(July 4, 2015 at 2:10 pm)Alex K Wrote: Now that you say it, the above "proof" in the OP is a nice illustration of one of the reasons why the TAG is wrong - the invalid steps are hidden because of delayed assumptions. In our wrong math argument, there is a step in the penultimate line that is invalid if one uses the info given in the first, but locally for individual steps everything looks fine. Likewise in TAG, the meaning of things is changed subtly towards the last step of the argument such that the first steps don't really work with the definitions used in the latter parts. With this trick, the TAG generates a statement that is much stronger than a valid proof could.
It is as sound as this:
I am nothing, since nothing is perfect and only god is perfect, therefore, I am god. Shit like that