Let me first tell you that in the first phases of this investigation my thoughts where that the specific quantum formalism would only play a limited role in all this, and most of all we needed to look for general non-Kolmogorovian and non-Boolean structures to model human thought. In the course of the investigations however at different times I was stumbled by the sheer power of the quantum formalism itself to model human thought, hence now I do believe that something deeper is touched upon than merely coping with non-Kolmogorovian and non-Boolean structures.
- Quantum theory is in some way a double layer mathematical theory. Calculations are done on the deeper layer of a complex vectors space, and then at the end of the calculation when contact is made with experiment, the deeper layer is squared (by taking literally the square of the absolute value of the complex numbers involved) to give rise to probabilities that can be compared with relative frequencies of outcomes of experiments. But not only calculations are done on this deeper underlying mathematical layer, for example, also when two or more systems are combined, this combining is done on the deeper layer, and this is what gives rise to the existence of the weird quantum phenomenon of entanglement. Recently we have proved that exactly this same entanglement exists when in human reasoning (very simple) concepts are combined (see:
http://arxiv.org/abs/1104.1322), which shows that 'the deep layer is also present in human reasoning'. In fact, before finding the explicit appearance of entanglement there were other signs in this direction, and in
http://uk.arxiv.org/abs/0810.5332 an attempt is made to describe what we have called 'the quantum conceptual mode of human thought', which resembles in some sense intuitive thought. A technically more difficult article goes further into this (
http://uk.arxiv.org/abs/0805.3850). Hence, at the actual stage of investigation, I do believe that more than just capturing the fuzziness of human thought is at stake. If this is true, it means that the Quantum Cognition approach to model human thought is definitely more powerful than, for example, the fuzzy set approach (with fuzzy logics), which indeed only captures the fuzzy aspect of human thought.
- A second possible reason, for me personally as a physicist at least, of why the quantum formalism works well in modeling human thought, is much more speculative, but worth mentioning. This second reason is not investigated within the Quantum Cognition community, since its focus is not on 'cognition' but on 'quantum physics' itself. So I work on it as a quantum physicist, alone at the moment (its too speculative still to engage young researchers in it at this stage), and mostly in elaborating a new type of interpretation of quantum theory itself. In this new interpretation quantum particles are seen as conceptual entities carrying conceptual information. This investigation is at this moment in a purely explorative phase, and for those interested there are three published articles (
http://uk.arxiv.org/abs/1004.2530,
http://uk.arxiv.org/abs/1004.2531,
http://uk.arxiv.org/abs/1005.3767). If this new interpretation is true, it would mean that the quantum formalism works so well to model human thought, "because" also microphysics quantum dynamics is a conceptual interaction process. Hence, the mathematics of the deep structure of a cognitive process would appear in both cases naturally.