Complete ? Really ?

Forgive me Doc, but, as you no doubt have guessed, my question was a rethorical trick. And it seems you fell into the trap.

Let us review your example of a complete statement :

(S) The mass of the proton at rest is 0.938 +/- 0.001 GeV

in light of your definition of 'complete' :

(D) A proposition is complete if it contains all the necessary assumptions and definitions that will make it a falsifiable model.

Let us suppose (S) indeed contains all the necessary assumptions. It certainly cannot be said to contain all the relevant definitions. What is a proton ? What is a GeV ? What does 'at rest' mean (for a proton) ?. These are more than rethorical questions, this time. As far as I am concerned, I roughly know what a proton is supposed to be and that a GeV is a Giga electron Volt. But I must confess that I do not remember very well what a Giga electron Volt is, and especially how to measure it. The term 'at rest' is probably even trickier since, if I am not mistaken, protons are never at rest in the kind of experiments we can do. So the 'mass at rest' is not something you measure directly but deduce (how ?) from measurements under different circumstances (which ones exactly ?). So (S) is definitely not complete according to (D).

Now is it 'completable' ? You can concievably transform (S) into another statement (S1) where 'proton', 'GeV' and 'at rest' have been replaced by short definitions (several lines long) of what these notions mean. But these definitions will inevitably contain other words like 'spin' or 'quark' or 'particle accelerator' or 'magnetic field' that will, in turn, require definition. Repeating the expansion process will yield a third statement (S2) where these words will have been similarly replaced by definitions. But why should (S2) be more complete than (S1) ? There is, in fact, every reason to believe (if you don't, just try) that (S2), being longer, will contain even more terms requiring definition. So from (S2) we will derive (S3), then (S4), etc. Now, is this series of statements going to stop at some point ? Logical Positivists believed it could and this is why R. Carnap (Der Logische Aufbau der Welt) or Otto Neurath tried to build very detailed systems to decompose any statement into a set of sense experience data readouts + predicitive structure. This project is generally considered to have failed and, indeed, has been abandoned. The coup de grâce seems to have come from W.V. Quine who said :

our statements about the external world face the tribunal of sense experience not individually but only as a corporate body.

and

The unit of empirical significance is the whole of science.

which means that Quine (and everyone else nowadays) believes that the sequence (S), (S1), ... (Sn),... cannot be meaningfully stopped until it contains 'the whole of science'. Now, 'the whole of science' is not a statement because it is not even precisely defined (what counts as science ? must we include definitions of ordinary words as well ?) So, none of the statements (S), (S1), ... (Sn), ... is a complete statement and what could be considered complete ('the whole of science') is not a statement. Ergo, there are no complete statements, since the above argument can be repeated for any starting statement (S).

Honestly, Doc, do you still believe your defintions of 'complete' and 'completable' are taking us anywhere ?