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In spite of this, the status of the quantified variable, individual or term, is still a moot point. The fact that proposition and individual are clearly distinguished does not avoid the question whether (Εχ)φχ is defined for an individual term x=aor for an objective individual x=a. e. language. Like Frege he has imposed a normative view, completely embedded in an unjustified ideal of generalized formalization. Formalism itself presupposes what is ought to explain, namely natural language and its intelligibility.

Since a propositional function refers to a class, to a set of values which gives its meaning, one should not be surprised to discover mathematical paradoxes of set theory in this connection14. But one can easily obtain a logical paradox in merely focus­ ing on a proposition. The paradox of the Liar (attributed to Epemenides of Crete) "All Cretans are liars" exemplifies this, as does "what I write in this sentence between quotation marks is false" : if this sentence is false, then what it says is true, and if it is true, it is false.

In general, if one generalizes without recourse to the intermediary stage (χ) φχ, thus -φx, one does not have to differentiate (χ) φχ from (Ey) φy by means of different symbols χ and y. Instead, one can simply write: out of φχ derive either (χ) φχ or (Ex) φχ and both types of possible expressions refer to true propositions only. Whereas, if one does use (χ) φχ, it signifies "all the propositions φχ". The economy consists in skipping this expression, which refers to all the prop­ osition φ, in order to include only the forms of true propositions in one's logic.

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