Hi Stephen,
Le 23-nov.-05, à 01:29, Stephen Paul King a écrit :
Does this assertion not assume a particular method of coding the
"true"
grammatical statements? Could we not show that if we allow for all
possible
encodings, symbol systems, etc. that *any* sequence will code a true
statement?
Sure. It is enough to decide to encode some truth, like "1 = 1" by any
strings. For example the string "6§yhY!!è" will effectively encode "1 =
1".
Now, for any effective coding procedure, you will only get a tiny part
of the true statements of arithmetic, by incompleteness.
And that is why we need to fix the encoding at the start. Then, in any
everything-like theory, we restrict the interpretation by the local
encoding/decoding made by local machines, ...
If not, the only possible TOE will be the inconsistent theory having
all formula as theorem. This does not discriminate anything and could
hardly be considered as providing a theory in the general sense of
scientific theory, given that any facts always confirm it and always
contradict it. It would be like to say that George Bush is the
president of France, adding (after the history teacher makes a
disappointment grin), "oh, but by France I mean that large north
american country". Cool: you will always be right!
Regards,
Bruno
http://iridia.ulb.ac.be/~marchal/
