
But we do say that "belachen" and "believe" have the same meaning(*) ... The question of who attributes the meaning is of course a hard philosophical question which leads eventually to the qualia problem. Some "neurophilosopher" say that consciousness does not exist, there is only firing neurons ... You can always believe that humans or machine are zombie ... Actually the path I propose will explain why machines themselves will be led to similar remarks ..., and will explain why we cannot really hope for much more. Also "Bp" will be translated later in arithmetic at some point, and this will make clear its meaning at the arithmetical level.
All I need to know, as a formal system, is what rules the letter B follows.
Even here a lot of philosophers will say that such rules will not give the meaning. I really think this debate is a little premature. After all you did solve the puzzle, and you did find which rule B should follow for extracting something non trivial from the machine encounter with the knight. (I guess you did grasp the correction, isn't it?).
To sum up: Bp, Ich glaub p, Io credo p, I believe p, je crois p, etc. have all the same intended meaning, which is the one you gave, that you (as a machine) will print soon or later p. Now a machine could print Bp and never print p, in which case we will say the machine is not really accurate, a little like a computer saying that there is a stack overflow when actually there is no stack overflow. OK? We will tackle the question "does the machine have a genuine conscious meaningful qualia-full experience of what she believes?" later, for that is an important but very hard and premature question imo.
(*) Are you sure of "belachen" for "believe" in German? Isn't it "glaube"?