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Re: Why is model theory needed? [superb answer]

From André G. Isaak <agisaak@gm.invalid>
Newsgroups sci.logic
Subject Re: Why is model theory needed? [superb answer]
Date 2023-04-08 17:05 -0600
Organization Christians and Atheists United Against Creeping Agnosticism
Message-ID <u0srvd$1efjp$1@dont-email.me> (permalink)
References (2 earlier) <u0sksm$1cruv$3@dont-email.me> <u0sli8$1d9v3$1@dont-email.me> <u0sm0o$1cruv$5@dont-email.me> <u0smle$1dgq2$1@dont-email.me> <u0sr63$1e8u5$1@dont-email.me>

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On 2023-04-08 16:51, olcott wrote:
> On 4/8/2023 4:34 PM, André G. Isaak wrote:
>> On 2023-04-08 15:23, olcott wrote:
>>> On 4/8/2023 4:15 PM, André G. Isaak wrote:
>>>> On 2023-04-08 15:04, olcott wrote:
>>>>> On 4/8/2023 3:27 PM, André G. Isaak wrote:
>>>>>> On 2023-04-08 13:16, olcott wrote:
>>>>>>> Well-formed formulas have meaning only when an interpretation is 
>>>>>>> given
>>>>>>> for the symbols. Mendelson
>>>>>>>
>>>>>>> No one seems to know why model theory is needed.
>>>>>>> A ∧ B → A is known to be true on the basis of the meaning of the 
>>>>>>> symbols, no model theory needed.
>>>>>>>
>>>>>>
>>>>>> ((A ∧ B) → A) is a statement which is true in *all* models, so of 
>>>>>> course you don't need to specify the model. And this is properly 
>>>>>> true on the basis of the meaning of the *connectives*, not the 
>>>>>> meaning of the symbols themselves.
>>>>>>
>>>>>> ((A ∧ B) → A) can be evaluated without reference to the symbols A 
>>>>>> or B.
>>>>>>
>>>>>> The same cannot be said for (A ∧ B). How would you evaluate (A ∧ 
>>>>>> B) as true or false without some model?
>>>>>>
>>>>>> André
>>>>>>
>>>>>
>>>>> *That was a very superb answer*
>>>>> My reply is to handle (A ∧ B) exactly the way that the syllogism
>>>>> handles them thousands of years before anyone thought of model theory.
>>>>>
>>>>> Since we didn't need model theory to do this thousands of years ago 
>>>>> why
>>>>> do we need it now?
>>>>
>>>> And what do syllogisms have to do with this? How exactly do you 
>>>> evaluate (A ∧ B) in absence of a model using syllogisms?
>>>>
>>>> André
>>>>
>>>
>>> Syllogisms never allowed semantics to be removed from logic thus there
>>> is no need to put semantics back in.
>>
>> Apparently you have a very idiosyncratic definition of 'syllogism'.
>>
>>> With the syllogism referring to A and B without having already defined
>>> them is simply flatly wrong.
>>
>> Aristotelian logic (from which we get the term 'syllogism') explicitly 
>> deals with symbolic terms independent of their semantics. He defines 
>> which forms constitute valid syllogisms *without* reference to the 
>> meanings of the terms involved. That's the entire foundation of logic 
>> -- to focus on the *form* an argument takes rather than the meanings 
>> of the terms involved.
>>
>> You should probably stop using the term 'syllogism' until you've 
>> actually *read* the works of Aristotle and his successors.
>>
>> André
>>
> 
> Try and provide an example of a correct syllogism that lacks sufficient
> semantics to evaluate whether it is true or false.

All As are Bs.
X is an A.
Therefore X is a B.

That's a perfectly valid syllogism despite the fact that I have provided 
no semantics for either A, B, or X.

> Basic structure
> A categorical syllogism consists of three parts:
> 
> Major premise
> Minor premise
> Conclusion
> 
> Each part is a categorical proposition, and each categorical proposition 
> contains two categorical terms.[13] In Aristotle, each of the premises 
> is in the form "All A are B," "Some A are B", "No A are B" or "Some A 
> are not B", where "A" is one term and "B" is another:

And you'll note that neither 'A' nor 'B' are defined in the above, 
because they don't have to be as we are focusing on the form of 
arguments rather than their contents.


-- 
To email remove 'invalid' & replace 'gm' with well known Google mail 
service.

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Why is model theory needed? olcott <polcott2@gmail.com> - 2023-04-08 14:16 -0500
  Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-08 12:36 -0700
    Re: Why is model theory needed? olcott <polcott2@gmail.com> - 2023-04-08 14:40 -0500
      Re: Why is model theory needed? Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-08 12:51 -0700
  Re: Why is model theory needed? André G. Isaak <agisaak@gm.invalid> - 2023-04-08 14:27 -0600
    Re: Why is model theory needed? olcott <polcott2@gmail.com> - 2023-04-08 15:35 -0500
    Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 16:04 -0500
      Re: Why is model theory needed? [superb answer] André G. Isaak <agisaak@gm.invalid> - 2023-04-08 15:15 -0600
        Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 16:23 -0500
          Re: Why is model theory needed? [superb answer] André G. Isaak <agisaak@gm.invalid> - 2023-04-08 15:34 -0600
            Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 14:43 -0700
            Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 17:51 -0500
              Re: Why is model theory needed? [superb answer] André G. Isaak <agisaak@gm.invalid> - 2023-04-08 17:05 -0600
                Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 18:20 -0500
                Re: Why is model theory needed? [superb answer] André G. Isaak <agisaak@gm.invalid> - 2023-04-08 17:30 -0600
                Re: Why is model theory needed? [superb answer] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-08 16:35 -0700
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 16:45 -0700
                Re: Why is model theory needed? [superb answer] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-08 17:12 -0700
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 17:17 -0700
                Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 19:25 -0500
                Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 19:21 -0500
                Re: Why is model theory needed? [superb answer] André G. Isaak <agisaak@gm.invalid> - 2023-04-08 18:46 -0600
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 17:52 -0700
                Re: Why is model theory needed? [superb answer] André G. Isaak <agisaak@gm.invalid> - 2023-04-08 18:57 -0600
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 18:00 -0700
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 18:27 -0700
                Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 20:30 -0500
                Re: Why is model theory needed? [superb answer] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-08 19:12 -0700
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-09 02:41 -0700
                Re: Why is model theory needed? [superb answer] olcott <polcott2@gmail.com> - 2023-04-08 20:21 -0500
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 16:23 -0700
                Re: Why is model theory needed? [superb answer] Julio Di Egidio <julio@diegidio.name> - 2023-04-08 16:25 -0700
    Re: Why is model theory needed? [superb answer][model] olcott <polcott2@gmail.com> - 2023-04-11 08:54 -0500
  Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 03:30 -0700
  Re: Why is model theory needed? Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-09 07:01 -0700
    Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 07:56 -0700
      Re: Why is model theory needed? Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-09 08:22 -0700
        Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 10:15 -0700
          Re: Why is model theory needed? Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-09 19:16 -0700
            Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 23:40 -0700
              Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 00:02 -0700
                Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 01:05 -0700
                Re: Why is model theory needed? Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-10 04:59 -0700
                Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 08:59 -0700
                Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-10 09:11 -0700
                Re: Why is model theory needed? [true] olcott <polcott2@gmail.com> - 2023-04-10 11:50 -0500
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-11 00:20 -0700
                Re: Why is model theory needed? [true] olcott <polcott2@gmail.com> - 2023-04-11 08:00 -0500
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-11 10:21 -0700
                Re: Why is model theory needed? [true] olcott <polcott2@gmail.com> - 2023-04-11 12:36 -0500
                Re: Why is model theory needed? [true] olcott <polcott2@gmail.com> - 2023-04-11 12:39 -0500
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-11 11:26 -0700
                Re: Why is model theory needed? [true] olcott <polcott2@gmail.com> - 2023-04-11 13:34 -0500
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-11 11:37 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-11 21:19 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-11 22:49 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 08:36 +0200
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-11 23:47 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 00:29 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 16:15 +0200
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 07:49 -0700
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 07:51 -0700
                Re: Why is model theory needed? [true] [Montague Grammar] olcott <polcott2@gmail.com> - 2023-04-12 10:22 -0500
                Re: Why is model theory needed? [true] [Montague Grammar] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 10:02 -0700
                Re: Why is model theory needed? [true] [Montague Grammar] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 10:10 -0700
                Re: Why is model theory needed? [true] [Montague Grammar] olcott <polcott2@gmail.com> - 2023-04-12 13:21 -0500
                Re: Why is model theory needed? [true] [Montague Grammar] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-12 11:56 -0700
                Re: Why is model theory needed? [true] [Montague Grammar] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 11:59 -0700
                Re: Why is model theory needed? [true] [Montague Grammar] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-12 12:13 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 19:48 +0200
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 11:11 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 11:53 -0700
                Re: Why is model theory needed? [true] olcott <polcott2@gmail.com> - 2023-04-12 14:12 -0500
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 12:17 -0700
                Re: Why is model theory needed? [true] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-11 22:35 -0700
                Re: Why is model theory needed? [true] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-12 12:28 -0700
                Re: Why is model theory needed? [true] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 12:33 -0700
                Re: Why is model theory needed? [true] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-12 13:29 -0700
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 14:04 -0700
                Re: Why is model theory needed? [true] Mostowski Collapse <bursejan@gmail.com> - 2023-04-12 14:06 -0700
                Re: Why is model theory needed? [true] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-12 14:14 -0700
                Re: Why is model theory needed? [true] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-12 14:16 -0700
              Re: Why is model theory needed? Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-10 04:16 -0700
    Re: Why is model theory needed? olcott <polcott2@gmail.com> - 2023-04-09 10:01 -0500
      Re: Why is model theory needed? Mostowski Collapse <bursejan@gmail.com> - 2023-04-09 08:15 -0700
        Re: Why is model theory needed? olcott <polcott2@gmail.com> - 2023-04-09 10:18 -0500
      Re: Why is model theory needed? Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-09 17:51 -0700
        Re: Why is model theory needed? [truth v provability] olcott <polcott2@gmail.com> - 2023-04-10 13:12 -0500
          Re: Why is model theory needed? [truth v provability] Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-12 19:15 -0700
            Re: Why is model theory needed? [truth v provability] Julio Di Egidio <julio@diegidio.name> - 2023-04-12 19:34 -0700
            Re: Why is model theory needed? [truth v provability] olcott <polcott2@gmail.com> - 2023-04-12 22:40 -0500
              Re: Why is model theory needed? [truth v provability] Mitchell Smith <mitchellsmith0860@gmail.com> - 2023-04-13 19:44 -0700
                Re: Why is model theory needed? [truth v provability] olcott <polcott2@gmail.com> - 2023-04-13 22:29 -0500
                Re: Why is model theory needed? [truth v provability] Ross Finlayson <ross.a.finlayson@gmail.com> - 2023-04-14 11:17 -0700
                Re: Why is model theory needed? [truth v provability] olcott <polcott2@gmail.com> - 2023-04-15 13:43 -0500
            Re: Why is model theory needed? [truth v provability] olcott <polcott2@gmail.com> - 2023-04-15 23:22 -0500

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