Nearly 60 years have passed since the notion of semantics was first used to explain Programming Languages. There was quite some divergence of opinions, at the time, in what the semantics of semantics was supposed to be. Today, in face of the plethora of different models and logical systems based thereupon, are we in a better position to address this socratic question? We analyse philosophical issues revolving around the Foundations of Formal Reasoning, Proof Cultures, Logical Frameworks, the Algebraic/Co-algebraic Duality, and Games. We put forward the thesis that, rather than being a drawback, plurality is what makes Semantics useful. In that Semantics of Computation is a “partita doppia”, a double check of what we think we understand in computing.