Re: LEM Re: [PEIRCE-L] Lowell Lecture 1.8

[John F Sowa]

Jerry and Kirstima,

Jerry

the issue of the "Law of the Excluded Middle” is a red herring to me.


Kirstima

LEM presents one of the three basic misassumptions in modern logic.


LEM is a convention used in a technical (mathematical) sense.
It's important to keep the conventions distinct from ordinary
(non-technical) uses of words.

Jerry

“Everything”, in my opinion, goes far beyond the ultra-simple notions
mathematical logic, mathematical formalisms, and  physical units of
representations 


Yes, of course.  You have to keep technical terms in logic distinct
from words in ordinary language that are spelled the same.

The term 'universe of discourse' is a technical term, which Boole
introduced in his famous book, _Laws of Thought_ (1854):

Now, whatever may be the extent of the field within which all the
objects of our discourse are found, that field may properly be termed
the universe of discourse. Furthermore, this universe of discourse
is in the strictest sense the ultimate subject of the discourse.


When Peirce was talking about logic, he followed the terminology
of Boole and de Morgen.  It's important to remember that context.

To avoid confusion, modern books on logic often use the term 'domain
of discourse' instead of 'universe of discourse'.  In this thread,
I suggest that we adopt the word 'domain'.

But when quoting Peirce, it's important to use his exact words.
To emphasize the distinction, we could write "universe [domain]"
in any quotation by Peirce that uses Boole's sense of 'universe'.

Peirce was a very clear thinker.  But sometimes his writings,
when taken out of context, may be confusing.  For any particular
context, it's important to note his assumptions in that *domain*.

John

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LEM Re: [PEIRCE-L] Lowell Lecture 1.8

[Jerry LR Chandler]

List , John:

I wrote:

"Because it violates the common sense of the meaning of natural language terms 
in the premise.”

John, your introducing the issue of the "Law of the Excluded Middle” is a red 
herring to me.  Let me add a word or two to clarify my intent.

My concern is rather esoteric from the attempt of mathematical / logical 
reasoning to reduce meaning to empty symbols.  
My concern is founded on the nature of the meanings of signs / signals / icons 
/ indexes and symbols.

The usage of the term “Everything” includes, I presume, all possible premises, 
irrespective of the symbolic origin of the premise. “Everything”, in my 
opinion, goes far beyond the ultra-simple notions mathematical logic, 
mathematical formalisms, and  physical units of representations (abstractions 
from nature).

The universe is what it is and the CSP writings challenges us find 
representations of all its emanations, not merely those that are concerned to 
the well-worn paths of predicate logic and ridiculous functions that ignore the 
observable nature of nature.

If one wishes to explore the pragmatic nature of “everything”, one could choose 
a significant concern, such as the practice of medicine or molecular biology.

Cheers

Jerry


> On Oct 11, 2017, at 1:20 AM, John F Sowa  wrote:
> 
> Jerry LRC, Jon AS, List,
> 
> Jerry
>>> [JFS] Since a contradiction is always false, a contradiction
>>> implies everything.
>> Everything?  While this assertion is widely repeated in
>> the literature, I think it is highly problematic.
> 
> It's widely repeated because it is a fundamental assumption
> of most versions of formal logic -- i.e., of every logic that
> assumes the Law of Excluded Middle (LEM).
> 
> But it is indeed problematic.  Brouwer, for example, rejected
> LEM for intuitionistic logic.
> 
> And even for systems that are based on LEM, nobody actually claims
> that everything has been proved.  Instead, they recognize that there
> is a mistake somewhere, and they start searching for it.
> 
> Jon
>> [JFS]  For modal logic, there are three options:
>> necessary, possible, and contingent (not necessary and not impossible).
>> Did you mean to say necessary, impossible, and contingent?
> 
> Yes.  I wrote that too hastily.  "not impossible" is a synonym
> for "possible".  For the three options, I should have written
> necessary, impossible, and contingent (possible and not necessary).
> 
> But after I sent that note, I did some googling, which led me
> to the article "Peirce and Brouwer" by Conor Mayo-Wilson:
> http://mayowilson.org/Papers/Peirce_Brouwer.pdf
> 
> Some excerpts:
> 
> page 1
>> In his 1908 "The Unreliability of the Logical Principles" Brouwer
>> rejected the law of excluded middle (LEM)...
>> Five years earlier, Peirce had reached similar conclusions...
> 
> p. 2
>> Peirce and Brouwer's common rejection of LEM is not simply a
>> coincidence, but rather, stems from a deep underlying similarity
>> in their respective philosophical analyses of the continuum.
> 
> p. 3
>> Peirce and Brouwer seemed to have no knowledge of each other's work.
>> Brouwer might have learned of Peirce's ideas on semiotics in the
>> 1920's through his association with Lady Welby... However, the two
>> most likely worked independently...
> 
> Fernando Zalamea also discusses Peirce and Brouwer in connection
> with the continuum.  But he doesn't mention Lady Welby:
> http://uberty.org/wp-content/uploads/2015/07/Zalamea-Peirces-Continuum.pdf
> 
> In any case, these sources indicate that Peirce began to reconsider
> his ideas about LEM around the same time as the Lowell lectures.
> His thoughts about the continuum seem to be the original reason.
> But by 1909, his thoughts led to 3-valued logic and a new way
> of representing and describing existential graphs.
> 
> John
> 
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> 
> 
> 
> 


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Re: [PEIRCE-L] Lowell Lecture 1.8

[kirstima]

List, John, Jerry and Jon,

LEM presents one of the three basic misassuptions in modern logic. For 
all I know CSP and Brouwer came to similar conclusions independently.  
They also offered their grounds and conclusions very differently.


There was a deep change in math and locic during and after the centuries 
1500-1600.


Arabic influence, for starters. Latinization of ancient greek 
philosophical heritage.


Modal logic was self-evident for Plato, Aristoteles etc.

Modern (especially formal) logic is just feebly trying to recover and 
gather together the remants after LEM & the other two mispremisses.


Kirsti







John F Sowa kirjoitti 11.10.2017 09:20:

Jerry LRC, Jon AS, List,

Jerry

[JFS] Since a contradiction is always false, a contradiction
implies everything.


Everything?  While this assertion is widely repeated in
the literature, I think it is highly problematic.


It's widely repeated because it is a fundamental assumption
of most versions of formal logic -- i.e., of every logic that
assumes the Law of Excluded Middle (LEM).

But it is indeed problematic.  Brouwer, for example, rejected
LEM for intuitionistic logic.

And even for systems that are based on LEM, nobody actually claims
that everything has been proved.  Instead, they recognize that there
is a mistake somewhere, and they start searching for it.

Jon

[JFS]  For modal logic, there are three options:
necessary, possible, and contingent (not necessary and not 
impossible).


Did you mean to say necessary, impossible, and contingent?


Yes.  I wrote that too hastily.  "not impossible" is a synonym
for "possible".  For the three options, I should have written
necessary, impossible, and contingent (possible and not necessary).

But after I sent that note, I did some googling, which led me
to the article "Peirce and Brouwer" by Conor Mayo-Wilson:
http://mayowilson.org/Papers/Peirce_Brouwer.pdf

Some excerpts:

page 1

In his 1908 "The Unreliability of the Logical Principles" Brouwer
rejected the law of excluded middle (LEM)...
Five years earlier, Peirce had reached similar conclusions...


p. 2

Peirce and Brouwer's common rejection of LEM is not simply a
coincidence, but rather, stems from a deep underlying similarity
in their respective philosophical analyses of the continuum.


p. 3

Peirce and Brouwer seemed to have no knowledge of each other's work.
Brouwer might have learned of Peirce's ideas on semiotics in the
1920's through his association with Lady Welby... However, the two
most likely worked independently...


Fernando Zalamea also discusses Peirce and Brouwer in connection
with the continuum.  But he doesn't mention Lady Welby:
http://uberty.org/wp-content/uploads/2015/07/Zalamea-Peirces-Continuum.pdf

In any case, these sources indicate that Peirce began to reconsider
his ideas about LEM around the same time as the Lowell lectures.
His thoughts about the continuum seem to be the original reason.
But by 1909, his thoughts led to 3-valued logic and a new way
of representing and describing existential graphs.

John



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Re: [PEIRCE-L] Lowell Lecture 1.8

[kirstima]

List, Jerry and John

Highly problematic, I agree. But it is not true that any 
contradiction,or all contradictions imply everything. Not logically, not 
really.


Everything does not mean the same as anything.  For CSP anything remains 
an open (vague) question UNTILL further studies & determinations on that 
basis.


On everything we can never definitely say.

On whichever moment in time (the current present), there always remains 
more to be found out.  - Or else there is no one to say anything.


Kirsti


Kirsti


Jerry LR Chandler kirjoitti 11.10.2017 00:22:

List, John:


On Oct 10, 2017, at 1:17 PM, John F Sowa  wrote:

Since a contradiction is always false, a contradiction implies
everything.


Everything?

While this assertion is widely repeated in the literature, I think it
is highly problematic.

Because it violates the common sense of the meaning of natural
language terms in the premise.

Cheers

Jerry



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RE: [PEIRCE-L] Lowell Lecture 1.9

[gnox]

John,

In Lowell 2, the pseudograph makes its appearance as "the blot", and I'm 
looking forward to our discussion of that when we come to it!

Gary f.

-Original Message-
From: John F Sowa [mailto:s...@bestweb.net] 
Sent: 11-Oct-17 23:39

Charles, Gary F, and Edwina,

Charles
> On what the sheet of assertions represents in EGs, I thought Peirce 
> said it represents TRUTH...

Yes, but that is because a blank sheet in EGs is a graph that says nothing 
false.  When I teach EG logic, I say "Silence is golden".

Charles
> if we frame a theory of language in terms of EG, that would explain 
> the fact that language in general presupposes truth.

It's best not to read too much into the truth value of the blank.
Its meaning in the EG system is determined by the rules of inference and the 
method of endoporeutic (outside-in evaluation) for determining the truth of any 
graph.

Gary
> Peirce does say that the sheet of assertion represents the universe of 
> discourse...

Yes.  And his rules of inference preserve truth.  So if you start with a blank 
sheet, which is true in every possible universe of discourse, any statement you 
derive from a blank sheet must be true in every universe of discourse.

In short, the blank is Peirce's only axiom.  Any statement derivable from the 
blank is a theorem.  The negation of the blank is an empty oval, which is 
always false.  Peirce called it the pseudograph.



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[PEIRCE-L] Lowell Lecture 1.10

[gnox]

Conclusion of Lowell Lecture 1 (EP2:256-7):

 

The ultimate purpose of the logician is to make out the theory of how
knowledge is advanced. Just as there is a chemical theory of dyeing which is
not exactly the art of dyeing, and there is a theory of thermodynamics which
is quite different from the art of constructing heat-engines; so
Methodeutic, which is the last goal of logical study, is the theory of the
advancement of knowledge of all kinds. But this theory is not possible until
the logician has first examined all the different elementary modes of
getting at truth and especially all the different classes of arguments, and
has studied their properties so far as these properties concern [the] power
of the arguments as leading to the truth. This part of logic is called
Critic. But before it is possible to enter upon this business in any
rational way, the first thing that is necessary is to examine thoroughly all
the ways in which thought can be expressed. For since thought has no being
except in so far as it will be embodied, and since the embodiment of thought
is a sign, the business of logical critic cannot be undertaken until the
whole structure of signs, especially of general signs, has been thoroughly
investigated. This is substantially acknowledged by logicians of all
schools. But the different schools conceive of the business quite
differently. Many logicians conceive that the inquiry trenches largely upon
psychology, depends upon what has been observed about the human mind, and
would not necessarily be true for other minds. Much of what they say is
unquestionably false of many races of mankind. But I, for my part, take
little stock in a logic that is not valid for all minds, inasmuch as the
logicality of a given argument, as I have said, does not depend on how we
think that argument, but upon what the truth is. Other logicians endeavoring
to steer clear of psychology, as far as possible, think that this first
branch of logic must relate to the possibility of knowledge of the real
world and upon the sense in which it is true that the real world can be
known. This branch of philosophy, called epistemology, or Erkenntnislehre,
is necessarily largely metaphysical. But I, for my part, cannot for an
instant assent to the proposal to base logic upon metaphysics, inasmuch as I
fully agree with Aristotle, Duns Scotus, Kant, and all the profoundest
metaphysicians that metaphysics can, on the contrary, have no secure basis
except that which the science of logic affords. I, therefore, take a
position quite similar to that of the English logicians, beginning with
Scotus himself, in regarding this introductory part of logic as nothing but
an analysis of what kinds of signs are absolutely essential to the
embodiment of thought. I call it, after Scotus, Speculative Grammar. I fully
agree, however, with a portion of the English school,- a school I may
observe which now has a large and most influential and scientific following
in Germany,- I agree, I say, with a portion of this school without thereby
coming into positive conflict with the others, in thinking that this
Speculative Grammar ought not to confine its studies to those conventional
signs of which language is composed, but that it will do well to widen its
field of view so as to take into consideration also kinds of signs which,
not being conventional, are not of the nature of language. In fact, as a
point of theory, I am of opinion that we ought not to limit ourselves to
signs but ought to take account of certain objects more or less analogous to
signs. In practice, however, I have paid little attention to these
quasi-signs. 

Thus there are, in my view of the subject, three branches of logic:
Speculative Grammar, Critic, and Methodeutic. 

 

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

 


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