Hey Nandric,
1) They are called "universal" quantifiers because they they say that the sentential function is true of everything, not because every generalization contains one.
2) Frege may not (or may) have used the word translated as "context", but there are at least three senses in which context was crucial to Frege's thinking. One is the so-called Context Principle, that only in the context of a sentence does a word have a meaning. Another is the idea of an opaque or intensional context, in which the principle of substitutional of co-referential terms salva vertitate does not hold -- or rather, as Frege would have it, in which we have to treat the customary sense as the referent in order that that principle hold. A third is in the case of determining the referents of indexicals.
3. There are ever so many kinds of sentences of which Frege never managed to give an adequate logical analysis, and while some progress has been made since his day, there remain many for which no such generally accepted analysis is forthcoming. These include sentences involving deontological elements, sentences involving attitude attributions, sentences involving explanation, and many more. So no, YOU can't analyze every sentence because you have read Frege.
4. Wittgenstein sure as heck did understand Frege's analysis of subject predicate sentences. he also took Frege's own context principle far more seriously than Frege himself did.
You are right about one thing. You haven't completed your study of Frege.
1) They are called "universal" quantifiers because they they say that the sentential function is true of everything, not because every generalization contains one.
2) Frege may not (or may) have used the word translated as "context", but there are at least three senses in which context was crucial to Frege's thinking. One is the so-called Context Principle, that only in the context of a sentence does a word have a meaning. Another is the idea of an opaque or intensional context, in which the principle of substitutional of co-referential terms salva vertitate does not hold -- or rather, as Frege would have it, in which we have to treat the customary sense as the referent in order that that principle hold. A third is in the case of determining the referents of indexicals.
3. There are ever so many kinds of sentences of which Frege never managed to give an adequate logical analysis, and while some progress has been made since his day, there remain many for which no such generally accepted analysis is forthcoming. These include sentences involving deontological elements, sentences involving attitude attributions, sentences involving explanation, and many more. So no, YOU can't analyze every sentence because you have read Frege.
4. Wittgenstein sure as heck did understand Frege's analysis of subject predicate sentences. he also took Frege's own context principle far more seriously than Frege himself did.
You are right about one thing. You haven't completed your study of Frege.