Conceptual engineering and inferential delegation

 In society there is a class of people called 'experts'  which are endowed with both cognitive and social preeminence. Some most common examples are doctors and lawyers which are contrasted with non-doctors or non-lawyers which we refer to as 'laymen'.  Experts generally possess more 'refined' versions of the layman's concepts.  Furthermore a public statement of a laymen in matters of health or law is delegated to the experts in a kind of inferential epokhe. The layman relieves himself of any obligation to provide reasons or draw inferences. He also (in general) acknowledges the imperfection and revisability of his own concepts.

We ask: what is the nature and social origin of this inferential delegation and this conscious conceptual engineering ?  What binds the lay and expert concepts together ? What is it that makes them aspects of the 'same' concept ?

This can be a difficult question for concepts which carry a strong historical and cultural baggage.  For example,  'marriage'.  Clearly the legal definition of 'marriage' can be changed more easily than the socio-cultural concept.  But there is a seemingly circular relationship between the two: the legal concept must have its 'origin' in the popular concept (i.e. in a majority consensus)  just as the popular concept 'must' accept that the legal concept as binding.  But what if under certain circumstances the legal concept became widely divergent from the popular one ? Would they still express the same concept ? For instance if people could legally marry frogs would the legal definition of marriage still correspond to the ordinary concept of marriage ?  One of course could answer that marriage has always been an essentially legal concept so the question boils down to whether the union of A and B should or should not enjoy certain special economic and legal benefits and obligations, a question that is obviously historically and socially contingent as well as subject to moral constraints.

One approach to study delegation is through the nature of disputes and the necessity of instituting an 'arbiter'.  Specially important in when disputes take a metalinguistic turn or at least have a metalinguistic component.  Most disputes of the form 'Is X Y ?' involve not only  inference according to agreed upon criteria for Y but disputes about these very criteria. This can be easily checked in social media by surveying multiple answers to questions  such as  'is X overrated ?' or  whether something should or not be included in 'top ten lists'.  The necessity of ending endless disputes may also be one motivation for devising various statistical metrics as a means of comparison for a given a concept. But this turns out to be problematic and creates new problems and disputes. 

Another position is that the very asking of 'Is X Y?' already implies that there is some agree-upon criteria Z for determining Y.   But there could be a multiplicity of accepted criteria Z,Z',Z'' for Y and X may fail one and satisfy another. So the dispute will take the form of weighing and comparing criteria for X which may involve invoking historical precedents. A counter-argument is given by the question 'Will it rain today?'. I do not think that this implies that there is any agree-upon criteria for weather-forecasting.  But, one could rejoin, if there are no criteria, what is the point of the question ?

Disputes over the correctness of a proof are quite rare in mathematics. If they do happen it is due to the sheer complexity and size of the proof or, on the other extreme, the elliptic, ambiguous and incomplete nature of the proof.  This provides  good motivation for the development of proof assistants and proof checkers and the 'formal mathematics' project.