[PEIRCE-L] Re: Lowell Lecture 2.6

[Jon Awbrey]

On 11/4/2017 11:19 AM, Stephen C. Rose wrote:

I suspect the fundamental reality of Peirce's thought was there at the
start and that his later work was consistent with what he had always
thought. After the PM was in place, everything was clarification.
The revolution lay in the work he anticipated would get done in future times
as a result of his basic insight which conflicted with the past in
a fundamental and world-changing way. It's a sort of forest and trees thing.

amazon.com/author/stephenrose



Exactly.

Jon

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[PEIRCE-L] Re: Lowell Lecture 2.6

[kirstima]

Jon,
You expressed my point even in what I did not put into words.

Kirsti

Jon Awbrey kirjoitti 3.11.2017 23:06:

Kirsti, List,

The Greek “dia-” means across, apart, or through.
And Peirce recognizes that one is often talking
to oneself or one's future self, so the number
of people that one is speaking across to is
indefinite.

Regards,

Jon

On 11/3/2017 4:50 PM, kirst...@saunalahti.fi wrote:

John, Jon, list

Some comments in response

In Peirce's view logic needs mathematical grounds, but I have not 
found anything to support the view that there should be such sharp 
distinction as you propose. – There were many, many classifications of 
sciences he developed over the years. Of which latest ones should be 
given precedence. According to Peirce, the expession 'should be' has 
no meaning, if no aim is involved. If and when it is agreed that 
Peirce was aiming at something better, then this becomes self-evident, 
does it not?


I have difficulties in understanding what is meant by

John:

Game theoretical semantics (GTS) is just a mathematical theory.
As pure mathematics, Peirce would not object to it.

My understanding of what Peirce meant by pure math just does not fit 
with this statement. I won't even try to express how and why. Instead, 
I take up the question at hand.


Hintikka's early lectures on game theory were addressed to 
philosophers and social scientists, as part of the curriculum of 
practical philosophy at Helsinki University.


Prisoner's dilemma played a major role. I wonder whether it has been 
taken up by the means of existential graphs? Would like very much to 
see it/them.


My interest lies in that it presents the Dilemma of Achilles and 
tortoise in other cloths. The (seemingly) physical problem is dressed 
up as a  (seemingly) social problem in Prisoner's Dilemma.


Peirce did not object to the former, he just solved it. Thus I see no 
reason why he would have objected the latter, he just would have shown 
it to be a pseudoproblem.


Both dilemmas exist. No doubt about that. – But are they real 
problems, is quite another kind of issue. An issue about the relations 
between thought and language, but not only.


As soon as the latter dilemma is given the name 'Prisoner's dilemma', 
a host of presuppositions are taken in. – Let's just make a seemingly 
tiny change. Let's call it 'Prisoners dilemma', thus omitting a 
grammatical detail, which deeply affects the meaning conveyed. – The 
logical move entails a move from one to many. Not something to be 
overlooked or dismissed, surely.


In GTS it has been. But now I have pointed it out, a needle in the 
haystock of GTS. If you feel no sting, then I must have overestimated 
your logical sensitivity.


I have studied Peirces writings on existential graphs in a preliminary 
way, just to get the general idea & to understand it's proper place 
within Peirce's philosophy. After testing the idea on the contents of 
further (and further…) reading CSP, it holds. After testing it in the 
light of your most valuable teachings, it seems to hold. - Which is 
why I get deeply puzzled if and when your views on CSP are not, well, 
congruent.


Also, I wish to point out the currently common (sense?) 
misunderstanding with the term DIALOGUE. The very word is taken as 
referring to a discussion involving two (and only two) participants. 
As if Greek 'DIA' would mean two, which it does not. It just means 
'between'.


Thus I find

Jon:

Peirce's explanation of logical connectives and quantifiers
in terms of a game between two players attempting to support
or defeat a proposition, respectively, is a precursor of many
later versions of game-theoretic semantics.

as neclecting something essential (in a Peircean view). The implied 
third is the audience ( from 'dear reader' on…). 'There is one…' 
claims a possibility. 'All…' claims a necessity. In between the lies 
the realm of probable inference, abduction, hypothesis & the lot.


The idea of continuity is of course needed to understand the the real 
nature both dilemmas and to solve them. Both are pseudoproblems, in 
the positive meaning of the term offered in EG. Really solving them, 
of course, goes beyond the proper realm of existential graphs. Gamma 
graphs would be needed.


But if the meaning of the term 'formal theory' is for starters defined 
as just a part of math, then … Well, what? Does math then mean 
anything else but 'formal'?


Wondering,

Kirsti


John F Sowa kirjoitti 2.11.2017 22:08:

Gary F, Jeff BD, Kirsti, Jon A,

I didn't respond to your previous notes because I was tied up with
other work.  Among other things, I presented some slides for a 
telecon

sponsored by Ontolog Forum.  Slide 23 (cspsci.gif attached) includes
my diagram of Peirce's classification of the sciences and discusses 
the
implications.  (For all slides: http://jfsowa.com/talks/contexts.pdf 
)


Among the implications:  The sharp distinction between "formal 
logic",
which is part of mathematics, from logic as a 

[PEIRCE-L] Re: Lowell Lecture 2.6

[Jon Awbrey]

On 11/2/2017 4:08 PM, John F Sowa wrote:
>
> Among the implications:  The sharp distinction between "formal logic",
> which is part of mathematics, from logic as a normative science and the
> many studies of reasoning in linguistics, psychology, and education.
>

John, List,

Peirce used the word “formal” in a sense that gave it a normative connotation.
That is the sense in which he defined “logic” as “formal semiotic”.

I think that raises some problems with the proposal of
a “sharp distinction between ‘formal logic’, which is
part of mathematics, from logic as a normative science”.

I don't think this means that “formal logic” is “formal formal semiotic”,
and as such a part of mathematics.  I think it simply means that logic
is inherently formal (= normative) and adding the adjective “formal”
is redundant.

Regards,

Jon

Links to a few relevant texts:

C.S. Peirce • On the Definition of Logic
https://inquiryintoinquiry.com/2012/06/01/c-s-peirce-%e2%80%a2-on-the-definition-of-logic/
Posted on June 1, 2012 by Jon Awbrey

Selections from C.S. Peirce, “Carnegie Application” (1902)

No. 12. On the Definition of Logic

Logic will here be defined as formal semiotic. A definition of a sign will be given which no more refers to human 
thought than does the definition of a line as the place which a particle occupies, part by part, during a lapse of time. 
Namely, a sign is something, A, which brings something, B, its interpretant sign determined or created by it, into the 
same sort of correspondence with something, C, its object, as that in which itself stands to C. It is from this 
definition, together with a definition of “formal”, that I deduce mathematically the principles of logic. I also make a 
historical review of all the definitions and conceptions of logic, and show, not merely that my definition is no 
novelty, but that my non-psychological conception of logic has virtually been quite generally held, though not generally 
recognized. (NEM 4, 20–21).


C.S. Peirce • Logic as Semiotic
https://inquiryintoinquiry.com/2012/06/04/c-s-peirce-%E2%80%A2-logic-as-semiotic/
Posted on June 4, 2012 by Jon Awbrey

Selection from C.S. Peirce, “Ground, Object, and Interpretant” (c. 1897)

Logic, in its general sense, is, as I believe I have shown, only another name for semiotic (σημειωτική), the 
quasi-necessary, or formal, doctrine of signs. By describing the doctrine as “quasi-necessary”, or formal, I mean that 
we observe the characters of such signs as we know, and from such an observation, by a process which I will not object 
to naming Abstraction, we are led to statements, eminently fallible, and therefore in one sense by no means necessary, 
as to what must be the characters of all signs used by a “scientific” intelligence, that is to say, by an intelligence 
capable of learning by experience. As to that process of abstraction, it is itself a sort of observation.


See Also:

The Difference That Makes A Difference That Peirce Makes : 14
https://inquiryintoinquiry.com/2017/06/24/the-difference-that-makes-a-difference-that-peirce-makes-14/
Posted on June 24, 2017 by Jon Awbrey

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[PEIRCE-L] Re: Lowell Lecture 2.6

[Jon Awbrey]

Kirsti, List,

The Greek “dia-” means across, apart, or through.
And Peirce recognizes that one is often talking
to oneself or one's future self, so the number
of people that one is speaking across to is
indefinite.

Regards,

Jon

On 11/3/2017 4:50 PM, kirst...@saunalahti.fi wrote:

John, Jon, list

Some comments in response

In Peirce's view logic needs mathematical grounds, but I have not found anything to support the view that there should 
be such sharp distinction as you propose. – There were many, many classifications of sciences he developed over the 
years. Of which latest ones should be given precedence. According to Peirce, the expession 'should be' has no meaning, 
if no aim is involved. If and when it is agreed that Peirce was aiming at something better, then this becomes 
self-evident, does it not?


I have difficulties in understanding what is meant by

John:

Game theoretical semantics (GTS) is just a mathematical theory.
As pure mathematics, Peirce would not object to it.

My understanding of what Peirce meant by pure math just does not fit with this statement. I won't even try to express 
how and why. Instead, I take up the question at hand.


Hintikka's early lectures on game theory were addressed to philosophers and social scientists, as part of the curriculum 
of practical philosophy at Helsinki University.


Prisoner's dilemma played a major role. I wonder whether it has been taken up by the means of existential graphs? Would 
like very much to see it/them.


My interest lies in that it presents the Dilemma of Achilles and tortoise in other cloths. The (seemingly) physical 
problem is dressed up as a  (seemingly) social problem in Prisoner's Dilemma.


Peirce did not object to the former, he just solved it. Thus I see no reason why he would have objected the latter, he 
just would have shown it to be a pseudoproblem.


Both dilemmas exist. No doubt about that. – But are they real problems, is quite another kind of issue. An issue about 
the relations between thought and language, but not only.


As soon as the latter dilemma is given the name 'Prisoner's dilemma', a host of presuppositions are taken in. – Let's 
just make a seemingly tiny change. Let's call it 'Prisoners dilemma', thus omitting a grammatical detail, which deeply 
affects the meaning conveyed. – The logical move entails a move from one to many. Not something to be overlooked or 
dismissed, surely.


In GTS it has been. But now I have pointed it out, a needle in the haystock of GTS. If you feel no sting, then I must 
have overestimated your logical sensitivity.


I have studied Peirces writings on existential graphs in a preliminary way, just to get the general idea & to understand 
it's proper place within Peirce's philosophy. After testing the idea on the contents of further (and further…) reading 
CSP, it holds. After testing it in the light of your most valuable teachings, it seems to hold. - Which is why I get 
deeply puzzled if and when your views on CSP are not, well, congruent.


Also, I wish to point out the currently common (sense?) misunderstanding with the term DIALOGUE. The very word is taken 
as referring to a discussion involving two (and only two) participants. As if Greek 'DIA' would mean two, which it does 
not. It just means 'between'.


Thus I find

Jon:

Peirce's explanation of logical connectives and quantifiers
in terms of a game between two players attempting to support
or defeat a proposition, respectively, is a precursor of many
later versions of game-theoretic semantics.

as neclecting something essential (in a Peircean view). The implied third is the audience ( from 'dear reader' on…). 
'There is one…' claims a possibility. 'All…' claims a necessity. In between the lies the realm of probable inference, 
abduction, hypothesis & the lot.


The idea of continuity is of course needed to understand the the real nature both dilemmas and to solve them. Both are 
pseudoproblems, in the positive meaning of the term offered in EG. Really solving them, of course, goes beyond the 
proper realm of existential graphs. Gamma graphs would be needed.


But if the meaning of the term 'formal theory' is for starters defined as just a part of math, then … Well, what? Does 
math then mean anything else but 'formal'?


Wondering,

Kirsti


John F Sowa kirjoitti 2.11.2017 22:08:

Gary F, Jeff BD, Kirsti, Jon A,

I didn't respond to your previous notes because I was tied up with
other work.  Among other things, I presented some slides for a telecon
sponsored by Ontolog Forum.  Slide 23 (cspsci.gif attached) includes
my diagram of Peirce's classification of the sciences and discusses the
implications.  (For all slides: http://jfsowa.com/talks/contexts.pdf )

Among the implications:  The sharp distinction between "formal logic",
which is part of mathematics, from logic as a normative science and the
many studies of reasoning in linguistics, psychology, and education.

Peirce was very clear about the infinity of 

Aw: [PEIRCE-L] Re: Lowell Lecture 2.6

[Helmut Raulien]

 
 

Supp-supplement: Please do not take my second example seriously, because: If the olden Indians have had a different concept about ways of existence, they nevertheless have used the term "exists" in the exactly same way as we do. And, if Lao Tse has thought, that there is no pure cut existing, he anyway has used the symbol for a (pure, real) cut in the same way that we do, in his yin-yang-graph, just has added the (existing) impurity by inserting the two oppositely coloured blots. So- universal logic exists, the devil´s advocate was wrong.



 
 

Supplement: Regarding what you wrote about "the object of logic that is common to all its avatars": Calling the avatars "languages" or "culturally different kinds of logic", I think it is very important to identify such a common object of logic, and maybe the EGs can help with that.

I think it is important, because it refutes cultural relativism, and corrobates e.g. Chomsky´s assumption of a universal grammar. I think that a scientifically corrobated universal way of thinking is important, because it helps to argue against the contemporary uprising of the political right-wingers in Europe and worldwide and their concept of "ethnopluralism".

I am still wondering about two examples: Some time ago, in the west other than in India, there wasn´t a "zero" in mathematics. What did people call it when they were broke? Did they have to decide whether they posessed something, or had debts?

The other example is: In the west, either something exists, or it doesn´t. But in ancient Indian wisdom there are four ways: Something exists / something doesn´t exist / something both exists and doesn´t exist / and something neither exists nor doesn´t exist. Well, is it possible to proove, that this Indian logic can not be expressed with, maybe somehow modified, EGs? And, can it be prooved, that the concept of "cut" is not just a false western concept, while in e.g. China they have this "Yin-Yang" graph, that illustrates that there cannot be a real cut: The negation always contains a small part of corrobation (negation of the negation)? Ok, my thoughts are going wild, don´t answer all my questions. I was just taking the role of a devil´s advocate- for real I pledge for universality and universal logic, as I had said before.

 




Jon, list,

thank you! "Not a without b" is much more simple, I sometimes think too complicatedly.

Reading the LL 7, and having read the Wikipedia article about EGs, I ask myself: Isnt that the same like in Spencer-Brown´s book "Laws of Form", except that Spencer-Brown says "distinction" instead of "cut"? Is there something new by "Laws of Form", e.g. the re-entry? And why did Spencer-Brown not mention Peirce in his book? Not nice, is it?

Best,

Helmut

 

 31. Oktober 2017 um 13:45 Uhr
 "Jon Awbrey" 
wrote:

 

Helmut, List,

Another way to read the form (a(b))
[in the existential interpretation]
is “not a without b”.

Peirce's approach in these lectures appeals to the line of thinking
that takes implications and the corresponding subject-predicate form
as basic, but that is not the only possible basis for a logical system
of syntax and not the only basis that Peirce himself took up in his many
syntactic experiments. In relating logical signs to logical objects it
normally proves best to remain flexible and to consider the object of
logic that is common to all its avatars.

Regards,

Jon

On 10/31/2017 3:34 AM, Helmut Raulien wrote:
> List,
> I have thought about how "if-then" translates from the cuts: If a cut would mean
> "it is not so, that", it would be: "It is not so, that it rains and it is not
> so, that a pear is ripe". This is not sufficient for translation, because an
> "and it" may be understood symmetrically, therefore it must be "and then" for
> a cut in a cut: "It is not so, that it rains, and then is not so, that a pear
> is ripe". Still insufficient, because it must be estimated, that the negation
> by the outer cut is valid for all outside, the whole universe (that it is not
> so not only in London, but everywhere): "It cannot be, that it rains and then
> is not so, that a pear is ripe". Now, by annihilating double negation, "It
> cannot be that then not" becomes "if, then".
> Best,
> Helmut

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[PEIRCE-L] Re: Lowell Lecture 2.6

[Jon Awbrey]

Helmut, List,

GSB mentioned CSP and also Christine Ladd-Franklin
in the chapter notes, appendices, and references
of his Laws of Form.  Just scanning very quickly,
I find refs on pages 90, 111, and 136 in my copy.

Almost in spite of its extremely elegant style, Laws of Form
did succeed in reviving a visual way of looking at logic that
Peirce had pioneered but that few other logicians took up with
any success in the intervening years.  It drew out and clarified
a number of insights into the mathematical forms and methods of
logic that Peirce had the depth of vision to peer into but did
not always have the opportunity to develop as far as possible.

Sorry, short on time ...
Will try to get back ...

Regards,

Jon

On 10/31/2017 12:06 PM, Helmut Raulien wrote:

Jon, list,
thank you! "Not a without b" is much more simple,
I sometimes think too complicatedly.
Reading the LL 7, and having read the Wikipedia article about EGs, I ask myself:
Isn't that the same like in Spencer-Brown´s book "Laws of Form", except that
Spencer-Brown says "distinction" instead of "cut"?  Is there something new by
"Laws of Form", e.g. the re-entry?  And why did Spencer-Brown not mention
Peirce in his book?  Not nice, is it?
Best,
Helmut

>

31. Oktober 2017 um 13:45 Uhr
"Jon Awbrey"  wrote:
Helmut, List,

Another way to read the form (a(b))
[in the existential interpretation]
is “not a without b”.

Peirce's approach in these lectures appeals to the line of thinking
that takes implications and the corresponding subject-predicate form
as basic, but that is not the only possible basis for a logical system
of syntax and not the only basis that Peirce himself took up in his many
syntactic experiments.  In relating logical signs to logical objects it
normally proves best to remain flexible and to consider the object of
logic that is common to all its avatars.

Regards,

Jon

On 10/31/2017 3:34 AM, Helmut Raulien wrote:

List,
I have thought about how "if-then" translates from the cuts: If a cut would mean
"it is not so, that", it would be: "It is not so, that it rains and it is not
so, that a pear is ripe". This is not sufficient for translation, because an
"and it" may be understood symmetrically, therefore it must be "and then" for
a cut in a cut: "It is not so, that it rains, and then is not so, that a pear
is ripe". Still insufficient, because it must be estimated, that the negation
by the outer cut is valid for all outside, the whole universe (that it is not
so not only in London, but everywhere): "It cannot be, that it rains and then
is not so, that a pear is ripe". Now, by annihilating double negation,
"It cannot be that then not" becomes "if, then".
Best,
Helmut




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Aw: [PEIRCE-L] Re: Lowell Lecture 2.6

[Helmut Raulien]

 
 

Supplement: Regarding what you wrote about "the object of logic that is common to all its avatars": Calling the avatars "languages" or "culturally different kinds of logic", I think it is very important to identify such a common object of logic, and maybe the EGs can help with that.

I think it is important, because it refutes cultural relativism, and corrobates e.g. Chomsky´s assumption of a universal grammar. I think that a scientifically corrobated universal way of thinking is important, because it helps to argue against the contemporary uprising of the political right-wingers in Europe and worldwide and their concept of "ethnopluralism".

I am still wondering about two examples: Some time ago, in the west other than in India, there wasn´t a "zero" in mathematics. What did people call it when they were broke? Did they have to decide whether they posessed something, or had debts?

The other example is: In the west, either something exists, or it doesn´t. But in ancient Indian wisdom there are four ways: Something exists / something doesn´t exist / something both exists and doesn´t exist / and something neither exists nor doesn´t exist. Well, is it possible to proove, that this Indian logic can not be expressed with, maybe somehow modified, EGs? And, can it be prooved, that the concept of "cut" is not just a false western concept, while in e.g. China they have this "Yin-Yang" graph, that illustrates that there cannot be a real cut: The negation always contains a small part of corrobation (negation of the negation)? Ok, my thoughts are going wild, don´t answer all my questions. I was just taking the role of a devil´s advocate- for real I pledge for universality and universal logic, as I had said before.

 




Jon, list,

thank you! "Not a without b" is much more simple, I sometimes think too complicatedly.

Reading the LL 7, and having read the Wikipedia article about EGs, I ask myself: Isnt that the same like in Spencer-Brown´s book "Laws of Form", except that Spencer-Brown says "distinction" instead of "cut"? Is there something new by "Laws of Form", e.g. the re-entry? And why did Spencer-Brown not mention Peirce in his book? Not nice, is it?

Best,

Helmut

 

 31. Oktober 2017 um 13:45 Uhr
 "Jon Awbrey" 
wrote:

 

Helmut, List,

Another way to read the form (a(b))
[in the existential interpretation]
is “not a without b”.

Peirce's approach in these lectures appeals to the line of thinking
that takes implications and the corresponding subject-predicate form
as basic, but that is not the only possible basis for a logical system
of syntax and not the only basis that Peirce himself took up in his many
syntactic experiments. In relating logical signs to logical objects it
normally proves best to remain flexible and to consider the object of
logic that is common to all its avatars.

Regards,

Jon

On 10/31/2017 3:34 AM, Helmut Raulien wrote:
> List,
> I have thought about how "if-then" translates from the cuts: If a cut would mean
> "it is not so, that", it would be: "It is not so, that it rains and it is not
> so, that a pear is ripe". This is not sufficient for translation, because an
> "and it" may be understood symmetrically, therefore it must be "and then" for
> a cut in a cut: "It is not so, that it rains, and then is not so, that a pear
> is ripe". Still insufficient, because it must be estimated, that the negation
> by the outer cut is valid for all outside, the whole universe (that it is not
> so not only in London, but everywhere): "It cannot be, that it rains and then
> is not so, that a pear is ripe". Now, by annihilating double negation, "It
> cannot be that then not" becomes "if, then".
> Best,
> Helmut

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Aw: [PEIRCE-L] Re: Lowell Lecture 2.6

[Helmut Raulien]

Jon, list,

thank you! "Not a without b" is much more simple, I sometimes think too complicatedly.

Reading the LL 7, and having read the Wikipedia article about EGs, I ask myself: Isnt that the same like in Spencer-Brown´s book "Laws of Form", except that Spencer-Brown says "distinction" instead of "cut"? Is there something new by "Laws of Form", e.g. the re-entry? And why did Spencer-Brown not mention Peirce in his book? Not nice, is it?

Best,

Helmut

 

 31. Oktober 2017 um 13:45 Uhr
 "Jon Awbrey" 
wrote:

 

Helmut, List,

Another way to read the form (a(b))
[in the existential interpretation]
is “not a without b”.

Peirce's approach in these lectures appeals to the line of thinking
that takes implications and the corresponding subject-predicate form
as basic, but that is not the only possible basis for a logical system
of syntax and not the only basis that Peirce himself took up in his many
syntactic experiments. In relating logical signs to logical objects it
normally proves best to remain flexible and to consider the object of
logic that is common to all its avatars.

Regards,

Jon

On 10/31/2017 3:34 AM, Helmut Raulien wrote:
> List,
> I have thought about how "if-then" translates from the cuts: If a cut would mean
> "it is not so, that", it would be: "It is not so, that it rains and it is not
> so, that a pear is ripe". This is not sufficient for translation, because an
> "and it" may be understood symmetrically, therefore it must be "and then" for
> a cut in a cut: "It is not so, that it rains, and then is not so, that a pear
> is ripe". Still insufficient, because it must be estimated, that the negation
> by the outer cut is valid for all outside, the whole universe (that it is not
> so not only in London, but everywhere): "It cannot be, that it rains and then
> is not so, that a pear is ripe". Now, by annihilating double negation, "It
> cannot be that then not" becomes "if, then".
> Best,
> Helmut

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[PEIRCE-L] Re: Lowell Lecture 2.6

[Jon Awbrey]

Helmut, List,

Another way to read the form (a(b))
[in the existential interpretation]
is “not a without b”.

Peirce's approach in these lectures appeals to the line of thinking
that takes implications and the corresponding subject-predicate form
as basic, but that is not the only possible basis for a logical system
of syntax and not the only basis that Peirce himself took up in his many
syntactic experiments.  In relating logical signs to logical objects it
normally proves best to remain flexible and to consider the object of
logic that is common to all its avatars.

Regards,

Jon

On 10/31/2017 3:34 AM, Helmut Raulien wrote:

List,
I have thought about how "if-then" translates from the cuts: If a cut would mean
"it is not so, that", it would be: "It is not so, that it rains and it is not
so, that a pear is ripe". This is not sufficient for translation, because an
"and it" may be understood symmetrically, therefore it must be "and then" for
a cut in a cut: "It is not so, that it rains, and then is not so, that a pear
is ripe". Still insufficient, because it must be estimated, that the negation
by the outer cut is valid for all outside, the whole universe (that it is not
so not only in London, but everywhere): "It cannot be, that it rains and then
is not so, that a pear is ripe". Now, by annihilating double negation, "It 
cannot be that then not" becomes "if, then".

Best,
Helmut


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[PEIRCE-L] Re: Lowell Lecture 2.6

[Jon Awbrey]

Gary, List,

Peirce's introduction of the “blot” at this point is one of the places where
he touches on the “arithmetic” of logic underlying the “algebra” of logic,
a development that began with his taking up the empty sheet of assertion,
a “tabula rasa” or “uncarved block”, as a logical constant for truth.

The radical insight involved in this move would later be emphasized
by George Spencer Brown when he revived certain aspects of Peirce's
graphical approach to logic in the late 1960s.

More to follow, as I find the opportunity ...

Regards,

Jon

On 10/28/2017 4:38 AM, g...@gnusystems.ca wrote:

Continuing from Lowell 2.5:

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low
ell-lecture-ii/display/13608

In order to get an insight into how the scroll represents the conditional
proposition de inesse, we must make a little experimental research.

Thus far, we have no means of expressing an absurdity. Let us invent a sign
which shall assert that everything is true. Nothing could be more illogical
than that statement, inasmuch as it would render logic false as well as
needless. Were every graph asserted to be true, there would be nothing that
could be added to that assertion. Accordingly, our expression for it may
very appropriately consist in completely filling up the area on which it is
asserted. Such filling up of an area, may be termed a blot.

Take the conditional proposition de inesse, "If it rains then everything is
true[":]

That amounts to denying that it rains. But there is no need of making the
inner cut so large. Let us write

or even

This suggests that the relation which the cut asserts between the universe
of discourse and what is scribed within it is simply that what is scribed
within is false of the universe of discourse.

Then we may interpret

as meaning "It is false that it rains and that a pear is not ripe." But we
have already seen that this is precisely the whole meaning of the
conditional de inesse; namely that it is false that the antecedent is true
while the consequent is false. Thus, that which the cut asserts is precisely
that that which is on its bottom is not, as a whole, true.

 http://gnusystems.ca/Lowells.htm }{
Peirce's Lowell Lectures of 1903

https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii



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