On Sep 5, 3:32 pm, contact080...@jamesrmeyer.com wrote:
> Obviously MoeBlee is totally unaware of the fundamental principle of > mathematical equality - that when two expressions are to be asserted > to be equal, then they have the same properties in the syntax of the > mathematical language in which the equality is declared.
Whatever 'they have the same properties in the syntax ...' is supposed to mean, I am well aware of (though always still learning) the basics of mathematical equality syntactially as axiomatized (various ways) at first order and as defined at higher order, and as understood philosophically in such a sense as Leibniz, and as discussed in various articles on the subject, and as given its standard formal semantics, and as understood informally and naively in ordinary mathematics. And, ironically (with regard to your comment), it is non- standard notions of equality that I am not very well informed about.
Nothing I've said contradicts any ordinary sense of equality in mathematics.
> If MoeBlee > wants to play with his own non-standard notion of mathematical > equality, he is free to do so, but there is no reason why he should > expect anyone else to play along with him.
I've not used ANY non-stanard notion of equality whatsover. Moreover, you've not even MENTIONED any SPECIFIC remark I've made that you claim is non-standard, let alone any justification for your claim.
At this point, you're merely blowing smoke.
I explained to you PRECISELY how
Z(x) = Phi(the_standard_numeral(x)).
You don't get past that by making a FALSE, non-specific, and unexplained claim that I am using any "non-standard" notion of equality".
Nope, just ordinary mathematical equality.
You've now had ample opportunity to make your case that the Godel proof is in any way incorrect. At each point I've explained to you why your own criticisms are off-based. And along the way you've put words in my mouth to make utter strawmen and now you just resort to a false, non-specific, and unexplained claim about "non-standard equality". So, my patience is pretty much exhausted with you. I don't have unlimited time or interest to explain at each step why your notions are incorrect about the particulars in Godel's proof, and indeed, in your latest post, you abandoned addressing MY explanation of those particulars and instead just just swung wildly with your false claim about "non-standard equality". You've had more than your three wild swings and 'yer out!