On Jun 17, 4:32 am, Nam Nguyen <namducngu...@shaw.ca> wrote: > Transfer Principle wrote: > > > Of course, the reason for MoeBlee's response is that it's often hard > > to tell exactly what Nguyen is claiming at times. > > That's understandable: I had to response to different people with > different off-the-topic topics. For example, while I've *consistently* > claimed the symbols in the set of theorems can't be more than that > of the axiom sets, they kept forcing me to debate about the language > must be specified first, etc...; and in MoeBlee case he also kept talking > about Shoenfield' context or the context of "proof in a language", etc... > > > Indeed, I admit that I'm > > still trying to figure out exactly what Nguyen's claim is now. > > It's always the same (though with different renditions depending on whom > I was talking to; my opponents don't necessarily share exactly the same > interest or level of understanding in the matter). > > Basically my claim is: > > Given a formal system T, the set of T's theorems can *not* contain more > non-logical symbols than that of T's axiom-set.
And this is _false_ in Standard FOL! Are we talking about a standard definition of 'Formal System', or something else that you've made up? Please clarify this!
A formal system consists of a formal language (set of symbols and a grammar) and a deductive aparatus (logical axioms, non-logical axioms, and rules of inference). The axioms must be wffs in the language, but they do not need to include every symbol in the language. There _is no such requirement_ in, e.g., Shoenfield's presentation (which is pretty standard, I think). You've had the relevant passages quoted directly at you and still somehow managed to refuse to admit it, so I don't know if you'll accept this now.