Two theories I have looked in to are Ferdinand Sassure's Dyadic Semiotic System and Pierce's Triadic System.
A sign does not represent what the object means, for example the image of a cat makes us think automatically of a cat, however a the word cat does not look, take shape or sound like the actual animal.
Sassure believed that signs do not represent reality but construct it, we come to know the world through language. The relationship between the sign and signifier is not a matter of personal choice, "it is because the sign is arbitrary that knows no law other than tradition".
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Index: The signifier is no arbitrary directly connected to a sign. They refer to their objects through a causal link, for example, smoke is an index of fire and physical pain is an index for abnormality in the body. The relationship between the sign and the object is that they have something in common as the object generally effects the sign.
Icon: An icon is a sign that represents an object by resembling it, examples of these include pictures, maps and diagrams. The relationship is one of similarity. There is a relationship as the features of the signifier bare similarities to the signified.
Symbols: There is no relation or link between the referent and meaning. Symbols refer to their objects through law, rule, tradition, culture, institution and convention among others. Examples of this are words and numbers. This means with many things signs can be perceived by different viewers in many different ways. For example the referent of a mother may have other meanings to others such as mum, mom, mother or mam.
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