[PEIRCE-L] Re: Truth as Regulative or Real

[Jon Awbrey]

List,

Folks who were around a dozen years ago will remember all the fun and fuss we 
had when some rather absurd things about Peirce's theory of truth or the lack 
thereof popped up in various Wikipedious articles. Some of us eventually hashed 
out a fairly useful account of a Pragmatic Theory of Truth, at least IMHO.

Busy watching Goblet of Fire  for about the dozenth time now, where I am 
finding Rita Skeeter's theory of Alternative Truth especially poignant in view 
of current events, but I will dig up some old scraps of text later. 

Regards,

Jon

http://inquiryintoinquiry.com

> On Mar 9, 2017, at 5:17 PM, Jeffrey Brian Downard  
> wrote:
> 
> Jerry C., Jon S, List,
> 
> 
> With respect to the 13 items on the list. None is, taken by itself, a theory 
> of truth. Rather, they are statements made by a commentator on passages in 
> the published works and manuscripts, many of which are from different 
> contexts--and many of which seem to have been written by Peirce with 
> different purposes in mind. If we start with something more modest than a 
> theory, such as a definition of truth (verbal, logical or pragmatic), we can 
> see that Peirce was offering definitions of different senses of the 
> conception, and that the different senses were not wholly separate. Rather, 
> they are attempts to capture the meaning of conceptions pertaining to truth 
> where it functions as an ordinary end, and where it functions as a larger 
> ideal and where is taken as a relation between signs and objects, etc. Some 
> of these conceptions will be needed for the purpose of developing speculative 
> grammar, and others for the purpose of a critical logic and yet others for 
> the purpose of a methodeutic. Taken together, many if not most of the 
> statements Peirce has made about truth may turn out to be part of a larger 
> integrated semiotic theory. Others may turn out to be accounts of rival 
> conceptions of truth, or of ordinary notions, etc. As such, I suspect that 
> the 13 items can be sorted and organized, and some will turn out to be simply 
> false (e.g., 11).
> 
> 
> --Jeff
> 
> 
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354
> 
> 
>  
> From: Jon Alan Schmidt 
> Sent: Thursday, March 9, 2017 1:06 PM
> To: Jerry LR Chandler
> Cc: Peirce List
> Subject: Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and Boscovich 
> points.
>  
> Jerry C., List:
> 
> Almeder's 1985 Transactions article, "Peirce's Thirteen Theories of Truth," 
> does not spell out the list very clearly, but here is what I gather from the 
> text.
> Correspondence - "true propositions are simply the product of the destined 
> final opinion of the scientific community."
> Correspondence - truth is "an ideal limit of scientific progress, a limit 
> asymptotically approached (but never in fact reached) by successive advances 
> in scientific progress."
> Correspondence - "some propositions are true because they are what the 
> scientific community would endorse in the final opinion if the scientific 
> community were to continue inquiry forever."
> Coherence - "truth is simply what one gets when one's beliefs are verified or 
> fully authorized by standards of rationality proper to the scientific 
> community."
> Consensus - "similar to that ... adopted by Habermas and certain continental 
> hermeneuticists."
> Pragmatic - "the truth of a proposition is a function of whether it ... will 
> be asserted in the final opinion of the community," which is "destined as a 
> real product."
> Pragmatic - "the truth of a proposition is a function of whether it would be 
> ... asserted in the final opinion of the community," which is "approached as 
> an ideal limit."
> Pragmatic - "the truth of a proposition is a function of whether it ,,, would 
> continue to be endorsed were some final scientific opinion to emerge."
> Amalgam - "as if Peirce adopted some remarkably subtle theory that 
> consistently blends elements that are present every known theory of truth."
> Combination - "the meaning of 'true' is specified in terms of correspondence 
> while the conditions for applying the predicate are coherentist."
> Muddle - "Peirce's views on truth are basically incoherent or reflect 
> mutually inconsistent characterisations of the nature of truth."
> Received View - "whether Peirce defined truth in terms of correspondence or 
> coherence, he viewed truth as the product of the opinion that the scientific 
> community would ultimately reach were it to continue indefinitely long and 
> progressively in its research."
> Plausible View - "Peirce defined truth (with a capital T) as correspondence 
> and reckoned it the destined product the final opinion, and ... also defined 
> truth in terms of what are fully authorized in asserting under the current 
> standards of rationality and under the scientific method at any given moment."
> 

Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and Boscovich points.

[Jerry LR Chandler]

List:

In her book, Charles Peirces’s Pragmatic Pluralism, Rosenthal states:
… the literature on Peirce contains “no fewer than thirteen distinct 
interpretations of Peirce’s views on the nature of truth”, attributing the 
account to Robert Almeder.   

She apparently intends contrast CSP’s concept with the notions of 
correspondence and coherence.

(My source of this information is Google Books.)

Can anyone provide the putative listing of Almeter with the original text 
citations?

Cheers

Jerry



> On Mar 9, 2017, at 8:09 AM, John F Sowa  wrote:
> 
> Jerry, Clark, list,
> 
> In my response to Jeff B.D., I was defending the claim that board
> games are versions of mathematics.  But I definitely do *not* restrict
> math to board games or to set-theoretic models.
> 
> Jerry
>> Many mathematicians reject set theory as a foundation for mathematics
> 
> Yes. Peirce did and so do I. The four board games I cited illustrate
> diagrammatic reasoning.  But those diagrams use only discrete set
> theory.  Peirce also considered continuous diagrams, and so do I.
> I would also allow diagrams for any mathematical structures anyone
> might propose or discover -- including quantum-mechanical diagrams.
> 
 JFS
 Thanks for the reference.  On page 134, Béziau makes the
 following point, and Peirce would agree:
>>> JYB
>>> Universal logic is not a logic but a general theory of different
>>> logics.
>> Jerry
>> Analyze this quote. Is [JYB] saying anything more beyond
>> a contradiction of terms?
> 
> Peirce's semiotic is a general theory of all kinds of sign systems.
> Those systems include, as special cases, all natural languages and
> all versions of formal logic.  I agree with Montague that the
> underlying semantics of NLs and formal logics are essentially the
> same, but I would add that formal logics are weaker than NLs.
> 
> I interpreted JYB as saying that universal logic is a theory about
> logics in the same sense that CSP's semiotic is a theory about logics.
> But JYB's notion of universal logic is weaker than CSP's semiotic.
> 
>>> JYB
>>> This general theory is no more a logic itself than is
>>> meteorology a cloud.
>> Jerry
>> What the hell is this supposed to mean? Merely an ill-chosen metaphor?
> 
> My interpretation of JYB:  Universal logic is to any particular logic
> as meteorology is to clouds.
> 
> Jerry
>> Chemical isomers are not mathematical homomorphisms because of the
>> intrinsic nature of chemical identities. Thus, this reasoning is
>> not relevant to the composition of Boscovichian points.
> 
> I would not impose any restrictions on the kinds of diagrams or the
> mappings that define similarity.  If you can define a Boscovichian
> diagram for chemistry, I believe that Peirce's notion of diagrammatic
> reasoning could accommodate that diagram.
> 
> Implication:  Instead of defining a special kind of logic for every
> kind of subject matter, I would just change the kinds of diagrams
> -- quantum mechanical diagrams, Boscovichian diagrams, or whatever
> mathematical structures anyone might discover or imagine.
> 
> JLRC
>> Semiotics is not, in my view, a foundation for logic which is
>> grounded on antecedent and consequences.
> 
> That is a Fregean view of logic, not a Peircean view.  For his
> Begriffsschrift, Frege chose implication, negation, and the
> universal quantifier as his primitives.
> 
> For his algebraic logic, Peirce started with Boolean algebra and
> added quantifiers.  But he later switched to existential graphs.
> The early version distinguished Alpha (Boolean) from Beta (which
> added the line of identity).  But he later started with relational
> graphs (existence and conjunction) and added ovals for negation.
> 
> For beginning students, Boolean algebra is too abstract.  It just
> represents an NL sentence with a single letter like 'p'.  Peirce's
> relational graphs are a better starting point because they can be
> translated to and from actual NL sentences.  As a pedagogically
> sounder approach, I follow Peirce's later tutorials (circa 1909).
> See the first 25 slides of http://www.jfsowa.com/talks/egintro.pdf
> 
> Note slides 3 and 4 which come from Peirce's own intro in MS 145.
> In slide 8, I discuss one of CSP's examples that has a direct
> mapping to and from RDF -- the basic notation for the Semantic Web.
> 
> Many people believe RDF is a good starting point for logic.  I hate
> the RDF notation, but I use the comparison to show semantic webbers
> how a real logic can be defined on top of something like RDF.
> 
> Also note CSP's rules of inference (slide 25).  They are grounded
> in the need to preserve truth (as determined by endoporeutic).  And
> they apply equally well to Kamp's Discourse Representation Structures,
> which Kamp designed for NL semantics.
> 
> Note slide 31, which presents two *derived rules of inference*
> that are implied by the rules in slide 25.  These derived rules
> emphasize generalization and specialization.  I 

Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and Boscovich points.

[John F Sowa]

Jerry, Clark, list,

In my response to Jeff B.D., I was defending the claim that board
games are versions of mathematics.  But I definitely do *not* restrict
math to board games or to set-theoretic models.

Jerry

Many mathematicians reject set theory as a foundation for mathematics


Yes. Peirce did and so do I. The four board games I cited illustrate
diagrammatic reasoning.  But those diagrams use only discrete set
theory.  Peirce also considered continuous diagrams, and so do I.
I would also allow diagrams for any mathematical structures anyone
might propose or discover -- including quantum-mechanical diagrams.


JFS
Thanks for the reference.  On page 134, Béziau makes the
following point, and Peirce would agree:

JYB
Universal logic is not a logic but a general theory of different
logics.

Jerry
Analyze this quote. Is [JYB] saying anything more beyond
a contradiction of terms?


Peirce's semiotic is a general theory of all kinds of sign systems.
Those systems include, as special cases, all natural languages and
all versions of formal logic.  I agree with Montague that the
underlying semantics of NLs and formal logics are essentially the
same, but I would add that formal logics are weaker than NLs.

I interpreted JYB as saying that universal logic is a theory about
logics in the same sense that CSP's semiotic is a theory about logics.
But JYB's notion of universal logic is weaker than CSP's semiotic.


JYB
This general theory is no more a logic itself than is
meteorology a cloud.

Jerry
What the hell is this supposed to mean? Merely an ill-chosen metaphor?


My interpretation of JYB:  Universal logic is to any particular logic
as meteorology is to clouds.

Jerry

Chemical isomers are not mathematical homomorphisms because of the
intrinsic nature of chemical identities. Thus, this reasoning is
not relevant to the composition of Boscovichian points.


I would not impose any restrictions on the kinds of diagrams or the
mappings that define similarity.  If you can define a Boscovichian
diagram for chemistry, I believe that Peirce's notion of diagrammatic
reasoning could accommodate that diagram.

Implication:  Instead of defining a special kind of logic for every
kind of subject matter, I would just change the kinds of diagrams
-- quantum mechanical diagrams, Boscovichian diagrams, or whatever
mathematical structures anyone might discover or imagine.

JLRC

Semiotics is not, in my view, a foundation for logic which is
grounded on antecedent and consequences.


That is a Fregean view of logic, not a Peircean view.  For his
Begriffsschrift, Frege chose implication, negation, and the
universal quantifier as his primitives.

For his algebraic logic, Peirce started with Boolean algebra and
added quantifiers.  But he later switched to existential graphs.
The early version distinguished Alpha (Boolean) from Beta (which
added the line of identity).  But he later started with relational
graphs (existence and conjunction) and added ovals for negation.

For beginning students, Boolean algebra is too abstract.  It just
represents an NL sentence with a single letter like 'p'.  Peirce's
relational graphs are a better starting point because they can be
translated to and from actual NL sentences.  As a pedagogically
sounder approach, I follow Peirce's later tutorials (circa 1909).
See the first 25 slides of http://www.jfsowa.com/talks/egintro.pdf

Note slides 3 and 4 which come from Peirce's own intro in MS 145.
In slide 8, I discuss one of CSP's examples that has a direct
mapping to and from RDF -- the basic notation for the Semantic Web.

Many people believe RDF is a good starting point for logic.  I hate
the RDF notation, but I use the comparison to show semantic webbers
how a real logic can be defined on top of something like RDF.

Also note CSP's rules of inference (slide 25).  They are grounded
in the need to preserve truth (as determined by endoporeutic).  And
they apply equally well to Kamp's Discourse Representation Structures,
which Kamp designed for NL semantics.

Note slide 31, which presents two *derived rules of inference*
that are implied by the rules in slide 25.  These derived rules
emphasize generalization and specialization.  I believe that it is
more appropriate to say that logic is a theory of generalization
and specialization.  That includes implication as a special case
(p implies q iff p is more specialized than q).

There is much more to say, some of which I say in the slides
http://www.jfsowa.com/talks/ppe.pdf .  See slides 39 to 60.
In particular, note slide 59 about Turing oracles.

Clark

The problem with the game theoretical view of mathematics is
the question of realism.


I'm not sure what you mean by "game theoretical view".
There are three options, with some similarities among them:

 1. The idea that games like chess are mathematical systems.

 2. The point that Peirce's endoporeutic may be characterized
as an example of Hintikka's game theoretical semantics.

 3. Wittgenstein's