A Less Mysterious Solution to the Paradox of Analysis

Moore's paradox of analysis strikes me as having a simpler resolution than what recent commenters,  such as Richard Fumerton in "The Paradox of Analysis," have proposed. The major premise of the paradox, as Fumerton states it,

  

"If 'X is good' just means 'X is F' then the question 'Is what is F good?' has the same meaning as the question 'Is what is F, F?' " (478) 

is unsound because it assumes that an object being "good" is an identity statement (or at least, more charitably, that what is sought is an identity statement). One arrives at the paradox by assuming that an analysis just involves a chain of identities. In fact, what one wants here is an equivalence, conditions such that if and only if they obtain, something is good-- not an identity with the same intensional value under a different name. This latter notion just perpetuates the basic error of the Meno.

For example, an informative analysis of "good" could ask how its extension is formed by treating it as a binary relation and asking what sub-properties it restricts its members to, as restrictions on the equivalence class of x := the set of things that are good. Taking good as a relation G, we might propose, for instance, that when x is mapped to the set u of things with a positive utility value by the relation G, the statement "x is good" is true.

A logical analysis along the lines of the above without a necessary commitment to any one semantic interpretation could avoid being either merely lexicographical or mysteriously phenomenological. 

I'm not sure if it would be satisfying for all conceptual analyses to be only the product of equivalences, but I would claim that there is no satisfying conceptual analysis that is only the product of an identity. Indeed, since this is already an intuition most people have, Moore's reduction of conceptual analysis to an identity statement is what makes the paradox of analysis work. The only problem is that this reduction is wrong. In most cases, we do want an equivalence statement with a conceptual analysis to tell us how and when a concept obtains. (Maybe one could evoke Aristotle's four causes here and say that an informative analysis should not just give us a noun phrase that the concept noun stands in for but should give us one or more of these four constitutive explanations.)

For example, if the concept is "triangle," there might be an identity relation with "three-sided polygon," but this would not be informative-- it would just be a definition, a substitution of a noun phrase for the concept noun, not an analysis-- while adding, that "a triangle is any three-sided polygon such that it has three internal angles that sum to 180 degrees" would be informative (e.g., by this analytic definition we could claim that a three-sided polygon in non-Euclidean space might not be a triangle). So, one could say that a conceptual analysis can include identity definitions but cannot be constituted only by identity definitions.

Also, because a satisfying conceptual analysis, such as the analysis of "triangle," can be constituted only from a combination of equivalence statements and identity statements, we can at least say that there are some paradigm cases of analysis that do not require some phenomenal state in addition to succeed.