 An essential point here is that when a formula is construed as a natural number, then the numeral corresponding to that natural number can occur as the argument of a formula, thus enabling the syntax to “refer” to itself, so to speak (i.e., when a numeral is substituted into a formula the Gödel number of which the numeral represents). This will eventually allow Gödel to formalize the Liar paradox (with “provability” in place of “truth”) by substituting into the formula which says, ‘the formula, whose code is x, is unprovable,’ its own natural number code (or more precisely the corresponding numeral).