Re: how

On 6/18/2024 6:21 PM, Chris M. Thomasson wrote:

On 6/17/2024 5:04 PM, Jim Burns wrote:

On 6/16/2024 6:52 PM, Moebius wrote:

Am 16.06.2024 um 21:51 schrieb Moebius:

To put it in simple words:
/different/ means /not the same/.

>
We ask
what can we say (or not.say) about a and b
if they are (or are.not) the same?

a = 5 elephants
>
a = b
>
b must equal 5 elephants.
However, if we add in something, say:
>
a = 5 elephants
b = 5 cats
>
a = b?
>
Well, 5 = 5, but what they define is different...
>
Is that what you are getting at?

I might not have achieved the tone I was going for,
which was "chatting semi.technically"
instead of "obscure" and "mysterious".
What I am getting at  is that,
when we introduce equality into a formal system,
equality's axioms are something like
EQ1. x=x
EQ2. x=y ∧ P(x)  ⇒  P(y)
That is a way to say that a and b are "the same",
in a way in which we can put to use building
finite claim.sequences of only not.first.false.
Finite claim.sequences of only not.first.false
are only not.false. Sure, but
that's not very useful to us if we can't make
claims _about the things we want to explore_
Not every single time, but very, very often,
describing the things we want to explore
involves saying which things are the same and
which things are different.
_How_ do we say that?  One answer is EQ1 and EQ2.

a = 5 elephants
b = 5 cats
a = b?

In the physical sciences,
the wrong units of measurement turn something
into flaming nonsense.
How many stone.barns.per.fortnight does it take
to turn this light bulb on?
So, I would say
5 elephants ≠ 5 cats
But context matters.
I would also say
5 mammals = 5 mammals
I will courageously assert: it depends.