[FOM] Counterfactuals in relative computability theory

[Richard Grandy]

While Kripke’s theory is fairly widely accepted for proper names, it is much more controversial and less developed for natural kinds and “algorithm” is a kind word not a proper name.  Moreover, it is not at all clear whether “algorithm” is a natural kind.

Richard Grandy
Philosophy and Cognitive Sciences
Rice University
TX (stll in the USA, so far)




> On Aug 19, 2016, at 1:39 PM, Matthias Jenny <mj.
> enny at mit.edu> wrote:
> 
> 
> 
> On Thu, Aug 18, 2016 at 11:26 PM Timothy Y. Chow <tchow at alum.mit.edu <mailto:tchow at alum.mit.edu>> wrote:
> 
> 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.
> 
> I'm afraid I still don't understand why we're talking about 'algorithm' instead of about algorithms. My claim is that algorithms are necessary existents (if they exist, they exist necessarily, and if they don't, they couldn't exist). The semantics of 'algorithm' seems to me to be besides the point. Furthermore, I think it strikes me as distracting to talk about whether 'algorithm' is rigid in the way Kripke says proper names are. For even if we accept that proper names are rigid, this is usually put as follows: A proper name refers to the same individual in every possible world in which the name has a referent. This is to accommodate the fact that most individuals aren't necessary existents.
>  
> 
> 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."
> 
> The reason why I was hesitant to use the expression 'mathematically precise' is because, as I've tried to explain, the way you use this expression seems to me to pick out an epistemological property and not an ontological one.
> 
> Also, with all of that said, I wanted to remind you that my argument involving the idea that algorithms are necessary existents is only one of two arguments for the necessity of the Church-Turing thesis.
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