Discussion:
Symbolic Constants versus Variables
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Pete Olcott
2017-06-10 12:58:13 UTC
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A Constant is a specific individual that is
identified by its unique properties.
I am speaking in terms of formalized natural language semantics, not
some arbitrary convention of a branch of math.
Some unspecificied, specific individual is a constant?
A unique set of properties identify an individual represented by a constant.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Pete Olcott
2017-06-10 13:35:00 UTC
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https://plato.stanford.edu/entries/identity-indiscernible/
The Identity of Indiscernibles (hereafter called the Principle) is
usually formulated as follows: if, for every property F, object x has F
if and only if object y has F, then x is identical to y. Or in the
notation of symbolic logic: ∀F(Fx ↔ Fy) → x=y
https://en.wikipedia.org/wiki/Identity_of_indiscernibles
The identity of indiscernibles is an ontological principle that states
that there cannot be separate objects or entities that have all their
properties in common. That is, entities x and y are identical if every
predicate possessed by x is also possessed by y and vice versa; to
suppose two things indiscernible is to suppose the same thing under two
names.
*A Constant is a specific individual that is identified by its unique
properties.** (thus not bound to a quantifier).
**
**A Variable is an arbitrary member of a class of individuals. (in MTT
bound to a quantifier and a class). **
*
--
*(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)*
My statement to you about these matters
had been motivated by your statement concerning
the use of a meaning postulate to instantiate
a constant.
I had been clear that the standard account of
identity does not include the principle of identity
of indiscernibles.
As you can probably tell I really don't care about standard accounts or the received view, I only seek the actual facts buried underneath the divergent opinions.

When I correctly defined the principle of identity of indiscernibles, this was without even glancing at it for a moment. I had presumed that it was some screwy idea that two things could be identical in every possible way and still be two different things.
Definitions based upon the misconception that it
is part of the standard account can only lead
you further astray (if that is possible).
I can analytically separate the wheat from the chaff even if there is a universal consensus choosing the chaff and even if this choice really looks like it has a sound mathematical proof supporting it.

All of my ideas about these things come from my own mind. I typically don't even start with any other ideas besides my own as my initial basis.

https://www.amazon.com/Formal-Semantics-Introduction-Cambridge-Linguistics/dp/0521376106
The above book is the closest thing to an exception to this rule. The above book gave me a rich set of terminology that I could plug my own ideas.
For what this is worth, good luck to you
Mr. Olcott. A series of minor misfortunes
(beginnning with bedbugs) in my personal
life created stresses to which I did not
respond very well. So, I have wasted time
flaming you instead of being who I normally
am and doing what I normally do.
That is OK.
I had not planned on responding to you any
further. However, when I opened up my
browser this morning, I found my name in
the title of a new thread. So, it seemed
prudent to clarify how you twisted what had
been said to you.
mitch
It did turn out that the position you provided formed an excellent foundation for nailing down the gist of exactly what a constant is. Weirdly enough (as seems to always be the case) I totally figured out exactly what the essence of a constant is entirely on my own, and then later retroactively found that what you said anchoring my own position in an established position.

Personally I don't really care whether or not Gottfried Wilhelm Leibniz totally agrees with me or if everyone in the world is stuck on an emotional attachment to a misconception. As I have told you before I have an OCD like compulsion to discover and provide the mathematical foundation of Truth. This usually provides great joy to me, except when I work on it 16 hours per day everyday for two weeks or more.
--
(Γ ⊨ _FS A) ≡ (Γ ⊢ _FS A)
Jim Burns
2017-06-10 15:19:34 UTC
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Post by Pete Olcott
My statement to you about these matters
had been motivated by your statement concerning
the use of a meaning postulate to instantiate
a constant.
I had been clear that the standard account of
identity does not include the principle of identity
of indiscernibles.
As you can probably tell I really don't care about
standard accounts or the received view,
This is something that you should make clear as often as it
is necessary to drive home the point that _you are not_
_talking about what we are talking about_ . Instead of
doing that, you continually make remarks suggesting that
you are talking about the standard account. What you are
really not caring about is being understood.

(My own theory is that there is nothing in what you write
to be understood. You merely would like to present the
image of competence without doing any of the work of
acquiring competence. If you were writing science
fiction (where your "work" might earn more respect,
hint, hint), it would be called "technobabble".)

If I were writing about counter-examples to various theorems
about von Neumann ordinals, the Quine atom q = {q} = (q U {q})
would surely show how wrong the "standard account" is --
except that q is not well founded, so if we were talking about
q we wouldn't be talking about what q is supposedly a counter-
-example to, the standard account of von Neumann ordinals.

This is the difference between _being read_ correctly and
being read incorrectly. I can't imagine a more important
"detail" to care about.
Post by Pete Olcott
I only seek the actual facts buried underneath
the divergent opinions.
You can't have it both ways. You can't both ignore
the standard account and look for facts beneath it.
Post by Pete Olcott
When I correctly defined the principle of identity
of indiscernibles, this was without even glancing
at it for a moment. I had presumed that it was some
screwy idea that two things could be identical in
every possible way and still be two different things.
In solid state physics, the entropy of a certain number
of electrons in certain orbitals is calculated as though
the electrons can be (are) "identical in very possible way
and still be two different things".

(For example, if an imaginary crystal had three states
and two electrons, named Kurt and Alfred, the wave
functions
psi( Kurt, Alfred, (empty) )
and
psi( Alfred, Kurt, (empty) )
are counted as one wave function.)

This is not a small difference.
It's the difference between predictions wildly at odds
with what we observe and predictions that permit us to
build such devices as you are reading this on.

I don't expect that my informing you of this will change
your "100% certain knowledge" in any way.

E pur si muove.
Pete Olcott
2017-06-10 16:22:53 UTC
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<div class="moz-cite-prefix">On 6/10/2017 10:19 AM, Jim Burns wrote:<br>
</div>
<blockquote cite="mid:873cb3ac-638a-854c-58e9-***@att.net"
type="cite">On 6/10/2017 9:35 AM, Pete Olcott wrote:
<br>
<blockquote type="cite">On 6/10/2017 8:00 AM, mitch wrote:
<br>
</blockquote>
<br>
<blockquote type="cite">
<blockquote type="cite">My statement to you about these matters
<br>
had been motivated by your statement concerning
<br>
the use of a meaning postulate to instantiate
<br>
a constant.
<br>
<br>
I had been clear that the standard account of
<br>
identity does not include the principle of identity
<br>
of indiscernibles.
<br>
</blockquote>
<br>
As you can probably tell I really don't care about
<br>
standard accounts or the received view,
<br>
</blockquote>
<br>
This is something that you should make clear as often as it
<br>
is necessary to drive home the point that _you are not_
<br>
_talking about what we are talking about_ . Instead of
<br>
doing that, you continually make remarks suggesting that
<br>
you are talking about the standard account. What you are
<br>
really not caring about is being understood.
<br>
</blockquote>
<br>
I am not talking about any of the commonly accepted (received view)
misconceptions of others. I am diligently striving to translate my
insights into conventional terminology and conventional notational
conventions. <br>
<br>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<p class="MsoNormal"><span style="font-family:&quot;Arial Unicode
MS&quot;">A formula A is
a syntactic consequence within some formal system FS of a set <span
lang="ZH-CN">Γ</span>
of formulas if there is a formal proof in FS of A from the set <span
lang="ZH-CN">Γ</span>:   </span><b><span
style="font-family:&quot;Segoe UI Symbol&quot;;
mso-fareast-font-family:&quot;Arial Unicode
MS&quot;;mso-bidi-font-family:&quot;Arial Unicode MS&quot;;
background:yellow;mso-highlight:yellow">Γ ⊢ <sub>FS</sub> A</span><u1:p></u1:p></b><span
style="font-family:&quot;Arial Unicode MS&quot;"> <br>
<br>
<font size="+1"><b>Translation to MTT notational conventions:</b><b><o:p></o:p></b></font></span><b><span
style="font-family:&quot;Arial Unicode MS&quot;" lang="ZH-CN"> 
Γ
⊢ </span></b><b><sub><span style="font-family:&quot;Arial
Unicode MS&quot;">FS</span></sub></b><b><span
style="font-family:&quot;Arial Unicode MS&quot;"> A  <span
lang="ZH-CN">≡ </span><span
style="background:yellow;mso-highlight:yellow">( <span
lang="ZH-CN">∃Γ ⊂</span>
FS (<span lang="ZH-CN">Γ ⊢</span> A) )</span></span><u1:p></u1:p></b><span
style="font-family:&quot;Arial Unicode MS&quot;"><o:p></o:p></span>
</p>
<p class="MsoNormal"><span style="font-family:&quot;Arial Unicode
MS&quot;"><br>
Named predicate (of predicate logic PL) impossible to prove and
impossible
to refute:<b> <span
style="background:yellow;mso-highlight:yellow">G( ~<span
lang="ZH-CN">∃Γ ⊂</span> PL (<span lang="ZH-CN">Γ ⊢</span>
G) )</span> </b><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-family:&quot;Arial Unicode
MS&quot;">If the 1931 Incompleteness
Theorem is correct then the much simpler expression above
equally proves that
there are some sentences of predicate logic that are neither
provable nor
refutable. <br>
</span></p>
<p class="MsoNormal"><span style="font-family:&quot;Arial Unicode
MS&quot;"><br>
</span></p>
<p class="MsoNormal"><font face="Arial Unicode MS">There is no need
to go through the convoluted process of converting expressions
into enormous strings of numeric digits in an attempt to provide
this proof within arithmetic. One can simply generalize the gist
of the whole proof (within predicate logic instead of limited to
arithmetic) as the concise expression above. <br>
</font></p>
<p class="MsoNormal"><font face="Arial Unicode MS"><br>
</font></p>
<p class="MsoNormal"><b><font face="Arial Unicode MS">Perhaps with
the missing piece (translation to MTT) provided, others can
finally see what I am saying. <br>
</font></b></p>
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<o:p></o:p></font></p>
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<blockquote cite="mid:873cb3ac-638a-854c-58e9-***@att.net"
type="cite">
<blockquote type="cite">I only seek the actual facts buried
underneath
<br>
 the divergent opinions.
<br>
</blockquote>
<br>
You can't have it both ways. You can't both ignore
<br>
the standard account and look for facts beneath it.
<br>
</blockquote>
<br>
Many of these divergent opinions are merely enormously convoluted
misconceptions, I generally ignore those. <br>
<br>
<blockquote cite="mid:873cb3ac-638a-854c-58e9-***@att.net"
type="cite">
<br>
<blockquote type="cite">When I correctly defined the principle of
identity
<br>
of indiscernibles, this was without even glancing
<br>
at it for a moment. I had presumed that it was some
<br>
screwy idea that two things could be identical in
<br>
 every possible way and still be two different things.
<br>
</blockquote>
<br>
In solid state physics, the entropy of a certain number
<br>
of electrons in certain orbitals is calculated as though
<br>
the electrons can be (are) "identical in very possible way
<br>
and still be two different things".
<br>
</blockquote>
<br>
If they also share an identical point in Space-Time then they are
one and the same thing. If they do not share an identical point in
Space-Time then they are discernibly different things. <br>
<br>
<blockquote cite="mid:873cb3ac-638a-854c-58e9-***@att.net"
type="cite">
<br>
  (For example, if an imaginary crystal had three states
<br>
   and two electrons, named Kurt and Alfred, the wave
<br>
   functions
<br>
      psi( Kurt, Alfred, (empty) )
<br>
   and
<br>
      psi( Alfred, Kurt, (empty) )
<br>
   are counted as one wave function.)
<br>
</blockquote>
<br>
One can imagine the misconception that is thing is not itself. This
can be discerned as a misconception on the basis that its meaning
postulates do not coherently fit together. <br>
<br>
<blockquote cite="mid:873cb3ac-638a-854c-58e9-***@att.net"
type="cite">
<br>
This is not a small difference.
<br>
It's the difference between predictions wildly at odds
<br>
with what we observe and predictions that permit us to
<br>
build such devices as you are reading this on.
<br>
<br>
I don't expect that my informing you of this will change
<br>
your "100% certain knowledge" in any way.
<br>
<br>
E pur si muove.
<br>
<br>
</blockquote>
<br>
<br>
<p><br>
</p>
<div class="moz-signature">-- <br>
<p class="western" style="margin-bottom: 0in"><b><font
face="Arial, sans-serif"><font style="font-size: 12pt"
size="2">(Γ
</font><font style="font-size: 12pt" size="2">⊨ </font><sub><font
style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A) ≡ (</font><font style="font-size: 12pt" size="2">Γ </font><font
style="font-size: 12pt" size="2">⊢
</font><sub><font style="font-size: 8pt" size="2">FS</font></sub><font
style="font-size: 12pt" size="2">
A)</font></font></b></p>
<p class="western" style="margin-bottom: 0in"><br>
</p>
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