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Apr 4, 2021, 2:30:23 PM4/4/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Paradisaical Logic and the After Math • Comment 1

https://inquiryintoinquiry.com/2021/04/04/paradisaical-logic-and-the-after-math-comment-1/

Re: Peter Cameron • Cultures, Tribes, or Just an Illusion?

https://cameroncounts.wordpress.com/2012/04/01/cultures-tribes-or-just-an-illusion/

Re: Peirce List

https://list.iupui.edu/sympa/arc/peirce-l/2012-04/thrd1.html#00004

https://list.iupui.edu/sympa/arc/peirce-l/2021-03/thrd7.html#00205

https://list.iupui.edu/sympa/arc/peirce-l/2021-04/thrd1.html#00001

All,

One of many recurring themes — you might call it “The Power of

Negative Thinking” — arose this time on the Peirce List and it

took me back to a piece I wrote nine Aprils ago and that took

me even further back to the very doors I first walked through

into the wonderland of logic à la Peirce.

I fixed the links broken by the ravages of time and the impings

of web developers and I added more links to the original context

of discussion. A partial transcript follows.

Paradisaical Logic and the After Math

=====================================

https://inquiryintoinquiry.com/2012/04/09/paradisaical-logic-and-the-after-math/

Not too coincidentally with the mention of Peirce’s existential graphs,

a tangent of discussion elsewhere brought to mind an old favorite passage

from Peirce, where he is using his entitative graphs to expound the logic

of relatives. Here is the observation I was led to make.

Paradisaical Logic

==================

Negative operations (NOs), if not more important than

positive operations (POs), are at least more powerful

or generative, because the right NOs can generate all

POs, but the reverse is not so.

Which brings us to Peirce’s amphecks, NAND and NNOR,

either of which is a sole sufficient operator for

all boolean operations.

Amphecks ( https://oeis.org/wiki/Ampheck )

NAND ( https://oeis.org/wiki/Logical_NAND )

NNOR ( https://oeis.org/wiki/Logical_NNOR )

In one of his developments of a graphical syntax for logic,

that described in passing an application of the Neither-Nor

operator, Peirce referred to the stage of reasoning before

the encounter with falsehood as “paradisaical logic, because

it represents the state of Man’s cognition before the Fall.”

Here’s a bit of what he wrote there —

C.S. Peirce • Relatives of Second Intention

https://inquiryintoinquiry.com/2012/04/07/c-s-peirce-relatives-of-second-intention/

Resources

=========

Logic Syllabus ( https://oeis.org/wiki/Logic_Syllabus )

Peirce’s 1870 Logic Of Relatives

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview

Regards,

Jon

https://inquiryintoinquiry.com/2021/04/04/paradisaical-logic-and-the-after-math-comment-1/

Re: Peter Cameron • Cultures, Tribes, or Just an Illusion?

https://cameroncounts.wordpress.com/2012/04/01/cultures-tribes-or-just-an-illusion/

Re: Peirce List

https://list.iupui.edu/sympa/arc/peirce-l/2012-04/thrd1.html#00004

https://list.iupui.edu/sympa/arc/peirce-l/2021-03/thrd7.html#00205

https://list.iupui.edu/sympa/arc/peirce-l/2021-04/thrd1.html#00001

All,

One of many recurring themes — you might call it “The Power of

Negative Thinking” — arose this time on the Peirce List and it

took me back to a piece I wrote nine Aprils ago and that took

me even further back to the very doors I first walked through

into the wonderland of logic à la Peirce.

I fixed the links broken by the ravages of time and the impings

of web developers and I added more links to the original context

of discussion. A partial transcript follows.

Paradisaical Logic and the After Math

=====================================

https://inquiryintoinquiry.com/2012/04/09/paradisaical-logic-and-the-after-math/

Not too coincidentally with the mention of Peirce’s existential graphs,

a tangent of discussion elsewhere brought to mind an old favorite passage

from Peirce, where he is using his entitative graphs to expound the logic

of relatives. Here is the observation I was led to make.

Paradisaical Logic

==================

Negative operations (NOs), if not more important than

positive operations (POs), are at least more powerful

or generative, because the right NOs can generate all

POs, but the reverse is not so.

Which brings us to Peirce’s amphecks, NAND and NNOR,

either of which is a sole sufficient operator for

all boolean operations.

Amphecks ( https://oeis.org/wiki/Ampheck )

NAND ( https://oeis.org/wiki/Logical_NAND )

NNOR ( https://oeis.org/wiki/Logical_NNOR )

In one of his developments of a graphical syntax for logic,

that described in passing an application of the Neither-Nor

operator, Peirce referred to the stage of reasoning before

the encounter with falsehood as “paradisaical logic, because

it represents the state of Man’s cognition before the Fall.”

Here’s a bit of what he wrote there —

C.S. Peirce • Relatives of Second Intention

https://inquiryintoinquiry.com/2012/04/07/c-s-peirce-relatives-of-second-intention/

Resources

=========

Logic Syllabus ( https://oeis.org/wiki/Logic_Syllabus )

Peirce’s 1870 Logic Of Relatives

https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Overview

Regards,

Jon

Apr 6, 2021, 10:11:29 AM4/6/21

to ontolo...@googlegroups.com, Cybernetic Communications, Laws of Form, Peirce List, Structural Modeling, SysSciWG

Dear Jon,

I'm not sure if I understand, but in an old post you said:

" " is "true".

"( )" is "false".

"a b" is "a and b"

"(a)" is "not a"

"((a)(b)) is "a or b"

"(a(b))" is "a implies b"

etc.

"( )" is "false".

"a b" is "a and b"

"(a)" is "not a"

"((a)(b)) is "a or b"

"(a(b))" is "a implies b"

etc.

By these we can append:

NAND = (a b)

NNOR= (a)(b)

and then we can construct the duality, with the sign /=, like this:

NAND/=(NNOR)

So the power of negative thinking is NAND if all the variable are true the solution is false or say in an other way just a false variable make true the solution. In NNOR if all variable are false the solution is trueor in an other way if just a variable is true the solution is false.

So:

a b NAND NNOR (NNOR)

V V F F V

V F V F V

F V V F V

F F V V F

regards

Mauro

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"[..] events are primarily linguistic or cognitive in nature. That is, the world does not really contain events. Rather, events are the way by which agents classify certain useful and relevant patterns of change."

Allen and Fergusson

Allen and Fergusson

"No, no. *History of Eternity*. At first I wanted to find every single one of the buyers to apologize because of the book and also to thank them for what they had done. There is an explanation for that. If you think of thirty-seven people—those people are real, I mean every one of them has a face of his own, a family, he lives on his own particular street. Why, if you sell, say two thousand copies, it is the same thing as if you had sold nothing at all because two thousand is too vast—I mean, for the imagination to grasp. While thirty-seven people—perhaps thirty-seven are too many, perhaps seventeen would have been better or even seven—but still thirty-seven are still within the scope of one's imagination."

Apr 6, 2021, 10:46:27 AM4/6/21

to ontolo...@googlegroups.com, Cybernetic Communications, Laws of Form, Peirce List, Structural Modeling, SysSciWG

Hi Mauro,

I won’t be getting my computer back till my wife gets done with her zoom conference so I’ll just post this link to a bit about “sole sufficient operators” in boolean algebra or propositional calculus.

Sole Sufficient Operator

See also —

Ampheck

Regards,

To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/CAAhN2n5rw8WSWXNKxoHHoKb5hDC4KXpZN-Ccv-7xkM52cR-DiA%40mail.gmail.com.

Apr 7, 2021, 8:00:39 PM4/7/21

to Cybernetic Communications, Laws of Form, Ontolog Forum, Peirce List, Structural Modeling, SysSciWG

Cf: Paradisaical Logic and the After Math • Comment 2

http://inquiryintoinquiry.com/2021/04/07/paradisaical-logic-and-the-after-math-comment-2/

Re: Peirce List

https://list.iupui.edu/sympa/arc/peirce-l/2021-04/thrd1.html#00005

::: Mauro Bertani

https://pilot.list.iupui.edu/sympa/arc/peirce-l/2021-04/msg00014.html

[Note: Cleaned up yesterday's copy and added a few resource links.]

Dear Mauro,

My access to the internet is limited today — maybe

I can make a start toward addressing your comments

by linking to an article on “sole sufficient operators”

in boolean algebra and propositional calculus.

• Sole Sufficient Operator

https://oeis.org/wiki/Sole_sufficient_operator

There's more information about Peirce's “amphecks”,

tantamount to what we now call Nand and Nnor in

the following article.

• Ampheck ( https://oeis.org/wiki/Ampheck )

• Logical NAND ( https://oeis.org/wiki/Logical_NAND )

• Logical NNOR ( https://oeis.org/wiki/Logical_NNOR )

Regards,

Jon

http://inquiryintoinquiry.com/2021/04/07/paradisaical-logic-and-the-after-math-comment-2/

Re: Peirce List

https://list.iupui.edu/sympa/arc/peirce-l/2021-04/thrd1.html#00005

::: Mauro Bertani

https://pilot.list.iupui.edu/sympa/arc/peirce-l/2021-04/msg00014.html

[Note: Cleaned up yesterday's copy and added a few resource links.]

Dear Mauro,

My access to the internet is limited today — maybe

I can make a start toward addressing your comments

by linking to an article on “sole sufficient operators”

in boolean algebra and propositional calculus.

• Sole Sufficient Operator

https://oeis.org/wiki/Sole_sufficient_operator

There's more information about Peirce's “amphecks”,

tantamount to what we now call Nand and Nnor in

the following article.

• Ampheck ( https://oeis.org/wiki/Ampheck )

• Logical NAND ( https://oeis.org/wiki/Logical_NAND )

• Logical NNOR ( https://oeis.org/wiki/Logical_NNOR )

Regards,

Jon

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