Re: [PEIRCE-L] Modal Logic and Pragmaticism

[Jon Alan Schmidt]

List:

In 1903, Peirce introduced broken cuts signifying possible falsity in the
Gamma part of Existential Graphs (EG). By 1906, they had evolved into
various tinctures within ordinary cuts for different kinds of possibility,
actuality, and intention. However, in 1911, he definitively abandoned that
approach in favor of simply shading oddly enclosed areas to distinguish
them from evenly enclosed areas and stated, "I shall now have to add a
*Delta *part in order to deal with modals" (RL 376, R 500:3). A 1909 Logic
Notebook entry (
https://list.iupui.edu/sympa/arc/peirce-l/2022-05/msg0/jpgz4WTat3_Ee.jpg,
R 339:509[340r]) might be what he had in mind, showing five graphs in which
a heavy line of compossibility (LoC, my term) denotes some possible state
of things (PST) where each proposition represented by a letter attached to
it would be true.

Implementing a formal system of modal logic with this notation is a matter
of working out the appropriate transformation rules associated with LoCs,
for which Peirce does not offer any guidance. They are presumably similar
to what he establishes for lines of identity in Beta EG, but not identical
because an LoC crossing a boundary between different areas denotes some PST
where the entire graph within that boundary would be false, like a broken
cut in Gamma EG. Accordingly, any such LoC is always attached to all the
letters enclosed by the outermost boundary that it crosses, branching in
any area with more than one subgraph. Iterated modalities correspond to
multiple LoCs attached to the same letter(s) and interpreted from the
outside inward (*endoporeutically*) as "possibly" for each LoC and "not"
for each boundary.

With these conventions, the only axiom for Delta EG besides the blank sheet
signifying tautology is the unattached LoC. It may be added or removed in
any area, signifying "there is some PST where tautology would be true," or
placed across the inner boundary of an otherwise empty scroll, signifying
"there is no PST where tautology would be false." Peirce's Alpha EG
permissions are maintained for individual subgraphs consisting of letters
with or without shading and/or attached LoCs, except that they may not be
iterated/deiterated through boundaries crossed only by other LoCs. His
Gamma permissions for converting solid cuts into broken cuts and vice-versa
correspond to the characteristic axiom of system T, which (best I can tell)
Delta EG implements with the following permissions.

1. Erasure - Any unshaded LoC may be broken, and any resulting loose end of
an LoC extending into that area from the surrounding shaded area must be
retracted outward across the boundary.
2. Insertion - Any shaded LoCs not already attached to the same letter may
be joined to each other, and any LoC in the surrounding unshaded area may
be extended inward across the boundary to be so joined.
3. Iteration/Deiteration - Any subgraph attached to an LoC may be
duplicated on another branch of the same LoC in the same area or a more
enclosed area, and any such duplicate subgraph may be removed.
4. Scrolling - A ring-shaped area, containing only LoCs that cross both its
boundaries, may be added or removed around any subgraph in any area.
5. Attachment - An unshaded LoC may be added to any individual subgraph or
simultaneously to multiple subgraphs in the same area.
6. Release - Any LoC whose outermost portion is shaded may be removed
simultaneously from every subgraph to which it is attached.


Moreover, although Peirce includes a few Gamma graphs with nested broken
cuts in R S-1, his Logic Notebook graphs with LoCs are all of modal degree
one. Taking this as another hint, Delta EG implements "basic modal
logic"--the system that I advocate renaming P for Pollock, Parry, Peirce,
and pragmaticism (
https://list.iupui.edu/sympa/arc/peirce-l/2022-04/msg00013.html)--with all
these permissions plus the restriction that no letter may be attached to
more than one LoC. On the other hand, appending the following permissions
instead implements S4.

7a. Iteration/Deiteration - Any LoC may be duplicated with another LoC
attached to all the same letters and crossing all the same boundaries, and
any such duplicate LoC may be removed.


Replacing these with the following permissions implements S5.

7b. Equivalence - A shaded LoC may be added to any subgraph with at least
one LoC, and an unshaded LoC not otherwise attached may be removed from any
subgraph unless it is the innermost LoC attached to it.


In a previous post (below), I listed several advantages of Delta EG with
LoCs over Gamma EG with broken cuts. Another is the ability to implement T
with strictly diagrammatic permissions and restrictions, as well as even
weaker systems such as D by omitting #5-6 or K by also further restricting
#1-2. By contrast, Ma Minghui and Ahti-Veikko Pietarinen treat Gamma EG as
merely an alternative notation in which the appropriate modal axioms and
inference rules can be stipulated (
https://www.researchgate.net

Re: [PEIRCE-L] Modal Logic and Pragmaticism

[Jon Alan Schmidt]

List:

There are numerous formal systems of modal logic, which are differentiated
by which axioms and inference rules they add to classical logic. The
attached diagram shows the most discussed ones, arranged from weakest
(left) to strongest (right) and showing how they are contained within each
other. As indicated, those in the bottom row treat only classical
tautologies and (for S1-S3) their added modal axioms as necessarily true,
while the others extend this to all their theorems; in fact, that is the
sole difference between S0.5 and T (sometimes called M). C. I. Lewis
introduced S1-S5, and the two strongest of these are now generally
considered to be the "best" for most purposes, as John P. Burgess observes.

JPB: The question Which is the right validity logic? has been answered at
the sentential level, which is the only level that will be considered here:
it is the system known as *S5*. This result is essentially established
already in Carnap (1946).
The question Which is the right demonstrability logic? goes back to the
earliest days of modern modal logic. ... To the extent that there is any
consensus or plurality view among logicians today, I take the view to be
that the right demonstrability logic is *S4*. (
https://doi.org/10.1305/ndjfl/1039096306, 1999, p. 82)


On the other hand, John L. Pollock proposes a "Basic Modal Logic" and calls
it B, although it is very different from the system named B after L. E. J.
Brouwer and shown in the attachment as containing T and contained in S5 but
independent of S4. Pollock's approach is to eliminate all "iterated"
modalities, which correspond to compounded expressions like "possibly
possible" and "necessarily possibly necessary." He describes his motivation
and results as follows (https://www.jstor.org/stable/2270778, 1967).

JLP: [W]hen philosophers and logicians *apply* modal logic to concrete
problems, they rarely need principles which involve iterated modalities.
For most practical purposes, principles involving only one layer of
modalities are all that are needed. This suggests that if we try to
construct a theory of modal logic in which there are no iterated
modalities, we can avoid most of the controversy and still have a theory
that is strong enough for all of the normal uses to which modal logic is
put. (p. 355)

JLP: [A]ll of the controversy over which theory of propositional modal
logic is correct stems from disagreement about principles involving
iterated modalities. S1-S5 and M[=T] are the most common theories of
propositional modal logic, and ... we see that they all give exactly the
same theorems not involving iterated modalities. Thus there is a very real
sense in which B is *basic* modal logic. B gives us the core theorems that
everyone accepts. (p. 363)


Jean Porte summarizes, "Indeed, *S1-S5* and Feys' *T* all have the same
theses of modal degree at most one and, among the systems which have this
property, *S5* is the strongest, and *S0.5* is the weakest" (
https://doi.org/10.1305/ndjfl/1093883250, 1980, p. 672). In other words,
all theorems of S5 in which no propositional variable is within the scope
of more than one modal operator, which together comprise Pollock's B, are
also theorems of S0.5-S4 and T, as well as the Brouwer-inspired B.
Moreover, "A formula of modal order greater than one is a thesis of S0.5 if
and only if it is a substitution instance of a first-order thesis" (p. 675).

Accordingly, Pollock's B matches E. J. Lemmon's original specification for
S0.5 (https://www.jstor.org/stable/2964179, 1957, pp. 180-181), except that
such substitution is precluded. Lemmon even anticipates this in a footnote,
referencing William T. Parry's brief suggestion of the same idea, which he
calls S.1 (https://www.jstor.org/stable/2266559, 1953, p. 328). As
indicated in the attachment, without such a limitation, infinitely many
higher-degree modalities are irreducible in all the systems shown except
S3-S5. Even in S3 and S4, there are 42 and 14 non-equivalent modalities,
respectively.

By contrast, as G. E. Hughes and M. J. Cresswell point out, "Every formula
of higher than first degree is reducible in S5 to a first-degree formula."
They go on to present "an effective procedure for reducing any wff of
higher than first degree to one of first degree by equivalence
transformations" (
http://www.stoqatpul.org/lat/materials/huges_cresswell_modal_logic.pdf, 1996,
pp. 98-101). Jean-Louis Gardies adds, "Due to this, every thesis of S5 may
be related to a thesis being its translation in [Pollock's] B," although
"different theses of S5 may have the same corresponding thesis of the first
modal degree" (
https://filozof.uni.lodz.pl/~filozof/wp-content/uploads/logicatr/Gardies2.pdf,
1998, p. 32).

Personally, I find this very appealing. After all, what does it mean to
assert, "There is some possible state of things where there would be some
possible state of things where the proposition A would be true"? Why and
how is it different from merely asserting, "

re: [PEIRCE-L] Modal Logic and Pragmaticism

[John F Sowa]

Jon,

Your recent note reminded me of one I had started in reply to one of yours on 
April 9th. But I got distracted by miscellaneous details, such as income tax. 
So I finished the earlier note and include it here.

I have much more to say about modal logic, but I'll save that for another note. 
 For a quick overview, see the 6-page article on "Five Questions on Epistemic 
Logic", http://jfsowa.com/pubs/5qelogic.pdf .  For more, see "Worlds, Models, 
and Descriptions" http://jfsowa.com/pubs/worlds.pdf .  Both articles relate the 
discussions of 21st century methods to pioneering work by Peirce.

John

--

JAS: According to Peirce, classical logic as implemented using the Alpha 
(propositional) and Beta (first-order predicate) parts of his Existential 
Graphs (EG) is applicable only to a universe of discourse that is definite, 
individual, and real.

Important point: Peirce's writings are precise. A single word or phrase, if 
omitted or ignored, may distort or even reverse the meaning of the whole. In 
the following quotation, the words creator and fictive are critical.

CSP: The sheet on which the graphs are written (called the sheet of assertion), 
as well as each portion of it, is a graph asserting that a recognized universe 
is definite (so that no assertion can be both true and false of it), individual 
(so that any assertion is either true or false of it), and real (so that what 
is true or false of it is independent of any judgment of man or men, unless it 
be that of the creator of the universe, in case this is fictive); any graph 
written upon this sheet is thereby asserted of that universe; and any multitude 
of graphs written disconnectedly upon the sheet are all asserted of the 
universe. (R 491:29, 1903)

In the same year, Peirce defined fictive: "For the fictive is that whose 
characters depend upon what characters somebody attributes to it" (EP2:209). 
That is true of every theory of pure mathematics. Its creator is the 
mathematician who specifies the axioms.

When mathematics is applied to physical reality, the fictive universe of 
discourse (Uod) may be more definite than the physical UoD. But there is a 
third UoD of experimental observations. Because of errors in measurement, 
mappings among all three UoDs are, at best, approximations.

In the book Photometric Researches (1878), Peirce described his methods for 
using logic and mathematics to analyze, relate, and reason about the three 
UoDs: mathematical, physical, and experimental. Although he had not yet 
developed his terminology of UoDs, the methods he describes in that book are 
good illustrations of his later theories. See 
http://jfsowa.com/peirce/PRexcerpts.pdf

JAS: However, [Peirce] also maintains that reality itself is general rather 
than strictly individual, such that some assertions are legitimately 
indeterminate.

That comment is not implied by the quotation you selected:

CSP: To speak of the actual state of things implies a great assumption, namely 
that there is a perfectly definite body of propositions which, if we could only 
find them out, are the truth, and that everything is really either true or in 
positive conflict with the truth. This assumption, called the principle of 
excluded middle, I consider utterly unwarranted, and do not believe it. Still, 
I hold that there is reason for thinking it to be very nearly true. (NEM 3:758, 
1893)

You quoted everything up to, but not including the sentence in italics. It 
explains why Newtonian mechanics, a definite mathematical theory, can be "very 
nearly true" for anything we observe without special instruments.

JAS: In these passages, Peirce refers to the "great assumption" that every 
proposition is either true or false as "the principle of excluded middle." 
However, in today's standard logical terminology, this is instead designated as 
the semantic principle of bivalence and distinguished from the (so-called) law 
of excluded middle, which is that either a proposition or its negation must be 
true-or, equivalently, that a proposition and its negation cannot both be 
false. Accordingly, there are at least two basic approaches for deviating from 
classical logic to facilitate treating some propositions as neither true nor 
false.

That paragraph requires clarification and qualification. I'll comment on the 
issues as they arise.

JAS: Intuitionistic logic rejects the law of excluded middle by denying that 
the negation of a false proposition must be true.

That is not what Brouwer said. He claimed that without a constructive proof, 
nobody can know whether a theory is true or false. Therefore, intuitionism 
prohibits theories that assume entities without any method for constructing 
them. But in any theory that can be proved by constructive methods, the 
negation of a false statement is indeed true. For more about intuitionism, 
search for "intuition" in the Handbook on Mathematical Logic, edited by Jon 
Barwise: http://jfsowa.com/temp/Barwise

Re: [PEIRCE-L] Modal logic

[Jerry Rhee]

ecome clearer about a subject, I find that Aristotle has
>> also become clearer."
>>
>> I would make that same comment about Peirce.”
>>
>> Then is it obvious to you that Peirce and Aristotle (among others) are
>> talking about one great big thing that has relation to several similar
>> things?
>>
>> it seems to me that the logician ought to recognize what our ultimate
>> aim is.
>>
>> .. it is clear that this one ultimate End must be the Good, and indeed
>> the Supreme Good.
>>
>> Will not then a knowledge of this Supreme Good be also of great
>> practical importance for the conduct of life? Will it not better
>> enable us to attain our proper object, like archers having a target to
>> aim at?
>>
>> If this be so, we ought to make an attempt to determine at all events
>> in outline what exactly this Supreme Good is, and of which of the
>> sciences or faculties it is the object.
>>
>> That is, if nothing is complete which has no end and only one thing is
>> the ultimate aim,
>>
>> then why do I find it so bizarre to justify our actions with:
>>
>> _ _
>>
>> _because_ Peirce..
>>
>> _because_ Aristotle..
>>
>> _because_ ultimate aim?
>>
>> I would greatly appreciate someone explaining this joke to me so that
>> I may
>>
>> _redirect my attention to the subject_,
>>
>> recognize that it is clear it has a reality, in _some_ mode of being,
>>
>> which is independent of what anyone thinks about it,
>>
>> “become clearer” and lead to a modification of those habits
>>
>> 3. Aristotle. Have read and thought more about Aristotle than about
>> any other man.
>>
>> Best,
>>  Jerry R
>>
>> On Wed, Jan 3, 2018 at 6:47 AM,  wrote:
>>
>> John Sowa wrote,
>>>
>>> “I like to quote a comment that Hilary Putnam made about
>>> Aristotle: "Whenever I become clearer about a subject, I find that
>>> Aristotle has also become clearer."
>>>
>>> I would make that same comment about Peirce.”
>>>
>>> Amen to that! And if I may clarify more minutely:
>>>
>>> Becoming clearer about a _subject_ begins with assuming —
>>> provisionally at least — that it has a reality, in _some_ mode of
>>> being, which is independent of what anyone thinks about it. This
>>> reality involves the _possibility_ of perceiving the real difference
>>> between true and false thoughts about it.
>>>
>>> Finding that Peirce has become clearer _about that subject_ means
>>> perceiving the _real relations_ between its reality and Peirce’s
>>> actual words about it. The reality _of those relations_ consists in
>>> the fact that they are what they are independently of what anyone
>>> thinks about them. But the increase in clarity which I find in
>>> Peirce is a result of _my thoughts_ about the real subject coming
>>> into greater conformity with _Peirce’s actual words_ about it.
>>>
>>> This clarity may turn out (upon further study of both the subject
>>> and Peirce’s words) to be an illusion. But in any case, it results
>>> from Peirce’s actual words _redirecting my attention to the
>>> subject_, to some extent. Only in this way can my thoughts about the
>>>
>>> subject (or about Peirce’s thoughts) gain a measure of
>>> independence from my own previous habits of language usage (or of
>>> reading Peirce). To me, “becoming clearer” refers to a
>>> modification of those habits.
>>>
>>> I know, it’s like explaining a joke, which takes all the fun out
>>> of it. But what could be more Peircean?
>>>
>>> Gary f.
>>>
>>> -Original Message-
>>> From: John F Sowa [mailto:s...@bestweb.net]
>>> Sent: 3-Jan-18 03:04
>>> To: peirce-l@list.iupui.edu
>>> Subject: Re: [PEIRCE-L] Modal logic
>>>
>>> On 1/1/2018 7:07 AM, Auke van Breemen wrote:
>>>
>>> I am quite sure Peirce felt rationally necessitated to be of the
>>>>
>>>
>>> opinion that it is not allowed to favor his suggestions after they
>>>>
>>> pop
>>>
>>> up only on the basis that they are written by him.
>>>>
>>>
>>> I agree. But Peirce would also insist that readers should make a
>>> clear distinction between his exact words and anybody else's
>>> interpretation. Note how strongly he objected to the version of
>>> pragmatism by 

Re: [PEIRCE-L] Modal logic

[kirstima]

habits

3. Aristotle. Have read and thought more about Aristotle than about
any other man.

Best,
 Jerry R

On Wed, Jan 3, 2018 at 6:47 AM,  wrote:


John Sowa wrote,

“I like to quote a comment that Hilary Putnam made about
Aristotle: "Whenever I become clearer about a subject, I find that
Aristotle has also become clearer."

I would make that same comment about Peirce.”

Amen to that! And if I may clarify more minutely:

Becoming clearer about a _subject_ begins with assuming —
provisionally at least — that it has a reality, in _some_ mode of
being, which is independent of what anyone thinks about it. This
reality involves the _possibility_ of perceiving the real difference
between true and false thoughts about it.

Finding that Peirce has become clearer _about that subject_ means
perceiving the _real relations_ between its reality and Peirce’s
actual words about it. The reality _of those relations_ consists in
the fact that they are what they are independently of what anyone
thinks about them. But the increase in clarity which I find in
Peirce is a result of _my thoughts_ about the real subject coming
into greater conformity with _Peirce’s actual words_ about it.

This clarity may turn out (upon further study of both the subject
and Peirce’s words) to be an illusion. But in any case, it results
from Peirce’s actual words _redirecting my attention to the
subject_, to some extent. Only in this way can my thoughts about the
subject (or about Peirce’s thoughts) gain a measure of
independence from my own previous habits of language usage (or of
reading Peirce). To me, “becoming clearer” refers to a
modification of those habits.

I know, it’s like explaining a joke, which takes all the fun out
of it. But what could be more Peircean?

Gary f.

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net]
Sent: 3-Jan-18 03:04
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Modal logic

On 1/1/2018 7:07 AM, Auke van Breemen wrote:


I am quite sure Peirce felt rationally necessitated to be of the



opinion that it is not allowed to favor his suggestions after they

pop


up only on the basis that they are written by him.


I agree. But Peirce would also insist that readers should make a
clear distinction between his exact words and anybody else's
interpretation. Note how strongly he objected to the version of
pragmatism by William James. He even replaced the word 'pragmatism'
with 'pragmaticism' to avoid any confusion.

As I said in my note about ways of studying Peirce, the first is
trying to determine exactly what he said. But there may be 5, 7, or
indefinitely (infinitely?) many ways of interpreting, building on,
using, and extending his work.


Filling in gaps tentatively due to inaccessible manuscripts offers

a


chance to check our understanding at some future time, as well of

the


text as of the object the text tries to understand.


Yes, of course. There has been a century of developments that
Peirce could not have known. Even for those subjects he knew very
well, he did not provide an exhaustive analysis of every detail. We
must fill in those gaps, but we also have to be clear about the
sources.

And by the way, I like to quote a comment that Hilary Putnam made
about Aristotle: "Whenever I become clearer about a subject, I find
that Aristotle has also become clearer."

I would make that same comment about Peirce.

John

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Re: [PEIRCE-L] Modal logic

[Jerry Rhee]

John, list,



Thanks for bringing attention to my mistake.

I ought to have said one big thought that is unlike any other thing,

for how, then, can it be an ultimate aim and be like similar things?

__



"To speak truth, and be skillful with bow and arrow" –

so seemed it alike pleasing and hard to the people from whom comes my name
–

the name which is alike pleasing and hard to me



A thousand goals have there been hitherto, for a thousand peoples have
there been.

Only the fetter for the thousand necks is still lacking;

there is lacking the one goal.  As yet humanity hath not a goal.



But pray tell me, my brethren, if a goal of humanity be still lacking,

is there not also still lacking- humanity itself?-  Thus spake Zarathustra.



I return to the Gods.

Can we suppose any of them to be squint-eyed, or even to have a cast in the
eye?

Have they any warts?  Or are they free from imperfections?

Let us grant you that.  Are they all alike in the face?


For if they are many, then one must necessarily be more beautiful than
another,

and then there must be some Deity not absolutely most beautiful.



Or if their faces are all alike, there would be an Academy in heaven;

for if one God does not differ from another,

there is no possibility of knowing or distinguishing them.


With best wishes,

Jerry R

On Thu, Jan 4, 2018 at 2:37 PM, John F Sowa  wrote:

> On 1/3/2018 3:17 PM, Jerry Rhee wrote:
>
>> [JFS] I like to quote a comment that Hilary Putnam made about Aristotle:
>>>
>>> "Whenever I become clearer about a subject, I find that Aristotle has
>>> also become clearer."
>>>
>>> I would make that same comment about Peirce.
>>>
>>> [JR] Then is it obvious to you that Peirce and Aristotle (among others)
>> are talking about one great big thing that has relation to several similar
>> things?
>>
>
> No.  They had many big thoughts.  But their terminology and ways
> of thinking were different from each other and from currently
> popular paradigms.  It requires quite a bit of hard thought to
> learn and appreciate their ways of thinking.
>
> John
>
>
> -
> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
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> .
>
>
>
>
>
>

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Re: [PEIRCE-L] Modal logic

[John F Sowa]

On 1/3/2018 3:17 PM, Jerry Rhee wrote:

[JFS] I like to quote a comment that Hilary Putnam made about Aristotle:

"Whenever I become clearer about a subject, I find that Aristotle has 
also become clearer."


I would make that same comment about Peirce.

[JR] Then is it obvious to you that Peirce and Aristotle (among others) 
are talking about one great big thing that has relation to several 
similar things?


No.  They had many big thoughts.  But their terminology and ways
of thinking were different from each other and from currently
popular paradigms.  It requires quite a bit of hard thought to
learn and appreciate their ways of thinking.

John

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Re: [PEIRCE-L] Modal logic

[Jerry Rhee]

Dear gary, list,



If what Gary adds of John about Putnam is true,



 “I like to quote a comment that Hilary Putnam made about Aristotle:

"Whenever I become clearer about a subject, I find that Aristotle has also
become clearer."

I would make that same comment about Peirce.”



Then is it obvious to you that Peirce and Aristotle (among others) are
talking about one great big thing that has relation to several similar
things?



it seems to me that the logician ought to recognize what our ultimate aim
is.



.. it is clear that this one ultimate End must be the Good, and indeed the
Supreme Good.

Will not then a knowledge of this Supreme Good be also of great practical
importance for the conduct of life? Will it not better enable us to attain
our proper object, like archers having a target to aim at?

If this be so, we ought to make an attempt to determine at all events in
outline what exactly this Supreme Good is, and of which of the sciences or
faculties it is the object.



That is, if nothing is complete which has no end and only one thing is the
ultimate aim,

then why do I find it so bizarre to justify our actions with:



*because* Peirce..

*because* Aristotle..

*because* ultimate aim?



I would greatly appreciate someone explaining this joke to me so that I may



*redirect my attention to the subject*,

recognize that it is clear it has a reality, in *some* mode of being,

which is independent of what anyone thinks about it,

“become clearer” and lead to a modification of those habits



3. *Aristotle*. Have read and thought more about Aristotle than about any
other man.



Best,
Jerry R

On Wed, Jan 3, 2018 at 6:47 AM,  wrote:

> John Sowa wrote,
>
> “I like to quote a comment that Hilary Putnam made about Aristotle:
> "Whenever I become clearer about a subject, I find that Aristotle has also
> become clearer."
>
> I would make that same comment about Peirce.”
>
>
>
> Amen to that! And if I may clarify more minutely:
>
>
>
> Becoming clearer about a *subject* begins with assuming — provisionally
> at least — that it has a reality, in *some* mode of being, which is
> independent of what anyone thinks about it. This reality involves the
> *possibility* of perceiving the real difference between true and false
> thoughts about it.
>
>
>
> Finding that Peirce has become clearer *about that subject* means
> perceiving the *real relations* between its reality and Peirce’s actual
> words about it. The reality *of those relations* consists in the fact
> that they are what they are independently of what anyone thinks about them.
> But the increase in clarity which I find in Peirce is a result of *my
> thoughts* about the real subject coming into greater conformity with *Peirce’s
> actual words* about it.
>
>
>
> This clarity may turn out (upon further study of both the subject and
> Peirce’s words) to be an illusion. But in any case, it results from
> Peirce’s actual words *redirecting my attention to the subject*, to some
> extent. Only in this way can my thoughts about the subject (or about
> Peirce’s thoughts) gain a measure of independence from my own previous
> habits of language usage (or of reading Peirce). To me, “becoming clearer”
> refers to a modification of those habits.
>
>
>
> I know, it’s like explaining a joke, which takes all the fun out of it.
> But what could be more Peircean?
>
>
>
> Gary f.
>
>
>
> -Original Message-
> From: John F Sowa [mailto:s...@bestweb.net]
> Sent: 3-Jan-18 03:04
> To: peirce-l@list.iupui.edu
> Subject: Re: [PEIRCE-L] Modal logic
>
>
>
> On 1/1/2018 7:07 AM, Auke van Breemen wrote:
>
> > I am quite sure Peirce felt rationally necessitated to be of the
>
> > opinion that it is not allowed to favor his suggestions after they pop
>
> > up only on the basis that they are written by him.
>
>
>
> I agree.  But Peirce would also insist that readers should make a clear
> distinction between his exact words and anybody else's interpretation.
> Note how strongly he objected to the version of pragmatism by William
> James.  He even replaced the word 'pragmatism' with 'pragmaticism' to avoid
> any confusion.
>
>
>
> As I said in my note about ways of studying Peirce, the first is trying to
> determine exactly what he said.  But there may be 5, 7, or indefinitely
> (infinitely?) many ways of interpreting, building on, using, and extending
> his work.
>
>
>
> > Filling in gaps tentatively due to inaccessible manuscripts offers a
>
> > chance to check our understanding at some future time, as well of the
>
> > text as of the object the text tries to understand.
>
>
>
> Yes, of course.  There has been a century of development

RE: [PEIRCE-L] Modal logic

[gnox]

John Sowa wrote,

“I like to quote a comment that Hilary Putnam made about Aristotle:  "Whenever 
I become clearer about a subject, I find that Aristotle has also become 
clearer."

I would make that same comment about Peirce.”

 

Amen to that! And if I may clarify more minutely:

 

Becoming clearer about a subject begins with assuming — provisionally at least 
— that it has a reality, in some mode of being, which is independent of what 
anyone thinks about it. This reality involves the possibility of perceiving the 
real difference between true and false thoughts about it.

 

Finding that Peirce has become clearer about that subject means perceiving the 
real relations between its reality and Peirce’s actual words about it. The 
reality of those relations consists in the fact that they are what they are 
independently of what anyone thinks about them. But the increase in clarity 
which I find in Peirce is a result of my thoughts about the real subject coming 
into greater conformity with Peirce’s actual words about it.

 

This clarity may turn out (upon further study of both the subject and Peirce’s 
words) to be an illusion. But in any case, it results from Peirce’s actual 
words redirecting my attention to the subject, to some extent. Only in this way 
can my thoughts about the subject (or about Peirce’s thoughts) gain a measure 
of independence from my own previous habits of language usage (or of reading 
Peirce). To me, “becoming clearer” refers to a modification of those habits.

 

I know, it’s like explaining a joke, which takes all the fun out of it. But 
what could be more Peircean?

 

Gary f.

 

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 3-Jan-18 03:04
To: peirce-l@list.iupui.edu
Subject: Re: [PEIRCE-L] Modal logic

 

On 1/1/2018 7:07 AM, Auke van Breemen wrote:

> I am quite sure Peirce felt rationally necessitated to be of the 

> opinion that it is not allowed to favor his suggestions after they pop 

> up only on the basis that they are written by him.

 

I agree.  But Peirce would also insist that readers should make a clear 
distinction between his exact words and anybody else's interpretation.  Note 
how strongly he objected to the version of pragmatism by William James.  He 
even replaced the word 'pragmatism' with 'pragmaticism' to avoid any confusion.

 

As I said in my note about ways of studying Peirce, the first is trying to 
determine exactly what he said.  But there may be 5, 7, or indefinitely 
(infinitely?) many ways of interpreting, building on, using, and extending his 
work.

 

> Filling in gaps tentatively due to inaccessible manuscripts offers a 

> chance to check our understanding at some future time, as well of the 

> text as of the object the text tries to understand.

 

Yes, of course.  There has been a century of developments that Peirce could not 
have known.  Even for those subjects he knew very well, he did not provide an 
exhaustive analysis of every detail.  We must fill in those gaps, but we also 
have to be clear about the sources.

 

And by the way, I like to quote a comment that Hilary Putnam made about 
Aristotle:  "Whenever I become clearer about a subject, I find that Aristotle 
has also become clearer."

 

I would make that same comment about Peirce.

 

John


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Re: [PEIRCE-L] Modal logic

[John F Sowa]

On 1/1/2018 7:07 AM, Auke van Breemen wrote:

I am quite sure Peirce felt rationally necessitated to be of
the opinion that it is not allowed to favor his suggestions
after they pop up only on the basis that they are written by him.


I agree.  But Peirce would also insist that readers should
make a clear distinction between his exact words and anybody
else's interpretation.  Note how strongly he objected to the
version of pragmatism by William James.  He even replaced the
word 'pragmatism' with 'pragmaticism' to avoid any confusion.

As I said in my note about ways of studying Peirce, the first
is trying to determine exactly what he said.  But there may be
5, 7, or indefinitely (infinitely?) many ways of interpreting,
building on, using, and extending his work.


Filling in gaps tentatively due to inaccessible manuscripts offers
a chance to check our understanding at some future time, as well
of the text as of the object the text tries to understand.


Yes, of course.  There has been a century of developments that
Peirce could not have known.  Even for those subjects he knew
very well, he did not provide an exhaustive analysis of every
detail.  We must fill in those gaps, but we also have to be
clear about the sources.

And by the way, I like to quote a comment that Hilary Putnam
made about Aristotle:  "Whenever I become clearer about a
subject, I find that Aristotle has also become clearer."

I would make that same comment about Peirce.

John

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RE: [PEIRCE-L] Modal logic

[Auke van Breemen]

John,

You wrote:
Maybe.  But these are issues for which we could benefit from more easily 
accessible resources -- such as well organized and cross referenced 
transcriptions of all of Peirce's MSS.
It would also be useful to have all of the MSS cross linked to everything that 
any and all Peirce scholars have written about any or all the MSS.
John

When a student I bought a reproduction on a second hand market for the picture 
frame only. Since I did not have a fitting image, I decided to keep the image, 
that was and still is in very bad state. After some weeks I knew the image 
would stay for an indefinite time period. Pictured are three women, each with a 
bible. In the middle an intensely, close reading older woman, to her left a 
young lady keeping the book at a distance, as if reading very critical. To her 
right a middle aged woman that looks away from the book into the world, as if 
checking what has been said. I am of the opinion that every serious text 
deserves all three kinds of reading.

Filling in gaps tentatively due to inaccessible manuscripts offers a chance to 
check our understanding at some future time, as well of the text as of the 
object  the text tries to understand.

As one may ask whether the ladies primarily want to understand the immediate 
object (the bible book) or the dynamical object, one may ask the same question 
with the work of Peirce. I am quite sure Peirce felt rationally necessitated to 
be of the opinion that it is not allowed to favor his suggestions after they 
pop up only on the basis that they are written by him. The goal, uncovering the 
dynamical object, in the interrogative mode on all suggestions, carefully 
considering all accessible facts concerning the objects, utilizing the social 
possibilities the community of investigators offers on the subject, will 
determine the conclusions in the end.

Best,

Auke

-Oorspronkelijk bericht-
Van: John F Sowa [mailto:s...@bestweb.net] 
Verzonden: maandag 1 januari 2018 5:14
Aan: peirce-l@list.iupui.edu
Onderwerp: Re: [PEIRCE-L] Modal logic

Jerry and Auke,

In the Worlds article, my primary goal was to convince readers that a 
definition of modality in terms of laws and facts is more fruitful than a 
definition in terms of possible worlds.

The final paragraph of that article summarizes what I was trying to show.  (See 
below.)  What Peirce himself said about modality and his Gamma graphs is 
fragmentary, and I don't claim to know what he would have said in answer to 
your questions.

JLRC
> Can you provide the names of the four subdivisions of the universe of 
> actualities?

Since Peirce didn't attach any names to those subdivisions, I won't attempt to 
do so.  Don Roberts reproduced Peirce's diagram on p. 94 of his book on 
existential graphs.  But he doesn't name them either.

But by analogy with the labels Peirce assigned to the subdivisions of 
possibilities and necessities, I would guess that the 3rd and 4th subdivisions 
of actualities would represent something actual with respect to an observer or 
to some other person.  Peirce may have had some ideas in mind, but hadn't made 
a final decision.

AvB
> I would say...

Maybe.  But these are issues for which we could benefit from more easily 
accessible resources -- such as well organized and cross referenced 
transcriptions of all of Peirce's MSS.

It would also be useful to have all of the MSS cross linked to everything that 
any and all Peirce scholars have written about any or all the MSS.

John


 From the final paragraph of http://jfsowa.com/pubs/worlds.pdf

The combination of semiotics with Dunn's semantics of laws and facts provides a 
theoretical foundation for modality and intentionality that captures more of 
the intended interpretation than a undefinable relation R over an undefined set 
W. An important promise of this combination is the ability to support 
multimodal reasoning as a kind of metalevel reasoning about the source of the 
laws and facts. Instead of complex axioms for each mode with even more complex 
interactions between modes, it enables the laws to be partitioned in a 
hierarchy that represents grades of necessity or levels of entrenchment:  
logical, physical, economic, legal, social, cultural, or personal (Sowa 2003). 
Exploring the full implications of Peirce's semiotics is far beyond the scope 
of this article, but the outline presented here suggests a wealth of resources 
waiting to be developed.


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Re: [PEIRCE-L] Modal logic

[John F Sowa]

Jerry and Auke,

In the Worlds article, my primary goal was to convince readers
that a definition of modality in terms of laws and facts is
more fruitful than a definition in terms of possible worlds.

The final paragraph of that article summarizes what I was trying
to show.  (See below.)  What Peirce himself said about modality
and his Gamma graphs is fragmentary, and I don't claim to know
what he would have said in answer to your questions.

JLRC

Can you provide the names of the four subdivisions of the universe
of actualities?


Since Peirce didn't attach any names to those subdivisions, I won't
attempt to do so.  Don Roberts reproduced Peirce's diagram on p. 94
of his book on existential graphs.  But he doesn't name them either.

But by analogy with the labels Peirce assigned to the subdivisions
of possibilities and necessities, I would guess that the 3rd and 4th
subdivisions of actualities would represent something actual with
respect to an observer or to some other person.  Peirce may have had
some ideas in mind, but hadn't made a final decision.

AvB

I would say...


Maybe.  But these are issues for which we could benefit from
more easily accessible resources -- such as well organized
and cross referenced transcriptions of all of Peirce's MSS.

It would also be useful to have all of the MSS cross linked
to everything that any and all Peirce scholars have written
about any or all the MSS.

John


From the final paragraph of http://jfsowa.com/pubs/worlds.pdf

The combination of semiotics with Dunn's semantics of laws and facts 
provides a theoretical foundation for modality and intentionality that 
captures more of the intended interpretation than a undefinable relation 
R over an undefined set W. An important promise of this combination is 
the ability to support multimodal reasoning as a kind of metalevel 
reasoning about the source of the laws and facts. Instead of complex 
axioms for each mode with even more complex interactions between modes, 
it enables the laws to be partitioned in a hierarchy that represents 
grades of necessity or levels of entrenchment:  logical, physical, 
economic, legal, social, cultural, or personal (Sowa 2003). Exploring 
the full implications of Peirce's semiotics is far beyond the scope of 
this article, but the outline presented here suggests a wealth of 
resources waiting to be developed.

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RE: [PEIRCE-L] Modal logic (was Nativity scenes

[Auke van Breemen]

Jerry, list,

 

A good question. 

 

Looking in  <http://jfsowa.com/pubs/worlds.pdf> 
http://jfsowa.com/pubs/worlds.pdf I find:

 

Existents. This universe includes "Objects whose Being consists in their Brute 
reactions, and of, second, the Facts (reactions, events, qualities, etc.) 
concerning those Objects Every member of this Universe is either a Single 
Object subject, alike to the Principles of Contradiction and to that of 
Excluded Middle, or it is expressible by a proposition having such a singular 
subject."

 

I would say two are mentioned:

 

2. Objects whose Being consists in their Brute reactions

3. the Facts (reactions, events, qualities, etc.) concerning those Objects

 

I am inclined to speculate, and welcome alternatives:

1 could be subjective, so feeling

4 operative goals 

 

 

  Possibilitiesactualities  
 necessitated

1.  Subjective possibility  - feeling   
- compelled 
  
2.  Objective possibility   - Objects .. brute reactions
- determined  
3.  Social possibility  - Facts concerning objects  
- commanded
4.  Interrogative mode- goals   
  - rationally necessitated 

 

 

Happy new year!

 

Auke

 

 

Van: Jerry LR Chandler [mailto:jerry_lr_chand...@icloud.com] 
Verzonden: maandag 1 januari 2018 0:13
Aan: John F Sowa ; Peirce List 
Onderwerp: Re: [PEIRCE-L] Modal logic (was Nativity scenes

 

John:

 

In For a six-page review of these issues with references,

see  <http://jfsowa.com/pubs/5qelogic.pdf> http://jfsowa.com/pubs/5qelogic.pdf .

 

You wrote:

Peirce considered three universes: actualities, possibilities, and the 
necessitated. He subdivided each universe in four ways to define 12 modes. In 
the universe of possibilities, for example, he distinguished objective 
possibility (an alethic mode), subjective possibility (epistemic), social 
possibility (deontic), and an interrogative mode, which corresponds to 
scientific inquiry by hypothesis and experiment. For the necessitated, he 
called the four subdivisions the rationally necessitated, the compelled, the 
commanded, and the determined. Most of his writings on these topics were 
unpublished, and he changed his terminology from one manuscript to the next. 
Peirce admitted that a complete analysis and classification would be “a labor 
for generations of analysts, not for one” (MS 478:165).

 

It provides the subdivisions of two of the three universes. 

Can you provide the names of the four subdivisions of the universe of 
actualities?

 

Thank you 

 

Happy New Year to All!

 

Cheers

Jerry

 

 

On Dec 31, 2017, at 9:04 AM, John F Sowa < <mailto:s...@bestweb.net> 
s...@bestweb.net> wrote:

 

Historical note:  Aristotle claimed that necessity and possibility
are determined by the laws of nature.  Leibniz introduced possible
worlds with necessity as truth in all possible worlds, and
possibility as truth in at least one.

Carnap was a strict nominalist who followed Mach in claiming
that the laws of science are *nothing but* summaries of
observable data.  He even considered *truth* to be outside
the realm of "scientific" method.  But Tarski's model theory
convinced him that truth could be defined in observable terms.
Carnap later (1947) combined Leibniz and Tarski.

Hintikka introduced "model sets", which consisted of sets
of propositions that are true of the possible worlds.  He also
introduced an alternativity relation among model sets.

Kripke went back to sets of worlds and related the accessibility
relation (identical to Hintikka's alternativity) to the axioms
for modality that C. I. Lewis had introduced.

Nominalists preferred sets of worlds to sets of sets of propositions.
But Quine would not accept modality with either version.

But in 1973, Michael Dunn introduced a beautiful solution
that Peirce would love, but the nominalists would hate:
treat each possible world as a pair (facts, laws).

For a six-page review of these issues with references,
see  <http://jfsowa.com/pubs/5qelogic.pdf> http://jfsowa.com/pubs/5qelogic.pdf .

For more detail (26 pages), see  <http://jfsowa.com/pubs/worlds.pdf> 
http://jfsowa.com/pubs/worlds.pdf .

 

 


 
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Re: [PEIRCE-L] Modal logic (was Nativity scenes

[Jerry LR Chandler]

John:

In For a six-page review of these issues with references,
> see http://jfsowa.com/pubs/5qelogic.pdf  
> .

You wrote:
Peirce considered three universes: actualities, possibilities, and the 
necessitated. He subdivided each universe in four ways to define 12 modes. In 
the universe of possibilities, for example, he distinguished objective 
possibility (an alethic mode), subjective possibility (epistemic), social 
possibility (deontic), and an interrogative mode, which corresponds to 
scientific inquiry by hypothesis and experiment. For the necessitated, he 
called the four subdivisions the rationally necessitated, the compelled, the 
commanded, and the determined. Most of his writings on these topics were 
unpublished, and he changed his terminology from one manuscript to the next. 
Peirce admitted that a complete analysis and classification would be “a labor 
for generations of analysts, not for one” (MS 478:165).


It provides the subdivisions of two of the three universes. 
Can you provide the names of the four subdivisions of the universe of 
actualities?

Thank you 

Happy New Year to All!

Cheers
Jerry

 

> On Dec 31, 2017, at 9:04 AM, John F Sowa  wrote:
> 
> Historical note:  Aristotle claimed that necessity and possibility
> are determined by the laws of nature.  Leibniz introduced possible
> worlds with necessity as truth in all possible worlds, and
> possibility as truth in at least one.
> 
> Carnap was a strict nominalist who followed Mach in claiming
> that the laws of science are *nothing but* summaries of
> observable data.  He even considered *truth* to be outside
> the realm of "scientific" method.  But Tarski's model theory
> convinced him that truth could be defined in observable terms.
> Carnap later (1947) combined Leibniz and Tarski.
> 
> Hintikka introduced "model sets", which consisted of sets
> of propositions that are true of the possible worlds.  He also
> introduced an alternativity relation among model sets.
> 
> Kripke went back to sets of worlds and related the accessibility
> relation (identical to Hintikka's alternativity) to the axioms
> for modality that C. I. Lewis had introduced.
> 
> Nominalists preferred sets of worlds to sets of sets of propositions.
> But Quine would not accept modality with either version.
> 
> But in 1973, Michael Dunn introduced a beautiful solution
> that Peirce would love, but the nominalists would hate:
> treat each possible world as a pair (facts, laws).
> 
> For a six-page review of these issues with references,
> see http://jfsowa.com/pubs/5qelogic.pdf  
> .
> 
> For more detail (26 pages), see http://jfsowa.com/pubs/worlds.pdf 
>  .


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RE: [PEIRCE-L] Modal logic (was Nativity scenes

[Auke van Breemen]

John,

Thanks, the text behind the links appears to be interesting. Zeman got me 
thinking about tinctures and sheets.  Your http://jfsowa.com/pubs/5qelogic.pdf 
has a lot to offer.

Best,

Auke

-Oorspronkelijk bericht-
Van: John F Sowa [mailto:s...@bestweb.net] 
Verzonden: zondag 31 december 2017 16:05
Aan: peirce-l@list.iupui.edu
Onderwerp: [PEIRCE-L] Modal logic (was Nativity scenes

On 12/31/2017 7:14 AM, Auke van Breemen wrote:
> I am unsure about the place of modality, but maybe it just boils down 
> to a firstness and secondness view on the issue.

Historical note:  Aristotle claimed that necessity and possibility are 
determined by the laws of nature.  Leibniz introduced possible worlds with 
necessity as truth in all possible worlds, and possibility as truth in at least 
one.

Carnap was a strict nominalist who followed Mach in claiming that the laws of 
science are *nothing but* summaries of observable data.  He even considered 
*truth* to be outside the realm of "scientific" method.  But Tarski's model 
theory convinced him that truth could be defined in observable terms.
Carnap later (1947) combined Leibniz and Tarski.

Hintikka introduced "model sets", which consisted of sets of propositions that 
are true of the possible worlds.  He also introduced an alternativity relation 
among model sets.

Kripke went back to sets of worlds and related the accessibility relation 
(identical to Hintikka's alternativity) to the axioms for modality that C. I. 
Lewis had introduced.

Nominalists preferred sets of worlds to sets of sets of propositions.
But Quine would not accept modality with either version.

But in 1973, Michael Dunn introduced a beautiful solution that Peirce would 
love, but the nominalists would hate:
treat each possible world as a pair (facts, laws).

For a six-page review of these issues with references, see 
http://jfsowa.com/pubs/5qelogic.pdf .

For more detail (26 pages), see http://jfsowa.com/pubs/worlds.pdf .

John


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