When you consider the computational parameters of anything, physical or abstract, that you can observe, mathematical definitions force you down only a few possible paths. There are only two types of systems in the abstract: those with discernable high order patterns, and those without.
Systems with discernable high order patterns asymptotically approach certainty that they are finite state systems, as a function of the size of the dataset. For things like emotions and general human cognitive function, for which we have enormous datasets with clear high order patterns, the odds of these being the output of anything other than finite state machinery is about the same as the odds of me being God i.e. so infinitesimally small as to be effectively zero. To frame it another way, there are a lot of truly crazy ideas that have a higher probability of being correct than these not being the output of finite state systems.
Systems for which there are no discernable patterns give two possibilities. First, the system may be finite state but simply have no discernable high order patterns within the predictive limits of your brain(*). Strong cryptographic PRNGs (like the RC4 algorithm) are examples of this. Second, the system may be truly infinite state. There is no way to tell between the two except by either looking inside the black box as it were, or re-testing for high order patterns on bigger hardware.
(*) As should be self-evident, if the brain was an infinite state system it should be able to discern high order patterns in all finite state systems, such as cryptographic PRNGs. That even trivial PRNGs do not have transparent high order patterns to humans is tantamount to proof that our brains are relatively limited finite state systems.
But my question was more to the epistemological point of how do you know that emotions can be measured or discerned. (For Lurkers, post 990.)
The issue is one of perception, how do you know you have observed an emotion like pain or love or grief? How could you ever know that you have observed all such emotions in all the possible manifestations, degrees and meanings?
For instance, how could anyone know the array of emotions that the various players would experience after the annihilation of a third of the world's population by an act of terror? Unless you can read my mind, you have no way of knowing the love, pain or grief I have already experienced much less that which I may experience under such unknown circumstances.
Lurkers may enjoy this link to view the issues: Epistemological Problems of Perception
I would also submit the difference caused by aspect of the observer due to dimensionality.