1.2 A statement made in language does not directly express a truth about the world.

1.2.1 Since any formal definition of a word must use only other words, the process cannot “bottom out.” One must either accept some undefined terms or face infinite regress.

1.2.1.1 A formalized language, in which every term is either undefined or defined precisely through undefined terms, can thus make statements only about its undefined terms. A statement about a defined term reduces to a statement about undefined terms.

1.2.1.2 Undefined terms are in and of themselves meaningless. They are placeholders.

1.2.2 The assignment of truth values to statements in a formal language makes a claim as to how our undefined terms behave structurally.

1.2.2.1 By assigning truth values in a manner consistent with our some notion of deduction, we create a language which embodies a form of logic.

1.2.2.2 A language which embodies a form of logic which has not been contradicted by scientific investigation is quite useful. Such a language has the possibility of describing the world.

1.2.2.3 Any abstract structure is best described in a language which has a similar notion of deduction. Newtonian mechanics can be expressed in the language of calculus. Quantum mechanics can be expressed in the language of functional analysis. Quantum mechanics does not make Newtonian mechanics useless. Newtonian mechanics still makes coherent assertions within its language. The question of finding the natural language in which to speak of a certain topic is essential to any precise communication.

1.2.3 The properties a language guarantees about its undefined terms allows for meaning to be ascribed.

1.2.3.1 If one observes a system exhibiting properties that are mirrored by the undefined terms in a language, one can in some sense “perform the isomorphism” between the two and use the language to speak about the objects.

1.2.3.2 The meaning of a language is therefore not inherent to the language. It comes from our ability to use the language to mirror something else. The language does not mirror something else in and of itself.

1.2.3.3 Thus, we find a flaw with the picture theory of logic. One could say that logic is a picture, but it is wrong to say that it is a picture of the world. A picture is an object itself. By saying that one object or structure represents another, we must be saying that one can find an isomorphism between the two. It is only through perceiving the relations of a picture to the world that we can speak of the picture being any sort of representation. It is not inherent.