Full Idea
There are two problems with defining the quantifiers in terms of conjunction and disjunction. The general statements are unspecific, and do not say which things have the properties, and also they can't range over infinite objects.
Gist of Idea
Conjunctive and disjunctive quantifiers are too specific, and are confined to the finite
Source
Michael Morris (Guidebook to Wittgenstein's Tractatus [2008], 5C)
Book Reference
Morris,Michael: 'Guidebook to Wittgenstein's Tractatus' [Routledge 2008], p.218
A Reaction
That is, the universal quantifier is lots of ands, and the existential is lots of ors. If there only existed finite objects, then naming them all would be universal, and the infinite wouldn't be needed.