The main problem of the natural sciences is, and it's always been, quello di allontanare le componenti psicologiche dallo sviluppo della knowledge e di trovare un language perfect. L’obiettivo ideale sarebbe quello di rendere la knowledge, a "calculation". Recall Leibniz:
The attempt to found Science Its A language logically perfect was considered by Frege (1848-1925), Russel(1872-1970), Ludwig Wittgenstein (1889-1951) and by logical positivism.
In Tractatus Logico-Philosophicus, Wittgenstein è alla search di un’epurazione del language dalle componenti che non rispettano la sintassi della logic.
Foto di Ludwig Wittgenstein
The starting point is to identify the correspondence between the reality of world and that of the logic and language.
He says that logical propositions are tautologies, esse non dicono anything on world. Che relazione ci deve be tra un fatto (as laid down) and another fact, perché il primo possa be simbolo del secondo?
L’enunciato deve be “immagine” del fatto rappresentato e la proposizione è un modello della realtà, as we think. Structure world (logic) and that of the language match: "What the picture must have in common with reality, to be able to represent – correttamente o falsamente – è la forma logic, that is, the form of reality ".
Propositions, per be dotate di sense, They must respect not only the grammar rules, but also logical ones. La struttura logic del fatto, It is shown by the structure of the structure of the proposition, nothing in fact corresponds to the logical objects, solo la “forma logic” gli corrisponde.
The logic It is shown by language, but not described. In order to show the logical form, we should situate ourselves with the bringing out of the logic, vale a dire, fuori dal world.
The truth and falsehood depend on the correlation between what is expressed from the image (his sense) it's the realty. The sense of a proposition is the ability to express the "link between objects" , dove le funzione complesse sono funzioni di truth delle singole componenti.
In summary we can say that the structure of the logic shows that of reality, ma non afferma anything of world. The only expressions with common sense are those that have a logical form correctly and they say something about world: describe atomic facts, possible states of affairs.
Interestingly, the differences of position on the metaphysics of the two thinkers.
Per Wittgenstein la metafisica è un uso scorretto del linguaggio e la buona philosophy è quella che chiarifica la logic of thoughts. Statements of metaphysics that are not factual (not describe states of affairs) nor tautological (logical laws) I am "not meaning" so "everything that can be said, one must say clearly, the rest one must be silent ". But at this point you may be wondering: how can the tractatus describe the use and structure of language if all that is with sense should be riconducibile ad esserti fattuali?
A language that speaks the language, nella concezione di Wittgenstein, not a "nonsense"?
Il Tractatus non può dire anything sul rapporto tra reality and language, but to show up and tell how the same Wittgenstein, You should use his work, as a ladder: climb to the top and then get rid of it (although one would wonder how we can once climbed down). it's the same Wittgenstein, in the final phase of his thought, It is released by the logic, which becomes one of the many language games. The logic It is one among the linguistic systems, but it is not the only or the privileged.
The search of a universal feature that realized the correspondence between reality, language and thought, capace di ricostruire in modo perfetto la relazione tra le cose del world e tutte le possibili combinazioni linguistiche è stata definitivamente abbandonato con il theorem di incompletezza di Gödel: in a self-consistent system there are logical propositions true that can not be proved logically. Basically an ideal computer, that could work with the first-order logic would not be able to carry out all the steps necessary logic to the demonstration. Exist of the steps of the algorithm, whose propositions would Undecidable (They can be neither proved nor disproved).
Recall that Gödel's theorems have definitely thwarted attempt, started by Frege, e poi preso in carico da Russel di fondare l’intera math sulla logica.