Path: ...!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail
From: Mild Shock <janburse@fastmail.fm>
Newsgroups: sci.logic,comp.theory
Subject: Re: Truth Bearer or Truth Maker
Date: Wed, 24 Jul 2024 23:52:54 +0200
Message-ID: <v7rt3n$9vte$1@solani.org>
References: <v7rohj$9t9k$2@solani.org> <v7rpra$1sv5t$2@dont-email.me>
 <v7rsko$9vkk$1@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 21:52:55 -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:OaTEckl4CyoO47gRFddGmNektZY=
In-Reply-To: <v7rsko$9vkk$1@solani.org>
X-User-ID: eJwFwYEBwDAEBMCVJPGPcSj2H6F3eDz8TAkqFhskU109ZxoRW/1Sxcx9EZZtk3V6LldGYvQWvBdtbB3xH1yMFe8=
Bytes: 4693
Lines: 115


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 3:34 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/
>>>
>>
>> Because the received view has never gotten past Quine's
>> nonsense rebuttal of the analytic synthetic distinction
>> no other expert on truth-maker theory made much progress.
>>
>> {true on the basis of meaning expressed in language}
>> conquers any of Quine's gibberish.
>>
>> 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.
>>
>>> A world of truthmakers?
>>> https://philipp.philosophie.ch/handouts/2005-5-5-truthmakers.pdf
>>>
>>
>> This seems at least reasonably plausible yet deals with things besides
>> {true on the basis of meaning expressed in language}
>>
>>> 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.
>>
>