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Topic: Must equality "=" be defined as the identity relation or as "the
same"?

Replies: 12   Last Post: Apr 28, 2012 3:05 AM

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kirby urner

Posts: 3,678
Registered: 11/29/05
Re: Must equality "=" be defined as the identity relation or as "the same"?
Posted: Apr 26, 2012 8:43 PM
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On Thu, Apr 26, 2012 at 2:55 PM, Paul Tanner <upprho@gmail.com> wrote:

<< SNIP >>

> When I said "no matter how we interpret "="" I meant within the
> boundary created by the definitions I gave.
>


Right, and what I'm saying is that, given developments in STEM, we
know our AMNs ("amens" or animated math notations) are tending to
repurpose the "=" symbol to mean "assignment operator".

Curricula which either (a) bleep over the assignment operator role or
worse (b) heap scorn on "computer languages" in bigoted fashion,
should be discontinued forthwith, most obviously.

I'm saying that not making room for other meanings of "=" is out of
step with STEM, and that the math teachers are falling behind in
failing to update their lingo. No "math objects" even, a minimal
requirement.

In terms of passing our standards, we see a "no go". NCTM may be
trying to palm off CCS (Common Core Standards) on "private
corporations" but from my viewpoint here in Silicon Forest, there was
no implicit nor explicit groundswell of support for this new
"standards movement".

Common Core was mainly for the convenience of big publishing, still
having pipe dreams of continuing the wood pulp publishing industry in
its humongously wasteful form, as if teachers pushing such abuse of
world resources could have any credibility with their still-thinking
students.

>> If "=" is a naming device, used to assign names to objects, then all
>> the above theorems are blown out of the water, thanks to disagreement
>> on definitions.

>
> It depends on whether this use of "=" as a naming device is within the
> boundary created by the definitions I gave. If it is within, then the
> theorems apply, if not, then they don't. It's not so much that they
> are "blown out of the water" as it is that they simply don't apply
> because the definitions for the symbols are not compatible.
>


Right. So then it's more a question of "your meme pool or mine?" and
I'm suggesting that STEM needn't get sidetracked into propositional
calculus based on Frege's wrong turn (he was a greater logician than
Russell, most in my circle seem to think, alluding to our earlier "top
ten" thread).

Happy Birthday to Wittgenstein (today) by the way. I'm off to a
lecture in celebration (though on a different topic -- we'll find a
connection).

Blog post, party hats:

http://controlroom.blogspot.com/2012/04/hb2u-lw.html

http://worldgame.blogspot.com/2012/04/philosophical-investigations.html

> Well, except for the special uses in some parts of computer science of
> the same symbols like "=", just about all of mathematics including the
> use of symbols is based on sets and logic. Take away sets and logic
> and the result is that there isn't much left, including in computer
> science.


Actually, take away sets and logic and you have everything up to the
historical point where those disciplines invented themselves. Of
course "logic" goes back a long way, converges with rhetoric, part of
the old trivium / quadrivium and all that.

sets are of fading importance to foundationalists on many branches.

New foundations are always in the works, as its an industry, not a
finished product.

That is the promise of Logic: many secure jobs, if you keep applying
yourselves etc.

However, in K-12 we're not about indulging these foundationalists to
the nth degree, any more so than creationists (of whatever stripe).

And where the focus is STEM, we don't segregate the "computer stuff"
into a separate bin and tout mathematics as an aloof-and-above subject
(how ugly / dark ages).

More airtime for "=" as "assignment operator" is a hallmark /
signature of a thinking / working curriculum. I would encourage
parents to sniff closely.

If it doesn't pass this sniff test, one of many, and if only
expensive wood pulp is offered, then definitely you're invited to join
the resistance.

Speaking of which, here's another movie about Occupy, this one out of
Portland, my home town.

http://worldgame.blogspot.com/2012/04/occupation-nation-movie-review.html
(lots of history)

Kirby



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