Paradox of Analysis

I'm doing this from memory so I will use Sellars' version:

1. The concept Male Parent is the analysis of the concept Father
2. The concept Father = the concept Male Parent
3. The concept Father is the analysis of the concept Father

What leads us to befuddlement is that (1) should be true. (3) should be false. So what about (2)?

We might argue: "Look, (1) is true. The concept Male Parent and the concept Father mean the same thing. So (2) is true." But then we should think that (1) and (3) express the same sort of information. But they don't. So maybe (2) is false. But then how can (1) be true? If we can analyze concept X in terms of concept Y, don't X and Y have to mean the same thing?

Thus, befuddlement.

It should be easy to argue that (1) is true. We have a complex concept, being a Male Parent, and a simple concept, being a Father. We are analyzing the complex one into the simple one. Let us say that this isn't a logical truth, but an analytic one.

So then (2) has to be false. It is saying that a complex concept is identical to a simple one. This is false.

So then we can deny (3). An analysis is supposed to break down a complex concept into a simple one.

King considers examples like:

4. If x is a father, then x is a male parent
5. If x is a father, then x is a human adult male with offspring

When we explicate their logical form, we get

6. For all x [ [x is a father] iff [ [x is a male] & [x is a parent] ] ]
7. For all x [ [x is a father] iff [ [x is a human] & [x is an adult] & [x is a male] & [x is a parent] ] & [for some y [ y is an offspring of x] ] ] ]

So while both (4) and (5) are kinds of analysis for what it is to be a father, (5) is deeper. This is shown by (6) and (7).

If we consider the original example:

1. The concept Male Parent is the analysis of the concept Father
2. The concept Father = the concept Male Parent
3. The concept Father is the analysis of the concept Father

It seems we should indeed deny (2). I think Frege would appeal to there being two different senses. Sellars to there being to distinct functional classes, a •Father• and a •Male Parent•. King, it seems to me, two different concepts.

We can also see that the property of being a male parent is different from that of being a father. One is simple, one is complex. The concepts are likewise different. This is why we call (1) an analysis, whereas (3) is not. And if we were to take (3) to be an analysis at all, it would be an incredibly shallow one. As (4) - (7) shows, we can have various levels of analysis.