Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Franklin Ransom]

Ben, Gary F,

I like Gary's suggestion about "throwing everything" into the predicate or
into the subject. However, not quite everything gets thrown in, right?
There still needs to be some bare minimum subject if everything gets thrown
into the predicate, and some bare minimum predicate if everything gets
thrown into the subject. I'm not sure this works.

Ben, I thought to myself of that possibility, namely of erasing the subject
and letting the rhema or term remain. But I don't see how propositions and
arguments can really be like terms in this sense, since propositions
certainly require subjects and arguments do because they require premisses
in the form of propositions.

But, I was looking through Natural Propositions to make sure I understood
the "throwing everything in" idea, and I found a quote from Peirce that
Frederik included in his text that seems pertinent. NP, p.84, quoted from
"Pragmatism", 1907, 5.473:

The interpretant of a proposition is its predicate; its object is the
> things denoted by its subject or subjects (including its grammatical
> objects, direct and indirect, etc.).


So this says that the subject-term represents the object of the
proposition, while the predicate-term represents the interpretant of the
proposition. We should probably imagine that interpretants don't all come
down to being cases of predicate-terms. But if we consider that the
conclusion of an argument is the argument's interpretant, and comes in the
form of a proposition, and that such proposition itself can be interpreted
by way of its predicate, then propositions and arguments can ultimately be
interpreted as predicate terms. A term, in this way, as an interpretant,
signifies all the characters of the propositions and arguments leading to
it, while denoting, by way of its determination from such determining
signs, the object(s) of the determining signs. What do you think?

Franklin



On Sun, Nov 8, 2015 at 2:14 PM, Benjamin Udell  wrote:

> Gary F., Franklin,
>
> Gary, you wrote,
>
> I’m not sure what Peirce meant by saying in 1893 that every proposition
> and every argument can be regarded as a term, or what advantage a logician
> would gain by regarding them that way.
> [End quote]
>
> In "Kaina Stoicheia" III. 4. (EP 2:308), 1904,
> http://www.iupui.edu/~arisbe/menu/library/bycsp/stoicheia/stoicheia.htm
> Peirce says:
>
> [] If we erase from an argument every monstration of its special
> purpose, it becomes a proposition; usually a copulate proposition, composed
> of several members whose mode of conjunction is of the kind expressed by
> "and," which the grammarians call a "copulative conjunction." If from a
> propositional symbol we erase one or more of the parts which separately
> denote its objects, the remainder is what is called a *rhema*; but I
> shall take the liberty of calling it a *term*. Thus, from the proposition
> "Every man is mortal," we erase "Every man," which is shown to be
> denotative of an object by the circumstance that if it be replaced by an
> indexical symbol, such as "That" or "Socrates," the symbol is reconverted
> into a proposition, we get the *rhema* or *term* "_ is mortal." []
> [End quote]
>
> Somewhere Peirce also notes that a proposition is a medadic term.
>
> Best, Ben
>
> On 11/8/2015 1:48 PM, g...@gnusystems.ca wrote:
>
> Franklin,
>
> I’m not sure what Peirce meant by saying in 1893 that every proposition
> and every argument can be regarded as a term, or what advantage a logician
> would gain by regarding them that way. But to me it sounds like a precursor
> of his (much later) observation that one can analyze a proposition by
> “throwing everything” into the predicate *or* by throwing everything into
> the subject. Maybe his comment in the Regenerated Logic also works in both
> directions.
>
> In the Kaina Stoicheia passage, when Peirce says that the “totality of the
> predicates of a sign” is “called its logical *depth*,” and that the
> “totality of the subjects … of a sign is called the logical *breadth,*”
> the sign he is referring to has to be a proposition, because only
> propositions include subjects and predicates. Each subject and each
> predicate can be called a “term,” but it’s the breadth and depth of the
> whole sign, the proposition, that Peirce is defining here, not the breadth
> or depth of the terms (which is what he defined in ULCE). And, as you say,
> propositions and arguments also have information (which for Peirce is the
> logical product of breadth and depth).
>
> Gary f.
>
> } The birth and death of the leaves are the rapid whirls of the eddy whose
> wider circles move slowly among the stars. [Tagore] {
>
> http://gnusystems.ca/wp/ }{ *Turning Signs*
> gateway
>
>
>
> -
> PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON
> PEIRCE-L to this message. PEIRCE-L posts should go to
> peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L
> but to l

Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Franklin Ransom]

Gary F, list,

I confess that I am finding myself somewhat confused about this passage
from KS. If he meant specifically propositions, why not call them
propositions and not signs? Then again, he doesn't call them terms either,
so that doesn't help my view either. I'm wondering if there is something
deliberately vague here about what predicates ("essential parts") and
subjects ("substantial parts") apply to.

In the quote from 1893, it's clear that the logical breadth and depth of
propositions is not the same as that of terms from ULCE. But in KS, the way
depth and breadth are presented as relating to characters and real objects
is exactly how they are presented in ULCE when applied to terms. If Peirce
still held to the view that the depth and breadth of propositions had to do
with "the total of fact which it asserts of the state of things to which it
is applied" and "the aggregate of possible states of things in which it is
true", respectively, that is certainly very different from what is being
explained in KS. Did he change his views here?

Then there's an earlier part in KS, p.304 of EP 2, to consider: "But, in
the third place, every sign is intended to determine a sign of the same
object with the same signification or *meaning*. Any sign, B, which a sign,
A, is fitted so to determine, without violation of its, A's, purpose, that
is, in accordance with the "Truth," even though it, B, denotes but a part
of the objects of the sign, A, and signifies but a part of its, A's,
characters, I call an *interpretant* of A. What we call a "fact" is
something having the structure of a proposition, but supposed to be an
element of the very universe itself. The purpose of every sign is to
express "fact," and by being joined with other signs, to approach as nearly
as possible to determining an interpretant which would be the *perfect
Truth*, the absolute Truth, and as such (at least, we may use this
language) would be the very Universe."

Note that *every* sign determines another sign (the interpretant) of the
same object with the same signfication, and the interpretant does in fact
have breadth and depth, and in the same sense that terms in UCLE and signs
in KS have breadth and depth, as denoting objects and signifying
characters. Since any sign, to be a sign, will have an interpretant, it
seems clear that whether it is a term, proposition, argument, or any sign
whatsoever, it must have breadth and depth (if it had no breadth, there
would be no object, and if it had no depth, it would signify nothing about
the object). But not only does every sign have breadth and depth, every
sign has them in the sense of denoting objects and signifying characters.

How to understand this? Do predicates and subjects simply apply to
propositions only, or do they apply generally to all signs?

Franklin

On Sun, Nov 8, 2015 at 1:48 PM,  wrote:

> Franklin,
>
>
>
> I’m not sure what Peirce meant by saying in 1893 that every proposition
> and every argument can be regarded as a term, or what advantage a logician
> would gain by regarding them that way. But to me it sounds like a precursor
> of his (much later) observation that one can analyze a proposition by
> “throwing everything” into the predicate *or* by throwing everything into
> the subject. Maybe his comment in the Regenerated Logic also works in both
> directions.
>
>
>
> In the Kaina Stoicheia passage, when Peirce says that the “totality of
> the predicates of a sign” is “called its logical *depth*,” and that the
> “totality of the subjects … of a sign is called the logical *breadth,*”
> the sign he is referring to has to be a proposition, because only
> propositions include subjects and predicates. Each subject and each
> predicate can be called a “term,” but it’s the breadth and depth of the
> whole sign, the proposition, that Peirce is defining here, not the breadth
> or depth of the terms (which is what he defined in ULCE). And, as you say,
> propositions and arguments also have information (which for Peirce is the
> logical product of breadth and depth).
>
>
>
> Gary f.
>
>
>
> } The birth and death of the leaves are the rapid whirls of the eddy whose
> wider circles move slowly among the stars. [Tagore] {
>
> http://gnusystems.ca/wp/ }{ *Turning Signs* gateway
>
>
>
> *From:* Franklin Ransom [mailto:pragmaticist.lo...@gmail.com]
> *Sent:* 8-Nov-15 12:32
> *To:* peirce-l@list.iupui.edu 1 
> *Subject:* Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction
>
>
>
> Gary F, list,
>
>
>
> Gary, thank you, thank you so much for finding that quote about the
> information of propositions and arguments! I spent so many hours, and not
> just yesterday, trying to find that quote again. I'll have to keep it
> somewhere I'll be sure to find it. Btw, it's 407, not 406, at least in the
> Intelex version on Past Masters.
>
>
>
> Now, you said:
>
>
>
> One place where Peirce uses the terms *breadth* and *depth* in reference
> to the proposition (rather than the term) is “Kaina Stoicheia”

Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Benjamin Udell]

Gary F., Franklin,

Gary, you wrote,

   I’m not sure what Peirce meant by saying in 1893 that every
   proposition and every argument can be regarded as a term, or what
   advantage a logician would gain by regarding them that way.
   [End quote]

In "Kaina Stoicheia" III. 4. (EP 2:308), 1904, 
http://www.iupui.edu/~arisbe/menu/library/bycsp/stoicheia/stoicheia.htm

Peirce says:

   [] If we erase from an argument every monstration of its special
   purpose, it becomes a proposition; usually a copulate proposition,
   composed of several members whose mode of conjunction is of the kind
   expressed by "and," which the grammarians call a "copulative
   conjunction." If from a propositional symbol we erase one or more of
   the parts which separately denote its objects, the remainder is what
   is called a /rhema/; but I shall take the liberty of calling it a
   /term/. Thus, from the proposition "Every man is mortal," we erase
   "Every man," which is shown to be denotative of an object by the
   circumstance that if it be replaced by an indexical symbol, such as
   "That" or "Socrates," the symbol is reconverted into a proposition,
   we get the /rhema/ or /term/ "_ is mortal." []
   [End quote]

Somewhere Peirce also notes that a proposition is a medadic term.

Best, Ben

On 11/8/2015 1:48 PM, g...@gnusystems.ca wrote:


Franklin,

I’m not sure what Peirce meant by saying in 1893 that every 
proposition and every argument can be regarded as a term, or what 
advantage a logician would gain by regarding them that way. But to me 
it sounds like a precursor of his (much later) observation that one 
can analyze a proposition by “throwing everything” into the predicate 
*/or/* by throwing everything into the subject. Maybe his comment in 
the Regenerated Logic also works in both directions.


In the Kaina Stoicheia passage, when Peirce says that the “totality of 
the predicates of a sign” is “called its logical /depth/,” and that 
the “totality of the subjects … of a sign is called the logical 
/breadth,/” the sign he is referring to has to be a proposition, 
because only propositions include subjects and predicates. Each 
subject and each predicate can be called a “term,” but it’s the 
breadth and depth of the whole sign, the proposition, that Peirce is 
defining here, not the breadth or depth of the terms (which is what he 
defined in ULCE). And, as you say, propositions and arguments also 
have information (which for Peirce is the logical product of breadth 
and depth).


Gary f.

} The birth and death of the leaves are the rapid whirls of the eddy 
whose wider circles move slowly among the stars. [Tagore] {


http://gnusystems.ca/wp/ }{ /Turning Signs/ gateway

*From:* Franklin Ransom [mailto:pragmaticist.lo...@gmail.com]
*Sent:* 8-Nov-15 12:32
*To:* peirce-l@list.iupui.edu 1 
*Subject:* Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

Gary F, list,

Gary, thank you, thank you so much for finding that quote about the 
information of propositions and arguments! I spent so many hours, and 
not just yesterday, trying to find that quote again. I'll have to keep 
it somewhere I'll be sure to find it. Btw, it's 407, not 406, at least 
in the Intelex version on Past Masters.


Now, you said:

One place where Peirce uses the terms /breadth/ and /depth/ in 
reference to the proposition (rather than the term) is “Kaina 
Stoicheia” (1904), EP2:305:e


I'm confused. I had just read that passage again yesterday, and then 
again when you quoted it. But I don't see reference to the breadth and 
depth in reference to the proposition. Rather, it is still to terms, 
understood with respect to the roles they play in propositions and how 
such roles determine the information a given term signifies. This is 
just what we find in ULCE; there is nothing new in Kaina Stoicheia. 
Perhaps I have misunderstood something?


Returning to the quote from the note to CP2:407, I wonder what he 
meant that "[i]n fact, every proposition and every argument can be 
regarded as a term." I recall Stjernfelt said in NP, p.79, that "both 
Rhemes and Dicisigns may be seen as potential or truncated Arguments 
rather than autonomous figures:", and he goes on to quote Peirce:


I have maintained since 1867 that there is but one primary and
fundamental logical relation, that of illation, expressed by
/ergo/. A proposition, for me, is but an argumentation divested of
the assertoriness of its premiss and conclusion. This makes every
proposition a conditional proposition at bottom. In like manner a
"term," or class-name, is for me nothing but a proposition with
its indices or subjects left blank, or indefinite. ("The
Regenerated Logic, 1896, 3.440)

However, this goes in the direction of arguments, not in the direction 
of terms. How can every proposition and every argument be regarded as 
a term? If he had said this before explaining how the concept of 
information applies to propositions and argument

RE: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[gnox]

Franklin,

 

I’m not sure what Peirce meant by saying in 1893 that every proposition and 
every argument can be regarded as a term, or what advantage a logician would 
gain by regarding them that way. But to me it sounds like a precursor of his 
(much later) observation that one can analyze a proposition by “throwing 
everything” into the predicate or by throwing everything into the subject. 
Maybe his comment in the Regenerated Logic also works in both directions.

 

In the Kaina Stoicheia passage, when Peirce says that the “totality of the 
predicates of a sign” is “called its logical depth,” and that the “totality of 
the subjects … of a sign is called the logical breadth,” the sign he is 
referring to has to be a proposition, because only propositions include 
subjects and predicates. Each subject and each predicate can be called a 
“term,” but it’s the breadth and depth of the whole sign, the proposition, that 
Peirce is defining here, not the breadth or depth of the terms (which is what 
he defined in ULCE). And, as you say, propositions and arguments also have 
information (which for Peirce is the logical product of breadth and depth).

 

Gary f. 

 

} The birth and death of the leaves are the rapid whirls of the eddy whose 
wider circles move slowly among the stars. [Tagore] {

  http://gnusystems.ca/wp/ }{ Turning Signs gateway

 

From: Franklin Ransom [mailto:pragmaticist.lo...@gmail.com] 
Sent: 8-Nov-15 12:32
To: peirce-l@list.iupui.edu 1 
Subject: Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

 

Gary F, list,

 

Gary, thank you, thank you so much for finding that quote about the information 
of propositions and arguments! I spent so many hours, and not just yesterday, 
trying to find that quote again. I'll have to keep it somewhere I'll be sure to 
find it. Btw, it's 407, not 406, at least in the Intelex version on Past 
Masters.

 

Now, you said:

 

One place where Peirce uses the terms breadth and depth in reference to the 
proposition (rather than the term) is “Kaina Stoicheia” (1904), EP2:305:e 

 

I'm confused. I had just read that passage again yesterday, and then again when 
you quoted it. But I don't see reference to the breadth and depth in reference 
to the proposition. Rather, it is still to terms, understood with respect to 
the roles they play in propositions and how such roles determine the 
information a given term signifies. This is just what we find in ULCE; there is 
nothing new in Kaina Stoicheia. Perhaps I have misunderstood something?

 

Returning to the quote from the note to CP2:407, I wonder what he meant that 
"[i]n fact, every proposition and every argument can be regarded as a term." I 
recall Stjernfelt said in NP, p.79, that "both Rhemes and Dicisigns may be seen 
as potential or truncated Arguments rather than autonomous figures:", and he 
goes on to quote Peirce:

 

I have maintained since 1867 that there is but one primary and fundamental 
logical relation, that of illation, expressed by ergo. A proposition, for me, 
is but an argumentation divested of the assertoriness of its premiss and 
conclusion. This makes every proposition a conditional proposition at bottom. 
In like manner a "term," or class-name, is for me nothing but a proposition 
with its indices or subjects left blank, or indefinite. ("The Regenerated 
Logic, 1896, 3.440)

 

However, this goes in the direction of arguments, not in the direction of 
terms. How can every proposition and every argument be regarded as a term? If 
he had said this before explaining how the concept of information applies to 
propositions and arguments, I would have thought that he simply meant they can 
be regarded as terms insofar as they too have information. But since he 
concludes with that statement, my guess is that he meant something more by it. 
But what? Or maybe I'm reading too much into it, and he just meant to say 
exactly that, that like terms, propositions and arguments also have information.

 

Franklin

 


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Re: [PEIRCE-L] RE: Peirce's Categories

[Benjamin Udell]

Jeff D., list,

I re-read my post below and realize that my main two points probably got 
lost in the chatter, and they were in support of you. I meant


1. that it does make sense to speak of hypotheses in phaneroscopy since 
it makes sense (in Peirce's later opinion and FWIW in mine) to speak of 
reasoning in phaneroscopy, and
2. that (although I had raised loosely Peirce-based doubts about it in 
earlier messages) mathematical hypotheses are comparable, in regard to 
their potential for shedding explanatory light, with hypotheses in other 
fields, so your desire to compare phaneroscopic hypotheses with 
mathematical ones makes sense.


* * *

I didn't go far enough in saying how imaginary and complex numbers are 
hypotheses that help simplify (and indeed explain) things about real 
numbers. An example that I vaguely remembered from some book but didn't 
dig up till the other day:


   The impetus to study complex numbers proper first arose in the 16th
   century when algebraic solutions for the roots of cubic and quartic
   polynomials were discovered by Italian mathematicians (see Niccolò
   Fontana Tartaglia, Gerolamo Cardano). It was soon realized that
   these formulas, even if one was only interested in real solutions,
   sometimes required the manipulation of square roots of negative numbers.
   [End quote from https://en.wikipedia.org/wiki/Complex_number ]

As regards non-Archimedean numbers, I didn't know till yesterday that 
p-adic numbers are non-Archimedean. They were regarded, like the 
nonstandard reals later on, as playthings by some, but are now regarded 
as co-equal to the reals, according to (peirce-l member) Joseph W. 
Dauben in "Abraham Robinson and Nonstandard Analysis: History, 
Philosophy, and Foundations of Mathematics" in _History and Philosophy 
of Modern Mathematics_. If nonstandard reals are just another way of 
talking about certain limits, why not vice versa? That idea is probably 
riskier than I know, since I don't know enough about math. And then of 
course there are further things, such as superreals and surreals.


Best, Ben

On 11/4/2015 9:41 AM, Benjamin Udell wrote:


Jeff D., Jon A., list,

Jeff, you wrote,

Peirce points out that inquiry in phenomenology is different in a
number of respects from inquiry in the other parts of philosophy. 
He says:  It can hardly be said to involve reasoning; for

reasoning reaches a conclusion, and asserts it to be true however
matters may seem; while in Phenomenology there is no assertion
except that there are certain seemings; and even these are not,
and cannot be asserted, because they cannot be described. CP
2.197  Having said that, he makes a very interesting remark:
“Phenomenology can only tell the reader which way to look and to
see what he shall see.”  This remark makes me think that one of
the tasks of phenomenology might be to articulate precepts that
can guide us in making and analyzing our observations.  As such, I
have a hunch that we might learn something by drawing a more
detailed comparison between the precepts that guide us in doing
math and the “precepts” that might guide our observational activities.
[End quote]

That remark by Peirce 
http://www.commens.org/dictionary/entry/quote-minute-logic-chapter-ii-section-ii-why-study-logic-1 
was made circa 1902 in "Minute Logic." Even then he goes on to say 
"The question of how far Phenomenology does reason will receive 
special attention." Two or so years later, circa 1904 he does allow of 
proof (a kind of reasoning) in phaneroscopy 
http://www.commens.org/dictionary/term/phaneroscopy. I'm not sure how 
he arrived from the first position to the second; maybe he decided 
that reasoning in phaneroscopy asserts a conclusion as true, not 
_/despite/_ how things seem but instead _/on the basis of/_ how things 
seem. Maybe reasoning isn't automatically supposed to assert a 
conclusion as holding in spite of appearances. Reasoning could still 
assert a conclusion as holding in spite of something. If the 
question's other elements are brought back in, then the idea seems 
that phaneroscopy asserts a conclusion as true, not _/despite/_ how 
things seem, much less _/on the basis of/_ physical, psychological, 
metaphysical, etc. explanations of the seemings, — but instead _/on 
the basis of/_ how things seem _/even despite/_ various (physical, 
psychological, metaphysical, etc.) explanations of the seemings.


On the comparability of mathematical hypotheses with hypotheses in 
other fields, something that has occurred to me is that maybe Peirce 
went too far in regarding mathematical hypotheses not as scientific 
acts and leaving it at that. A context of this, in the history of 
mathematics, has finally come back to me. Various new abstractions 
were introduced, not quite as explanations, but still as simplifiers.


As Peirce points out, mathematicians dislike exceptions. In real 
numbers without imaginary numbers, e

Aw: Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Helmut Raulien]

Hi!

"degenerate" supposes a devolution, but there is none. Reference to an interpretant is thirdness, but if the interpretant relation does not contain thirdness, because it is not an argument, but eg. a rheme: Then it is not degenerated, because it has not been an argument before. If the object relation is not a symbol, then it cannot be anyway, even if it wanted to, at least not within this actual sign. Hypothesis forming as a result of abduction, or probability increase as a result of induction are inferences, so might or might not they lead to deduction in the following signs, or are they all inside each sign? Peirce said, that all three modes of interpretant are there, always. So, maybe in any case of mind action, all three kinds of inference are there too: In the listening to a street cry, the deduction is: I have heard this cry, and i dont know by whom and why it has been uttered, so I dont know what it is about". This deduction exists, even if this chain of thoughts has not been thought, just by the would-be-possibility of the mind of being able to explain it in other cases of more premisses.  And in case of a motive, of course. Ockham would have cut all this away with his razor, but he was a nominalist. So the non-nominalist perhaps would say: The nonexistence of something is a reality, so something that exists, at least if a vacuum can be defined: The would-be-vacuum, or unfilled-capacity-vacuum. The concept of interpretation contains thirdness, but there are interpretants that dont, so within them there exists a nonexistance of elements that otherwise might exist. This is a recursive ontology, but not a concept of degeneration, I think. And it is weird. But this weirdness has to be suffered, if you dont want to be a nominalist.

Was this weird? Am I talking nonsense?

Helmut



Von: "Benjamin Udell" 
 



Jerry, list,

Apropos of your comment on Peirce's idea that all mental action takes the form of inference:


The latter is stunning from the perspective that inferences require a conclusion (!) and for me, at least, passing thoughts float by without apparent motivation and often without a hint of closure, just a gentle fade.


Back on Sept. 20, 2015, I wrote to peirce-l:


[] There's a statement in [my blog] it that I've corrected. I said that, in the pervasive absence of such heuristic merits as nontriviality, natural simplicity, etc., no mind would bother with inference. It might be better [to] say more narrowly that no mind would bother with _reasoning_, in the sense of explicit, consciously weighed inference. I wasn't thinking with Peirce's exemplary broadness. Inference without those heuristic merits would amount to remembering (... ∴ p, ∴ p, ∴ p, ∴ ...), free-associative or at any rate wild supposition, and so on; one might call them degenerate cases of inference but, in their seasons, they have their merits, and arguably need to be taken into account for Peirce's idea that all of a mind's action is a continuum of inference.


A pretty wild play of the imagination is, it cannot be doubted, an inevitable and probably even a useful prelude to science proper.
— Peirce, CP 1.235 (1902). Snifter clink to Gary Fuhrman http://gnusystems.ca/wp/index.php/2015/09/15/wild-science/ 


[End quote]


My notion there was that remembering amounts to a kind of equipollential deduction without nontriviality, and that free-associative or wild supposition amounts to a kind of abductive inference without explanatory instinctual naturalness or simplicity.

Best, Ben

On 11/8/2015 9:34 AM, Benjamin Udell wrote:


Jerry, list,

On mental action as always having the form of inference (i.e., inference as the form of all mental action): Peirce goes even further and says that all mental action conforms to the formula of _valid_ inference.

See "Some Consequences of Four Incapacities" (1868), CP5.264-317, also W2:211-41, in particular CP 5.266-79,
beginning
  "In accepting the first proposition",
continuing through
"It is a consequence, then, of the first two principles whose results we are to trace out, that we must, as far as we can, without any other supposition than that the mind reasons, reduce all mental action to the formula of valid reasoning."
and ending with
"In every fallacy, therefore, possible to the mind of man, the procedure of the mind conforms to the formula of valid inference."

On the sample as index of the whole:

1867 | On a New List of Categories | W 2:58; CP 1.559
http://www.commens.org/dictionary/entry/quote-new-list-categories-5


In an argument, the premises form a representation of the conclusion, because they indicate the interpretant of the argument, or representation representing it to represent its object. The premises may afford a likeness, index, or symbol of the conclusion. In deductive argument, the conclusion is represented by the premises as by a general sign under which it is contained. In hypotheses, something like the conclusion is proved, that is, the premises form a like

Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Franklin Ransom]

Gary F, list,

Gary, thank you, thank you so much for finding that quote about the
information of propositions and arguments! I spent so many hours, and not
just yesterday, trying to find that quote again. I'll have to keep it
somewhere I'll be sure to find it. Btw, it's 407, not 406, at least in the
Intelex version on Past Masters.

Now, you said:

One place where Peirce uses the terms *breadth* and *depth* in reference to
> the proposition (rather than the term) is “Kaina Stoicheia” (1904), EP2:305:
> e


I'm confused. I had just read that passage again yesterday, and then again
when you quoted it. But I don't see reference to the breadth and depth in
reference to the proposition. Rather, it is still to terms, understood with
respect to the roles they play in propositions and how such roles determine
the information a given term signifies. This is just what we find in ULCE;
there is nothing new in Kaina Stoicheia. Perhaps I have misunderstood
something?

Returning to the quote from the note to CP2:407, I wonder what he meant
that "[i]n fact, every proposition and every argument can be regarded as a
term." I recall Stjernfelt said in NP, p.79, that "both Rhemes and
Dicisigns may be seen as potential or truncated Arguments rather than
autonomous figures:", and he goes on to quote Peirce:

I have maintained since 1867 that there is but one primary and fundamental
> logical relation, that of illation, expressed by *ergo*. A proposition,
> for me, is but an argumentation divested of the assertoriness of its
> premiss and conclusion. This makes every proposition a conditional
> proposition at bottom. In like manner a "term," or class-name, is for me
> nothing but a proposition with its indices or subjects left blank, or
> indefinite. ("The Regenerated Logic, 1896, 3.440)


However, this goes in the direction of arguments, not in the direction of
terms. How can every proposition and every argument be regarded as a term?
If he had said this before explaining how the concept of information
applies to propositions and arguments, I would have thought that he simply
meant they can be regarded as terms insofar as they too have information.
But since he concludes with that statement, my guess is that he meant
something more by it. But what? Or maybe I'm reading too much into it, and
he just meant to say exactly that, that like terms, propositions and
arguments also have information.

Franklin

On Sun, Nov 8, 2015 at 9:36 AM,  wrote:

> Franklin, regarding this point:
>
> [ I would also like to point out that "Upon Logical Comprehension and
> Extension" (ULCE) only deals with terms, not propositions or arguments. I
> seem to recall that in his later years Peirce had specified what
> information would be like for propositions and arguments, but after looking
> around a bit, I can't find a text to cite and I don't exactly recall how it
> worked, only that it didn't work the same way for them as for terms. ]
>
>
>
> You may be thinking of this note to CP2:406:
>
> [[ I restricted myself to terms, because at the time this chapter was
> first written (1867), I had not remarked that the whole doctrine of breadth
> and depth was equally applicable to propositions and to arguments. The
> breadth of a proposition is the aggregate of possible states of things in
> which it is true; the breadth of an argument is the aggregate of possible
> cases to which it applies. The depth of a proposition is the total of fact
> which it asserts of the state of things to which it is applied; the depth
> of an argument is the importance of the conclusions which it draws. In
> fact, every proposition and every argument can be regarded as a term.—1893.
> ]]
>
>
>
> One place where Peirce uses the terms *breadth* and *depth* in reference
> to the proposition (rather than the term) is “Kaina Stoicheia” (1904),
> EP2:305:e
>
>
>
> [[ If a sign, *B*, only signifies characters that are elements (or the
> whole) of the meaning of another sign, *A*, then *B* is said to be a
> *predicate* (or *essential part*) of *A*. If a sign, *A*, only denotes
> real objects that are a part or the whole of the objects denoted by another
> sign, *B*, then *A* is said to be a *subject* (or *substantial part*) of
> *B*. The totality of the predicates of a sign, and also the totality of
> the characters it signifies, are indifferently each called its logical
> *depth*. This is the oldest and most convenient term. Synonyms are the
> *comprehension* of the Port-Royalists, the *content* (*Inhalt*) of the
> Germans, the *force* of DeMorgan, the *connotation* of J.S. Mill. (The
> last is objectionable.) The totality of the subjects, and also,
> indifferently, the totality of the real objects of a sign is called the
> logical *breadth*. This is the oldest and most convenient term. Synonyms
> are the *extension* of the Port-Royalists (ill-called *extent* by some
> modern French logicians), the *sphere* (*Umfang*) of translators from the
> German, the *scope* of DeMorgan, the *de

Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Benjamin Udell]

Jerry, list,

Apropos of your comment on Peirce's idea that all mental action takes 
the form of inference:


   The latter is stunning from the perspective that inferences require
   a conclusion (!) and for me, at least, passing thoughts float by
   without apparent motivation and often without a hint of closure,
   just a gentle fade.

Back on Sept. 20, 2015, I wrote to peirce-l:

   [] There's a statement in [my blog] it that I've corrected. I
   said that, in the pervasive absence of such heuristic merits as
   nontriviality, natural simplicity, etc., no mind would bother with
   inference. It might be better [to] say more narrowly that no mind
   would bother with _/reasoning/_, in the sense of explicit,
   consciously weighed inference. I wasn't thinking with Peirce's
   exemplary broadness. Inference without those heuristic merits would
   amount to remembering (... ∴ /p/, ∴ /p/, ∴ /p/, ∴ ...),
   free-associative or at any rate wild supposition, and so on; one
   might call them degenerate cases of inference but, in their seasons,
   they have their merits, and arguably need to be taken into account
   for Peirce's idea that all of a mind's action is a continuum of
   inference.

   A pretty wild play of the imagination is, it cannot be doubted,
   an inevitable and probably even a useful prelude to science proper.
   — Peirce, CP 1.235 (1902). Snifter clink to Gary Fuhrman
   http://gnusystems.ca/wp/index.php/2015/09/15/wild-science/

   [End quote]

My notion there was that remembering amounts to a kind of equipollential 
deduction without nontriviality, and that free-associative or wild 
supposition amounts to a kind of abductive inference without explanatory 
instinctual naturalness or simplicity.


Best, Ben

On 11/8/2015 9:34 AM, Benjamin Udell wrote:


Jerry, list,

On mental action as always having the form of inference (i.e., 
inference as the form of all mental action): Peirce goes even further 
and says that all mental action conforms to the formula of _/valid/_ 
inference.


See "Some Consequences of Four Incapacities" (1868), CP5.264-317, also 
W2:211-41, in particular CP 5.266-79,

beginning
  "In accepting the first proposition",
continuing through
"It is a consequence, then, of the first two principles whose results 
we are to trace out, that we must, as far as we can, without any other 
supposition than that the mind reasons, reduce all mental action to 
the formula of valid reasoning."

and ending with
"In every fallacy, therefore, possible to the mind of man, the 
procedure of the mind conforms to the formula of valid inference."


On the sample as index of the whole:

1867 | On a New List of Categories | W 2:58; CP 1.559
http://www.commens.org/dictionary/entry/quote-new-list-categories-5

In an argument, the premises form a representation of the
conclusion, because they indicate the interpretant of the
argument, or representation representing it to represent its
object. The premises may afford a likeness, index, or symbol of
the conclusion. In deductive argument, the conclusion is
represented by the premises as by a general sign under which it is
contained. In hypotheses, something like the conclusion is proved,
that is, the premises form a likeness of the conclusion. [—]
That it is different with induction another example will show.

/S/′, /S/″, /S/‴, and /S^iv / are taken as samples of the
collection /M/;
/S/′, /S/″, /S/‴, and /S^iv / are /P/:
.·. All /M/ is /P/

Hence the first premise amounts to saying that "/S/′, /S/″, /S/‴,
and /S^iv /" is an index of /M/. Hence the premises are an index
of the conclusion.
[End quote]

See also this remark by Peirce in 1903 
http://www.commens.org/dictionary/entry/quote-harvard-lectures-pragmatism-lecture-v-deleted-passage-0


Best, Ben

On 11/7/2015 8:20 PM, Jerry LR Chandler wrote:


List:

Does anyone have the citations for the two statements with respect to 
indices and mental acts as "forms" of  inferences?  I am curious 
about the textual origins in view of the following feelings.


The first suggests a role for the connection between sin-sign and 
index as a consequence of the antecedent analysis of the sin-sign.


The latter is stunning from the perspective that inferences require a 
conclusion (!) and for me, at least, passing thoughts float by 
without apparent motivation and often without a hint of closure, just 
a gentle fade.


Cheers

Jerry

On Nov 7, 2015, at 1:53 PM, Franklin Ransom wrote:


Ben, list,

You wrote:

If the sample is an index, as he later said, of the whole, what 
sort of actual index indicates a hypothetical, potential whole?


Yes, that is a good point. He must have changed his views, but I'm 
not sure exactly how. I just re-read the paragraph in Kaina 
Stoicheia where he introduces depth, breadth, and information, but 
there is not much there, and certainly nothing about how they relate 
to inference. He clearly s

RE: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[gnox]

Franklin, regarding this point:

[ I would also like to point out that "Upon Logical Comprehension and 
Extension" (ULCE) only deals with terms, not propositions or arguments. I seem 
to recall that in his later years Peirce had specified what information would 
be like for propositions and arguments, but after looking around a bit, I can't 
find a text to cite and I don't exactly recall how it worked, only that it 
didn't work the same way for them as for terms. ]

 

You may be thinking of this note to CP2:406:

[[ I restricted myself to terms, because at the time this chapter was first 
written (1867), I had not remarked that the whole doctrine of breadth and depth 
was equally applicable to propositions and to arguments. The breadth of a 
proposition is the aggregate of possible states of things in which it is true; 
the breadth of an argument is the aggregate of possible cases to which it 
applies. The depth of a proposition is the total of fact which it asserts of 
the state of things to which it is applied; the depth of an argument is the 
importance of the conclusions which it draws. In fact, every proposition and 
every argument can be regarded as a term.—1893. ]]

 

One place where Peirce uses the terms breadth and depth in reference to the 
proposition (rather than the term) is “Kaina Stoicheia” (1904), EP2:305:

 

[[ If a sign, B, only signifies characters that are elements (or the whole) of 
the meaning of another sign, A, then B is said to be a predicate (or essential 
part) of A. If a sign, A, only denotes real objects that are a part or the 
whole of the objects denoted by another sign, B, then A is said to be a subject 
(or substantial part) of B. The totality of the predicates of a sign, and also 
the totality of the characters it signifies, are indifferently each called its 
logical depth. This is the oldest and most convenient term. Synonyms are the 
comprehension of the Port-Royalists, the content (Inhalt) of the Germans, the 
force of DeMorgan, the connotation of J.S. Mill. (The last is objectionable.) 
The totality of the subjects, and also, indifferently, the totality of the real 
objects of a sign is called the logical breadth. This is the oldest and most 
convenient term. Synonyms are the extension of the Port-Royalists (ill-called 
extent by some modern French logicians), the sphere (Umfang) of translators 
from the German, the scope of DeMorgan, the denotation of J.S. Mill. 

Besides the logical depth and breadth, I have proposed (in 1867) the terms 
information and area to denote the total of fact (true or false) that in a 
given state of knowledge a sign embodies. ]]

 

Gary f.

 

} The future ain't what it used to be. [Yogi Berra] {

  http://gnusystems.ca/wp/ }{ Turning Signs gateway

 

From: Franklin Ransom [mailto:pragmaticist.lo...@gmail.com] 
Sent: 7-Nov-15 23:34
To: Peirce List 
Subject: Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

 

Jerry, list,

 

Well, this turned out longer than I anticipated.

 

You wrote:

 

BTW, this is just another example of CSP's usage of his chemical knowledge to 
ground his logical explorations.

 

Yes, I was surprised some such reference to chemistry and its importance in 
influencing Peirce's work wasn't in your first post; I suppose you were winding 
up for the pitch. There is a very decidedly chemistry-centric direction that 
your posts take here on Peirce-L. I think it's important to notice that I'm not 
a chemistry whiz, but that I will do my best to keep up. For what it's worth, I 
would like to point out that I see no reason to deny your claims about the 
important influence of developments in chemistry on Peirce's work in logic. I 
just don't always see the relevance in a given discourse.

 

What is the information content of a symbol (as a diagram, icon, index or any 
term) if the change of the sign does not indicate a change in information?

 

Recent extension of the discussion point out that both "breadth" and "depth" 
can be viewed as changes in the distinctiveness of the sign (or information 
content.)

 

This question needs some clarification before it can be answered. When you say 
"What is the information content of a symbol (as a diagram, icon, index, or any 
term)," it is unclear whether you mean for diagrams, icons, indices, and any 
term to be understood as a symbol. Strictly speaking, icons and indices cannot 
be symbols, a diagram is a type of icon, and terms, well, that depends on how 
one means term; in particular, it matters if one envisions dicisigns as 
involving terms (rhemes?), or whether one restricts terms to propositions 
proper, and then specifically the predicate term. My guess is that you 
understand all of this, but your wording was vague, and I wanted to be clear 
that we are specifically talking about symbols. If you want to include 
diagrams, icons, indices, and any term, then it is important to note that icons 
only serve content for information; indi

Re: [PEIRCE-L] Vol. 2 of Collected Papers, on Induction

[Benjamin Udell]

Jerry, list,

On mental action as always having the form of inference (i.e., inference 
as the form of all mental action): Peirce goes even further and says 
that all mental action conforms to the formula of _/valid/_ inference.


See "Some Consequences of Four Incapacities" (1868), CP5.264-317, also 
W2:211-41, in particular CP 5.266-79,

beginning
  "In accepting the first proposition",
continuing through
"It is a consequence, then, of the first two principles whose results we 
are to trace out, that we must, as far as we can, without any other 
supposition than that the mind reasons, reduce all mental action to the 
formula of valid reasoning."

and ending with
"In every fallacy, therefore, possible to the mind of man, the procedure 
of the mind conforms to the formula of valid inference."


On the sample as index of the whole:

1867 | On a New List of Categories | W 2:58; CP 1.559
http://www.commens.org/dictionary/entry/quote-new-list-categories-5

   In an argument, the premises form a representation of the
   conclusion, because they indicate the interpretant of the argument,
   or representation representing it to represent its object. The
   premises may afford a likeness, index, or symbol of the conclusion.
   In deductive argument, the conclusion is represented by the premises
   as by a general sign under which it is contained. In hypotheses,
   something like the conclusion is proved, that is, the premises form
   a likeness of the conclusion. [—]
   That it is different with induction another example will show.

   /S/′, /S/″, /S/‴, and /S^iv / are taken as samples of the collection
   /M/;
   /S/′, /S/″, /S/‴, and /S^iv / are /P/:
.·. All /M/ is /P/.

   Hence the first premise amounts to saying that "/S/′, /S/″, /S/‴,
   and /S^iv //^/" is an index of /M/. Hence the premises are an index
   of the conclusion.
   [End quote]

See also this remark by Peirce in 1903 
http://www.commens.org/dictionary/entry/quote-harvard-lectures-pragmatism-lecture-v-deleted-passage-0 
.


Best, Ben

On 11/7/2015 8:20 PM, Jerry LR Chandler wrote:


List:

Does anyone have the citations for the two statements with respect to 
indices and mental acts as "forms" of  inferences?  I am curious about 
the textual origins in view of the following feelings.


The first suggests a role for the connection between sin-sign and 
index as a consequence of the antecedent analysis of the sin-sign.


The latter is stunning from the perspective that inferences require a 
conclusion (!) and for me, at least, passing thoughts float by without 
apparent motivation and often without a hint of closure, just a gentle 
fade.


Cheers

Jerry


On Nov 7, 2015, at 1:53 PM, Franklin Ransom wrote:


Ben, list,

You wrote:

If the sample is an index, as he later said, of the whole, what
sort of actual index indicates a hypothetical, potential whole?


Yes, that is a good point. He must have changed his views, but I'm 
not sure exactly how. I just re-read the paragraph in Kaina Stoicheia 
where he introduces depth, breadth, and information, but there is not 
much there, and certainly nothing about how they relate to inference. 
He clearly still has the basic ideas there so many decades later, but 
how to apply them in light of changes to his views in semiotics?


If all mental action has the form of inference, then they all
must be related to inferences in some way.


Yes, exactly my thought.

Franklin

On Sat, Nov 7, 2015 at 12:03 PM, Benjamin Udell > wrote



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