Re: universe of discourse

[And Rosta <a.rosta@UCLAN.AC.UK>]

Bob on the universe of discourse:
> [My apologies; I have been too busy with family estate matters to
> follow closely the last two weeks.  I will try to fill in soon.]
>
>    >> The number 3 does not exist in the universe of discourse which
>    >> is restricted to the set of even numbers.
>
>  > What is a universe of discourse?
>
> That topic within which you and your interlocutor are talking.
>
> The phrase is based on a container metaphor.  The idea is that a
> discussion may stay, like two people, within a garden, house or
> particular cosmos.

This is how I understood it. So if you're in the garden and
say "every flower is yellow", it might mean "every flower in
the garden".

Going by what you say, a universe of discourse is then not the
same thing a s a possible world (contra Lojbab).

> A second metaphor might refer to traditional Western music and say
> that a specific discussion remains within a particular key.
> (Hmmm... you will note here that the music metaphor is expressed using
> a territorial or container metaphor, too... )
>
> A third metaphor might use the concept of saliency: that those
> utterances that are meaningful within a discussion are those that leap
> out or poke at you, `are salient'.
>
> Utterances or knowledge that is not salient to the discussion have no
> effect on the truth value of assertions in that discussion.  This is
> why, in at least one universe of discourse, you can truthfully say
> that `unicorns leap like gazelles'.
>
>
> As for even numbers:
>
> Some years ago, one of my teachers pointed out that there is a kind of
> mathematical container or universe that relates to addition and
> multiplication among even numbers that does not occur with odd
> numbers.
>
>   * When you add two even numbers, the sum is an even number; and
>     when you multiply two even numbers, the product is an even number.
>
>     The result of the two operations is a number that is also and
>     always even.
>
>     But
>
>   * when you add two odd numbers, the product is an even number; and
>     when you multiply two odd numbers, the product is an odd number.
>
>     The result of the two operations is a number that may be odd and
>     may be even.
>
> In the jargon I was taught many years ago, the even integers
> {..., -4, -2, 0, 2, 4, ...}  with the usual operations of addition
> and multiplication form a "commutative ring".  The odd integers do not.
>
>     <even number> + <even number> ==> <even number>
>                 2 + 2              => 4
>     <even number> * <even number> ==> <even number>
>                 2 * 6              => 12
>
>     <odd number> + <odd number>   ==> <even number>
>                3 + 5               => 8
>     <odd number> * <odd number>   ==> <odd number>
>                3 * 7               => 21
>
> The universe of even numbers and the universe of odd numbers are very
> different.

Lojbab seemed to be saying that it is possible to construct
a world containing only even numbers. This is what I cannot
conceive of. I can of course easily understand a discussion
focused entirely on even numbers, where odd numbers are
irrelevant, and where {ro namcu} might be intended to mean
"all even numbers".

--And