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John Cowan wrote:
> Well, let's see what you do reckon as a nominal definition, if anything. Is it legitimate
> to treat "10 newtons" as nominally equivalent to "10 kg m / sec^2"?
No, not strictly. Unlike Cicero vs. Tully there is more than a name here. The units allow
the values which they modify to be compared through the execution of process and perhaps
then declared commensurate.
> Then you must hold that a copy of an algorithm is distinct from the original, even when
> there are no bound variables in the algorithm?
I think that you are confusing the execution of an algorithm, and the outcome of that
execution, with the statement of the algorithmic process. The execution of the copy and of
the original proceed identically against the same input and render the same result. The
original text of the algorithmic process and a copy of that text enjoy, at their most
distanced, an aliased relationship like that of Tully and Cicero.
> It seems to me that on your ontology there is no such thing as a general purpose tool, for
> every document is utterly distinct from every other, requiring a special purpose processor
> tailored to its idiosyncrasies.
That is the pathological case. In hope of avoiding it for most instances, we follow general
rules in processing which understand the difference between commensuration elaborated
through processes appropriate to units stated in original content and simple nominal
aliasing, or for that matter between element content and attribute values.
> How can you bring yourself to say that the current price of T is in any way commensurable
> with the current price of MSFT, just because they are both *said* to be measured in
Because I (or my software) executes many processes each day in which a dollar (or in more
correctly stated units, a stated currency per share versus a given counterparty in a given
market) value is elaborated through the operation of such processes as order execution,
comparison matching, delivery on settlement, etc. They are commensurable precisely because
they are made so on each occasion through the execution of process.