concepts section: copyright Robert Ellis 2011


Isomorphism is the concept of 'being the same shape' used in representationalist accounts of meaning. Criticism of the assumptions involved in isomorphism is one of the bases of argument used to support a non-dualistic theory of meaning in Middle Way philosophy.

In a representationalist account of meaning, meaning is said to arise from the way in which a symbol ('symbol' here including words, terms, sentences and more abstract symbols) represents an object. This 'representation' takes a number of possible forms, from a direct physical resemblance to the object in the world, to a resemblance to an object in our minds, to a resemblance to the agreed social conventions on the use of a term. The last of these is the Wittgensteinian understanding of meaning, often misunderstood to be a pragmatic theory: but it is not pragmatic at all, just another representational theory with a different idea of what object is represented by a symbol. The weakness that all these representational accounts of meaning have in common is their reliance on isomorphism.

According to isomorphism, meaning arises from a similarity between the object and the symbol. When one considers cruder versions of isomorphism (like the idea that the symbol "dog" gains its meaning from its similarity to dogs in the world) it is obvious that this is not the case. However, even if our understanding of meaning takes into account the ways in which words and other symbols are merely conventional, isomorphism is still assumed between what people agree that a symbol means and the symbol, in order to make the symbol meaningful.

Isomorphism of any kind is flawed, because whatever similarity exists between symbol and object is relative, ambiguous, and dependent on our selection of important features in the object. For example, if I claim that the meaning of the symbol "dog" is equivalent to the object "the way in which people use the word 'dog'", any similarity between the two is dependent on the features of how people happen to use the word that I happen to pick out and focus on. I may or may not include wolves, soft toys, or sausages in a bread roll. Indeed, there is no reason why I might not meaningfully use the word in a completely new sense, to refer to tables, aliens or beetles. The consistency of meaning I give to my new use of language might be a purely 'internal' one, between different instances of my using that word. However, isomorphism attempts to legislate what words may or may not mean in the face of a potentially massive flux of pragmatic divergences, by tying them to objects.

The alternative to isomorphism is to adopt a genuinely pragmatic approach to meaning. One good starting point for this is the linguistic philosophy of George Lakoff, which bases meanings on our physical experience, developed through metaphorical extension. This shows isomorphism to be a completely mistaken way to approach meaning. Although there are some occasions when our words gain their meaning for us by their relationship to a situation we believe to be the case, that constructed "reality" in its turn is only understood because of its relationship to our physical experience. Cognitive and emotional elements of meaning are thus equally necessary to a larger context, and neither isomorphic representations nor expression of oneself provide enough of a basis by themselves to explain meaning satisfactorily.

Related discussion:

'Representationalism and expressivism' from thesis


Fragmentation of meaning

Integration of meaning

The Middle Way and language


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