In the paper, 

* *Aldo Antonelli and Robert May*, [**Frege's new science**](http://dx.doi.org/10.1305/ndjfl/1038336844), *Notre Dame J. Form. Log.* **41** (2000), no. 3, 242–-270, [MR 1943495](http://ams.org/mathscinet-getitem?mr=1943495).

the authors give the following quote of Frege, from his paper "Über die Grundlagen der Geometrie"\*:

> 
> What I call a proposition *tout court* or a real proposition is a group of of signs that expresses a thought [has a sense—my comment]; however, whatever only has the grammatical form [i.e. being a well-formed formula—my comment] of a proposition I call a pseudo-proposition.†
> 
> 
> 

Since it is well-known that $$R \notin R \Leftrightarrow R \in R$$ (this is actually true if both $R \notin R$ and $R \in R$ are false, but then this seems to contradict the Law of Excluded Middle), can one rightly attribute either a reference (since they are 'propositions', their reference must be, according to Frege, either The True, or The False) or a sense (what would that be, exactly) to "$R \notin R$" or "$R \in R$"? And if not, are "$R \notin R$", "$R \in R$" pseudo-propositions?

Furthermore, since $$R \notin R \Leftrightarrow R \in R$$ can be derived from Basic Law V, shouldn't Basic Law V be restricted to apply only to "real propositions"? And how might that be done in the context of the *Grundgesetze*? 

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\*In *Jahresbericht der Deutschen Mathematiker Vereinigung*, vol. 15 (1906), pp. 293-309, 377-403, 423-30.  

†English translation by E-H. W. Kluge in *Gottlob Frege, On the Foundations of Geometry and Formal Theories of Arithmetic*, Yale University Press, 1971, p.69.