The logic of time and its perils

The discussion on reductionism here and earlier at Bill Vallicella's has segued into one on identity and composition.  Bill has brought up the familiar lump/statue, hand/fist examples.  He and others argue that the lump that the sculptor transforms into a statue, or the hand that is clenched into a fist are 'numerically distinct' from said statue and fist.  I take this to mean that they are distinct objects: the statue does not refer to the same object as the lump, the fist does not refer to the same thing as the hand.  This seems wrong to me, but they have an argument, which is more than I have.  Actually, they have two arguments, one modal, the other temporal.  The modal argument I'll have to put to one side as I'm not at all sure I understand what their claim is.  I do understand their temporal argument.  It goes like this.

At time t1 when the sculptor begins his work we have just a lump. At time t2 after he has finished we have a lump and we have a statue.  The lump has the property of existing at time t1 but the statue does not have this property.   The statue and lump are thus discernible and therefore by the converse of the law of Identity of Indiscernibles, they are not identical.

 What are we to make of this?  Firstly, the argument is not this one:

At t2:  there is a lump and there is a statue;  therefore, there are at least two things.

Nor, using a for the lump, b for the statue, F for is a lump and G for is a statue, is it

At t2: Fa and Gb; ergo a ≠ b.

Rather, using H for existed at time t1:

Ha and ~Hb; ergo a≠b.

There seem to be several steps in this.

1. We introduce two related concepts F and G under the condition that if at any time something is G then it must also be F but not conversely.  Being a hand and being a fist, say, or being a lump and being a statue.  
2. We consider a situation in which at some earlier time t1 there is an F but no G and at a later time t2 there is an F and a G.
3. We stipulate that there are at most two things under consideration and introduce a name a to denote the F and b to denote the G.  Nothing we have said so far requires a and b to be identical or be distinct, ie refer to the same thing or different things.
4. Lastly we introduce the predicate H meaning existed at time t1.

We can now claim that Ha, because a is the F and the F existed at t1.  And we can further claim that ~Hb because b is the G and the G did not exist at t1. Finally, wheeling on the big gun of Identity of Indiscernibles, we conclude that a≠b.
  
It all looks very good.  But surely it's invalid.  Here is a counter-example:  let F denote being a person, let G denote being an adult. Clearly, being an adult implies being a person, but not conversely.  Consider just me, DB, born 1952, and let t1 be 1960 before I was an adult.  Take t2 to be 2000.  a denotes the person and the person existed in 1960.  b denotes the adult and the adult did not exist in 1960.  All the conditions for our argument are in place so it appears a cannot co-refer with b.   But they must co-refer: DB is the only object in sight.

 I conclude that we must treat arguments of this form with care. But how does it go wrong?  First of all note that in some situations the argument delivers the right result.  Suppose DB dies in 1961 but SB is born that year and these are the only objects.  This too meets the conditions with DB the F at t1 and SB both F and G at t2.  But DB≠SB.  The argument claims that

a. The G does not exist at t1

is necessarily true, but this cannot follow.  My suggestion is that, by an ambiguity of scope, this is seen as

b. The G does not exist at t1,

and this is taken to be equivalent to

c. There is no G at t1

which is one of the premises and hence true. But, of course, (b) does not follow from (c), as the counter-example shows.  Why should (b) and (c) be seen as equivalent? I think because we see (b) as an assertion, at time t1, of the proposition The G does not exist, and we would assent to this, if present at time t1, because there really is no G at that time. We cannot know that by t2 there will be a G in existence for the G to refer to, and that it may turn out to be the F.