Are these
uninterpreted symbols?
If you have a logical calculus, it is often assumed that it is legitimate to choose to substitute expressions with meaning for the uninterpreted symbols of the system.
An element of a logical calculus (the propositional calculus) would be this:
If either p or q and not-p then q.
C K(Apq) Np q
It is legitimate it is said to substitute for p a meaningful proposition, and to substitute another meaningful proposition for q.
This then yields the meaningful argument:
If either I'm in bed or you're a Dutchman, and I'm not in bed then you're a Dutchman.
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Are these
uninterpreted symbols?
1+1=1
1+0=0
0+1=0
0+0=0
What would be an interpretation?
A true sentence conjoined with a true sentence is a true sentence
A true sentence conjoined with a false sentence is a false sentence
A false sentence conjoined with a true sentence is a false sentence
A false sentence conjoined with a false sentence is a false sentence
I say these things just to start lines of thought.