SV: SV: On logic and fuzziness

Narayan S. Raja raja at IFA.HAWAII.EDU
Mon Nov 9 20:52:13 UTC 1998

```On Mon, 9 Nov 1998, H.M.Hubey wrote:

> > LMF: I wish it were that easy. You really owe us a precise definition of such a distance.
>
> Definition of distance is precise and well known.
>
>         d(x,z) <= d(x,y) + d(y,z)
>
> It means simply that if I take a detour (to go to z from x) via y then
> the
> sum of the two distances which comprise the detour (i.e. d(x,y)+d(y,z))
> must be greater than or equal to the direct distance d(x,z). Any kind
> of a function that satisfies this can be called a distance metric.

Y
/|
/ |
/  |
/   |
/    |
X-----Z

Here is a simple case where d(x,z) is not <= d(x,y) + d(y,z)

A precise definition of distance presupposes
a precise definition of the "space" (to put
it simplistically, at least how many dimensions
are involved)!  Is there a precise and uncontroversial
definition of "linguistic space", or even of
"evolutionary phonological space"?  I doubt it.

Regards,

Narayan Sriranga Raja (also a comp. scientist and electrical engineer)

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