[FOM] Counterfactuals in relative computability theory

[Timothy Y. Chow]

Matthias Jenny wrote:
> On Thu, Aug 18, 2016 at 5:23 PM Timothy Y. Chow <tchow at alum.mit.edu> wrote:
>> 2. If a connection can be established between a particular word, such as
>> "algorithm," and an "abstract object," then the word also retains its
>> identity across all possible worlds.
[...]
> But even aside from that, I certainly don't subscribe to 2.
> In fact, I'm not sure if I understand what you mean by it.

Frankly, *I* don't understand it either.  I offered it only as a tentative 
reconstruction of part of your thinking, which I don't understand.  So a 
detailed discussion of what it means is probably not fruitful; it's enough 
that you say that it's not what you meant.

The point is that I don't see how you're arriving at the conclusion that 
"algorithm" is rigid.  If you were to say, "The name `Barack Obama' is 
rigid," then I would presume that you're simply agreeing with Kripke's 
view of names.  But "algorithm," on the face of it, is not a name. 
You're saying that it "picks out" an "abstract object" but I don't quite 
understand this either since there are different ways of "picking out" 
objects that have radically different behavior when you move across 
possible worlds.

Further complicating the matter is that you are arguing that "algorithm" 
is "fully precise" but perhaps not "mathematically precise" because the 
latter concept is unclear to you.  You maintain this even though by far 
the majority view in discussions of the Church-Turing thesis is that the 
side of the equation with the word "algorithm" (as opposed to the other 
side, which involves "Turing machine") is informal and *not* precise.  So 
I don't know what you mean by "fully precise" if it's not the same as 
"mathematically precise."

In the end, all I'm saying is that there are a lot of details here to be 
filled in, and if you can fill them in successfully, then you're frying a 
pretty big fish, since you're introducing new notions of precision and 
algorithm as they relate the possible worlds.  That's quite a general 
claim.

Tim