The use of saying a = b

Wittgenstein says “Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all.” (Tractatus Logico-Philosophicus, 5.5303)

So why are identity statements useful? Does Tully = Cicero say something different than Tully = Tully or Cicero = Cicero? If you can substitute identicals are they not the same? They are the same as far as truth goes, but belief_r(Tom,now,’~=’,’Tully’,’Cicero’) can be true. This is because Tom doesn’t know that Tully = Cicero. Tom’s belief is in symbols – the symbols ‘Tully’, and ‘Cicero’. (Using quotation marks to name symbols is a convenience, I will now name ‘Tully’ Barbara and ‘Cicero’ Nancy. We have then belief-R(Tom,now,’~=’,Barbara,Nancy) We also have Barbara = ‘Tully’ and Nancy = ‘Cicero’. We know, but Tom does not that Tully = Cicero. It is also true that for Tom Barbara is a symbol for Tully and that Nancy is a symbol for Cicero. So we have Symbol_0r(Tom.now,Nancy,Cicero) and Symbol_0r(Tom,now,Barbara,Tully) It may be that Tom read separately about Cicero (Tully) one place using the symbol Nancy the other the symbol Barbara, and they were about separate parts of his life, and that one of the books had a typo in his date of birth 100 years off so that he has evidence, though wrong, that they are different people. It is also true that Symbol_0r(Tom,now,Barbara,Cicero) and Symbol_0r(Tom,now,Nancy,Tully), but Tom himself doesn’t know it. It is true however because Cicero = Tully. So as I define Tom believes (though not belief_r) Tully = Cicero , this is true, because belief_r(Tom,now,’=’,Barbara,Barbara) and Symbol_0r(Tom,now,Barbara,Tully) and Symbol_0r(Tom.now,Barbara,Cicero), Tom will not realize this although someone else could say it of him. But still we will have belief_r(Tom,now,’~=’,Barbara,Nancy). And the Symbol_0r relations also hold so another person could also say of Tom that he believed as well Cicero ~= Tully. If someone convinces him about the typo he may change his mind and realize the identity and then we have belief_r(Tom,now,’=’,Barbara,Nancy). Or that Tom would say Tully = Cicero.

On Quotation

I am only using quotation of individual words, and do not permit substitution into quotation. The entity between the quotes is not a symbol, it corresponds in form to a symbol, but, between quotes forms a symbol for the symbol it is formed from. This is very convenient – It would be confusing to have to call ‘Tully’ Barbara and ‘Cicero’ Nancy. But it is this convenience that causes so much confusion also. For you might think that if Tully = Cicero, then you can substitute Tully for Cicero in ‘Cicero’, getting ‘Tully’. But it must be clear that this is a mistake for ‘Tully’ and ‘Cicero’ are distinct names. Most of these philosophical confusions come from mixing up symbols with what they are symbols of, which is perhaps inherent in the very nature of symbolism.