One of the assumptions in the substitution problem was the indiscernibility of identicals:
Fa and a=b implies Fb
Is this always true? A slightly different way of expressing the law is that if Fa, and if 'a' denotes exactly what 'b' denotes then Fb. But in this form the law is clearly not valid. Suppose there is a shortage of red paint, and that only Ferraris are red. Then it follows that if Ferraris are fast, then red cars are fast, and conversely. But it does not follow that if John thinks Ferraris are fast, then he thinks that red cars are fast – perhaps he is imagining a red reliant Robin that he once saw. I.e. F = ‘John thinks that every – is fast’ and a = ‘Ferrari’ and b = ‘red car’. Then Fa and the fact that ‘a’ denotes everything that ‘b’ denotes does not entail Fb.
You will object that indiscernibility of identicals applies only when a and b are proper names. Proper names are referring terms, not common terms like ‘Ferrari’ or ‘red car’. I reply: what is a referring term? If it is defined as something to which indiscernibility of identicals necessarily applies, then the ‘Shakespeare’ arguments in the previous posts suggest that indiscernibility of identicals does not apply to ordinary proper names at all.