However two different ideas lie behind these translation schemes.

For Russell and Whitehead we are to carry out this translation to give a perfect clarity to our language and, in so doing, we come closer to a mirroring of the world itself. The clearest exposition of this Matching theory (world and Language) was given by Wittgenstein in his first book "Tractatus Logico-Philosophicus". Here a Word relates directly to an Object, while a Sentence relates to a State-of-Affairs (i.e. a combination of objects) in the world. Russell, very strongly behind this vision of the world stated by Wittgenstein, conceived of his Symbolic logic, i.e. the translations of "muddy" sentences into his clear ones, was the way to ensure the correct matching of our sentences to the real world. When we work on the appropriate translations of our sentences we come to have a one to one matching with the world.

Turing's system, however, leads us not to any matching scheme, but revolves around the notion of translation of information itself. The translation of information is seen as only that. The only occurrence which we can be assured of is that in the translation and the internal usage of the language by the machine (in this case the 0-1 language) there will be a change of state of the machine. This is tantamount to saying that if we set out the rules which we believe and therefore the language we are to use in this methodology (the one we think is "right") we are going to reach certain states of operating, or, to put it for us, we are going to reach certain conclusions. We, or the machine, is going to act in certain ways.