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Re: Why is model theory needed?

Newsgroups sci.logic
Date 2023-05-31 21:12 -0700
References (14 earlier) <7d2ce2bb-efb1-4bbe-abe0-9e92a0b32dcfn@googlegroups.com> <2f4d8289-0602-4517-a217-210682a0c14cn@googlegroups.com> <df1b3f91-45de-44e6-b7e1-f8d28d15b35fn@googlegroups.com> <92fb36db-7b5b-4267-b182-155ba2a0d03bn@googlegroups.com> <d7beecff-eaa0-422b-811a-5b756cea9f1cn@googlegroups.com>
Message-ID <d5c007bd-7747-4106-b983-c3ccbe0e3623n@googlegroups.com> (permalink)
Subject Re: Why is model theory needed?
From Ross Finlayson <ross.a.finlayson@gmail.com>

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On Wednesday, May 31, 2023 at 1:10:17 PM UTC-7, Dan Christensen wrote:
> On Wednesday, May 31, 2023 at 2:50:58 PM UTC-4, Ross Finlayson wrote: 
> > On Wednesday, May 31, 2023 at 8:39:03 AM UTC-7, Dan Christensen wrote: 
> > > On Wednesday, May 31, 2023 at 11:28:54 AM UTC-4, Ross Finlayson wrote: 
> > > > On Wednesday, May 31, 2023 at 8:21:19 AM UTC-7, Dan Christensen wrote: 
> > > > > On Wednesday, May 31, 2023 at 5:09:14 AM UTC-4, Mild Shock wrote: 
> > > > > 
> > > > > > Dan Christensens proof still uses a lot of double negation 
> > > > > > removal, is not constructive as it is presented currently: 
> > > > > > http://www.dcproof.com/UniversalSet.htm 
> > > > > Double negation removal is a legitimate method of proof accepted by the vast majority of mathematicians. Must be frustrating as hell for you, Mr. Collapse. (Hee, hee!) 
> > > > > Dan 
> > > > > 
> > > > > Download my DC Proof 2.0 freeware at http://www.dcproof.com 
> > > > > Visit my Math Blog at http://www.dcproof.wordpress.com 
> > > > So are a bunch of derivation rules in the contrapositive about 
> > > > implications, the direct variety: legitimate derivation rules, 
> > > > that applied to "material implications": result garbage. 
> > > > 
> > > A proof of said "garbage" would be nice, but I won't hold my breath.
> > Well it's simple, you apply the contrapositive to material implication, 
> > but don't know whether you're negating thusly what _was_ a true, 
> > or, ..., _wasn't_, a false, all vacuous. 
> >
> [snip] 
> 
> You are making no sense. 
> 
> 1. A => B 
> Premise 
> 
> 2. ~B 
> Premise 
> 
> 3. A 
> Premise 
> 
> 4. B 
> Detach, 1, 3 
> 
> 5. ~B & B 
> Join, 2, 4 
> 
> 6. ~A 
> Conclusion, 3 
> 
> 7. ~B => ~A 
> Conclusion, 2 
> 
> 8. A => B => [~B => ~A] 
> Conclusion, 1 
> 
> This result doesn't depend of the truth value of either A or B. What combination of truth values do you imagine would negate this result? Alternatively, which is the first invalid statement here and why.
> Dan 
> 
> Download my DC Proof 2.0 freeware at http://www.dcproof.com 
> Visit my Math Blog at http://www.dcproof.wordpress.com



I've been looking at it and what I need to figure out is about when a premise is discharged, 
how to build for it cases, because otherwise there's only one case.  I.e., a premise can be 
made multiple times, and has to be discharged each time.  The idea is that putting it in 
multiple orders, it gets discharged out various ways, or "last wins", and then the various 
ways together contradict each other.  (That ~A => B and ~A => ~B contradict each other, 
because B and ~B contradict each other.)

The other way is about the proof of "completeness", which allows the "vacuity", and basically 
looking into an "infinite inference", then for example about what happens when there is an 
infinite chain of inferences, how it would roll around contradicting itself.

...Then of course showing that with "direct implication" the resulting contradictions don't follow.

About the contrapositive and derivation rules, is that with direct implication (or here, 
just plain "implication", and only the affirmatory not the vacuous, vis-a-vis the causal 
and coincident), that (~A -> B) -> (~B -> A), but also that (~A -> ~B) -> (B -> A).  

A -> ~B --> B -> ~A
A -> B --> ~B -> ~A
~A -> ~B --> B -> A
~A -> B --> ~B -> A


Also there's the bit about "eliminate double negative" is just written in those.

About the vacuous, it's about as simple as having a set theory 
with no empty set (no empty domain of entailment), thus that 
the "monotonicity that makes the completeness that makes the 
sasisfiability", is kind of the same when everything's framed in the affirmatory.

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Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-30 15:05 -0700
  Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-30 15:14 -0700
    Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-30 15:57 -0700
    Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-30 18:45 -0700
      Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 01:42 -0700
        Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 01:55 -0700
          Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 02:09 -0700
            Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 08:21 -0700
              Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 08:28 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 08:39 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 11:50 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 11:58 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 13:10 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 21:12 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 21:35 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 11:43 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 12:40 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 12:54 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-01 14:24 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 14:55 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 15:18 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-03 08:31 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-03 09:10 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-02 08:19 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-02 11:20 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-03 08:27 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-03 08:31 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-03 13:53 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-03 13:57 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-03 14:04 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-03 14:13 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-04 07:47 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-04 08:26 -0700
                Re: Why is model theory needed? Mild Shock <janburse@fastmail.fm> - 2023-06-04 17:53 +0200
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-04 15:31 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:21 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:30 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:39 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-04 17:49 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-05 08:20 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-05 10:56 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-05 13:16 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-05 13:17 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:10 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 14:07 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-05 15:09 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-05 17:51 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-05 22:54 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-06 18:44 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-06 21:02 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-07 11:42 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-07 13:48 -0700
                Re: Why is model theory needed? Mild Shock <janburse@fastmail.fm> - 2023-06-07 23:43 +0200
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-08 12:14 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-08 12:19 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 10:54 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 10:54 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 11:35 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-09 11:53 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 11:58 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 15:27 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-09 11:59 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 15:27 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-06 18:43 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 05:18 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 05:20 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 10:53 -0700
                Re: Why is model theory needed? Mild Shock <janburse@fastmail.fm> - 2023-06-09 21:28 +0200
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 15:27 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 15:28 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 15:45 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 15:51 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-09 15:51 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-09 15:57 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 16:03 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 16:09 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-09 16:19 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-09 16:20 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 16:21 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 16:28 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-09 16:28 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-10 08:25 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-10 09:08 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-10 09:13 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-10 12:52 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-10 13:21 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-11 08:25 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-11 08:44 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-11 09:06 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-11 10:55 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-11 11:54 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-11 13:12 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-11 13:59 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-11 15:26 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-11 15:31 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-11 15:34 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-12 08:31 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 08:39 -0700
                Re: Why is model theory needed? Jeffrey Rubard <theleasthappyfella@gmail.com> - 2023-06-12 08:56 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-12 09:00 -0700
                Re: Why is model theory needed? Jeffrey Rubard <theleasthappyfella@gmail.com> - 2023-06-12 09:07 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 09:22 -0700
                Re: Why is model theory needed? Jeffrey Rubard <theleasthappyfella@gmail.com> - 2023-06-12 13:30 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-12 09:37 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 09:50 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-12 10:13 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 10:27 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 10:35 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 10:40 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 10:48 -0700
                Re: Why is model theory needed? Jeffrey Rubard <theleasthappyfella@gmail.com> - 2023-06-12 13:29 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-12 16:07 -0700
                Re: Why is model theory needed? Jeffrey Rubard <theleasthappyfella@gmail.com> - 2023-06-12 13:30 -0700
                Re: Why is model theory needed? Jeffrey Rubard <theleasthappyfella@gmail.com> - 2023-06-12 13:31 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-12 14:27 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-12 14:31 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-12 14:33 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-12 08:31 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-12 08:30 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-06-10 12:51 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-10 15:13 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-10 15:19 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-11 08:25 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-10 08:24 -0700
              Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 13:05 -0700
        Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 08:15 -0700
          Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 11:41 -0700
            Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 11:48 -0700
            Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 12:52 -0700
              Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 13:06 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 13:28 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-05-31 18:53 -0700
              Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:18 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 13:53 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 13:58 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 14:06 -0700
                Re: Why is model theory needed? Jeffrey Rubard <jeffreydanielrubard@gmail.com> - 2023-05-31 14:08 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 15:57 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-05-31 16:46 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-05-31 17:31 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 02:48 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 03:02 -0700
                Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-06-01 08:19 -0700
                Re: Why is model theory needed? Jeffrey Rubard <rehashedrubard@gmail.com> - 2023-06-01 08:42 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 07:07 -0700
                Re: Why is model theory needed? Dan Christensen <Dan_Christensen@sympatico.ca> - 2023-06-01 11:03 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 11:08 -0700
                Re: Why is model theory needed? Mild Shock <bursejan@gmail.com> - 2023-06-01 11:14 -0700

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