We assume that if we use the symbol ‘+’ then that symbol must have a meaning. Not only that, but also that meaning must be in the mind somehow before its use. That is, we may assume that certain “conscious states or events” must have “accompanied” (372) the use of ‘+’. Perhaps, however, we can use ‘+’ without any meaning or different mental events or states. That is, without things in addition to the cognition of the actual use of ‘+’.
It could be the case that the use of ‘+’ has a normative dimension. That is, it is not a case of what ‘+’ means, but what it should mean. Or, more correctly, how it should be used. Of course, we can now ask if there can be examples of use, of any kind, that can function without meaning or separate mental events or processes. However, Heidegger talked, in his Being and Time, of a particular use of a hammer without its users thinking at all about the nature of the hammer or hammers generally or what function it fulfils. That is, he simply uses the hammer. He knows how the hammer should be used, in the Wittgensteinian normative sense, but he does not rely on an intellectual attitude to the hammer.
Back to the normative status of ‘+’. We know what it should do, but this knowledge doesn’t depend on mental meaning or meaning of any description. What is determinate is not the meaning of ‘+’, but the rules of its usage. So if there are any meanings to understand, it is not the meaning of ‘+’, but the meanings of the rules that determine its usage.
What all this means is that
‘+’ does not mean +
If we accept meaning, then ‘+’ could mean slinmp. It is not the meaning of ‘+’ that determines that 2 + 2 = 4, but the use of the symbols in it.
It may therefore follow that if the symbol ‘+’ doesn’t depend on meanings, then it doesn’t depend on private mental events or processes either. Therefore the use of ‘+’ may depended, instead, on what the community takes the symbol ‘+’ to be, not what they think it means. Indeed, it is precisely because ‘+’ doesn’t depend on meanings, which are essentially private, that it can be used in a public or communal manner. If it depended on private meanings, then it couldn’t be captured in a public discourse and it couldn’t be communicated intersubjectively from a person’s private meaning to other people who cannot be aware of that person’s private mental states and processes. If the use of ‘+’ depended on private meanings, then, as with the ‘private language argument’, there would be no going right or wrong with an individual’s use of ‘+’. That is, no one could tell him, and he couldn’t even tell himself, whether or not he is going right or going wrong.
However, if the individual cannot know if he is going right or wrong, what happens when we take the community as a whole? That is, perhaps the community as a whole can’t know if it’s going right or wrong. The community itself would need another community, or a larger community, to guarantee its correct use of ‘+’. Each member of the community can’t depended on other members of the community to determine whether or not he is using ‘+’ correctly, or even on a larger subsection of the community, because other members of the community are by definition using ‘+’ in the same way, just as the private individual outside the community cannot compare his present uses of ‘+’ to other of his past uses and see if his present use is correct. So just as the private individual doesn’t rely on external sources of justification in his use of ‘+’, so too the community doesn’t rely on external sources to justify its uses.
*) Meanings can’t be facts or be factual because the things that determine facts or explain the facts must themselves contain meanings. Meanings are not facts, but what they mean can have a factual status. That is, it is a fact that the word ‘cat’ is invariably used to refer to cats. But then the fact is not the word’s meaning, but the situation that people use that word, ‘cat’, to refer to cats. Indeed, in that case the word ‘cat’ may not need some kind of internal and abstract meaning. That is, ‘cat’ means cat because the word ‘cat’ is used to refer to cats. Nothing more is needed. No mental item and no abstract meaning, nothing but the usage and nothing but the communal rules that determine the use of the word ‘cat’. Why do philosophers cry out for something more than this? Because communal rules change and they are not shared between different communities. And what if there are communities within communities (as there are)? What the realist wants is something determinate. Something timeless or out of time. Something essential and non-contingent. Something that can settle disputes once and for all. Something that can firmly answer, say, the question: What does ‘justice’ mean?