The discussion revolves around the validity of a method involving existential generalization and logical notation in the context of predicate logic. The original poster presents a logical statement and attempts to derive a conclusion using various logical principles.
Some participants have provided feedback on the notation, suggesting that the original poster's general approach is correct while also raising questions about the quantification of variables and the implications of symmetry in the relation R. The discussion is ongoing, with multiple interpretations being explored.
There are concerns regarding the clarity of notation and the fixed nature of the variable a, which is not quantified in the original statement. This has led to further questioning about the definitions and assumptions underlying the logical expressions presented.
Terrell said:∃x¬R(x,a) --> ¬∃R(a,x)
thank you stephen!Stephen Tashi said:As fresh_42 pointed out, the usual notation would be something like ##\lnot( \exists x ( R(a,x) )##
Your general approach is correct.
yes i missed an "x" there. how was "a" not quantified?fresh_42 said:I have trouble to understand your notation. ##\lnot R(x,a)## suggests, that it is a statement, whereas ##\exists R(a,x)## looks like an element somewhere. Furthermore ##a## isn't quantified.
Well, is ##a## fixed? Then it could be taken as part of ##R##, if ##R## is symmetric, which I don't know. Or does it mean for all ##a##, or there is an ##a##? Since it is in all occurrences of ##R## I tend to put it into the definition of ##R## to get rid of it, as it seems to be unnecessary. But then there are ##R(a,x)## and ##R(x,a)## and I don't know. what is the difference between them.Terrell said:yes i missed an "x" there. how was "a" not quantified?