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| From | Mild Shock <janburse@fastmail.fm> |
|---|---|
| Newsgroups | comp.theory, sci.logic |
| Subject | Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) |
| Date | 2024-07-24 23:54 +0200 |
| Message-ID | <v7rt7c$9vte$3@solani.org> (permalink) |
| References | (12 earlier) <v7p4mt$8bl4$1@solani.org> <v7ph81$1dv95$1@dont-email.me> <v7roel$9t9k$1@solani.org> <v7rp4t$1sv5t$1@dont-email.me> <v7rt6b$9vte$2@solani.org> |
Cross-posted to 2 groups.
This view of a logic is extremply powerful.
For example we can already define a property
of a logic. For example we could say a logic
L is consistent, if it doesn't explode, i.e.
if it doesn't prove anything, i.e. if there
exists a sentences with is not in the logic:
L consistent :<=> exists A (A e S & ~(A e L))
Or take page 18 of the BLACK BOOK by
Chagrov & Zakharyaschev, Modal Logic - 1997
https://global.oup.com/academic/product/modal-logic-9780198537793
L has disjunction property :<=>
(A v B e L <=> A e L v B e L)
Theorem: Classical logic does not have disjunction property
Proof: Classical logic has LEM, i.e. p v ~p e L,
but it is neither the case p e L nor ~p e L.
Q.E.D.
Mild Shock schrieb:
> But obviously sometimes sentences are
> decidable, and sometimes not. Since
> this depends on "True" and "L".
>
> Actually modern logic does it much simpler,
> you don't need to prescribe or explain what
> a "True" and "L" does, in that you repeat
>
> nonsense like for example:
>
> > A truth maker is any sequence of truth preserving operations
> > that links an expression x of language L to its semantic meaning
> > in language L. The lack of such a connection in L to x or ~x
> > means that x is not a truth-bearer in L.
>
> Its much much easier to define a "logic".
> You just take a language of sentences S.
> And define a "logic" L as a subset of S.
>
> You can imagine that L was defined as follows:
>
> L := { A e S | True(L, A) }
>
> But this is not necessarely the case how L is
> conceived, or how L comes into being.
>
> So a logic L is just a set of sentences. You
> don't need the notion truth maker or truth bearer
> at all, all you need to say you have some L ⊆ S.
>
> You can then study such L's. For example:
> - classical logic
> - intuitionistic logic
> - etc..
>
> olcott schrieb:
>> On 7/24/2024 3:33 PM, Mild Shock wrote:
>>> But truth bearer has another meaning.
>>> The more correct terminology is anyway
>>> truth maker, you have to shift away the
>>>
>>> focus from the formula and think it is
>>> a truth bearer, this is anyway wrong,
>>> since you have two additional parameters
>>> your "True" and your language "L".
>>>
>>> So all that we see here in expression such as:
>>>
>>> [~] True(L, [~] A)
>>>
>>> Is truth making, and not truth bearing.
>>> In recent years truth making has received
>>> some attention, there are interesting papers
>>> concerning truth makers. And it has
>>>
>>> even a SEP article:
>>>
>>> Truthmakers
>>> https://plato.stanford.edu/entries/truthmakers/
>>>
>>> A world of truthmakers?
>>> https://philipp.philosophie.ch/handouts/2005-5-5-truthmakers.pdf
>>>
>>> olcott schrieb:
>>>
>>>> The key difference is that we no long use the misnomer
>>>> "undecidable" sentence and instead call it for what it
>>>> really is an expression that is not a truth bearer, or
>>>> proposition in L.
>>
>> A truth-bearer is any expression of language that can
>> be true or false. Self-contradictory expressions are not
>> truth bearers.
>>
>>
>
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Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 11:42 -0500
""self contradictory"" (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-22 22:18 +0200
Re: ""self contradictory"" (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-22 15:32 -0500
Re: ""self contradictory"" (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-22 22:46 +0200
Re: ""self contradictory"" (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-22 22:49 +0200
Re: ""self contradictory"" (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-22 16:42 -0500
Re: ""self contradictory"" (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 00:49 +0200
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 20:01 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 19:11 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 20:17 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 19:44 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 21:42 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 21:12 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-22 22:56 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-22 23:07 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 07:30 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 09:55 -0500
Re: Analytic Truth-makers Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:57 +0200
"undecidable" / "unentscheidbar" (Was Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 23:02 +0200
Re: "undecidable" / "unentscheidbar" (Was Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 23:13 +0200
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 19:25 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 14:02 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-23 09:58 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:36 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-23 15:43 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:44 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-23 22:52 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-23 19:18 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-24 22:33 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) olcott <polcott333@gmail.com> - 2024-07-24 15:45 -0500
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-24 23:54 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Mild Shock <janburse@fastmail.fm> - 2024-07-24 23:54 +0200
Re: Gödel's Basic Logic Course at Notre Dame (Was: Analytic Truth-makers) Richard Damon <richard@damon-family.org> - 2024-07-24 19:57 -0400
Re: Analytic Truth-makers Wasell <wasell@example.com> - 2024-07-23 16:51 +0200
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 11:26 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 22:15 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 21:45 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 23:03 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 22:17 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-23 23:27 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-23 23:09 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-24 07:28 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-24 09:20 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-24 19:57 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-24 19:44 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-24 21:05 -0400
Re: Analytic Truth-makers olcott <polcott333@gmail.com> - 2024-07-25 09:12 -0500
Re: Analytic Truth-makers Richard Damon <richard@damon-family.org> - 2024-07-25 19:35 -0400
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