In Wittgenstein's Tractatus Logico-Philosophicus, the opening proposition can be read as a definition:
- The world is everything that is the case.
As such, which kind of definition is it: nominal, or real?
That is, is Wittgenstein merely describing the usage of the word, "world", or is he providing an explanation of the meaning of the concept, world? (Or some third option?)
Wittgenstein is stating a model of our 'world'. It consists of 'facts' which is 'everything that is the case'.
Nominalism is the position that there no such things as universals. Wittgenstein does not answer this question, he evades it because this is not his concern. It may be the 'case' universals exist, or it may be the 'case' that universals do not exist. Whichever is the 'case', the simple sentence of the first opening proposition constructs the right model by choosing 'everything that is the case'.
Wittgenstein is basically affirming here the correspondance theory of truth.
Let us just look at the first four sentences together how they are written in German:
1. Die Welt ist alles, was der Fall ist.
2. Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.
3. Das logische Bild der Tatsachen ist der Gedanke.
4. Der Gedanke ist der sinnvolle Satz.
A reasonable translation would be
1. The world is everything that is the case.
2. That which is the case, the fact, is the existence of states of affairs.
3. The logical image of the facts is the thought.
4. The thought is the meaningful sentence.
This suggests two very different layers: the world on the one hand and its logical image, meaningful sentences, on the other.
To decide the question of nominalism vs. realism I think it is important to know a bit more, namely that the German terms have very specific connotations. And a main thing to consider here is that he essentially contrasts states of affairs with thoughts. This strongly suggests that the intention is to contrast material and ideal existence as well since the connotation is that which happens in the objective material world vs. that which happens in the logical idealist world of our thoughts.
Indeed, that is the common reading of the Tractatus: Wittgenstein champions a correspondence theory of truth and at the same time links meaning to truth, ie. only those sentences that are a logical mapping of facts (=true) are meaningful. It also means nothing we say or think is actually a fact in this view, it is always a logical mapping thereof and the two have to be kept apart.
Due to his later discussion of morals and religion, though, some people argue that the end of the book kind of turns itself against how it started off. This is discussed in other question threads, though, and not relevant for the question at hand.
We can come to grips with these notions looking at the main threads running through them: Nominal definition is language-based and language-driven, while real definition is reality-based and reality-driven. The distinction is comparable to that between the notions of sentence and proposition (it is a vice or virtue of German terminology that it does not distinguish them). Nominal definition is grounded in and addresses our language-dependent constraints on our decisions and behaviour. On the other side, real definition is disposed to breach the patterns and constraints of language and ready to transform them by our ever-furthering probes into reality.
Having said that, rather than try to categorise actual definitions as purely nominal or purely real, we should direct our attention on the focus of a definition, especially when the topic of discussion is a philosophical work in which word-world relationship is one of the main issues dealt with.
In Tractatus Logico-Philosophicus, Wittgenstein offers us a deeply fundamental view of our reality, setting forth a framework of, we may say, primordial metaphysics. His conception of world is a key element of this "worldview." Analogous to a physicist who depicts the fundamental nature of the Universe without bothering with thought-experiments populated by exotic creatures, he aims at not describing or correcting a particular linguistic behaviour, or clarifying a confusion about a pair of sense and reference, and the like, but laying bare the philosophical essence of our reality ('factuality' may be another term to employ on one interpretation), that would serve as a basis for a series of core questions of philosophy.
Stock examples of this distinction mostly contrast ordinary ways of seeing things with their scientific determinations (e.g., water with H2O), however, that needn't be and Wittgenstein's usage of "world" is a bona fide real definition.
For Wittgenstein this is the same, because you can not speak about the world other than in terms of language, and a statement can either only be true or false. The sum of all true statements (those that are 'the case') describe/represent the 'world'.
