Re: how (quantities and units, implicits and explicits, intensional and extensional)

On 06/18/2024 05:45 PM, Jim Burns wrote:

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:

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

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

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

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I might not have achieved the tone I was going for,
which was "chatting semi.technically"
instead of "obscure" and "mysterious".
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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)
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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.
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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_
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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.
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_How_ do we say that?  One answer is EQ1 and EQ2.
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a = 5 elephants
b = 5 cats
a = b?

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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?
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So, I would say
5 elephants ≠ 5 cats
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But context matters.
I would also say
5 mammals = 5 mammals
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I will courageously assert: it depends.
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https://www.youtube.com/watch?v=T9roz5F13q4&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY&index=15
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"If 1/oo = 0, what if you add oo/oo = 1?"
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What you got there is extensionality and intensionality,
that extensionally X mammals is X mammals, while,
intensionally, it depends:  on the individuals.
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Nice thing about language:  it's built into the words.
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"In-di-vidual."
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