Re: Equivalence relations and "is a sibling of"


Arturo Magidin wrote:
In article <1152409461.069956.110550@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<sttscitrans@xxxxxxxxx> wrote:
Recently, I came across "is a sibling of" being used
as an example of an equivalnce relation and as an example
of a relation that is not an equivelence relation.

The usual explanation of why "is a sibling of" is not an equivalence
relation is that it is not reflexive because "A cannot be a sibling of
A".
or "A cannot be his own sibling" . On the other hand, "is the same
height as"
seems to be always accepted as an equivalence relation.
"A is the same height as A" or " I am the same height as myself",
however
both seem as linguistically strange as "I am my own sibling ".

"Linguistically" they may seem to be the same. However, in English,
the word "sibling" does not apply to one person alone. An only child
is said to "have no siblings", we do not sy that "he has no siblings
other than him/her self". However, "have the same height" does not
suffer from the same ad hoc exclusion as sibling.

Basically, for the height relation H, (X,Y) is in H if Height(X) =
Height(Y)
and it is, therefore, also true that (A,A) is in H. "To be a sibling
of" means
"to have the same two biological parents as"

Actually, a "sibling" is "one of two or more individuals having a
common parent," according to Merriam-Webster. (In fact, it is not
restricted to biological parents; adopted children are considered
'siblings', as far as I am aware). The second definition in M-W is
"one of two or more things related by a common tie or characteristic",
with the example "the sedan's smaller sibling" given.

In both cases, you will see that it is specified that it has to "one
of two or more".

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"
while "I have the same colour of eyes as you/they do" is generally
acceptable.
As you say "the word "sibling" does not apply to one person alone"
but then neither does "as tall as" etc.
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

.

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