RE: RE: [PEIRCE-L] Lowell Lecture 2.5

[gnox]

Helmut,

 

What we’re depicting is not an if-then-routine but a proposition; and the 
scroll is not a set-subset-graph like a Venn diagram. I think those familiar 
ideas (i.e. your interpretive habits) are getting in the way of your following 
what Peirce is actually saying. But that happens a lot, to readers of Peirce. 
It’s happened to me too.

 

Gary f. 

 

From: Helmut Raulien [mailto:h.raul...@gmx.de] 
Sent: 26-Oct-17 14:08
To: g...@gnusystems.ca
Cc: peirce-l@list.iupui.edu
Subject: Aw: RE: [PEIRCE-L] Lowell Lecture 2.5

 

Gary, list,

I have understood nothing, except, that you may depict an if-then-routine as a 
set-subset-graph on a blackboard, and also may partially cut off the surface, 
or stick patches on it. If there is more to it metaphorically or so, I surely 
am stupid.

Best,

Helmut


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Aw: RE: [PEIRCE-L] Lowell Lecture 2.5

[Helmut Raulien]

Gary, list,

I have understood nothing, except, that you may depict an if-then-routine as a set-subset-graph on a blackboard, and also may partially cut off the surface, or stick patches on it. If there is more to it metaphorically or so, I surely am stupid.

Best,

Helmut

 

26. Oktober 2017 um 19:03 Uhr
 g...@gnusystems.ca
wrote:




List,

 

I have a lot to say about 2.5, so I’ll insert my comments into the text below.

 

Gary f.

 



From: g...@gnusystems.ca [mailto:g...@gnusystems.ca]
Sent: 25-Oct-17 16:35



 

Continuing from Lowell 2.4,

https://www.fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii/display/13604:

 

[Lowell 2.5:] The question of the proper way of expressing a conditional proposition de inesse in a system of existential graphs has formed the subject of an elaborate investigation with the reasoning of which I will not trouble you.

 

[Gf:] Those who don’t mind being troubled with this reasoning can find a few clues in CP 4.435:

[[ If a system of _expression_ is to be adequate to the analysis of all necessary consequences, it is requisite that it should be able to express that an expressed consequent, C, follows necessarily from an expressed antecedent, A. …. In order to form a new and reasonable convention for this purpose we must get a perfectly distinct idea of what it means to say that a consequent follows from an antecedent. It means that in adding to an assertion of the antecedent an assertion of the consequent we shall be proceeding upon a general principle whose application will never convert a true assertion into a false one. This, of course, means that so it will be in the universe of which alone we are speaking. But when we talk logic — and people occasionally insert logical remarks into ordinary discourse — our universe is that universe which embraces all others, namely The Truth, so that, in such a case, we mean that in no universe whatever will the addition of the assertion of the consequent to the assertion of the antecedent be a conversion of a true proposition into a false one. But before we can express any proposition referring to a general principle, or, as we say, to a “range of possibility,” we must first find means to express the simplest kind of conditional proposition, the conditional de inesse, in which “If A is true, C is true” means only that, principle or no principle, the addition to an assertion of A of an assertion of C will not be a conversion of a true assertion into a false one. …

This conditional de inesse has to be expressed as a graph in such a way as distinctly to express in our system both a and c, and to exhibit their relation to one another. To assert the graph thus expressing the conditional de inesse, it must be drawn upon the sheet of assertion, and in this graph the expressions of a and of c must appear; and yet neither a nor c must be drawn upon the sheet of assertion. How is this to be managed? Let us draw a closed line which we may call a sep (sæpes, a fence), which shall cut off its contents from the sheet of assertion. Let this sep together with all that is within it, considered as a whole, be called an enclosure, this close, being written on the sheet of assertion, shall assert the conditional de inesse; but that which it encloses, considered separately from the sep, shall not be considered as on the sheet of assertion. Then, obviously, the antecedent and consequent must be in separate compartments of the close. In order to make the representation of the relation between them iconic, we must ask ourselves what spatial relation is analogous to their relation. Now if it be true that “If a is true, b is true” and “If b is true, c is true,” then it is true that “If a is true, c is true.” This is analogous to the geometrical relation of inclusion. So naturally striking is the analogy as to be (I believe) used in all languages to express the logical relation; and even the modern mind, so dull about metaphors, employs this one frequently. It is reasonable, therefore, that one of the two compartments should be placed within the other. But which shall be made the inner one? … In order to decide which is the more appropriate mode of representation, one should observe that the consequent of a conditional proposition asserts what is true, not throughout the whole universe of possibilities considered, but in a subordinate universe marked off by the antecedent. This is not a fanciful notion, but a truth. ]]

 

[Lowell 2.5:]  Suffice it to say that it is found that there is essentially but one proper mode of representing it. Namely, in order to assert of the universe of discourse that if it rains then a pear is ripe I must put on the blackboard this: 



I draw the two ovals which I call a scroll in blue because I do not want you to regard them as ordinary lines. I want you to join me in making believe that they are cuts through the surface, and that inside the outer one the skin of the board has been strip

RE: [PEIRCE-L] Lowell Lecture 2.5

[gnox]

List,

 

I have a lot to say about 2.5, so I’ll insert my comments into the text
below.

 

Gary f.

 

From: g...@gnusystems.ca [mailto:g...@gnusystems.ca] 
Sent: 25-Oct-17 16:35

 

Continuing from Lowell 2.4,

https://www.fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903
-lowell-lecture-ii/display/13604:

 

[Lowell 2.5:] The question of the proper way of expressing a conditional
proposition de inesse in a system of existential graphs has formed the
subject of an elaborate investigation with the reasoning of which I will not
trouble you.

 

[Gf:] Those who don’t mind being troubled with this reasoning can find a few
clues in CP 4.435:

[[ If a system of expression is to be adequate to the analysis of all
necessary consequences, it is requisite that it should be able to express
that an expressed consequent, C, follows necessarily from an expressed
antecedent, A. …. In order to form a new and reasonable convention for this
purpose we must get a perfectly distinct idea of what it means to say that a
consequent follows from an antecedent. It means that in adding to an
assertion of the antecedent an assertion of the consequent we shall be
proceeding upon a general principle whose application will never convert a
true assertion into a false one. This, of course, means that so it will be
in the universe of which alone we are speaking. But when we talk logic — and
people occasionally insert logical remarks into ordinary discourse — our
universe is that universe which embraces all others, namely The Truth, so
that, in such a case, we mean that in no universe whatever will the addition
of the assertion of the consequent to the assertion of the antecedent be a
conversion of a true proposition into a false one. But before we can express
any proposition referring to a general principle, or, as we say, to a “range
of possibility,” we must first find means to express the simplest kind of
conditional proposition, the conditional de inesse, in which “If A is true,
C is true” means only that, principle or no principle, the addition to an
assertion of A of an assertion of C will not be a conversion of a true
assertion into a false one. …

This conditional de inesse has to be expressed as a graph in such a way as
distinctly to express in our system both a and c, and to exhibit their
relation to one another. To assert the graph thus expressing the conditional
de inesse, it must be drawn upon the sheet of assertion, and in this graph
the expressions of a and of c must appear; and yet neither a nor c must be
drawn upon the sheet of assertion. How is this to be managed? Let us draw a
closed line which we may call a sep (sæpes, a fence), which shall cut off
its contents from the sheet of assertion. Let this sep together with all
that is within it, considered as a whole, be called an enclosure, this
close, being written on the sheet of assertion, shall assert the conditional
de inesse; but that which it encloses, considered separately from the sep,
shall not be considered as on the sheet of assertion. Then, obviously, the
antecedent and consequent must be in separate compartments of the close. In
order to make the representation of the relation between them iconic, we
must ask ourselves what spatial relation is analogous to their relation. Now
if it be true that “If a is true, b is true” and “If b is true, c is true,”
then it is true that “If a is true, c is true.” This is analogous to the
geometrical relation of inclusion. So naturally striking is the analogy as
to be (I believe) used in all languages to express the logical relation; and
even the modern mind, so dull about metaphors, employs this one frequently.
It is reasonable, therefore, that one of the two compartments should be
placed within the other. But which shall be made the inner one? … In order
to decide which is the more appropriate mode of representation, one should
observe that the consequent of a conditional proposition asserts what is
true, not throughout the whole universe of possibilities considered, but in
a subordinate universe marked off by the antecedent. This is not a fanciful
notion, but a truth. ]]

 

[Lowell 2.5:]  Suffice it to say that it is found that there is essentially
but one proper mode of representing it. Namely, in order to assert of the
universe of discourse that if it rains then a pear is ripe I must put on the
blackboard this: 



I draw the two ovals which I call a scroll in blue because I do not want you
to regard them as ordinary lines. I want you to join me in making believe
that they are cuts through the surface, and that inside the outer one the
skin of the board has been stripped off disclosing another surface below.
This I call the bottom or area. Therefore “It rains” is not scribed on the
blackboard or, as I say, is not scribed on the sheet of assertion. For what
is scribed on that sheet is asserted to be true of the universe of
discourse; while the statement “It rains” is a mere supposition. Let us say
that tha

Re: [PEIRCE-L] Lowell Lecture 2.4

[Franklin Ransom]

Gary F, Jeff, Mike,

Thanks for the reference, Jeff.

I thought that the question of consequentiae might be more complicated than
being able to relate it to the terms of formal symbolic logic, but I wanted
to see what your thoughts were on it, and so I do. The confirmation is much
appreciated.

-- Franklin

On Oct 25, 2017 8:05 PM, "Mike Bergman"  wrote:

> Hi Jeff,
>
>
> Thank you. The Bellucci reference is excellent and timely. I found a PDF
> online at http://www.academia.edu/download/41369857/Bellucci_
> CSP_consequences.pdf; some of the Abelard quotes are translated at
> http://johnmacfarlane.net/abelard.pdf.
>
>
> Best, Mike
>
> On 10/25/2017 6:18 PM, Jeffrey Brian Downard wrote:
>
> Franklin, Gary F, List,
>
>
> In *Reading Peirce Reading*, Richard Smyth suggests that many logicians,
> such as Quine, make the error of   making assignments to the truth table
> for the conditional in a rather arbitrary fashion. Peirce, on the other
> hand, is developing a logical theory that seeks to explain why some
> inferences that we take to be good or bad really are valid or invalid. As
> such, he is setting up a semantic assignment of values to the truth table
> that is not arbitrary.
>
>
> Here, in the second lecture, he trying to show us how to set up
> mathematical system of logic that will enable us to analyze examples of
> reasoning more carefully and exactly. As such, he is trying to avoid the
> temptation of developing a logical system that prejudges the questions
> we're trying to answer in the normative theory of logic.
>
>
> For background on the relation between these different accounts of the
> conditional, it might be worth looking atFrancesco Bellucci
> 's "Charles S.
> Peirce and the Medieval Doctrine of *consequentiae".*
> See: http://www.tandfonline.com/doi/full/10.1080/01445340.
> 2015.1118338?scroll=top&needAccess=true&
>
>
> In this article, he provides a historical reconstruction of what Peirce
> was drawing from in the medieval doctrine, and how this account of the
> conditional shape his understanding of the relation of implication.
>
>
> --Jeff
>
>
> Jeffrey Downard
> Associate Professor
> Department of Philosophy
> Northern Arizona University
> (o) 928 523-8354 <(928)%20523-8354>
> --
> *From:* Franklin Ransom 
> 
> *Sent:* Wednesday, October 25, 2017 1:51:13 PM
> *To:* peirce-l@list.iupui.edu 1
> *Subject:* RE: [PEIRCE-L] Lowell Lecture 2.4
>
> Gary F,
>
> If I try to picture the Philonian and Diodoran interpretations in terms of
> truth value tables, they essentially correspond to material and strict
> implication, respectively. But I'm not sure how the distinction between
> ordinary consequence and simplex de inesse fits in. Would that have more to
> do with modal logic (possible vs...actual?), which the gamma graphs aim to
> treat of, and which you are suggesting is where the Philonian or material
> approach becomes problematic?
>
> -- Franklin
>
>
> On Oct 25, 2017 4:22 PM,  wrote:
>
> Franklin, list,
>
>
>
> The distinction between the conditional “simplex de inesse” and other
> if-then propositions is that the “simplex” is indeed simpler, and
> absolutely exact from a logical point of view, which removes all possible
> ambiguity from the interpretation of it. It asserts no connection at all
> between the truth of the antecedent and the truth of the consequent
> *except* that when the former is true, the latter is true, “never mind
> the why or wherefore.” This means that there is no way to falsify the
> conditional proposition as a whole *except* to observe that the
> antecedent is true *and* the consequent is false. The proposition as a
> whole — contrary to the “ordinary language” usage and the Diodoran point of
> view — remains perfectly true if *both* antecedent and consequent are in
> themselves false.
>
>
>
> The *significance* of this distinction should become more clear as Peirce
> proceeds to define the “scroll” as the diagram representing the conditional 
> *de
> inesse*. The reading of the scroll follows from the stipulation “that in
> logic we are to understand the form “If A, then B” to mean “Either A is
> impossible or in every possible case in which it is true, B is true
> likewise,” or in other words it means “In each possible case, either A is
> false or B is true.”
>
> From this Peirce will derive the meaning of the cut as *negation of what
> is inside the cut*. It seems to me, in hindsight, that right here on the
> ground level of the whole EG system lies a design feature that will later
> become problematic for the gamma part of EGs, i.e. for modal logic. That’s
> why I’m trying to understand why Peirce felt compelled to design them in
> the way he did.
>
>
>
> The significance of the distinction becomes amplified, I think, as soon as
> we take a step beyond exact logic into metaphysics. But we’re not ready to
> talk about that yet. Or at least I’m not, I’m still trying to clar