According the Wittgenstein in his Philosophical Investigations, the purpose of philosophy is “not to resolve a contradiction by means of a mathematical or logico-mathematical discovery, but to make it possible for us to get a clear view of the state of mathematics that troubles us: the state of affairs before the contradiction is resolved” (Wittgenstein, 50). Language, like mathematics, comprises an agreed-upon set a rules which we must follow in order to understand one another; language as a whole is a kind of “game” and the rules of language comprise the mechanism or “technique” necessary for it to function. However the imperfect nature of these rules is such that we tend to get “entangled” in them; we try to express ourselves accurately but the method at our disposal, that is to say language, only allows for an approximate expression of meaning and occasionally produce contradictions. For Wittgenstein, the philosophical problem is not to resolve these contradictions but rather to understand the particular rule entanglement that caused them to appear in the first place.
Wittgenstein points out that when the single word “Slab!” means the same thing as the sentence “Bring me a slab!,” this meaning is derived in contrast to the meanings of other possible sentences containing the word “slab” such as “Hand me a slab,” “Bring him a slab,” or “Bring two slabs” (Wittgenstein, 9). It is a feature of our language that we are able to produce different sentences using the same word (“slab”), each with different meaning, and it is because of this available variety of sentences and their associated meanings that we are able to select the one particular combination of words (“Bring me a slab!”) which in contrast to all the others has the same meaning as the single word (“Slab!”). As Wittgenstein points out, “someone who did not understand our language, a foreigner, who had fairly often heard someone giving the order: “Bring me a slab!”, might believe that this whole series of sounds was one word corresponding perhaps to the word for “building-stone” in his language” (Wittgenstein, 9). The foreigner would not conceive of “Bring me a slab!” as a sentence with multiple words because to him there would not be other combinations of the word “slab” with different meanings. To the foreigner, “Bring me a slab!” is a single thought or idea; he sees no need to break the sound down into multiple words. But Wittgenstein questions whether even those who master the language are conscious of the fact that the sentence “Bring me a slab!” contains four words as they are actually uttering it. For Wittgenstein, the thought comes first; then we express the thought by arranging words in a specific order according to the rules of language (Wittgenstein, 108).The fact that the single word “Slab!” and the word for “building-stone” in the foreigner’s language can mean the same thing as the four-word sentence “Bring me a slab!” suggests that mastery of language may be entirely unrelated to the ability to derive meaning from utterances.
Meaning, as Wittgenstein also points out, is indestructible, “for it must be possible to describe the state of affairs in which everything destructible is destroyed. And this description will contain words; and what corresponds to these cannot then be destroyed, for otherwise the words would have no meaning” (Wittgenstein, 27). There is a distinction here between the meaning of the word and the actual person or object that the name or word refers to in the real world. What the word corresponds to – its meaning – must not be the same as the actual thing referred to since the word still has meaning even when the thing referred to by the word no longer exists. For Wittgenstein, the meaning of the word is not the actual thing it refers to but rather what makes it such that the word is useful as an instrument of our language or a “paradigm that is used in connection with the name in the language-game” (Wittgenstein, 27).
For Wittgenstein, “to have understood the definition means to have in one’s mind an idea of the thing defined, and that is a sample or picture. So if I am shown various different leaves and told ‘This is called a leaf’, I get an idea of the shape of a leaf, a picture of it in my mind” (Wittgenstein, 34). But Wittgenstein then rightfully asks: “What does the picture of a leaf look like when it does not show us any particular shape, but what is common to all shapes of leaf?” We tend to think we understand what a simple thing like a leaf is but this understanding is composed of pictures of leaves in one’s mind which are only samples or particular instances of the shape of a leaf; none of these mental images convey what is common or essential to all leaves. As Wittgenstein further explains, “If you look at them you will not see something common to all, but similarities, relationships” (Wittgenstein, 31). The meaning of “leaf” is in fact “a complicated network of similarities, overlapping and criss-crossing,” which Wittgenstein refers to as “family resemblances” (Wittgenstein, 32).
 Wittgenstein, L. (1953). Philosophical investigations;. New York: Macmillan.