If I may use a crude simile for illustration, Wittgenstein posits that knowledge, or language, or science, is like a pile of cordwood. Each individual piece of wood represents a proposition that mirrors or pictures a fact in the world. These pieces of wood are neatly stacked on top of each other in accordance with the logical rules for concatenating propositions. This includes implication (for causation) and universal quantifiers (for scientific principles). The pile of wood rests firmly on a bottom layer of “elementary propositions,” upon which the rest are compounded. The nature of these elementary propositions is left somewhat unspecified, save for the fact that they are empirical. They could pertain to the simplest sensations (as in Bertrand Russell’s logical atomism), or they could be related to something appropriate to the subject matter (perhaps atoms, molecules, cells, etc.).
All that language can convey is what is contained within that woodpile. Anything outside of it is considered nonsense. Any part of that woodpile is logically founded upon the elementary propositions at its base. There are limitations to how high one can build the woodpile. This is all that we can know, neatly stacked up in this orderly pile of wood.
The most well-known consequence of this philosophical system is that certain areas of discourse are deemed nonsense. This includes philosophy, religion, morality, aesthetics, and so on. The traditional topics of philosophy are effectively out of bounds. We are unable to discuss the world as a whole, the relation of knowledge to the world, the nature of the self, and other such matters, because they do not form part of our woodpile and we cannot step outside of it to do so.
It is an elegant and beautiful system, and a theory of language. I will refrain from complaining because, within this system, I am unable to engage in any philosophy. As Wittgenstein concludes, “What we cannot speak about we must pass over in silence.” I admire the beauty and integrity with which Wittgenstein articulates his vision, such that it becomes like a Zen koan.
One minor point before I conclude. The facts in the world that propositions are supposed to mirror seem to me to be metaphysical projections. They strangely resemble propositions, yet they are supposed to exist in the world. If I look out my window, I see trees and houses, but I do not perceive facts. Wittgenstein says many things about facts, enough to make me uncertain if I am making a valid point. He states, for example, that they are the logical structure which propositions and the world have in common. He also contends that one cannot speak of this logical structure, because to do so, one would have to be outside the woodpile. So I will continue to ponder in silence.
As a footnote, all of the above pertains to the early Wittgenstein of the Tractatus, as distinct from the later Wittgenstein of the Philosophical Investigations.