There have been some discussions about intuitionistic logic and the
claim that Peirce anticipated aspects of Brouwer's version of
intuitionistic logic
However, Peirce and Brouwer were on
opposite sides of fundamental issues about the nature of mathematics.
Peirce maintained that mathematical
Alex and William,
I agree with Mario B. that a foundation
for ontology based on systems is far and away superior to a foundation
based on physical things -- primarily because systems presuppose
non-physical mathematics and the supra-physical laws that govern the
physical things/stuff.
Without
Jon AS,
I'm writing an article about Peirce's writings on logic
in 1911, which I'll post to P-list soon. And I'm glad that we can agree
on that point.
JFS> However, Peirce and Brouwer were on
opposite sides of fundamental issues about the nature of mathematics.
... In general, Brouwer's assu
Gary R,
I'm glad you asked.GR> Please explain how this
"blocks the
way of inquiry" for folk like me who are apparently radically deficient
in mathematics and logic so simply can't see it as such.
Intuitionistic logic is a restriction on the
permissible rules of inference. That makes it impossib
Avril,
As I said in my note, I believe that Mario Bunge's view
that an ontology based on systems is quite good. I also agree with the
quotations you cited in your note.
But one thing that is
missing from most discussions of ontology is a definition of 'reality'
that specifically includes mathe
Jon AS,
I'm tied up with other deadlines, and I'll post a longer
article that goes into all the details in a few more days.
Re
rejecting R669: In R670, CSP explicitly stated that the scroll is
equivalent to a nest of two negations (12 June 1911). On the next day, he
wrote that it's so easy to
Edwina and Jon AS,
Just two short points:
1. There
is nothing derogatory about the word 'opinion'. If you consult a
physician about some issue, he or she will perform some diagnostics and
state an opinion about your condition and what treatment, if any, should
be performed. If it's anything s
Jon AS,
As I said, I'm writing a longer article in which I cover
all the details Just a short preview of coming
attractions:
1. The story about paradisaical logic is used in
R669 to justify the derivation of negation from a scroll. In L376, Peirce
happens to use the same term for a logic wit
Jon AS,
I admit that Peirce does not use the word scroll
in r670. But he draws some scrolls, and he shows one EG as a scroll
and another with shaded ovals and says that they are
"equivalent".
If you look at the times and dates, his
remark about heaven & hell was the first entry during the
Jon AS,
JAS> Remember, "nobody can claim that
anything other than an exact quotation is what Peirce intended"
Thank you for emphasizing my point. The only solid evidence we
have of what Peirce intended is what he wrote before and after June 1911.
But the developments during the century after
Jon AS, List,
Before getting into any speculation, I'll mention
some undeniable
facts:
1. R699 has the title
"Assurance through reasoning", it begins with a
paragraph
about necessary deduction and probable deduction, and it
contains a
summary of the EG system from the early days up to and
inclu
Jon AS, Ahti, Francesco, List,
JAS> I have taken the liberty
of adding Francesco Bellucci (who has
posted to Peirce-L in the past)
and Ahti-Veikko Pietarinen to the cc:
line. I also changed the
subject line.
Thank you. That may help get closure on this
topic.
First, the undeniable facts: In
Jon AS. List,
Your comments helped me state the following four
points more clearly.
I believe they have been established beyond any
reasonable doubt. If
you're not convinced, I suggest that you
forward this note to any Peirce
scholar(s) anywhere in the world and
ask whether they have any doub
Dear Ahti and Francesco,
As you know, I believe that Peirce's
insight of June 1911 led him
to develop a new version of EGs that is
superior to the older ones.
I have refuted Jon's claims, point
by point, and I stopped answering
him when they became repetitious
and irrelevant. But he continues
Dear Francesco,
FB> as to the "evidence from the
century after Peirce", this evidence is
certainly relevant to
determining whether Peirce was right or wrong in
this or that idea
that he had, but I'm not sure it is fully relevant to
determining
whether we are right or wrong about whether Peirce h
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(For some mysterious reason, the content of my previous note
disappeared.}
As background reading material about phaneroscopy, I
recommend some
important papers by Tony Jappy. Unlike many
publications that talk
only about abstract issues, Tony J illustrates
the abstract analysis
with specific ex
Dear Tony, Jon AS, List,
I sent a note (copy below) to
Peirce-L, in which I recommended some
of your work for ongoing
discussions of phaneroscopy. But Jon
objected to my saying that your
subject matter is phaneroscopy:
JAS> Jappy's paper further
clarifies that phenomenology/phaneroscopy
provid
Cathy, Edwina, List,
I strongly agree with your concerns, and I
broadened the title line.
My publications are mostly in technical
areas, but I have been working
on computational linguistics -- the
task of analyzing and relating
anything and everything that people
write or speak to
computional
Jon AS, List,
I renamed the subject line to emphasize the stages
prior to the derivation of the three branches of normative
logic.
JAS> I have corrected the subject line since the cited
writings by Jappy
and quoted statements by Peirce are not about
phaneroscopy at all, but about
speculative
On 8 November 1913, Peirce described a version of EGs that is identical
to the 1911 version. See the copy below. My summary:
A
universe of discourse is described by the graphs scribed on a sheet
of assertion (AKA phemic sheet). The structure and meaning of an EG
is
determined by five conventi
Gary F> For me at least, veracity only applies to stories or
propositions that are publicly verifiable.
But a huge amount of
information that we get every day is reported by people whose observations
cannot be verified by any other sources. When your friends or family
discuss their experie
Alex,
Everybody on planet Earth knows and uses an excellent
Knowledge Query Language every day. It's our native language or some
other NL that we choose to use or are required to use for some
purpose.
But KQL is a bad acronym, because it puts too much emphasis
on the Q. It's better to emphasi
The attached file, diag.txt, contains a review of the book
Diagrammatic Immanence: Category Theory and Philosophy, which
contains a chapter about Peirce. Since the book is written for
non-mathematicians, it uses diagrams to explain the ideas, rather than the
more complex terminology of categor
Robert, I took a course in algebraic topology way back when, and I
appreciate the power of category theory and commutative
diagrams.
But in recommending that book review, I wanted to tell
people who have trouble with math that the presentation is written for an
audience that does not have any s
Since Jon Awbrey no longer subscribes to Peirce-L, I'm sending this
note about another book he cited. See below for the title, authors, and
the publisher's summary.
The Springer website for this book also
includes two URLs for free copies of the table of contents and Chapter 2
Iconicity in Pei
Robert, List,
I strongly agree with you:
RM> My criticism is precisely about the fact that De Tienne
starts with
phaneroscopy and forgets that the formal structures he believes in
discovering are
inherited from mathematics on which they depend.
At
the end of this note is the opening section of
Robert and Gary F,
The issue you're debating is caused by the
ambiguity in Peirce's use of the word 'logic'. In his 1903 classification
of the sciences, the word 'logic' appears in two places: mathematics of
logic is the first of three branches of mathematics. But logic proper is
a branch o
Jack RKC> When you say that the phaneron (or any phenomenon) always
has three
elements, I was wondering (rhetorically), "Yes, but as defined by
who?"
That short sentence about the phaneron covers an immense
amount of complexity. The categories of 1-ness, 2-ness, and 3-ness
classify the three k
Robert,
I changed the subject line to emphasize the word
element, Which is
Peirce's own word for the constituents of
the phaneron. In fact, the
word element, which occurs over
800 times in CP, is one of Peirce's
favorite words. He replaced the
term speculative grammar with
Stechiology (from th
Jon AS,
Peirce's definition of mathematics is consistent with
the mainstream
of mathematical thinking since antiquity. There are
many versions
of the philosophy of mathematics, but Peirce's version
is still
at the forefront of modern research.
JAS>
anyone is free to disagree with Peirce's defi
Different people have different ways of thinking and talking. That is
important, because the world is so complex, so diverse, and so
dynamic
that no single method could comprehend and describe it all.
Peirce's
method of diagrammatic thinking, which is the foundation for
his logic
and philosophy
William,
I agree with nearly everything you wrote.
WF> I think [modal logic is] more of a playground.
I like
the word playground. It's a source of thesis topics for
professors to assign to their graduate students who publish papers
that nobody who has a day job would read.
WF> There are
lots
Edwina,
Yes. That is a major advantage of diagrams:
ET> I agree that diagrams are more fundamental than words, since
their
attributes are less open to multiple interpretations. That
includes
both the written and spoken word, with the latter overlaid
with
meanings provided by tone and rhythm a
Terry, Jack, Helmut, Edwina, List,
TLR> Perhaps our knowledge
base isnt either learned
or innate (per exclusive disjunction), but both learned
and innate.
The nature/nuture/culture issues have been
debated for centuries, and there is a lot of evidence that is sometimes
clear and sometimes am
William and Alex,
John McCarthy made a very clear distinction in
an article with the title "Modality, Si. Modal logic,
No!"
Modality involves reasoning about possibility and
necessity. In short, it involves *metalevel* reasoning about the laws,
rules, requirements, etc, that determine what is
Robert> This leads me to a final question to be discussed: should
the
classification of sciences according to Peirce be considered as a
kind
of imperative to be respected or can phenomenology be approached
from
the logic that depends on it according to this
classification?
There is no conflict
In my previous note, I accidentally typed the word 'nominalists' twice,
In the corrected version below, the second occurrence is changed to
'scientists'.
Actuality consists of everything that
exists in space and time. It's
what nominalists claim is
everything. But they have no answer to the
On 8 Nov. 1913, Peirce summarized his final position on EGs, and it is
identical to his 1911 EGs. Nobody has shown any evidence for any other
opinion, no matter what their purpose may be.
Case
closed.
John
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Mihai Nadin> Diagrammatic thinking is more or less mathematical
thinking.
Peirce made the point that all mathematical
reasoning, including algebra,
is diagrammatic. But diagrams can also
include reasoning that most
people would not call mathematics -- but
Peirce's definition of diagram
is broad
Edwina, Helmut, Jon A, List,
The term 'weasel word' for emergence
has negative connotations. I wouldn't suggest the negativity, but I admit
that it hides a wide range of interpretants that deserve to be analyzed in
more detail.
I agree that the early stages of interpretation are so
rapid (fract
Helmut> "Emergence" for me seems to be a not yet
logically fully explained phenomenon.
That's true. There are
various hypotheses, but none of them are sufficient to explain the
result. That is typical for most unsolved problems.
In short, the
word emergence is a placeholder to be replaced wh
Edwina> All [the word emergence] means in my reference is 'coming
into being'; i.e., becoming
a morphology, a form, whether in the mode of being of
1ns,2ns,3ns.
Yes. That is all it means. Jon A called it a 'weasel
word' as a sign of deprecation because it names a phenomenon without
explaining
Edwina,
I agree with you. The question of how life emerged is
important, and it's important to explore all the possible ways in which it
might have emerged on earth and on other planets or moons in the solar
system, galaxy, or universe.
I also implied that Peirce would have
approved of the wor
Robert, List,
That quotation shows how mathematics is used in
phaneroscopy:
CSP: Thus, the mathematician does two very
different things: namely,
he first frames a pure hypothesis stripped
of all features which do
not concern the drawing of consequences from
it, and this he does
without inquir
Jon AS, List,
JFS: As Peirce explained in many passages in his
writings, mathematics
is the universe of all possibilities.
JAS> Please provide exact quotations of the "many passages"
where Peirce
supposedly equates mathematics with "the universe
of all possibilities."
That question has two pa
Gary R, Edwina, List,
See the attached file JFS_Aug6.txt for my
answers to JAS.
And thanks, Edwina, for the following quotation.
Any form, when considered apart from the matter, is always a mathematical
pattern.
CSP: that which is communicated from the Object through the
Sign to
the Interpreta
Jack KRC> At the risk of being pedantic, what is meant by
"mathematical" here?
That question is important for
understanding what Peirce meant in saying that Phaneroscopy depends on
mathematics.
The simplest and clearest definition: "Anything
that can be completely specified by a definition sta
Jon AS, Edwina, Jack, Gary F, List,
JFS: The simplest and
clearest definition [of the adjective
'mathematica'l':
"Anything that can be completely specified by a
definition
stated in any branch of mathematics."
JAS: That is not a
definition, it is a tautology.
No. Jack asked "what is
meant
I uploaded a preliminary version of my slides for tomorrow's talk at
http://jfsowa.com/talks/uql.pdf
I'll post an updated version this
evening or tomorrow morning at the same URL.
For further
information, see the announcement below by Ken Baclawski.
John
--
This is a reminder
Jon AS, Gary F, List,
JAS: the question is simply whether
Peirce ever explicitly states that
"mathematics is the universe
of all possibilities." If not, then nobody
can definitively
claim that this is what he intended.
The assumption that
mathematics specifies all of what Peirce called
"real
I uploaded new slides for today's talk:
http://jfsowa.com/talks/uql.pdf
Slides 19 and 20 are the most
important additions.
John
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Edwina, List
ET> Who will judge whether X-person's
reading or Y-person's reading
'represents its author's original
intent? Who has this capacity to
make such a judgment?
The author is the only person who has the right to state his or her
intent. Following is one of Peirce's clearest statemen
Bernard, Gary F, List.
The confusion in this case is caused by a
failure to distinguish two kinds of dependency: (1) which science depends
on which other sciences for its fundamental principles and its data; (2)
which sources do the scientists depend on for their ideas, inspirations,
purposes,
Jerry,
I agree with your point about the difference between
signs and semiosis. But I would like to state it more generally: It's the
difference between the content of a subject (such as a science), the
actions by the people (typically scientists) who are doing the
development, and the actions
Gary F and Jerry,
A computer theorem prover that generates all
possibilities and
systematically eliminates (by deduction) the ones
that generate
contradictions could be called an abduction machine.
GF: In the present context, this would imply that abduction is
essentially mathematical, or at l
Robert, List,
I strongly agree with your approach, and I would
like to add three
quotations by Peirce (copied below). They show
that De Tienne has
misunderstood the role of mathematics in Peirce's
philosophy.
But I am not claiming that ADT does not understand
Peirce, People were
doing mathemat
Jerry and Edwina,
I found three quotations by Peirce that
directly contradict the three sentences in ADT's slide 25, (Copies below
my signature)
In the first sentence of that slide, ADT belittles
Peirce's life's work: "we cannot
count on mathematicians to help
figure out what goes on in
expe
and (c) the application of
mathematics in other theoretical
>> and practical sciences.
>
>
>
> What are the distinctions that
being referred to?
>
> Are they merely semantic
distinctions?
>
> How do these distinctions relate to the
writings of CSP?
>
>
There have been some comments about Peirce-L breaking into Tribes. I
don't believe that a tribal breakdown is good. But if there are any,
my tribe is Peirce's. He had a broad range of talents in many
fields,
but as he said himself, his philosophy "has been
entirely the fruit of
this outgrowth
Sorry about the typo.
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Gary F,
It's ironic that you should talk about tribalism. As
you might know, there have been other discussions offline about the
"triumvirate" of GR, GF, and JAS. You constantly cite each
other's notes with great praise, and ignore or browbeat others.
One
of the worst examples is a comment yo
> On 8/17/2021 12:18 PM, John F. Sowa wrote:
>>
>>
>> Sorry about the typo.
>>
>
> Looking more like Tribble-ism all the time
...
>
> Jon
>
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Jerry, Gary F, List,
I agree that Gary's example of a cedar tree
is good. And a phaneroscopic analysis of the experience shows precisely
where the mathematical reasoning comes in. This example does not involve
any deep deduction, but any analysis that is sufficiently detailed for
expression i
Gary F, List,
That's a good summary of what ADT wrote. But
good examples are far
more important than more jargon. I can't see
any justification for
ADT's jargon.
GF: But De Tienne
chooses to emphasize the primacy of mathematics,
and thus presents
positiveness as a result of a process that
André was correct in claiming that phaneroscopy must involve a
transition from experience in the phaneron to something that can be
interpreted by ordinary common sense. But he made a mistake in
claiming
that it could not be mathematical.
See below for
five quotations by CSP, which make the foll
graphs, (c) is by definition iconic, and (d) is easy for
non-mathematicians to understand: 'diagram'.
For quotations
by Peirce about these issues, see the attached file
transition.txt.
John
Subject:Transition to diagrams (was ADT slide 25
From: "John F. Sowa"
Gary F, Helmut, List,
I agree with Gary that "there are no
perfect choices when it comes to
naming such things" and we
should "weed out the choices most likely to
cause
confusion."
HR: In mathematical language, the sentence
"possibility implies a
relation to what exists" is false.
Maybe in or
Gary F, List,
GF: we agree that De Tiennes reference to a
transition out of
mathematics in slide 25 can be confusing, and you
say that we can
avoid the confusion by adopting the word 'diagram'
for ADT's slide
25. ... Do you mean substituting the word diagram
for some part of
slide 25?
Helmut, List,
JFS: I agree with Gary that "there are no
perfect choices when it
comes to naming such things" and we
should "weed out the choices most
likely to cause
confusion."
HR: But if we weed out too many terms, we may
not be able to talk
anymore! Can we not instead "count on
mathematic
>
>
> Helmut, List,
>
>
JFS: I agree with Gary that "there are no
> perfect choices
when it
> comes to naming such things" and we
>
should "weed out the choices most
> likely to cause
>
confusion."
>
> HR: But if we weed out too many
terms, we may
> not be able to talk
> anymore! Can we
My only excuse is that it's after midnight.
Helmut, List,
JFS: I agree with Gary that "there are no perfect choices
when it
comes to naming such things" and we should "weed
out the choices most
likely to cause confusion."
HR:
But if we weed out too many terms, we may not be able to talk
anym
Helmut,
Technical terms are important when a completely new
concept has been invented for which there is no convenient term in the
common vocabulary. If a new term is necessary, it's important to choose
some combination of common words that is not likely to create ambiguities
or confusions.
T
Jerry, List,
I strongly agree that the term 'qualitative
possibility' is a good term
for the applications you mentioned. I
would never suggest the word
'diagram' as a replacement for the term
'qualitative possibility' in
those contexts.
My
recommendation is a revision (copied below) of slide
Gary F, Helmut, Jerry, List,
Thanks, Gary, for that quotation.
I often search CP and EP before
commenting on Peirce's terms, and I
admit that I should have done
that. I agree that in Peirce's
quotation for "positive qualitative
possibility", it is a
useful term -- especially in the context o
Gary F, List,
Please don't attribute anything to me that I did
not say. I totally
agree with the following point.
GF:
Slide 31, following up on slide 30, make it perfectly clear that
the
key word in Peirces work on phenomenology (before and after he
renamed it phaneroscopy) is experience.
Gary R, List,
I have a high regard for ADT's expertise about
Peirce's entire body of
work and his understanding of the
interconnections and developments
over the years. But ADT is not a
mathematician or logician, and
Peirce was.
GR: But this
is just your opinion, John, and it seems to me that
Robert M, Gary F, Gary R, Jon AS, List,
I changed the subject
line to emphasize the role of diagrams in Peirce's
thought in general
and in phenomenology/phaneroscopy in particular. I
cited some of
these quotations in previous notes, and I copied others
from a note
by Robert. All of them are re
Jeff, List,
JBD: Some have suggested that the aim of
phenomenology is to provide
an analysis and account of human
consciousness.
Peirce made a sharp distinction between
phaneroscopy, the science that
provides the raw data for all the
empirical sciences, and psychology,
which is one of the psy
Edwina, Gary F, List,
ET: Thank you for this excellent
post... I'd like to note that I
think a key problem with the
arguments over 'where does mathematics
or phaneroscopy fit into this
process' is the old issue of the
differentiation of Mind and Matter
and their relations.
ET: I feel that D
Ediwina, Jon AS, Jeff JBD, List
I changed the subject line to
clarify and emphasize the distinction.
ET: the distinction
between pure and applied mathematics is very
fuzzy. I'd suspect it's
the same in phenomenology. But I do support
and agree with [Jeff's]
agenda of using both mathematics a
Jon AS, Gary F, List,
We must always distinguish the subject
matter of any science from the
people who (a) develop the science or
(b) apply the science.
The dependencies among the sciences,
which Comte noted and Peirce
adopted after reading Comte's
classification, show how each science
depend
Jeff, Edwina, Gary F, Jon AS, List,
On this issue, I agree with
Jeff that the support of the sciences
(all of them) was uppermost in
Peirce's mind. But I admit that a
more explicit statement of the
issues would have been desirable.
JBD: I have yet to see an
explanation of Peirce's phenomenolo
Jon A,
Thank you for emphasizing the need to consider and
analyze concrete examples. I have often mentioned Peirce's book,
Photometric Researches, as a textbook example of how to do
phaneroscopy, methodeutic, and all subsequent steps to produce an
important contribution to science.
But many ot
The Halloween goblin apparently replaced my name with "N/A"
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Mike,
Common Logic (CL) is a very general version of logic, and OWL is just a
tiny subset of the capabilities of CL. Peirce's existential graphs, with
a small extension, have the full expressive power of CL.
For an overview of the issues and the mappings to and from EGs, see
http://jfs
Jon A and Jerry LRC,
There are multiple issues here: (1) The syntax of the logical notation,
(2) The number of participants related by a particular relation, and (3)
the question whether a relation that relates N participants can be replaced
by two or more relations, each with a fewer numb
Ed,
I used the verb 'give' as an example of an obligatory triad: any act of
giving must have three participants. The mapping to three dyadic relations is
a purely syntactic transformation that replaces the verb "give" with a gerund
'giving' and three linguistic dyads. But the node labeled '
Azamat> I have an impression that many big problems in science and
technology could be solved by recognizing Data as a Prime Ontological
Category
Yes, of course. That is absolutely true The failure to recognize and
emphasize that point is the primary reason why the ISO standard for
onto
Azamat,
The words 'data' and 'information' represent special cases of signs.
The word 'data' is Latin for "that which has been given" and the word
'information' is an English word, derived from Latin, for that which
informs. But the word 'sign' is the general term that includes signs fr
Barry> Landgrebe and I have been working on a BFO physics Ontology and on
a mathematics Ontology, separate from BFO.
I'm glad to hear that you're finally developing an ontology for
mathematics and that it's independent of the current BFO.
Since it's impossible to do modern physics witho
Lars> I think we revolve around the same basic problem: is there anything
called 'abstraction' beyond instances of abstract cognition?
Yes. Those things are called "patterns". And the formal study of
patterns is called "mathematics". And the foundation for cognition in
every living thing
Lars,
I added the word 'women' to the subject line because I wanted to mention a
debate in 1958 that was both humorous and enlightening: "The ontological
status of women and abstract entities",
http://jfsowa.com/ontology/church.htm
In 1947, Nelson Goodman and Willard Van Orman Quine publis
Avril,
Before saying anything further, I'd like to recommend Wittgenstein's term
"Sprachspiel", which is usually translated as "language game', but a better
translation might be "language play", "language practice", or just "language
context". One of Ludwig W's ,most relevant discussions
JLRC: On some occasions, CSPeirce's logical notation included the
multiplication sign, an operation that may conflict with the scientific
notation of chemistry and the notion of a natural object
Yes. That is the reason why Peano began the practice of turning letters
upside down and backwards
Dear Ulysses,
UP: Does the metaphor of "the ground" or "grounding" in semiosis have an
association to the "ground" in electrical circuits?
Short answer: The ground in electrical circuits is not a metaphor. It
literally means a connection to something connected to the ground, such as a
wate
Alex, Matteo, Igor, Lists,
A one-dimensional structure is often an awkward approximation to some
n-dimensional structure. For example, C. S. Peirce invented the
one-dimensional notation for predicate calculus (which Peano modified by
introducing letters drawn upside-down and backwards). Bu
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.
Jon,
I'm glad that you found Dunn's semantics for modal logic useful. But
where did you find any MSS about Delta graphs?
John
t
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Is there an errata sheet for NEM or anybody who should be notified about
errors in it?
When I studied and wrote about Peirce's 1911 EGs, I used a transcription
of the mislabeled MS 514, which was mistakenly dated 1909. Since Peirce
had written some MSS with different versions of EGs with la
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