Path: ...!3.eu.feeder.erje.net!feeder.erje.net!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: Mild Shock <janburse@fastmail.fm>
Newsgroups: comp.theory,sci.logic
Subject: =?UTF-8?Q?Re:_G=c3=b6del's_Basic_Logic_Course_at_Notre_Dame_=28Was:?=
 =?UTF-8?Q?_Analytic_Truth-makers=29?=
Date: Wed, 24 Jul 2024 23:54:52 +0200
Message-ID: <v7rt7c$9vte$3@solani.org>
References: <v7m26d$nrr4$1@dont-email.me>
 <e41a2d324173031e1fe47acc0fd69b94b7aba55e@i2pn2.org>
 <v7msg0$sepk$1@dont-email.me>
 <3fb77583036a3c8b0db4b77610fb4bf4214c9c23@i2pn2.org>
 <v7much$sepk$2@dont-email.me>
 <9577ce80fd6c8a3d5dc37b880ce35a4d10d12a0e@i2pn2.org>
 <v7n3ho$t590$1@dont-email.me>
 <7d9b88425623e1166e358f1bce4c3a2767c36da0@i2pn2.org>
 <v7naae$120r5$1@dont-email.me> <v7o64d$7r0l$1@solani.org>
 <v7ogdr$17h8r$9@dont-email.me> <v7p499$8bb2$5@solani.org>
 <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>
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8; format=flowed
Content-Transfer-Encoding: 8bit
Injection-Date: Wed, 24 Jul 2024 21:54:52 -0000 (UTC)
Injection-Info: solani.org;
	logging-data="327598"; mail-complaints-to="abuse@news.solani.org"
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:91.0) Gecko/20100101
 Firefox/91.0 SeaMonkey/2.53.18.2
Cancel-Lock: sha1:ZQIduXcXnqmi55jIDTawqqLLcmk=
X-User-ID: eJwFwYEBwDAEBMCVSPzTcRD2H6F3uFS2G0HDYmPvMRRX61t0jH5WXZTwCefLyRjBKcVJ0PHiUl6nCHWrflU9FZM=
In-Reply-To: <v7rt6b$9vte$2@solani.org>
Bytes: 4790
Lines: 102

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.
>>
>>
>