Lambda the Ultimate

The following is from Alberto Coffa's book The Semantic tradition from Kant to Carnap: To the Vienna Station (p. 153). The intellectual context in which this discussion occurs is a bit complex, and I am not going to try to explain it here (do read the book, if you are interested). While the philosophical debate was obviously not about the semantics of programming languages, I think trying to think how it applies to that case is an interesting exercise...

...what we need is not to add to that system a theory of types, but to throw that system away and replace it by one that does not allow such misleading symbolic configurations. The idea was illustrated at a meeting with Vienna circle representatives, when Wittgenstein agreed that the following was a good explanation of the intended point: In a normal language such as German or English, not only can we formulate the statements 'A is north of B' and 'B is north of A' but we can also formulate their conjunction, and someone could be misled into thinking that there is a conceivable circumstance that this new configuration represents. The Russellian strategy for avoiding this difficulty would be to add a rule forbidding the introduction of conjunctions of that sort. The Wittgensteinian strategy was to adopt a different system of representation, in this case a map, in which one could still say the meaningful, that A is north of B, or that B is north of A, but could no longer display a configuration of symbols corresponding to the old 'A Is north of B and vice versa' (Waismann, Wiener Kreis, pp, 79-80).