[FOM] Counterfactuals in relative computability theory

[Timothy Y. Chow]

Matthias Jenny wrote:

> On Wed, Aug 17, 2016 at 12:10 AM Timothy Y. Chow <tchow at alum.mit.edu> wrote:
>
>> If you can give a coherent account of all this then I think that that 
>> should be the main focus of your work, since you'd be frying a much 
>> bigger fish than the vacuity thesis.
>>
> I still don't see why this is so. As I tried to explain, it seems to me 
> that the notion of mathematical precision that you have in mind is of 
> epistemological significance, not of ontological. It's only if it were 
> of ontological significance that it would matter for the question 
> whether algorithms are necessary existents.

I'm also having difficulty following your train of thought, so what 
follows is conjectural.

It sounds like your thinking proceeds along roughly the following lines.

1. So-called "abstract objects" retain their identity across all possible 
worlds, at least if they are "fully precise."

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.

3. The connection in 2 is an ontological one.  Whether the connection is 
known by people in the actual world is irrelevant to the above 
considerations.

Assuming this reconstruction of your views is approximately correct, there 
are many non-obvious features.  In step 2, it is known that there are 
different ways that a word or phrase can be connected with an object. 
Specifically, a name such as "Barack Obama" can pick out a particular 
person.  So can a phrase such as "the current president of the United 
States."  However, according to the standard account, these behave very 
differently across different possible worlds.  So it's not enough to say 
vaguely that there is some kind of "picking out" going on; in the case of 
most interest to you, a clear account of the relationship between 
"algorithm" and the allegedly "fully precise abstract object" that it is 
supposedly "picking out" must be given.  There are further complications 
because you're drawing a distinction between "fully precise" and 
"mathematically precise" that I don't think most people will understand 
without further elucidation, especially for a word that, in the context of 
Church's thesis, is widely regarded as being *not* "fully precise."

Sorting all these issues out is what I was referring to as "bigger fish to 
fry" because they involve very general issues such as the nature of 
vagueness and precision and the way they relate to identity across 
possible worlds, and the way you're thinking about them does not seem to 
line up with standard accounts.

Tim