@kennethamy,
It doesn't change that it's a "hope" or "belief", but
the task is converting each "hope" and "belief" into language with conditions. I think this is where Wittgenstein's exercise really comes into play:
"Wittgenstein first asks the reader to perform a thought experiment: to come up with a definitionof the word "game". While this may at first seem a simple task, he then goes on to lead us through the problems with each of the possible definitions of the word "game". Any definition which focuses on amusement leaves us unsatisfied since the feelings experienced by a world class chess player are very different from those of a circle of children playing Duck Duck Goose. Any definition which focuses on competition will fail to explain the game of catch, or the game of solitaire. And a definition of the word "game" which focuses on rules will fall on similar difficulties. Wittgenstein's point is not that it is impossible to define "game", but that
we don't have a definition, and we don't need one, because even without the definition, we
use the word successfully. Everybody understands what we mean when we talk about playing a game, and we can even clearly identify and correct inaccurate uses of the word, all without reference to any definition that consists of necessary and sufficient conditions for the application of the concept of a game"
-Wikipedia
Similarly, as noted, one could use the
word "belief" with different meanings implied. One could use it interchangeably with "think", while another may use it interchangeably with "know". Intensity varies: A religious zealot who shouts, "I
believe in God!", is much different than me nonchalantly stating, "Yeah, I
believe my mother is in the other room".
If we are to attempt to lay necessary and sufficient conditions out for "hope" or "belief" or "game", we must all be playing the same "language-game", we must all participate in clarification, come to an understanding. Otherwise, language
will not help us in clarifying. "Belief", like "Game",
I don't feel has a general set of conditions. So, we could postulate what conditions
may precede "belief" in particular situations, just as we could postulate what conditions
may precede "game" in particular situations such as, "Bob and Joe go outside to play a game of catch", or "The professional chess champion is playing the game of chess".
And we've already done this. What else shall we do?