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. 

[PEIRCE-L] Survey of Abduction, Deduction, Induction, Analogy, Inquiry

[Jon Awbrey]

Peircers,

Questions about the role of abductive hypothesis formation
in scientific inquiry have been coming up with increasing
frequency on the science side of the blogosphere lately,
so I started putting together a catablog of my previous
posts on the subject.

Survey of Abduction, Deduction, Induction, Analogy, Inquiry • 1
===

This is a Survey of blog and wiki posts on three elementary forms of
inference recognized by a logical tradition extending from Aristotle
through C.S. Peirce and how these inferential rudiments are combined
to compose the more complex patterns of analogy and inquiry.

[24 urls omitted from this email, see the following blog post]

http://inquiryintoinquiry.com/2017/03/08/survey-of-abduction-deduction-induction-analogy-inquiry-%e2%80%a2-1/

More to be added later ...

Regards,

Jon

--

inquiry into inquiry: https://inquiryintoinquiry.com/
academia: https://independent.academia.edu/JonAwbrey
oeiswiki: https://www.oeis.org/wiki/User:Jon_Awbrey
isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
facebook page: https://www.facebook.com/JonnyCache

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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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