Absolutely—but what is missing is a discussion of context. It isn’t enough to just say that 2+2=4 is true, or that a particular octopus is false; we need to know what the context of evaluation is.
2+2=4 has a standard context, namely the natural numbers N. “2+2=4” (without qualification) asserts that N satisfies 2+2=4. So the fact that one can imagine a non-standard context where “2+2=4″ means something false (like “Paris is the capital of the UK”) doesn’t really have any bearing.
In my use of the expression “2+2=4” I refer not merely to a function that maps contexts to propositions, but to one specific proposition, which has meaning in and of itself. (That’s basically what a proposition is—a little chunk of semantics.)
And about that proposition it is meaningless to affirm or deny that it exists only in people’s minds. To be fair, I think it’s equally meaningless to say that the proposition “exists in” physical processes where someone puts two nuts next to two other nuts and then has four nuts.
2+2=4 has a standard context, namely the natural numbers N...
Agreed. For efficiency in communication we often assume normative contexts. For the statement “2+2=4” it makes sense for us to rely on its implicit context. To make sense of a statement like “Is that octopus true or false?”, we will need to make the context of evaluation explicit.
In my use of the expression “2+2=4” I refer not merely to a function that maps contexts to propositions, but to one specific proposition, which has meaning in and of itself.
I’m not certain I understand this as you mean it, so I’ll respond generally and see how you reply.
The idea that something can have “a meaning in and of itself” is false. This is equivalent to “objective truth”. All meaning is relative to some context.
You can certainly have a conception of “a proposition that has meaning in and of itself”, but that conception exists within the context of your mind, and the proposition with that nature is non-existent.
2+2=4 has a standard context, namely the natural numbers N. “2+2=4” (without qualification) asserts that N satisfies 2+2=4. So the fact that one can imagine a non-standard context where “2+2=4″ means something false (like “Paris is the capital of the UK”) doesn’t really have any bearing.
In my use of the expression “2+2=4” I refer not merely to a function that maps contexts to propositions, but to one specific proposition, which has meaning in and of itself. (That’s basically what a proposition is—a little chunk of semantics.)
And about that proposition it is meaningless to affirm or deny that it exists only in people’s minds. To be fair, I think it’s equally meaningless to say that the proposition “exists in” physical processes where someone puts two nuts next to two other nuts and then has four nuts.
Agreed. For efficiency in communication we often assume normative contexts. For the statement “2+2=4” it makes sense for us to rely on its implicit context. To make sense of a statement like “Is that octopus true or false?”, we will need to make the context of evaluation explicit.
I’m not certain I understand this as you mean it, so I’ll respond generally and see how you reply.
The idea that something can have “a meaning in and of itself” is false. This is equivalent to “objective truth”. All meaning is relative to some context.
You can certainly have a conception of “a proposition that has meaning in and of itself”, but that conception exists within the context of your mind, and the proposition with that nature is non-existent.
Perhaps you believe in dualism?