Holism and Compositionality
The relationship between compositionality and semantic holism has also been of interest to many philosophers of language. On the surface it would seem that these two ideas are in complete and irremediable contradiction. Compositionality is the principle that states that the meaning of a complex expression depends on the meaning of its parts and on its mode of composition. As stated before, holism, on the other hand, is the thesis that the meanings of expressions of a language are determined by their relations with the other expressions of the language as a whole. Peter Pagin, in an essay called Are Compositionality and Holism Compatible identifies three points of incompatibility between these two hypotheses. The first consists in the simple observation that while, for holism, the meaning of the whole would seem to precede that of its parts in terms of priority, for compositionality, the reverse is true, the meaning of the parts precedes that of the whole. The second incoherence consists in the fact that a necessity to attribute "strange" meanings to the components of larger expressions would apparently result from any attempt to reconcile compositionality and holism. Pagin takes a specific holistic theory of meaning – inferential role semantics, the theory according to which the meaning of an expression is determined by the inferences that it involves – as his paradigm of holism. If we interpret this theory holistically, the result will be that every accepted inference that involves some expression will enter into the meaning of that expression. Suppose, for example, that Fred believes that "Brown cows are dangerous". That is, he accepts the inference from "brown cows" to "dangerous." This entails that this inference is now part of the meaning of "brown cow." According to compositionality then, "cow implies dangerous" and "brown implies dangerous" are both true because they are the constituents of the expression "brown cow." But is this really an inevitable consequence of the acceptance of the holism of inferential role semantics? To see why it's not assume the existence of a relation of inference I between two expressions x and y and that the relation applies just in case F accepts the inference from x to y. Suppose that in the extension of I, there are the following pairs of expressions ("The sky is blue and leaves are green", "the sky is blue") and ("brown cow", "dangerous").
There is also a second relation P, which applies to two expressions just in case the first is part of the second. So, ("brown, "brown cow") belongs to the extension of P. Two more relations, "Left" and "Right", are required:
The first relation means that L applies between α,β and γ just in case α is a part of β and F accepts the inference between β and γ. The relation R applies between α, β, and γ just in case α is a part of γ and F accepts the inference from β to γ.
The Global Role, G(α), of a simple expression α can then be defined as:
The global role of consists in a pair of sets, each one composed of a pair of sets of expressions. If F accepts the inference from to and is a part of, then the couple is an element of the set which is an element of the right side of the Global Role of α. This makes Global Roles for simple expressions sensitive to changes in the acceptance of inferences by F. The Global Role for complex expressions can be defined as:
The Global Role of the complex expression β is the n- tuple of the global roles of its constituent parts. The next problem is to develop a function that assigns meanings to Global Roles. This function is generally called a homomorphism and says that for every syntactic function G that assigns to simple expressions α1...αn some complex expression β, there exists a function F from meanings to meanings:
This function is one to one in that it assigns exactly one meaning to every Global Role. According to Fodor and Lepore, holistic inferential role semantics leads to the absurd conclusion that part of the meaning of "brown cow" is constituted by the inference "Brown cow implies dangerous." This is true if the function from meanings to Global Roles is one to one. In this case, in fact, the meanings of "brown", "cow" and "dangerous" all contain the inference "Brown cows are dangerous"!! But this only true if the relation is one to one. Since it is one to one, "brown" would not have the meaning it has unless it had the global role that it has. If we change the relation so that it is many to one (h*), many global roles can share the same meaning. So suppose that the meaning of "brown "is given by M("brown"). It does not follow from this that L("brown", "brown cow", "dangerous") is true unless all of the global roles that h* assigns to M("brown") contain ("brown cow", "dangerous"). And this is not necessary for holism. In fact, with this many to one relation from Global Roles meanings, it is possible to change opinions with respect to an inference consistently. Suppose that B and C initially accept all of the same inferences, speak the same language and they both accept that "brown cows imply dangerous." Suddenly, B changes his mind and rejects the inference. If the function from meanings to Global Role is one to one, then many of B's Global Roles have changed and therefore their meanings. But if there is no one to one assignment, then B's change in belief in the inference about brown cows does not necessarily imply a difference is the meaning of the terms he uses. Therefore, it is not intrinsic to holism that communication or change of opinion is impossible.
Read more about this topic: Semantic Holism