No, I’m not defining a notion based on anyone’s whim/sensibilities; I fully agree that, to be meaningful, any account of ‘simplicity’ must be fully formalizable (a la K-complexity). However, I expect a full account of simplicity to include both elegance and parsimony based on the following kind of intuition:
a) There is in fact “stuff” out there b) Everything that actually exists consists of some orderly combination of this stuff, acting in an orderly manner according to the nature of the stuff c) All other things being equal, a theory is more simple if it posits less ‘stuff’ to account for the phenomena d) Some full account of simplicity should include both elegance (a la K-complexity) and this sense of parsimony in a sort of trade-off relationship, such that, for example, if all other things equal, there’s a theory A which is 5x more elegant but 1000x less parsimonious, and a theory B which is correspondingly 5x less elegant but 1000x more parsimonious, we should therefore favor theory B
My reasons for expecting there to be some formalization of simplicity which fully accounts for both of these concepts in such a way is, admittedly, somewhat based on whim/sensibility, as I cannot at this time provide such a formalization nor do I have any real evidence such a thing is possible (hence why this discussion is taking place in a thread entitled ‘Irrationality game’ and not in some more serious venue) - however, whim/sensibility is not inherent to the overall notion per se, i.e. I am not suggesting this notion of an elegance/parsimony trade-off is somehow true-but-not-formalizable or any such thing.
No, I’m not defining a notion based on anyone’s whim/sensibilities; I fully agree that, to be meaningful, any account of ‘simplicity’ must be fully formalizable (a la K-complexity). However, I expect a full account of simplicity to include both elegance and parsimony based on the following kind of intuition:
a) There is in fact “stuff” out there
b) Everything that actually exists consists of some orderly combination of this stuff, acting in an orderly manner according to the nature of the stuff
c) All other things being equal, a theory is more simple if it posits less ‘stuff’ to account for the phenomena
d) Some full account of simplicity should include both elegance (a la K-complexity) and this sense of parsimony in a sort of trade-off relationship, such that, for example, if all other things equal, there’s a theory A which is 5x more elegant but 1000x less parsimonious, and a theory B which is correspondingly 5x less elegant but 1000x more parsimonious, we should therefore favor theory B
My reasons for expecting there to be some formalization of simplicity which fully accounts for both of these concepts in such a way is, admittedly, somewhat based on whim/sensibility, as I cannot at this time provide such a formalization nor do I have any real evidence such a thing is possible (hence why this discussion is taking place in a thread entitled ‘Irrationality game’ and not in some more serious venue) - however, whim/sensibility is not inherent to the overall notion per se, i.e. I am not suggesting this notion of an elegance/parsimony trade-off is somehow true-but-not-formalizable or any such thing.