Statements are combinations of nouns and verbs and such like; Some statements are either true or false, and we can call these propositions. So, "The present king of France is bald" is a statement, but not a proposition.
Beliefs range over propositions. (arguably, they might be made to range over statements: Fred believes the present king of France is bald.)
Beliefs set out a relation of a particular sort between an agent and a proposition.
This relation is such that if the agent acts in some way then there is a belief and a desire that together are sufficient to explain the agent's action. Banno wants water; he believes he can pour a glass from the tap; so he goes to the tap to pour a glass of water.
The logical problem here, the philosophical interesting side issue, is that beliefs overdetermine our actions. There are other beliefs and desires that could explain my going to the tap.
We know some statement when at the least we believe it, it fits in with our other beliefs, and when it is true.
The "fits in with other beliefs" is a first approximation for a justification. Something stronger is needed, but material implication will not do.
Discard Gettier. The definition is not hard-and-fast.
It does not make sense to ask if we know X to be true; that's exactly the same as asking if we know X. The "we only know it if it is true" bit is only there because we can't know things that are false.
If you cannot provide a justification, that is, if you cannot provide other beliefs with which a given statement coheres, then you cannot be said to know it.
A belief that is not subject to doubt is a certainty.
Without a difference between belief and truth, we can't be wrong; if we can't be wrong, we can't fix our mistakes; without being able to fix our mistakes, we can't make things better.
The rules of language are stated post hoc.
In order for a rule to be made explicit, it must first be. That is, they cannot be explicated unless there is something to be explicated. Hence, there are rules for language use.
The rules of language are not binding in the way the rules of physics are; they are normative.
The rules of language can be usefully broken, and this is itself worthy of discussion - see "A nice derangement of epitaphs"
There is more to the way words are connected than the logical operators. These do not for instance describe the difference between statements, questions and commands, let alone rhetorical questions, metaphors, and so on. Logic is insufficient to set out the rules of language.
We can more or less circumscribe certain activities in order to understand what is happening; that is, we can set out parts of our use of language without having to set out the whole. We can look at the sorts of utterances that might occur during some activity. Importantly, such activities do not consist only of language, but involve interaction with stuff in the world. Such examples of language use might be found by observation, or set up by fiat.
These examples allow us to look at and understand something about the rules that are being use.
Wittgenstein called such examples "language games" with an eye towards three aspects: They involve not just language, but interaction with the things around us; they involve behaviour that can be set out in terms of rules; they are related to each other in ways he spoke of as a family resemblance.
Hence to claim that language games are not real is to misunderstand what they are.
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