Re: Equivalence relations and "is a sibling of"

In article <1152475103.311196.128470@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<sttscitrans@xxxxxxxxx> wrote:

[.snip.]

Naturally, if you ->redefine<- the word "sibling" to mean something
else, then the nature of the relation "is a sibling of" changes
accoringly. But under the common interpretation of "sibling", you need
two or more, so a person is not a sibling of him or herself.

Yes, it is true to say native speakers
would be puzzled by
"I am an only child and this is my sibling (pointing to myself)"
but they would also be puzzled by
"I am as tall as myself" or "I have the same colours of eyes as I/we
do"

The point is not that a "native speaker" might be puzzled. The point
is that the meaning of "sibling" is very specific, and it is NOT, as
you claim "have the same parents as".

If you were to give as an example the relation on the set of human
beings defined by xRy if and only if x
and y have the same biological parents, then this is a relation which
is DIFFERENT from the relation "xSy if and only if x and y are
siblings". You claimed originally that the latter was in fact the same
as the former, but it is not. The term "is a sibling of", in English,
requires that the two compared items be DIFFERENT. By contrast, "the
same X as" does not have such a linguistic requirement. I am not
contrasting the natural language use with mathematical use (I have
enough of that with the connective "or" to know they are not
identical). The point is that the notion of "sibling" comes with a
built-in prohibition against reflexivity, by the very meaning of the
word, where as "the same XXXX as" does not.

As I pointed out: if you REDEFINE the word "sibling" to mean "having
the same parents", then you would indeed have a point. But that
requires you to REDEFINE the term. If you consider the relation given
by the meaning of the word, it is irreflexive.

As you say "the word "sibling" does not apply to one person alone"
but then neither does "as tall as" etc.

That is where you are wrong. "Sibling" is explicit in its definition
in excluding reflexivity. By contrast, "tall" certainly does not:
tallness is an abstract measurement, and when you say "as tall as" you
are comparing those abstract measurements. "The same XXXX as" does not
preclude reflexivity; if you want to interpret "sibling" as meaning
"the same biological parents" (which is NOT the standard meaning),
then you'd be correct, but you would be using the term "sibling" as a
term of art, rather than via its standard meaning. By contrast, when
you say "the same height as" or "as tall as", you are using each and
every word in its ->standard<- meanings, even if you are applying it
in ways in which, in natural every day common language, you would not.

Either way the mathematical formulation of the relations
adds a sense that is not present in the usual natural language
contexts.
"I have the same parents as myself"
and
" I am the same height as myself"
seem equally implausible

Please read this carefully: "sibling" is NOT synonimous with "having
the same parents. As I noted in quoting the definition of the word
from the dictionary, it means "one of two or more XXXXXX".

I ->agree<- with you that the relation "having the same parents as" is
reflexive. That is the point you make above. I am saying that your
error lies in thinking that the relation "is a sibling of" and the
relation "have the same parents as" is identical; it is not. "Sibling"
carries a lot more linguistic baggage than "the same parents".

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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