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

[Jerry LR Chandler]

List, Jeff:

I concur with your elegantly phrased comments.

When I posted my request, I was hoping that the enumeration would be 
specifically indexed to textual references. So, I am a bit disappointed.

It would be nice mini-research project for an undergraduate student to collect 
CSP statements about truth with textual citations and post them online.  It 
would enhance the value of Almeder’s (incomplete) work.

Cheers

jerry


> On Mar 9, 2017, at 4:17 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."
> Almeder thinks that only #10, #11, and #13 "make any sense at all," and comes 
> out in favor of #13.
> 
> Regards,
> 
> Jon Alan Schmidt - Olathe, Kansas, USA
> 

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

[John F Sowa]

On 3/10/2017 8:57 AM, Jon Alan Schmidt wrote:

By contrast, Peirce's realism recognizes that "correspondence,
coherence, consensus, and instrumental reliability are all essential
and constitutive elements of truth--none is any more fundamental than
the others.  Moreover, each of these elements of truth is a necessary
condition for realizing the others.  Each one--properly understood and
fully explicated in accordance with the pragmatic maxim--implies the
others" (Paul Forster, p. 175).


Excellent point.

And by the way, Forster's book is good for what it does, but he always
compares Peirce to his predecessors or contemporaries.  In order to
understand the implications of CSP's work, it's essential to test
his ideas with the future -- both successes and failures.  Peirce
always insisted that the meaning of Thirdness is in the future.

For example, note that Rudolf Carnap, a good logician whose mind was
warped by Frege and Mach (hence logical positivism), refused to admit
Truth in his system.  But he finally admitted truth values, when Tarski
showed him the model-theoretic criterion.  But to the end of his life,
Carnap repeated Mach's claim that the laws of physics were nothing but
summaries of observations.

Historical studies are important, and Peirce studied the past more
than most of his contemporaries.  But it's important to confirm
his ideas by looking at successful applications -- *and* at major
failures caused by ignoring him.

The most spectacular failures were behaviorism and logical
positivism, which dominated a major part of the 20th century.
Quine didn't call himself a logical positivist, but he had
nothing better to offer.  Hao Wang, who earned a PhD with Quine,
called Q's philosophy "logical negativism".

Among their failures is the total absence of normative science
and value judgments.  They have nothing to say about the claims
"Greed is good" or "I'm OK. Pull up the gangplank."

John

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

[Clark Goble]

> On Mar 10, 2017, at 6:57 AM, Jon Alan Schmidt  
> wrote:
> 
> In chapter 8 of Peirce and the Threat of Nominalism, Paul Forster 
> argues--convincingly, I think--that the different "theories of truth" are 
> competitors only within  a nominalist epistemology and metaphysics.  By 
> contrast, Peirce's realism recognizes that "correspondence, coherence, 
> consensus, and instrumental reliability are all essential and constitutive 
> elements of truth--none is any more fundamental than the others.  Moreover, 
> each of these elements of truth is a necessary condition for realizing the 
> others.  Each one--properly understood and fully explicated in accordance 
> with the pragmatic maxim--implies the others" (p. 175).

I think the bigger issue is that correspondence presupposes an internalist 
scheme like Descartes or Kant and which tends to be presupposed in most 20th 
century approaches to epistemology which are still caught up in the methods of 
neo-Kantianism. If you adopt an externalist scheme like Peirce does then the 
very problem disappears. That’s why when I hear the word “correspondence” tied 
to Peirce (or Heidegger or any other number of 20th century figures who broke 
with internalism) I think that someone needs to clarify what they mean. If 
there’s no absolute inside or outside then the very need of correspondence, 
coherence and so forth disappears. Even the direct realism of say Scottish 
common sense philosophy becomes much more sensible without the echoes of the 
Cartesian division between mind and world in place.

We can talk about these things relative to Peirce, but almost always we’re 
speaking in terms of signs not minds. So correspondence is the relationship 
between an object conceived in a certain way and an interpretant conceived in a 
certain way. It’s useful for a certain type of analysis but isn’t the 
ontological problem it is in most philosophy.





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

[Jon Alan Schmidt]

Clark, Jeff, List:

In chapter 8 of *Peirce and the Threat of Nominalism*, Paul Forster
argues--convincingly, I think--that the different "theories of truth" are
competitors only within  a nominalist epistemology and metaphysics.  By
contrast, Peirce's realism recognizes that "correspondence, coherence,
consensus, and instrumental reliability are all essential and constitutive
elements of truth--none is any more fundamental than the others.  Moreover,
each of these elements of truth is a necessary condition for realizing the
others.  Each one--properly understood and fully explicated in accordance
with the pragmatic maxim--implies the others" (p. 175).

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Thu, Mar 9, 2017 at 5:42 PM, CLARK GOBLE  wrote:
>
> On Mar 9, 2017, at 3:17 PM, Jeffrey Brian Downard 
> wrote:
>
> 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.
>
> Exactly what I was going to point out. None of that really gets at a
> theory of truth. I agree completely.
>
> As John (Sowa) noted there are a lot of different issues at play here.
>

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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 

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

[John Collier]

I have thought of CSP as having much in common with the Common Sense 
philosophers. Their systematic scepticism in particular, and their emphasis on 
practical issues. The idea of atoms as we know not what exactly but small and 
localized and having properties that can interact with other properties seems 
rather Peircean to me. Open to further investigation.

I don’t know enough about what Peirce said about Boscovich. Pierce saw 
Boscovich as a precursor to argument by analogy, or hypothesis in note 1 of 
“Some Consequences of
Four Incapacities”, but there is nothing referring to atoms. However he did 
have much more to say, which I will come to below. Basically, Peirce was 
against atomistic combinations being explanatory, especially in biology

Atamspacker has a paper in which he mentions Peirce, but only with reference to 
abduction and semiotics, and also a paper referring to Boscovic (also about 
hypothesis) by Rὂssler, Otto E. (1991), ‘Boscovich covariance’, in Beyond 
Belief, ed. by J.L. Casti and A. Karlqvist (Boca Raton: CRC Press), pp. 65–87, 
which is an important paper. I can’t get access to the papers here at home, but 
Boscovician covariance championed by Rosseler more or less first my account, as 
I understand him. There is actually quite a bit of literature on the subject, 
but not lot in English. The covariance principle is a precursor to Einstein’s, 
and I think it tends to emphasize the extended field nature of Boscovician 
atoms rather than there point character. I see no problem with interpreting him 
as a field theorist rather than as an atomic theorist.

See also 
http://www.commens.org/encyclopedia/article/esposito-joseph-synechism-keystone-peirce%E2%80%99s-metaphysics,
 where Perice’s synechism is compared to Boscovic’s physics.  Here is an 
excerpt:

Atomism
“Synechism is incompatible with atomism at least in the sense in which atoms 
are regarded as irreducible and without parts. Another incompatibility would be 
that two atoms absolutely could not occupy the same space. They would be rigid 
bodies, to the extent that they were bodies, whose boundaries would mark a 
complete discontinuity with their surroundings. Peirce preferred to think of 
atoms the way his contemporaries regarded chemical compounds, as a system of 
components with an internal energy configuration: “Unless we are to give up the 
theory of energy, finite positional attractions and repulsions between 
molecules must be admitted. Absolute impenetrability would amount to an 
infinite repulsion at a certain distance. No analogy of known phenomena exists 
to excuse such a wanton violation of the principle of continuity as such a 
hypothesis is. In short, we are logically bound to adopt the Boscovichian idea 
that an atom is simply a distribution of component potential energy throughout 
space (this distribution being absolutely rigid) combined with inertia.” (CP 
6.242) (Boscovich, 1758)

Going on:

“A Boscovichian atom is a point of energy exerting a repulsive energy at 
approaching bodies, which is then turned into neutral and attractive force as 
the horizon of repulsive energy is breached. Ruggiero Giuseppe Boscovich, 
(1711-1787) was a Jesuit astronomer and mathematician and a precursor of the 
German Nature-Philosophers. He attempted to embed the laws of Newtonian physics 
into a simpler and more universal set of laws. Peirce appreciated the 
non-material and dynamic atomic model, but regarded the interaction of forces 
as more complex, as reflected in the differential equations that describe them: 
“But the equations of motion are differential equations of the second order, 
involving, therefore, two arbitrary constants for each moving atom or 
corpuscle, and there is no uniformity connected with these constants.” (CP 
6.101; 7.518) Forces are functions of space and time, and not of space alone, 
Peirce contended. Therefore, spatial configuration of two interacting bodies at 
any given time cannot be the basis for understanding subsequent configurations 
of those bodies. In the spirit of Boscovich, and of course Schelling and Hegel, 
Peirce wanted to reinterpret Newton’s laws using dynamic and relativistic terms:

… .one object being in one particular place in no way requires another object 
to be in any particular place. From this again it necessarily follows that each 
object occupies a single point of space, so that matter must consist of 
Boscovichian atomicules, whatever their multitude may be. On the same principle 
it furthermore follows that any law among the reactions must involve some other 
continuum than merely Space alone. Why Time should be that other continuum I 
shall hope to make clear when we come to consider Time. In the third place, 
since Space has the mode of being of a law, not that of a reacting existent, it 
follows that it cannot be the law that, in the absence of reaction, a particle 
shall adhere to its place; for that would be attributing to it an attraction 
for that place. 

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

[Jerry LR Chandler]

John:

CSP’s interpretation of Boscovich’ian atoms was unique to CSP, at least that is 
my reading. I could find the CSP text if it is a substantial issue. It was in a 
short note on the classification of the elements.
Note the dates of the two men.

Do you have a significant reason for introducing “Common Sense” philosophy into 
CSP’s view of “atoms”?  

Cheers
Jerry

> On Mar 8, 2017, at 9:41 PM, John Collier  wrote:
> 
> Interesting discussion, but one that bothers me a bit due to my reading of 
> Boscovic as an undergrad and my familiarity with the Scottish “Common Sense” 
> philosophers. 
>  
> My understanding of Boscovician atoms is that they are centres od force 
> fields that very in sign and intensity, being effective over varying 
> distances. The overall effect is a sinusoidal liker wave centred on the atom. 
> In this sense Boscovician atoms are not points, but have an extended scope, 
> which varies with distance. The point aspect stems from this filed being zero 
> at the centre, all the effects stemming from more distant fields centred on 
> the atom.
>  
> The Scottish Common Sense Philosophers, Like Thomas Young (usually classed as 
> an empiricist) took the view that we should treat a phenomena as it appears, 
> irrespective of its real nature, until we know more. In the Boscovician case 
> this would mean treating atoms as very small, but with the Boscovician field 
> properties, without reference to their smaller nature or their real 
> structure. Young, the wave theorist, was a follower of this school, and so 
> was, to some extent Maxwell.
>  
> So I think it is historically misleading to compare Boscovician atomism with 
> continuous views – I see no contradiction – much as the problem might be 
> interest in itself. I am more than a little reluctant to set up metaphysical 
> problems that aren’t supported by the science itself, and I think it requires 
> careful and unbiased historical study to ensure this is enforced.
>  
> John Collier
> Emeritus Professor and Senior Research Associate
> Philosophy, University of KwaZulu-Natal
> http://web.ncf.ca/collier 
>  
> From: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com] 
> Sent: Wednesday, 08 March 2017 6:51 PM
> To: Peirce List 
> Cc: Benjamin Udell ; Frederik Stjernfelt 
> ; Jeffrey Brian Downard ; Jeffrey 
> Goldstein ; Jon Alan Schmidt 
> ; Ahti-Veikko Pietarinen 
> ; John F Sowa 
> Subject: Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and Boscovich 
> points.
>  
> List, John:
> 
> I’m rather  pressed for time so only brief responses to your highly 
> provocative post. 
> Clearly, your philosophy of mathematics is pretty main stream relative to 
> mine.  But this is neither the time nor the place to develop these critical 
> differences.
> 
> My post was aimed directly at the problem of the logical composition of 
> Boscovich points.  This is inferred from CSP’s graphs and writings.
> I would ask that you describe your views on how to compose Boscovich points 
> into the chemical table of elements. Please keep in mind that each chemical 
> element represents logically a set of functors in the Carnapian sense. see: 
> p. 14, The Logical Syntax of Language.  
> 
> > On Mar 7, 2017, at 8:56 AM, John F Sowa  > > wrote:
> > 
> > Jerry,
> > 
> > We already have a universal foundation for logic.  It's called
> > "Peirce's semiotic”.
> 
> Semiotics is not, in my view, a foundation for logic which is grounded on 
> antecedent and consequences.
> Neither antecedents nor conclusions are intrinsic to the experience of signs 
> yet both are necessary for logic.  
> Logic is grounded in artificial symbols.  Applications of logic to the 
> natural world requires symbolic competencies appropriate to the 
> application(s).
> > 
> > JLRC
> >> the mathematics of the continuous can not be the same as the
> >> mathematics of the discrete. Nor can the mathematics of the
> >> discrete become the mathematics of the continuous.
> > 
> > They are all subsets of what mathematicians say in natural languages.
> 
> I reject this view of ‘subsets’ because of the mathematical physics of 
> electricity.
> Many mathematics reject set theory as a foundations for mathematics, 
> including such notables as S. Mac Lane (I discussed this personally with him 
> some decades ago.)  My belief is that numbers are the linguistic foundations 
> of mathematics and the physics of atomic numbers are the logical origin of 
> (macroscopic) matter and of the natural sciences. (Philosophical cosmology is 
> a different discourse.)
> 
> > 
> > For that matter, chess, go, and bridge are just as mathematical as
> > any other branch of mathematics.  They have different language games,
> > 

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

[John Collier]

Interesting discussion, but one that bothers me a bit due to my reading of 
Boscovic as an undergrad and my familiarity with the Scottish “Common Sense” 
philosophers.

My understanding of Boscovician atoms is that they are centres od force fields 
that very in sign and intensity, being effective over varying distances. The 
overall effect is a sinusoidal liker wave centred on the atom. In this sense 
Boscovician atoms are not points, but have an extended scope, which varies with 
distance. The point aspect stems from this filed being zero at the centre, all 
the effects stemming from more distant fields centred on the atom.

The Scottish Common Sense Philosophers, Like Thomas Young (usually classed as 
an empiricist) took the view that we should treat a phenomena as it appears, 
irrespective of its real nature, until we know more. In the Boscovician case 
this would mean treating atoms as very small, but with the Boscovician field 
properties, without reference to their smaller nature or their real structure. 
Young, the wave theorist, was a follower of this school, and so was, to some 
extent Maxwell.

So I think it is historically misleading to compare Boscovician atomism with 
continuous views – I see no contradiction – much as the problem might be 
interest in itself. I am more than a little reluctant to set up metaphysical 
problems that aren’t supported by the science itself, and I think it requires 
careful and unbiased historical study to ensure this is enforced.

John Collier
Emeritus Professor and Senior Research Associate
Philosophy, University of KwaZulu-Natal
http://web.ncf.ca/collier

From: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com]
Sent: Wednesday, 08 March 2017 6:51 PM
To: Peirce List 
Cc: Benjamin Udell ; Frederik Stjernfelt ; 
Jeffrey Brian Downard ; Jeffrey Goldstein 
; Jon Alan Schmidt ; 
Ahti-Veikko Pietarinen ; John F Sowa 

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

List, John:

I’m rather  pressed for time so only brief responses to your highly provocative 
post.
Clearly, your philosophy of mathematics is pretty main stream relative to mine. 
 But this is neither the time nor the place to develop these critical 
differences.

My post was aimed directly at the problem of the logical composition of 
Boscovich points.  This is inferred from CSP’s graphs and writings.
I would ask that you describe your views on how to compose Boscovich points 
into the chemical table of elements. Please keep in mind that each chemical 
element represents logically a set of functors in the Carnapian sense. see: p. 
14, The Logical Syntax of Language.

> On Mar 7, 2017, at 8:56 AM, John F Sowa 
> > wrote:
>
> Jerry,
>
> We already have a universal foundation for logic.  It's called
> "Peirce's semiotic”.

Semiotics is not, in my view, a foundation for logic which is grounded on 
antecedent and consequences.
Neither antecedents nor conclusions are intrinsic to the experience of signs 
yet both are necessary for logic.
Logic is grounded in artificial symbols.  Applications of logic to the natural 
world requires symbolic competencies appropriate to the application(s).
>
> JLRC
>> the mathematics of the continuous can not be the same as the
>> mathematics of the discrete. Nor can the mathematics of the
>> discrete become the mathematics of the continuous.
>
> They are all subsets of what mathematicians say in natural languages.

I reject this view of ‘subsets’ because of the mathematical physics of 
electricity.
Many mathematics reject set theory as a foundations for mathematics, including 
such notables as S. Mac Lane (I discussed this personally with him some decades 
ago.)  My belief is that numbers are the linguistic foundations of mathematics 
and the physics of atomic numbers are the logical origin of (macroscopic) 
matter and of the natural sciences. (Philosophical cosmology is a different 
discourse.)

>
> For that matter, chess, go, and bridge are just as mathematical as
> any other branch of mathematics.  They have different language games,
> but nobody worries about unifying them with algebra or topology.
>
Board games are super-duper simple relative to the mathematics of either 
chemistry and even more so wrt life itself.

> I believe that Richard Montague was half right:
>
> RM, Universal Grammar (1970).
>> There is in my opinion no important theoretical difference between
>> natural languages and the artificial languages of logicians; indeed,
>> I consider it possible to comprehend the syntax and semantics of
>> both kinds of languages within a single natural and mathematically
>> precise theory.

The logic of chemistry necessarily requires illations within sentences that 
logically connect both copula and 

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

[Clark Goble]

> On Mar 7, 2017, at 9:10 PM, John F Sowa  wrote:
> 
> On 3/7/2017 3:19 PM, Jeffrey Brian Downard wrote:
>> pure mathematics starts from a set of hypotheses of a particular sort,
>> and it does not seem obvious to me that these games are grounded
>> on such hypotheses.
> 
> More precisely, pure mathematics starts with axioms and definitions.
> A hypothesis is a starting point for a proof that also uses those
> axioms and definitions.
> 
> JBD
>> Peirce... uses tic-tac-toe in the Elements of Mathematics as
>> an example of how to take a kid's game, and then to examine it
>> in a mathematical spirit. Does this make the game a part of
>> mathematics?
> 
> It certainly does.  The axioms and definitions of tic-tac-toe
> can be stated in FOL.  From those axioms, you can prove various
> theorems.  For example, "From the usual starting position, if
> both players make the best moves at each turn, the game ends
> in a draw."

The problem with the game theoretical view of mathematics is the question of 
realism. This is why Godel made his argument about things not provable since he 
assumed they were true. While of course Wittgenstein’s model of language isn’t 
opposed to realism within mathematics there’s a difference between how we use 
the language of mathematics and what the objects of mathematics are. That is 
what are the relationship between the game and reality. 

Where this comes up is in semi-empirical methods such as Putnam suggested we 
apply to mathematics. As a practical matter there are unproven (and for all we 
know unprovable) mathematical theorems that are used as premises for other 
mathematical proofs. Perhaps this is still limited but I suspect it will 
accelerate in the future.

Again returning to language games of course while the notion can be abused a 
robust notion of language games is compatible with realism. But I think we have 
to think through carefully what sort of game we are playing if we’re going to 
use that as our metaphor.



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

[Jerry LR Chandler]

List, John:

I’m rather  pressed for time so only brief responses to your highly provocative 
post. 
Clearly, your philosophy of mathematics is pretty main stream relative to mine. 
 But this is neither the time nor the place to develop these critical 
differences.

My post was aimed directly at the problem of the logical composition of 
Boscovich points.  This is inferred from CSP’s graphs and writings.
I would ask that you describe your views on how to compose Boscovich points 
into the chemical table of elements. Please keep in mind that each chemical 
element represents logically a set of functors in the Carnapian sense. see: p. 
14, The Logical Syntax of Language.  

> On Mar 7, 2017, at 8:56 AM, John F Sowa  wrote:
> 
> Jerry,
> 
> We already have a universal foundation for logic.  It's called
> "Peirce's semiotic”.

Semiotics is not, in my view, a foundation for logic which is grounded on 
antecedent and consequences.
Neither antecedents nor conclusions are intrinsic to the experience of signs 
yet both are necessary for logic.  
Logic is grounded in artificial symbols.  Applications of logic to the natural 
world requires symbolic competencies appropriate to the application(s).
> 
> JLRC
>> the mathematics of the continuous can not be the same as the
>> mathematics of the discrete. Nor can the mathematics of the
>> discrete become the mathematics of the continuous.
> 
> They are all subsets of what mathematicians say in natural languages.

I reject this view of ‘subsets’ because of the mathematical physics of 
electricity.
Many mathematics reject set theory as a foundations for mathematics, including 
such notables as S. Mac Lane (I discussed this personally with him some decades 
ago.)  My belief is that numbers are the linguistic foundations of mathematics 
and the physics of atomic numbers are the logical origin of (macroscopic) 
matter and of the natural sciences. (Philosophical cosmology is a different 
discourse.)

> 
> For that matter, chess, go, and bridge are just as mathematical as
> any other branch of mathematics.  They have different language games,
> but nobody worries about unifying them with algebra or topology.
> 
Board games are super-duper simple relative to the mathematics of either 
chemistry and even more so wrt life itself. 

> I believe that Richard Montague was half right:
> 
> RM, Universal Grammar (1970).
>> There is in my opinion no important theoretical difference between
>> natural languages and the artificial languages of logicians; indeed,
>> I consider it possible to comprehend the syntax and semantics of
>> both kinds of languages within a single natural and mathematically
>> precise theory.

The logic of chemistry necessarily requires illations within sentences that 
logically connect both copula and predicates associated with electricity. This 
logical necessity is remote from the logic of the putative “universal 
grammars.”  (I presume that a balanced chemical equation is analogous to the 
concept of the term “sentence” in either normal language or mathematics.)
> 
> But Peirce would say that NL semantics is a more general version
> of semiotic.  Every version of formal logic is a disciplined subset
> of NL (ie, one of Wittgenstein's language games).


> JLRC
>> For a review of recent advances in logic, see
>> http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf,
>> 13 QUESTIONS ABOUT UNIVERSAL LOGIC.
> 
> Thanks for the reference.  On page 134, Béziau makes the following
> point, and Peirce would agree:
>> Universal logic is not a logic but a general theory of different
>> logics.

Analyze this quote.  Is he saying anything more beyond a contradiction of terms?

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

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

> 
> JYB, p. 137
>> we argue against any reduction of logic to algebra, since logical
>> structures are differing from algebraic ones and cannot be reduced
>> to them.  Universal logic is not universal algebra.
> 
> Peirce would agree.
> 
> JYB, 138
>> Universal logic takes the notion of structure as a starting
>> point; but what is a structure?
> 
> Peirce's answer:  a diagram.  Mathematics is necessary reasoning,
> and all necessary reasoning involves (1) constructing a diagram
> (the creative part) and (2) examining the diagram (observation
> supplemented with some routine computation).
> 
> What is a diagram?  Answer:  an icon that has some structural
> similarity (homomorphism) to the subject matter.

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. 
The reasoning behind chemical equations is not “necessary” in this sense of 
generality, but is always contingent on both the (iconic?) perplex numbers and 
the functors.
See, for example, Roberts, p. 22, 3.421.

> JYB, 145
>> Some wanted 

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

[John F Sowa]

On 3/8/2017 12:10 AM, Jeffrey Brian Downard wrote:

I'm trying to interpret Peirce's remarks about the importance
of stating the mathematical hypotheses of a system precisely
for the purpose of drawing conclusions with exactitude.


I certainly agree.  And the point I was trying to make is that
the *creative insight* comes first.  That is the discovery of
the diagram.  The diagram gives you *exactitude*.  Formalization
is a convenient notation -- and as Peirce noted, even algebra is
a linear diagram.

Note that tic-tac-toe, chess, go, bridge, and similar games
have very well defined diagrams.  The rules are usually stated
in natural languages, but they are (or can be) expressed with
as much precision as any system that is called mathematics.


That, I take it, is the kind of advance that was made by Euclid
and his predecessors in stating the postulates, definitions and
common notions with considerable (although still far from perfect)
precision.


I agree that Euclid's systematic treatment was an important
advance, and it stimulated a very active school in Alexandria.

But the Sumerians, Babylonians, and Egyptians had sophisticated
math for centuries before Pythagoras, who was a couple of
centuries before Euclid.

In fact, Plato was considered a better mathematician than
Aristotle, who was primarily a biologist.  But Aristotle's
systematic way of organizing and presenting his writings
inspired Euclid to organize his _Elements_.


The philosopher, on the other hand, must accept the vague
conceptions that are part and parcel of his inquiries--
warts and all.


All perception begins with vagueness.  Through experience,
certain aspects (icons) are distinguished as more important than
others.  Those are the things that are named.  Languages -- or
symbols in general -- "grow from icons".

Language is the great advantage of our species.  And mathematics
is just a systematic refinement of certain kinds of language games.
It didn't spring into existence with Euclid.  Scratches on bone
and monuments such as Stonehenge show that mathematics evolved
for millennia before Euclid.

The reason why philosophy is not as precise as physics is
that physicists have been studying the easy stuff -- things
that can be clearly distinguished, measured, and organized.
Quantum mechanics was a painful shock for many physicists.

John

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

[Jeffrey Brian Downard]

John S, List,

If my view of mathematics has been perverted, then the perversion wasn't caused 
by studying the works of the Bourbaki group (or something similar).  Rather, 
I'm trying to interpret Peirce's remarks about the importance of stating the 
mathematical hypotheses of a system precisely for the purpose of drawing 
conclusions with exactitude. That, I take it, is the kind of advance that was 
made by Euclid and his predecessors in stating the postulates, definitions and 
common notions with considerable (although still far from perfect) precision.

One of the great advantages, I take it, of working with mathematical hypotheses 
as opposed to philosophical conceptions is that the mathematician can make the 
hypotheses that serve as the starting points of the inquiries as clear as is 
needed. The philosopher, on the other hand, must accept the vague conceptions 
that are part and parcel of his inquiries--warts and all.

--Jeff






Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354

From: John F Sowa 
Sent: Tuesday, March 7, 2017 9:10 PM
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and Boscovich 
points.

On 3/7/2017 3:19 PM, Jeffrey Brian Downard wrote:
> pure mathematics starts from a set of hypotheses of a particular sort,
> and it does not seem obvious to me that these games are grounded
> on such hypotheses.

More precisely, pure mathematics starts with axioms and definitions.
A hypothesis is a starting point for a proof that also uses those
axioms and definitions.

JBD
> Peirce... uses tic-tac-toe in the Elements of Mathematics as
> an example of how to take a kid's game, and then to examine it
> in a mathematical spirit. Does this make the game a part of
> mathematics?

It certainly does.  The axioms and definitions of tic-tac-toe
can be stated in FOL.  From those axioms, you can prove various
theorems.  For example, "From the usual starting position, if
both players make the best moves at each turn, the game ends
in a draw."

The rules of chess, go, and bridge are also sufficiently precise
that they can be stated in FOL.  And the expert players of those
games have proved many theorems about them.  There is no definition
of pure mathematics that would exclude those four games (and many
others).

JBD
> What is more, the playing of those games does not need to a science
> that deduces theorems from hypotheses. They can be played on the
> basis of hunches, where the goal is simply to win and not to prove
> anything of a more general sort.

Of course.  That point is also true of arithmetic, geometry,
and other versions of mathematics.  Many people play games
with numbers and figures.  Do you remember the column on
mathematical games in the _Scientific American_?

For many years, that was a very popular feature by Martin Gardner.
In fact, I discovered Peirce's existential graphs from reading his
column in 1978.  Games are an excellent way to teach and learn math.

JBD
> Lacking an explicit statement of the hypotheses, we can only rely
> on unstated assumptions as unanalyzed common notions. Those will
> often suffice for practical purposes, but they won't suffice for
> developing mathematics as a pure science.

I suspect that your view of mathematics was perverted by studying the
Bourbaki (or something similar).  As remedial reading, I recommend
George Polya's books.  See the references and quotations in
http://www.jfsowa.com/talks/ppe.pdf

See below for an excerpt from slide 2 of ppe.pdf

John
__

“Mathematics — this may surprise or shock some — is never deductive
in its creation. The mathematician at work makes vague guesses,
visualizes broad generalizations, and jumps to unwarranted conclusions.
He arranges and rearranges his ideas, and becomes convinced of their
truth long before he can write down a logical proof... the deductive
stage, writing the results down, and writing its rigorous proof are
relatively trivial once the real insight arrives; it is more the
draftsman’s work not the architect’s.”

Paul Halmos (1968) Mathematics as a creative art,
_American Scientist_, vol. 56, pp. 375-389.
http://www-history.mcs.st-andrews.ac.uk/Extras/Creative_art.html

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

[John F Sowa]

On 3/7/2017 3:19 PM, Jeffrey Brian Downard wrote:

pure mathematics starts from a set of hypotheses of a particular sort,
and it does not seem obvious to me that these games are grounded
on such hypotheses.


More precisely, pure mathematics starts with axioms and definitions.
A hypothesis is a starting point for a proof that also uses those
axioms and definitions.

JBD

Peirce... uses tic-tac-toe in the Elements of Mathematics as
an example of how to take a kid's game, and then to examine it
in a mathematical spirit. Does this make the game a part of
mathematics?


It certainly does.  The axioms and definitions of tic-tac-toe
can be stated in FOL.  From those axioms, you can prove various
theorems.  For example, "From the usual starting position, if
both players make the best moves at each turn, the game ends
in a draw."

The rules of chess, go, and bridge are also sufficiently precise
that they can be stated in FOL.  And the expert players of those
games have proved many theorems about them.  There is no definition
of pure mathematics that would exclude those four games (and many
others).

JBD

What is more, the playing of those games does not need to a science
that deduces theorems from hypotheses. They can be played on the
basis of hunches, where the goal is simply to win and not to prove
anything of a more general sort.


Of course.  That point is also true of arithmetic, geometry,
and other versions of mathematics.  Many people play games
with numbers and figures.  Do you remember the column on
mathematical games in the _Scientific American_?

For many years, that was a very popular feature by Martin Gardner.
In fact, I discovered Peirce's existential graphs from reading his
column in 1978.  Games are an excellent way to teach and learn math.

JBD

Lacking an explicit statement of the hypotheses, we can only rely
on unstated assumptions as unanalyzed common notions. Those will
often suffice for practical purposes, but they won't suffice for
developing mathematics as a pure science.


I suspect that your view of mathematics was perverted by studying the
Bourbaki (or something similar).  As remedial reading, I recommend
George Polya's books.  See the references and quotations in
http://www.jfsowa.com/talks/ppe.pdf

See below for an excerpt from slide 2 of ppe.pdf

John
__

“Mathematics — this may surprise or shock some — is never deductive
in its creation. The mathematician at work makes vague guesses,
visualizes broad generalizations, and jumps to unwarranted conclusions.
He arranges and rearranges his ideas, and becomes convinced of their
truth long before he can write down a logical proof... the deductive
stage, writing the results down, and writing its rigorous proof are
relatively trivial once the real insight arrives; it is more the
draftsman’s work not the architect’s.”

Paul Halmos (1968) Mathematics as a creative art,
_American Scientist_, vol. 56, pp. 375-389.
http://www-history.mcs.st-andrews.ac.uk/Extras/Creative_art.html

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

[Jerry Rhee]

Dear list:



I think one can easily underestimate the possibilities of what one is doing
when one is playing games and potential consequences.



“The discussion of questions like these brings one face to face with
problems which offer as much intellectual challenge as quantum
indeterminacy or Bohr’s complementarity.  Theorists in general science have
staked out claims for a variety of fields in this area- games theory,
decision theory, systems theory, and the like.



It is not clear to the biologists wrestling with actual situations that
many of these “disciplines” amount to anything more than the formulation of
a lot of problems for which no solutions can be provided; there seems to be
a singular dearth of actually proved theorems which the biologists can take
over and employ.



Possibly the people who are trying to discover how to set up a computer to
learn to play good chess, or bridge, are among those most likely to make a
major contribution to the fundamental theory of evolution.”



~Conrad Waddington, Towards a Theoretical Biology, Nature, 1968

On Tue, Mar 7, 2017 at 2:19 PM, Jeffrey Brian Downard <
jeffrey.down...@nau.edu> wrote:

> Hi John S, List,
>
>
> You say:   For that matter, chess, go, and bridge are just as
> mathematical as
> any other branch of mathematics. They have different language games,
> but nobody worries about unifying them with algebra or topology.
>
> Peirce characterizes mathematics as a science in terms of the character
> of the hypotheses from which the inquiries proceed. He uses tic-tac-toe in
> the *Elements of Mathematics* as an example of how to take a kid's game,
> and then to examine it in a mathematical spirit. Does this make the game a
> part of mathematics? I would think not, for the simple reason that
> pure mathematics starts from a set of hypotheses of a particular sort , and
> it does not seem obvious to me that these games are grounded on such
> hypotheses. Those games could be studied in terms of such a formal system
> of hypotheses, but they need not be. What is more, the playing of those
> games does not need to a science that deduces theorems from hypotheses.
> They can be played on the basis of hunches, where the goal is simply to win
> and not to prove anything of a more general sort.
>
> Let's consider  a further example based on your own work involving
> the analysis of the geometric proofs in Euclid's Elements in terms of the
> Existential Graphs. One thing that seems to be essential to the proofs is
> the statement of the postulates as hypotheses. As such, the analysis of the
> arguments should start by the introduction of such postulates on the sheet
> of assertion--and then following the precepts articulated in the hypotheses
> as the diagrams are constructed. Lacking an explicit statement of the
> hypotheses, we can only rely on unstated assumptions as unanalyzed common
> notions. Those will often suffice for practical purposes, but they won't
> suffice for developing mathematics as a pure science. The scientific
> pursuit of such inquiries requires explicitly stated hypotheses, where all
> of the matter is removed from the conceptions and all that remains are the
> formal relations between the idealizations, otherwise it will not be
> possible to settle the question of whether or not specific
> conclusions follow deductively--much less build systems of theorems from
> such meager starting points.
>
>
> --Jeff
>
>
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354 <(928)%20523-8354>
>
>
> --
> *From:* Edwina Taborsky 
> *Sent:* Tuesday, March 7, 2017 8:54 AM
> *To:* Jerry LR Chandler; Peirce List; John F Sowa
> *Cc:* Benjamin Udell; Frederik Stjernfelt; Jeffrey Brian Downard; Jeffrey
> Goldstein; Jon Alan Schmidt; Ahti-Veikko Pietarinen
> *Subject:* Re: Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and
> Boscovich points.
>
>
>
> John Sowa - very nice outline of 'thinking', which is, as you say,
> diagrammatic.  And as you say, independent of any language or notation. The
> ability of the human species to 'symbolize', i.e., to transform that
> diagrammatic reasoning into symbols was certainly a massive evolutionary
> capacity. BUT, we must acknowledge that this transformation is just that, a
> transformation, and can mislead, mistransform from the one to the other.
> Then, we become rigid and 'stick to our words' and our 'symbolic meanings'
> and ignore the vitality of the diagram. I think that the triadic semiosis,
> with that mediative process, is a key factor in helping to prevent such
> rigidity.
>
> Edwina Taborsky
> --
> This message is virus free, protected by Primus - Canada's
> largest alternative telecommunications provider.
>
> http://www.primus.ca
>
> On Tue 07/03/17 9:56 AM , John F Sowa s...@bestweb.net sent:
>
> Jerry,
>
> We already have a universal foundation for logic. It's called
> "Peirce's 

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

[Jeffrey Brian Downard]

Hi John S, List,


You say:   For that matter, chess, go, and bridge are just as mathematical as

any other branch of mathematics. They have different language games,
but nobody worries about unifying them with algebra or topology.

Peirce characterizes mathematics as a science in terms of the character of the 
hypotheses from which the inquiries proceed. He uses tic-tac-toe in the 
Elements of Mathematics as an example of how to take a kid's game, and then to 
examine it in a mathematical spirit. Does this make the game a part of 
mathematics? I would think not, for the simple reason that pure mathematics 
starts from a set of hypotheses of a particular sort , and it does not seem 
obvious to me that these games are grounded on such hypotheses. Those games 
could be studied in terms of such a formal system of hypotheses, but they need 
not be. What is more, the playing of those games does not need to a science 
that deduces theorems from hypotheses. They can be played on the basis of 
hunches, where the goal is simply to win and not to prove anything of a more 
general sort.

Let's consider  a further example based on your own work involving the analysis 
of the geometric proofs in Euclid's Elements in terms of the Existential 
Graphs. One thing that seems to be essential to the proofs is the statement of 
the postulates as hypotheses. As such, the analysis of the arguments should 
start by the introduction of such postulates on the sheet of assertion--and 
then following the precepts articulated in the hypotheses as the diagrams are 
constructed. Lacking an explicit statement of the hypotheses, we can only rely 
on unstated assumptions as unanalyzed common notions. Those will often suffice 
for practical purposes, but they won't suffice for developing mathematics as a 
pure science. The scientific pursuit of such inquiries requires explicitly 
stated hypotheses, where all of the matter is removed from the conceptions and 
all that remains are the formal relations between the idealizations, otherwise 
it will not be possible to settle the question of whether or not specific 
conclusions follow deductively--much less build systems of theorems from such 
meager starting points.


--Jeff



Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354



From: Edwina Taborsky 
Sent: Tuesday, March 7, 2017 8:54 AM
To: Jerry LR Chandler; Peirce List; John F Sowa
Cc: Benjamin Udell; Frederik Stjernfelt; Jeffrey Brian Downard; Jeffrey 
Goldstein; Jon Alan Schmidt; Ahti-Veikko Pietarinen
Subject: Re: Re: [PEIRCE-L] Truth as Regulative or Real; Continuity and 
Boscovich points.


John Sowa - very nice outline of 'thinking', which is, as you say, 
diagrammatic.  And as you say, independent of any language or notation. The 
ability of the human species to 'symbolize', i.e., to transform that 
diagrammatic reasoning into symbols was certainly a massive evolutionary 
capacity. BUT, we must acknowledge that this transformation is just that, a 
transformation, and can mislead, mistransform from the one to the other. Then, 
we become rigid and 'stick to our words' and our 'symbolic meanings' and ignore 
the vitality of the diagram. I think that the triadic semiosis, with that 
mediative process, is a key factor in helping to prevent such rigidity.

Edwina Taborsky
--
This message is virus free, protected by Primus - Canada's
largest alternative telecommunications provider.

http://www.primus.ca

On Tue 07/03/17 9:56 AM , John F Sowa s...@bestweb.net sent:

Jerry,

We already have a universal foundation for logic. It's called
"Peirce's semiotic".

JLRC
> the mathematics of the continuous can not be the same as the
> mathematics of the discrete. Nor can the mathematics of the
> discrete become the mathematics of the continuous.

They are all subsets of what mathematicians say in natural languages.
In Wittgenstein's terms, they are "language games" that mathematicians
play with a subset of NL semantics. It's irrelevant whether they use
special symbols or words like 'set', 'integral', 'derivative' ...

For that matter, chess, go, and bridge are just as mathematical as
any other branch of mathematics. They have different language games,
but nobody worries about unifying them with algebra or topology.

I believe that Richard Montague was half right:

RM, Universal Grammar (1970).
> There is in my opinion no important theoretical difference between
> natural languages and the artificial languages of logicians; indeed,
> I consider it possible to comprehend the syntax and semantics of
> both kinds of languages within a single natural and mathematically
> precise theory.

But Peirce would say that NL semantics is a more general version
of semiotic. Every version of formal logic is a disciplined subset
of NL (ie, one of Wittgenstein's language games).

JLRC
> I am simply saying that the thought processes of the scientific
> community 

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

[Edwina Taborsky]

 

 BODY { font-family:Arial, Helvetica, sans-serif;font-size:12px; }
 John Sowa - very nice outline of 'thinking', which is, as you say,
diagrammatic.  And as you say, independent of any language or
notation. The ability of the human species to 'symbolize', i.e., to
transform that diagrammatic reasoning into symbols was certainly a
massive evolutionary capacity. BUT, we must acknowledge that this
transformation is just that, a transformation, and can mislead,
mistransform from the one to the other. Then, we become rigid and
'stick to our words' and our 'symbolic meanings' and ignore the
vitality of the diagram. I think that the triadic semiosis, with that
mediative process, is a key factor in helping to prevent such
rigidity.

Edwina Taborsky
 -- 
 This message is virus free, protected by Primus - Canada's 
 largest alternative telecommunications provider. 
 http://www.primus.ca 
 On Tue 07/03/17  9:56 AM , John F Sowa s...@bestweb.net sent:
 Jerry, 
 We already have a universal foundation for logic.  It's called 
 "Peirce's semiotic". 
 JLRC 
 > the mathematics of the continuous can not be the same as the 
 > mathematics of the discrete. Nor can the mathematics of the 
 > discrete become the mathematics of the continuous. 
 They are all subsets of what mathematicians say in natural
languages. 
 In Wittgenstein's terms, they are "language games" that
mathematicians 
 play with a subset of NL semantics.  It's irrelevant whether they
use 
 special symbols or words like 'set', 'integral', 'derivative' ... 
 For that matter, chess, go, and bridge are just as mathematical as 
 any other branch of mathematics.  They have different language
games, 
 but nobody worries about unifying them with algebra or topology. 
 I believe that Richard Montague was half right: 
 RM, Universal Grammar (1970). 
 > There is in my opinion no important theoretical difference between

 > natural languages and the artificial languages of logicians;
indeed, 
 > I consider it possible to comprehend the syntax and semantics of 
 > both kinds of languages within a single natural and mathematically

 > precise theory. 
 But Peirce would say that NL semantics is a more general version 
 of semiotic.  Every version of formal logic is a disciplined subset 
 of NL (ie, one of Wittgenstein's language games). 
 JLRC 
 > I am simply saying that the thought processes of the scientific 
 > community (and my thought processes) did not stop on April 19,
1914. 
 Peirce would certainly agree.  He said that building on the 
 foundations he laid "would be a labor for generations of analysts, 
 not for one" (MS 478).  The 20th c logicians who ignored Peirce were

 on the wrong track.  Many of them haven't yet reached the 14th c. 
 Peirce was far ahead of the 20th c because he did his homework. 
 JLRC 
 > For a review of recent advances in logic, see 
 > http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf [1], 
 > 13 QUESTIONS ABOUT UNIVERSAL LOGIC. 
 Thanks for the reference.  On page 134, Béziau makes the following 
 point, and Peirce would agree: 
 > Universal logic is not a logic but a general theory of different 
 > logics.  This general theory is no more a logic itself than is 
 > meteorology a cloud. 
 JYB, p. 137 
 > we argue against any reduction of logic to algebra, since logical 
 > structures are differing from algebraic ones and cannot be reduced

 > to them.  Universal logic is not universal algebra. 
 Peirce would agree. 
 JYB, 138 
 > Universal logic takes the notion of structure as a starting 
 > point; but what is a structure? 
 Peirce's answer:  a diagram.  Mathematics is necessary reasoning, 
 and all necessary reasoning involves (1) constructing a diagram 
 (the creative part) and (2) examining the diagram (observation 
 supplemented with some routine computation). 
 What is a diagram?  Answer:  an icon that has some structural 
 similarity (homomorphism) to the subject matter. 
 JYB, 138 
 > structuralism as we understand it is something still larger that 
 > includes linguistics, mathematics, psychology, and so on... 
 > what concerns us are not so much historical and  sociological 
 > considerations about the development of structuralism, but rather 
 > the issue of the ultimate view of structuralism as underlying 
 > mathematical structuralism and universal logic. 
 If you replace 'structuralism' with 'diagrammatic reasoning', 
 Peirce would agree. 
 JYB, 145 
 > Some wanted to go further and out of the formal framework, namely 
 > those working in informal logic or the theory of argumentation. 
 > The trouble is that one runs the risk of being tied up again in 
 > natural language. 
 See my comment above about Montague, Wittgenstein, and Peirce. 
 Universal logic (diagrammatic reasoning) is *independent of* any 
 language or notation.  The differences between the many variants 
 are the result of drawing different kinds of diagrams for sets, 
 continua, quantum mechanics, etc.  (Note Feynman diagrams.) 
 

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

[John F Sowa]

Jerry,

We already have a universal foundation for logic.  It's called
"Peirce's semiotic".

JLRC

the mathematics of the continuous can not be the same as the
mathematics of the discrete. Nor can the mathematics of the
discrete become the mathematics of the continuous.


They are all subsets of what mathematicians say in natural languages.
In Wittgenstein's terms, they are "language games" that mathematicians
play with a subset of NL semantics.  It's irrelevant whether they use
special symbols or words like 'set', 'integral', 'derivative' ...

For that matter, chess, go, and bridge are just as mathematical as
any other branch of mathematics.  They have different language games,
but nobody worries about unifying them with algebra or topology.

I believe that Richard Montague was half right:

RM, Universal Grammar (1970).

There is in my opinion no important theoretical difference between
natural languages and the artificial languages of logicians; indeed,
I consider it possible to comprehend the syntax and semantics of
both kinds of languages within a single natural and mathematically
precise theory.


But Peirce would say that NL semantics is a more general version
of semiotic.  Every version of formal logic is a disciplined subset
of NL (ie, one of Wittgenstein's language games).

JLRC

I am simply saying that the thought processes of the scientific
community (and my thought processes) did not stop on April 19, 1914.


Peirce would certainly agree.  He said that building on the
foundations he laid "would be a labor for generations of analysts,
not for one" (MS 478).  The 20th c logicians who ignored Peirce were
on the wrong track.  Many of them haven't yet reached the 14th c.
Peirce was far ahead of the 20th c because he did his homework.

JLRC

For a review of recent advances in logic, see
http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf,
13 QUESTIONS ABOUT UNIVERSAL LOGIC.


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

Universal logic is not a logic but a general theory of different
logics.  This general theory is no more a logic itself than is
meteorology a cloud.


JYB, p. 137

we argue against any reduction of logic to algebra, since logical
structures are differing from algebraic ones and cannot be reduced
to them.  Universal logic is not universal algebra.


Peirce would agree.

JYB, 138

Universal logic takes the notion of structure as a starting
point; but what is a structure?


Peirce's answer:  a diagram.  Mathematics is necessary reasoning,
and all necessary reasoning involves (1) constructing a diagram
(the creative part) and (2) examining the diagram (observation
supplemented with some routine computation).

What is a diagram?  Answer:  an icon that has some structural
similarity (homomorphism) to the subject matter.

JYB, 138

structuralism as we understand it is something still larger that
includes linguistics, mathematics, psychology, and so on...
what concerns us are not so much historical and  sociological
considerations about the development of structuralism, but rather
the issue of the ultimate view of structuralism as underlying
mathematical structuralism and universal logic.


If you replace 'structuralism' with 'diagrammatic reasoning',
Peirce would agree.

JYB, 145

Some wanted to go further and out of the formal framework, namely
those working in informal logic or the theory of argumentation.
The trouble is that one runs the risk of being tied up again in
natural language.


See my comment above about Montague, Wittgenstein, and Peirce.

Universal logic (diagrammatic reasoning) is *independent of* any
language or notation.  The differences between the many variants
are the result of drawing different kinds of diagrams for sets,
continua, quantum mechanics, etc.  (Note Feynman diagrams.)

Whatever the reasoning stuff may be, it would support NL-like
reasoning as a more general version of the 20th c kinds of logic.

I develop these points further in the following lecture on Peirce's
natural logic:  http://www.jfsowa.com/talks/natlogP.pdf

See also "Five questions on epistemic logic" and the references
cited there:  http://www.jfsowa.com/pubs/5qelogic.pdf

John

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

[Helmut Raulien]

 
 

Supplement:

Is there a crisis of systems theory, like I am feeling? If so, I have the hunch, that the reason for that is the blunt "Network" metaphor, whose wide use blocks the inquiry about structures, scales, continuity, processes, and so on. I feel, that the "Network" concept is normative in the way that it makes us think in a technocratic, instrumentalizing, neoliberalistic and digital way, and is wrong. But I want to exclude from this pre-critical feeling the use of the word "Network" by Norbert Elias, who, I think, uses it more elaborate, processural, and not so bluntly.




List,

I guess it might help to talk about time (and space) scales now, and about systems hierarchies with the sytems having different time (and space) scales. I think that synechism is connected to (Peircean) monism.

Eg. the dualism of mind and matter: Matter is effete mind. "Effete" is an unusual word for me (non-native speaker of English language), I think it means "weakened" or "exhausted". I would say, if something, some piece of mind, is exhausted, it goes slower, changes its time scale towards very slow.

With this slowliness, situations are conserved longer in their attractive states , meaning: Attractors (chaos theory) have a longer time of persistence, and it looks for faster (non-effete mind), as if there were discrete states countable with integer numbers.

I guess, that attractors are not like a trap, like once they occur, they remain forever, but that they remain only as long as a certain situation exists for them to keep them up.

So I think, that the obvious existence of discretenesses or integer numbers in nature is not a sign for dualism, but for the interaction of systems, positioned differently regarding their hierarchy towards each other, and their different time and space scales.

How all this is working and interacting exactly, would be interesting to argue about and to find out. I have the impression, that Peirce did not care much about this scale-problem, so I think that interdisciplinarity would be good. I think, that Stanley N. Salthe (Hi Stan!) might have something to contribute, and anybody occupied with systems theory, but I have the impression, that there nowadays is not much about systems theory, except when it is about psychological family-therapy or computing, which both I am not interested in. I rather am interested in natural sciences, like physics and biology (Why is the first plural, BTW, and the second singular? Non-native-speakers-question) and sociology.

Best,

Helmut

 

 04. März 2017 um 18:21 Uhr
 "Jerry LR Chandler"  wrote:
 


List, John:
 

 


On Mar 3, 2017, at 1:37 PM, Jon Alan Schmidt  wrote:
 

I am having a hard time following your thought process here,



Yes, you certainly do.  

 

And, I can identify several conjectures why this is the case.

 

At the top of the list of conjectures are the modes of explanation of abstract symbols.

 

Several symbolic competencies are reflected in CSP’s rumination, not just the usual literacy of alphabetic and perhaps mathematical symbols.

 

These multiple competencies and rule systems (legi-signs?) become entangled at the level of Bocovichian points.

 

At some point, one “must fish or cut bait” - that is, the mathematics of the continuous can not be the same as the mathematics of the discrete. Nor can the mathematics of the discrete become the mathematics of the continuous. 

 

The challenge to “modes of description” and “modes of explanation” that is common to all disciplines (including theology, metaphysics, mathematics, physics, chemistry, biology, medicine, the cognitive sciences and logic) must take this distinction into account.  

 

CSP refers to this as “representamen”.   Unfortunately, he omitted (as far as I am aware) the case where the sin-signs generated multiple symbol systems with different logics for each.  

(For a review of recent advances in logic, see; http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf, 

13 QUESTIONS ABOUT UNIVERSAL LOGIC.

 

In other words, I am simply saying that the thought processes of the scientific community (and my thought processes) did not stop on April 19, 1914. 

 

Cheers

 

Jerry

 

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

[Helmut Raulien]

List,

I guess it might help to talk about time (and space) scales now, and about systems hierarchies with the sytems having different time (and space) scales. I think that synechism is connected to (Peircean) monism.

Eg. the dualism of mind and matter: Matter is effete mind. "Effete" is an unusual word for me (non-native speaker of English language), I think it means "weakened" or "exhausted". I would say, if something, some piece of mind, is exhausted, it goes slower, changes its time scale towards very slow.

With this slowliness, situations are conserved longer in their attractive states , meaning: Attractors (chaos theory) have a longer time of persistence, and it looks for faster (non-effete mind), as if there were discrete states countable with integer numbers.

I guess, that attractors are not like a trap, like once they occur, they remain forever, but that they remain only as long as a certain situation exists for them to keep them up.

So I think, that the obvious existence of discretenesses or integer numbers in nature is not a sign for dualism, but for the interaction of systems, positioned differently regarding their hierarchy towards each other, and their different time and space scales.

How all this is working and interacting exactly, would be interesting to argue about and to find out. I have the impression, that Peirce did not care much about this scale-problem, so I think that interdisciplinarity would be good. I think, that Stanley N. Salthe (Hi Stan!) might have something to contribute, and anybody occupied with systems theory, but I have the impression, that there nowadays is not much about systems theory, except when it is about psychological family-therapy or computing, which both I am not interested in. I rather am interested in natural sciences, like physics and biology (Why is the first plural, BTW, and the second singular? Non-native-speakers-question) and sociology.

Best,

Helmut

 

 04. März 2017 um 18:21 Uhr
 "Jerry LR Chandler"  wrote:
 


List, John:
 

 


On Mar 3, 2017, at 1:37 PM, Jon Alan Schmidt  wrote:
 

I am having a hard time following your thought process here,



Yes, you certainly do.  

 

And, I can identify several conjectures why this is the case.

 

At the top of the list of conjectures are the modes of explanation of abstract symbols.

 

Several symbolic competencies are reflected in CSP’s rumination, not just the usual literacy of alphabetic and perhaps mathematical symbols.

 

These multiple competencies and rule systems (legi-signs?) become entangled at the level of Bocovichian points.

 

At some point, one “must fish or cut bait” - that is, the mathematics of the continuous can not be the same as the mathematics of the discrete. Nor can the mathematics of the discrete become the mathematics of the continuous. 

 

The challenge to “modes of description” and “modes of explanation” that is common to all disciplines (including theology, metaphysics, mathematics, physics, chemistry, biology, medicine, the cognitive sciences and logic) must take this distinction into account.  

 

CSP refers to this as “representamen”.   Unfortunately, he omitted (as far as I am aware) the case where the sin-signs generated multiple symbol systems with different logics for each.  

(For a review of recent advances in logic, see; http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf, 

13 QUESTIONS ABOUT UNIVERSAL LOGIC.

 

In other words, I am simply saying that the thought processes of the scientific community (and my thought processes) did not stop on April 19, 1914. 

 

Cheers

 

Jerry

 

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

[Jerry LR Chandler]

List, John:


> On Mar 3, 2017, at 1:37 PM, Jon Alan Schmidt  wrote:
> 
> I am having a hard time following your thought process here,

Yes, you certainly do.  

And, I can identify several conjectures why this is the case.

At the top of the list of conjectures are the modes of explanation of abstract 
symbols.

Several symbolic competencies are reflected in CSP’s rumination, not just the 
usual literacy of alphabetic and perhaps mathematical symbols.

These multiple competencies and rule systems (legi-signs?) become entangled at 
the level of Bocovichian points.

At some point, one “must fish or cut bait” - that is, the mathematics of the 
continuous can not be the same as the mathematics of the discrete. Nor can the 
mathematics of the discrete become the mathematics of the continuous. 

The challenge to “modes of description” and “modes of explanation” that is 
common to all disciplines (including theology, metaphysics, mathematics, 
physics, chemistry, biology, medicine, the cognitive sciences and logic) must 
take this distinction into account.  

CSP refers to this as “representamen”.   Unfortunately, he omitted (as far as I 
am aware) the case where the sin-signs generated multiple symbol systems with 
different logics for each.  
(For a review of recent advances in logic, see; 
http://www.jyb-logic.org/Universallogic13-bsl-sept.pdf, 
13 QUESTIONS ABOUT UNIVERSAL LOGIC.

In other words, I am simply saying that the thought processes of the scientific 
community (and my thought processes) did not stop on April 19, 1914. 

Cheers

Jerry



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

[Benjamin Udell]

Jerry, Jon S, list,

Jerry, you wrote,

   In MS 647, he compares a fact with "a chemical principle extracted
   therefrom by the power of Thought;”   That is, the notion of a fact
   is in the past tense.  It is completed and has an identity.  It is
   no longer is question about the nature of what happened during the
   occurrence.  Thus the separation from:  "in its Real existence it is
   inseparably combined with an infinite swarm of circumstances, which
   make no part of the Fact itself.”

Yes, there's something pastlike about facts, even supposed facts. The 
notion of fact seems to have a pastward perspective.


You continued,

   Now, compare this logical view of a chemical principle with the
   mathematical relation with the realism of matter in the synechism
   (EP1, 312-333.):

I'm not sure what comparison you were making. Your sentence above needs 
to be rewritten.


   Do you believe that CSP is asseerting that there exist two clear and
   distinctly different notions of mathematical points?
   That is, the Boscovichian points of discrete atoms as contrasted
   with the points of ”really continuous things, space, time and Law"?

   What would be an alternative hypothesis? That true continuity does
   not contain points?
   [End quote]

As far as I can tell from Web searches, a Boscovichian point is a point 
mass that can attract and repel. So, although it lacks shape, color, 
etc., it is still richer than a generic mathematical point. I suspect 
that Peirce would expect any point-particles that actually physically 
exist to be richer than generic mathematical points that one simply 
supposes in a physical continuum.


Peirce's general view is that a continuum _/has room for/_ points, or 
instants, or whatever kind of singularities, but, as Jon S. emphasizes, 
_/does not consist of/_ them, whether the given continuum is a 
mathematical hypothetical object or is physical. In Peirce's sense, one 
can say that a continuum "can contain" points, as long as one does not 
thereby mean that a continuum consists of points. (Sometimes it seems 
convenient to consider a line as a set of points, but I don't know 
whether Peirce was willing to do so even if just for convenience.)


You wrote,

   Would it be necessary for a legi-sign be something other than space
   and time because they would not be points??
   [End quote]

Legisigns aren't singular points but generals. Either way, they don't 
need to be outside of space and time (or some mathematical 
generalization of space and time), even in the case of a legisign that 
helps represent a mathematical point. Even a sign that is, itself, a 
singularity - some sort of extreme sinsign, I guess - does not need to 
be outside of space and time, since space and time can harbor it without 
being it (and other points). It's hard to think of sign, object, 
interpretant, semiosis, as quite outside of space and time. All thought 
is in signs because all thought takes time. Arguably mathematical 
objects at their most abstract are not spatio-temporal, and insofar as 
some serve as signs of others, those signs aren't spatio-temporal 
either. But our minds need to experiment diagrammatically with them in 
spacetime in order to learn anything about them. The idea that 
mathematical objects are anything more than the diagrammatic legisigns 
that represent them seems to require that those objects be more abstract 
than we can fully achieve. I.e., we seek to make the mathematical 
diagrammatic legisigns definite only in pertinent respects and vague in 
all others, but keep falling short, so to speak. Peirce in his section 
of "Truth and Falsity and Error," Baldwin's _Dictionary of Philosophy 
and Psychology_ v. 2, 1911, pages 718-720, reprinted in CP 5.565-573, 
see 567

http://www.gnusystems.ca/BaldwinPeirce.htm#Truth :

   These characters equally apply to pure mathematics. Projective
   geometry is not pure mathematics, unless it be recognized that
   whatever is said of rays holds good of every family of curves of
   which there is one and one only through any two points, and any two
   of which have a point in common. But even then it is not pure
   mathematics  until for points we put any complete determinations of
   any two-dimensional continuum. Nor will that be enough. A
   proposition is not a statement of perfectly pure mathematics until
   it is devoid of all definite meaning, and comes to this — that a
   property of a certain icon is pointed out and is declared to belong
   to anything like it, of which instances are given. The perfect truth
   cannot be stated, except in the sense that it confesses its
   imperfection. The pure mathematician deals exclusively with
   hypotheses. Whether or not there is any corresponding real thing, he
   does not care. His hypotheses are creatures of his own imagination;
   but he discovers in them relations which surprise him sometimes. A
   etaphysician may hold that this very forcing upon the
   mathematician's 

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

[Jon Alan Schmidt]

Jerry C., LIst:

Peirce makes it very clear elsewhere (and repeatedly) that a *true *continuum
does not contain *any *points or other definite, indivisible parts.  He
defines it as that which has *indefinite *parts, all of which have parts of
the same kind, such that it is *undivided* yet infinitely *divisible--*e.g.,
into infinitesimal lines rather than points.  Does that help at all?

Regards,

Jon Alan Schmidt - Olathe, Kansas, USA
Professional Engineer, Amateur Philosopher, Lutheran Layman
www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt

On Thu, Mar 2, 2017 at 5:59 PM, Jerry LR Chandler <
jerry_lr_chand...@icloud.com> wrote:

> List, Ben:
>
> Your recent posts contribute to a rather curious insight into CSP’s
> beliefs about the relationships between mathematics, chemistry and logic of
> scientific hypotheses.
>
> On Mar 2, 2017, at 10:58 AM, Benjamin Udell  wrote:
>
> from MS 647 (1910) which appeared in Sandra B. Rosenthal's 1994 book _Charles
> Peirce's Pragmatic Pluralism_:
>
> An Occurrence, which Thought analyzes into Things and Happenings, is
> necessarily Real; but it can never be known or even imagined in all its
> infinite detail. A Fact, on the other hand[,] is so much of the real
> Universe as can be represented in a Proposition, and instead of being, like
> an Occurrence, a slice of the Universe, it is rather to be compared to a
> chemical principle extracted therefrom by the power of Thought; and though
> it is, or may be Real, yet, in its Real existence it is inseparably
> combined with an infinite swarm of circumstances, which make no part of the
> Fact itself. It is impossible to thread our way through the Logical
> intricacies of being unless we keep these two things, the Occurrence and
> the Real Fact, sharply separate in our Thoughts. [Peirce, MS 647 (1910)]
>
> In that quote Peirce very clearly holds that not all will be known or can
> even be imagined.
>
> In MS 647, he compares a fact with "a chemical principle extracted
> therefrom by the power of Thought;”   That is, the notion of a fact is in
> the  past tense.  It is completed and has an identity.  It is no longer is
> question about the nature of what happened during the occurrence. Thus the
> separation from:  "in its Real existence it is inseparably combined with
> an infinite swarm of circumstances, which make no part of the Fact itself.
> ”
>
> Now, compare this logical view of a chemical principle with the
> mathematical relation with the realism of matter in the synechism (EP1,
> 312-333.):
>
> The things of this world, that seem so transitory to philosophers, are not
> continuous. They are composed of discrete atoms, no doubt *Boscovichian*
> * points (my
> emphasis)*. The really continuous things, Space, and Time, and Law, are
> eternal.”
>
> Do you believe that CSP is asseerting that there exist two clear and
> distinctly different notions of mathematical points?
> That is, the Boscovichian points of discrete atoms as contrasted with the
> points of ”really continuous things, space, time and Law"?
>
> What would be an alternative hypothesis? That true continuity does not
> contain points?
> Would it be necessary for a legi-sign be something other than space and
> time because they would not be points??
>
> Any ideas on the ontological status of Boscovichian points from your
> perspective of singularities?
>
> More precisely, what is the meaning of
>
> Synechism …  it is a regulative principle of logic, prescribing what sort
> of hypothesis is fit to be entertained and examined.??
>
> Is it possible that a “regulatory principle of logic” is a continuity in
> the sense of excluding Boscovichian points?
>
> Very confusing, to say the least.
>
> Cheers
>
> Jerry
>

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

[Jerry LR Chandler]

List, Ben:  

Your recent posts contribute to a rather curious insight into CSP’s beliefs 
about the relationships between mathematics, chemistry and logic of scientific 
hypotheses.

> On Mar 2, 2017, at 10:58 AM, Benjamin Udell  wrote:
> 
> from MS 647 (1910) which appeared in Sandra B. Rosenthal's 1994 book _Charles 
> Peirce's Pragmatic Pluralism_:
> 
> An Occurrence, which Thought analyzes into Things and Happenings, is 
> necessarily Real; but it can never be known or even imagined in all its 
> infinite detail. A Fact, on the other hand[,] is so much of the real Universe 
> as can be represented in a Proposition, and instead of being, like an 
> Occurrence, a slice of the Universe, it is rather to be compared to a 
> chemical principle extracted therefrom by the power of Thought; and though it 
> is, or may be Real, yet, in its Real existence it is inseparably combined 
> with an infinite swarm of circumstances, which make no part of the Fact 
> itself. It is impossible to thread our way through the Logical intricacies of 
> being unless we keep these two things, the Occurrence and the Real Fact, 
> sharply separate in our Thoughts. [Peirce, MS 647 (1910)]
> 
> In that quote Peirce very clearly holds that not all will be known or can 
> even be imagined.
> 
In MS 647, he compares a fact with "a chemical principle extracted therefrom by 
the power of Thought;”   That is, the notion of a fact is in the  past tense.  
It is completed and has an identity.  It is no longer is question about the 
nature of what happened during the occurrence. Thus the separation from:  "in 
its Real existence it is inseparably combined with an infinite swarm of 
circumstances, which make no part of the Fact itself.”

Now, compare this logical view of a chemical principle with the mathematical 
relation with the realism of matter in the synechism (EP1, 312-333.):

The things of this world, that seem so transitory to philosophers, are not 
continuous. They are composed of discrete atoms, no doubt Boscovichian 
 points (my emphasis). 
The really continuous things, Space, and Time, and Law, are eternal.”

Do you believe that CSP is asseerting that there exist two clear and distinctly 
different notions of mathematical points?
That is, the Boscovichian points of discrete atoms as contrasted with the 
points of ”really continuous things, space, time and Law"?

What would be an alternative hypothesis? That true continuity does not contain 
points?
Would it be necessary for a legi-sign be something other than space and time 
because they would not be points?? 

Any ideas on the ontological status of Boscovichian points from your 
perspective of singularities?

More precisely, what is the meaning of

Synechism …  it is a regulative principle of logic, prescribing what sort of 
hypothesis is fit to be entertained and examined.??


Is it possible that a “regulatory principle of logic” is a continuity in the 
sense of excluding Boscovichian points?

Very confusing, to say the least. 

Cheers

Jerry
 

 



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