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Symbols: Our brains are able to understand that some things stand for other things. For example, the sound we make when we say "food" stands for things we can eat. And with writing, we can say that words have meaning because they stand for things in the real world.
Association: A brand is what someone associates with a company. I associate McDonalds with delicious, unhealthy food.
Conditioning: And I can associate other things. I might feel bad when I hear a certain song because it was playing during a bad breakup.
Is associating things an entirely different process from linking things together to create symbols?
Conditioning is considered an example (type) of association by associationism, a school of philosophy in psychology that suggests that all mental processes may be based on similar or proximal mental states. Usually this idea is too broad and vague to be very practical to apply, but it has spawned a number of useful fields of study, including connectionism, a general strategy used in neural networks and learning modelling, and schemata, used in memory research.
Using connectionist models, artificial neural networks have demonstrated learning in a variety of subject areas, including operant and classical conditioning (examples of association), and handwriting recognition and sign reading (examples of symbols). This suggests that the process involved may be essentially the same.
One of the major challenges to basic associationism has been that in practice, associations do not seem to obey any straightforward rules. For example, children learn to associate words like "food" with their meaning very quickly with few (sometimes no) repetitions, while branding requires many more repetitions, and other associations (there is nothing intrinsically bad about this song) may never be learned. For this reason, more rigorous theories, such as conditioning, are preferred.