Path: ...!weretis.net!feeder8.news.weretis.net!reader5.news.weretis.net!news.solani.org!.POSTED!not-for-mail From: Mild Shock Newsgroups: sci.logic,comp.theory Subject: Re: Truth Bearer or Truth Maker Date: Wed, 24 Jul 2024 23:52:54 +0200 Message-ID: References: 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: 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. >> >