[PEIRCE-L] Re: [biosemiotics:8115] Pragmatism About Theoretical Entities

[Frederik Stjernfelt]

Dear Jon, lists,

Sorry again for an answer a bit belated.

Den 17/03/2015 kl. 20.22 skrev John Collier 
mailto:colli...@ukzn.ac.za>>:

Thanks, Frederik. I think that to properly call a view Platonist it must reject 
the existence of particulars in favour of universals. Russell fits this 
description because fairly early in his (long) career he explicitly rejected 
particulars, and argued that instances were combinations of “compossible” 
universals (whence his structuralism, and perhaps a “contraction to 
individuals”). One can be a Platonist about some domains but not others. For 
example there are Platonists about numbers and other parts of mathematics 
(Gödel), and there are the opposite about numbers (Mill and Phillip Kitcher, 
for example), but not necessarily about scientific laws. Hartrey Field famously 
rejected numbers altogether, at least with respect to the world of science.  
His motivation was an extreme nominalism.

Peirce was not a Platonist in the sense above, with his distinction between 
existing and being real. I suppose (no reason to think otherwise so far) that 
this extends to signs.

You're right. But Peircean Existence is not the same thing as individuals being 
completely determinate - here, he instead invokes the Scotist notion of 
"haecceity" to account for existence. As to his "more extreme", he means 
stronger rather than weaker. I think Peirce's idea is that when Scotus says 
that universals are "contracted" in particulars, Scotus thereby makes place ofr 
universals to be reducible to the classes of individuals instantiating them - 
here Peirce's continuity theory of universals make universals exceed any 
possible number of realizations of them, hence more strong.
But I am not quite sure how he slices it to get a position that is more extreme 
than (weaker than?) Duns Scotus, which is pretty weak, but still allows 
universals that are not instantiated. Or perhaps I am missing what he means by 
‘extreme’ here. I parted company with my coauthors of All Things Must Go over 
the existence of structures that don’t interact, for of which in principle we 
could have no knowledge. This seemed to me to violate a Peircean principle that 
they started the book with, which is basically the pragmatic principle.

Interesting!
Best
Frederik

In any case, we agree on openness of universals.

Regards,
John


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Re: [PEIRCE-L] Re: [biosemiotics:8115] Pragmatism About Theoretical Entities

[Jerry LR Chandler]

Frederik, John, List:

This philosophical exchange reflects on role of chemistry in CSP's philosophy. 

John writes:
>>  I parted company with my coauthors of All Things Must Go over the existence 
>> of structures that don’t interact, for of which in principle we could have 
>> no knowledge. This seemed to me to violate a Peircean principle that they 
>> started the book with, which is basically the pragmatic principle.

The chemical perspective on interactive structures is one of necessity.
A third emerges from a first and a second through interaction. 
In chemical theory, the independent first and the independent second BECOME 
relatives during the formation of the transition state. (As I recall, this 
theory was put forward about 1905, so that it's influence on CSP's writings was 
small.

Frederik writes:
>  I think Peirce's idea is that when Scotus says that universals are 
> "contracted" in particulars, Scotus thereby makes place ofr universals to be 
> reducible to the classes of individuals instantiating them - here Peirce's 
> continuity theory of universals make universals exceed any possible number of 
> realizations of them, hence more strong. 


>From the philosophy of chemistry perspective and its grounding in logic and 
>its relational physical predicates, this argument is very curious in its own 
>right. 
By invoking category theory, class theory and individuals, it is comparable to 
invoking individual nominals (the names of chemical elements, not nominalistic 
philosophy), classes of molecules such as hydrocarbons, sugars, and so forth, 
and the entire chemical plexus of all possible multi-sets of chemical elements. 

Is CSP's mathematical hypothesis relevant to his chemical language usage and 
correspondence between symbols as existent mathematical objects?
Such a correspondence between symbol systems is specifically excluded by CSP's 
definition of continuity as a welded whole without any mark of separation of 
parts of the whole.

But, in the current logic of chemical symbol system, very compound object 
entails the existence of firstness of chemical elements and multi-sets of 
chemical elements entail every compound object.  These mutual entailments are 
essential to the nature of individual identities.  Note that this logic entails 
NOT a contraction to individual identity, but rather a systematic EXPANSION to 
individual identity.

To sum up, this is merely another example of the uniqueness of the formal logic 
of the chemical and pan-chemical sciences.
In my opinion, these two posts adds another piece to the philosophical picture 
of why CSP's life-long quest for a universal logic that included chemical 
reasoning, ended as it did.

Cheers

Jerry




On Apr 20, 2015, at 7:33 AM, Frederik Stjernfelt wrote:

> Dear Jon, lists, 
> 
> Sorry again for an answer a bit belated. 
> 
> Den 17/03/2015 kl. 20.22 skrev John Collier :
> 
>> Thanks, Frederik. I think that to properly call a view Platonist it must 
>> reject the existence of particulars in favour of universals. Russell fits 
>> this description because fairly early in his (long) career he explicitly 
>> rejected particulars, and argued that instances were combinations of 
>> “compossible” universals (whence his structuralism, and perhaps a 
>> “contraction to individuals”). One can be a Platonist about some domains but 
>> not others. For example there are Platonists about numbers and other parts 
>> of mathematics (Gödel), and there are the opposite about numbers (Mill and 
>> Phillip Kitcher, for example), but not necessarily about scientific laws. 
>> Hartrey Field famously rejected numbers altogether, at least with respect to 
>> the world of science.  His motivation was an extreme nominalism.
>>  
>> Peirce was not a Platonist in the sense above, with his distinction between 
>> existing and being real. I suppose (no reason to think otherwise so far) 
>> that this extends to signs.
> 
> You're right. But Peircean Existence is not the same thing as individuals 
> being completely determinate - here, he instead invokes the Scotist notion of 
> "haecceity" to account for existence. As to his "more extreme", he means 
> stronger rather than weaker. I think Peirce's idea is that when Scotus says 
> that universals are "contracted" in particulars, Scotus thereby makes place 
> ofr universals to be reducible to the classes of individuals instantiating 
> them - here Peirce's continuity theory of universals make universals exceed 
> any possible number of realizations of them, hence more strong. 
>> But I am not quite sure how he slices it to get a position that is more 
>> extreme than (weaker than?) Duns Scotus, which is pretty weak, but still 
>> allows universals that are not instantiated. Or perhaps I am missing what he 
>> means by ‘extreme’ here. I parted company with my coauthors of All Things 
>> Must Go over the existence of structures that don’t interact, for of which 
>> in principle we could have no knowledge. This seem

Re: [PEIRCE-L] Natural Propositions, Ch. 10: Corollarial and Theorematic Experiments with Diagrams

[Frederik Stjernfelt]

Dear Ben,  Franklin, lists,

Den 19/04/2015 kl. 20.05 skrev Benjamin Udell 
mailto:bud...@nyc.rr.com>>:


Franklin, lists,

I agree with Jon, thanks for your excellent starting post.

You wrote,

[] Why can't corollarial reasoning, which involves observation and 
experimentation, reveal unnoticed and hidden relations? After all, on p.285-6, 
Frederik mentions the work of police detective Jorn "Old Man" Holm and his 
computer program, which Frederik describes as a "practical example of 
corollarial map reasoning" (p.285). In this example, Holm uses the corollarial 
reasoning to reveal information about the whereabouts of suspects. Doesn't the 
comparison of the map reasoning with suspects' testimony end up revealing 
unnoticed and hidden relations?



There's a distinction that some make between complexity and mere complication. 
Corollarial reasonings may accumulate mere complications until the result 
becomes hard to see, although it involves little if any complexity in, more or 
less, the sense of depth or nontriviality.

I don't know whether there's a theorematic approach to Jørn Holm's 
diagrammatization that would show its result in a nontrivial aspect, and anyway 
its diagrammatic, pictorial presentation already leaves one in no doubt that a 
pattern is revealed.

Certainly the comparison between Holm's map and suspects' testimony may give 
nontrivial results - but that comparison was not my point -
My argument, which I may not have made sufficiently clear in the chapter, is 
that the small step from having spatiotemporal cell phone information 
represented in long lists of coordinates - and to synthesize that same 
information in one geographical map, is a corollarial step. It does not contain 
any new information which was not already there in the list, but it brings the 
information together in one conclusive sign so as fo facilitate the charting of 
e.g. the trajectory of single cell phones on the map.

I admit it is more difficult, in general, to precisely extend the 
corollarial/theorematic distinction to applied cases - but as you can see I did 
the attempt picking map examples. The central problem for my pov seems to be 
that in applied cases you should not only include what is given in axiomatics 
(topographical maps largely respecting Euclidean geometry) but also in the more 
or less implicit ontological assumptions in the area of application - this is 
why i count Wegener's map experiment as theorematic. Taken as pure geometry, it 
is a trivial translation to move South America eastwards to compare its 
coastline with Africa's - but in terms of geology, it requires the addition of 
a "new idea" - namely that continents may move.

Best,
Frederik

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Re: [PEIRCE-L] Stjernfelt: Chapter 9

[Frederik Stjernfelt]

Dear Franklin, Cathy, Lists -

A small clarification: Peirce's BxD=A idea, I think, should not be taken a 
device for the arithmetic calculation of exact information size - it is rather 
the proposal of a general law relating Breadth and Depth. His idea comes from 
the simple idea that when intension is zero, there is no information, while 
when extension is zero, there is also no information - and that is the relation 
of the two factors in a product.  (It is a bit like his first Boole-inspired 
definition of universal quantification as a product - he defines truth as 1, 
falsity as 0,  then, in order to be true, each single case of a universal 
proposition should be true - if any single one of them is false, the total 
product of them all will be zero.)
The BXD=A idea allows him to investigate what happens if intension or extension 
are in- or decreased, etc. - even if not being able to express that in precise 
numbers.

Best
F


Den 20/04/2015 kl. 01.14 skrev Franklin Ransom 
mailto:pragmaticist.lo...@gmail.com>>:

Cathy, lists,

Well, look at this way: It is possible for there to be objects in the senses 
which are yet not perceived, because we do not yet have any idea of what it is 
to which we are looking. It takes a hypothesis to introduce a new idea to us to 
explain what it is, which hypothesis we can then put to the test. In order to 
do so, we must determine what kinds of characters to look for (deduction helps 
here) and then look for existent objects (induction) to learn whether the 
purported relations between characters obtain in fact, and in this way we come 
to understand the thing which we are experiencing. It is of course induction 
which gives us more information; abduction simply gives us the idea which needs 
to become informed, and deduction is merely explicative, based on relating the 
idea to other ideas and previously gathered information regarding those ideas.

Obviously, we cannot conduct induction without end, because that is a practical 
impossibility. Our 'sum', as you put it, far from being always an infinity, 
will very likely never be an infinity in practice, in whatever sense you mean 
to understand the application of infinity to a 'sum' of information. Of course, 
as an ideal, where science, the community of inquiry as such, continues to 
investigate, it is possible for the information of an idea to reach a much 
greater 'sum' than would otherwise be possible for individuals such as you or 
me. But it is a commonplace of science that ideas that work and continue to 
work are understood more thoroughly in their relations to other ideas over the 
course on inquiry. This means of course that not only the breadth, but also the 
depth of the idea continues to grow. As a result, typically, rather than 
tending to make comparisons moot, we start to see a hierarchy of ideas and 
related sciences appear.

Consider this passage: "The former [Cows] is a natural class, the latter [Red 
Cows] is not. Now one predicate more may be attached to Red Cows than to Cows; 
hence Mr. Mill's attempts to analyze the difference between natural and 
artificial classes is seen to be a failure. For, according to him, the 
difference is that a real kind is distinguished by unknown multitudes of 
properties while an artificial class has only a few determinate ones. Again 
there is an unusual degree of accordance among naturalists in making 
Vertebrates a natural class. Yet the number of predicates proper to it is 
comparatively small" (NP, p.238, quoting Peirce). We can see here that further 
simplifications are introduced, so taking what is learned about various 
vertebrates, a new idea, that of vertebrates, appears which simplifies the 
characters involved. Conversely, species under vertebrates will become much 
more determinate in terms of their characters, but be simplified with respect 
to their extension.

You said above: "Under synechism every real object has an infinite number of 
attributes, and every meaningful predicate or general term effectively has an 
infinite number of aspects, so a simple multiplication of B x D is pointless." 
And yet natural kinds appear, in which certain attributes, predicates, or 
aspects appear significant, and others do not. It is precisely the work of 
abduction to simplify what is observed so that what is essential is grasped, 
and not simply a never-ending multitude of characters. Such simplification is 
always with respect to a purpose. With respect to natural kinds, such purpose, 
or telos, is objective, and we see nature all around us selecting certain 
characters over others as more significant. If this were not true, natural 
science would be impossible. As to real objects, yes they have an infinite 
number, but not all of them are relevant to the purpose of interaction with the 
real object. Certain meaningful attributes are selected for in attention in 
order to aid conduct with respect to some purpose at hand. Information relevant 
to that purpose is

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[PEIRCE-L] Re: [biosemiotics:8363] Natural Propositions, Ch. 10:

[Frederik Stjernfelt]

Dear Franklin, lists -

Sorry for having rattled Franklin's empiricist sentiments with references to 
the a priori!
Empiricists seem to have an a priori fear of the a priori … but no philosophy 
of science has, as yet, been able to completely abolish the a priori - even 
logical positvism had to admit logic as a remaining a priori field 
(reinterpreting that as tautologies, that is true).
I should probably have given a note here to my own stance on the a priori - for 
the interested, I wrote a bit about it in ch. 8 of Diagrammatology (2007). My 
take on it there comes more from the early Husserl than from Peirce: the a 
priori has nothing to do with Kantian subjectivity, rather, it consists in 
dependence structures of objectivity - this makes it subject to fallibilism -  
the a priori charts necessities - these come in two classes, formal ontology 
and material ontology - the former holds for all possible objects, the latter 
for special regions of reality (like physics, biology, society) - no discipline 
can function without more or less explicit conceptual networks defining their 
basic ideas - being fallibilist, a priori claims develop with the single 
scientific disciplines …

I happen to think this Husserlian picture (for a present-day version, see Barry 
Smith) is compatible with Peirce's classification of the sciences where, as it 
is well known, the upper echelon is taken to be a priori in the sense of not at 
all containing empirical knowledge while the lower, "positive" levels inherit 
structures from those higher ones, co-determining the way they organize and 
prioritize their empirical material.
So, it is in this sense of "material ontology" that I speak of biogeographical 
ontology and and the ontology of human culture development involved in 
Diamond's argument. Given these assumptions, Diamond's argument, so I argue, is 
a priori. His conclusion that Eurasia privileges the spread of domesticated 
animals does not depend on the empirical investigation of early cultural 
contacts, human migrations or trade routes across the continent - but only on 
the general knowledge that climate is (largely) invariant along latitudes and 
that the spead of human cultures involves that of domesticated animals (the two 
ontologies I claim are involved).
As you can see my concept of ontology is deflated - which is also in concert 
with the ontological commitment in some Peircean ideas (cf. the idea that what 
exists is what must be there for true propositions to be true, 5.312) - so I do 
not participate in the analytical quest for the most meagre ontology possible … 
I would rather say that ontology should comprise general concepts necessary for 
the sciences at all levels (from elementary particles and genes to empires, 
wars, media and real estate …)

Best
F

Den 20/04/2015 kl. 04.07 skrev Franklin Ransom 
mailto:pragmaticist.lo...@gmail.com>>:

Ben, lists,

The connection you drew between the first and the fourth definitions of 
theorematic reasoning is quite interesting; I had not thought of conceptual 
analysis in quite that way. At least, though, the complexity of the diagram or 
icon is likely more complicated in the case of theorematic reasoning than in 
corollarial reasoning. I suppose I somehow think that a theorematic reasoning 
is often a previous corollarial reasoning but with something novel introduced, 
which would make the theorematic reasoning straightforwardly more complicated 
than the corollarial reasoning.

Part of my concern about the relationship between theorematic reasoning and 
abductive inference is that Frederik isn't just attempting to discuss 
mathematics when treating of theorematic diagrammatic reasoning. Rather, the 
significance is for all knowledge. Because the mathematical-diagrams are 
ubiquitous, and because Frederik takes the mathematical diagrams to be a 
priori, this means that all knowledge includes the a priori as a constituent 
element. This is a very Kantian move, repeated by C.I. Lewis in his Mind and 
the World-Order. I am quite wary of this move.

I think it very important the way you put the following: "The conclusions are 
aprioristically true only given the hypotheses, but the hypotheses themselves 
are not aprioristically true nor asserted to be true except hypothetically, and 
this hypotheticality is what allows such assurance of the conclusions, although 
even the hypothesis is upended if it leads to such contradictions as render the 
work futile". And then part of your quote from Peirce: "Mathematics merely 
traces out the consequences of hypotheses without caring whether they 
correspond to anything real or not. It is purely deductive, and all necessary 
inference is mathematics, pure or applied. Its hypotheses are suggested by any 
of the other sciences, but its assumption of them is not a scientific act." 
There are two things to be said about this. The first is that the hypotheses 
are originally suggested by experience. The second is that, even onc

[PEIRCE-L] Triadic Philosophy

[Stephen C. Rose]

Ontology consists of what is necessary for the achievement of the fusion of
truth and beauty.

Books http://buff.ly/15GfdqU

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RE: [PEIRCE-L] Peirce's 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2

[Jim Willgoose]

jon list.
 
Very nice work! I got stuck on the large number of objects that could be 
attached to a relative and drifted off into prime numbers, factors, subgroups 
and the 'conversion' formula(s). It is good to see a valuation for interpreting 
some of these things.  Given the arrays of zeroes and ones, I can begin to see 
how to replace the ":" sign with various operations that are less general.
 
Jim W
 
> Date: Sun, 19 Apr 2015 14:40:33 -0400
> From: jawb...@att.net
> To: peirce-l@list.iupui.edu
> Subject: [PEIRCE-L] Peirce's 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2
> 
> Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2
> http://inquiryintoinquiry.com/2015/04/19/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-comment-7-2/
> Date : April 19, 2015 at 1:00 pm
> 
> Peircers,
> 
> Note.  This post has a lot of math formatting,
> so please follow the link above for a more
> readable text.
> 
> Because it can sometimes be difficult to reconnect abstractions with
> their concrete instances, especially after the abstract types have
> become autonomous and taken on a life of their own, let us resort
> to a simple concrete case and examine the implications of what
> Peirce is saying about the relation between general relatives
> and individual relatives.
> 
> Suppose our initial universe of discourse has
> exactly two individuals, I and J.  Then there
> are exactly four individual dual relatives or
> ordered pairs of universe elements:
> 
> • I:I, I:J, J:I, J:J.
> 
> It is convenient arrange these in a square array:
> 
> ⎛ I:I I:J ⎞
> ⎝ J:I J:J ⎠
> 
> There are 2^4 = 16 dual relatives in general over this universe of discourse,
> since each one is formed by choosing a subset of the four ordered pairs and
> then “aggregating” them, forming their logical sum, or simply regarding them
> as a subset.  Taking the square array of ordered pairs as a backdrop, any one
> of the 16 dual relatives may be represented by a square matrix of binary 
> values,
> a value of 1 occupying the place of each ordered pair that belongs to the 
> subset
> and a value of 0 occupying the place of each ordered pair that does not belong
> to the subset in question.  The matrix representations of the 16 dual 
> relatives
> or dyadic relations over the universe {I, J} are displayed below:
> 
> ⎛ 0 0 ⎞ ⎛ 1 0 ⎞ ⎛ 0 0 ⎞ ⎛ 1 0 ⎞
> ⎝ 0 0 ⎠ ⎝ 0 0 ⎠ ⎝ 0 1 ⎠ ⎝ 0 1 ⎠
> 
> ⎛ 0 1 ⎞ ⎛ 1 1 ⎞ ⎛ 0 1 ⎞ ⎛ 1 1 ⎞
> ⎝ 0 0 ⎠ ⎝ 0 0 ⎠ ⎝ 0 1 ⎠ ⎝ 0 1 ⎠
> 
> ⎛ 0 0 ⎞ ⎛ 1 0 ⎞ ⎛ 0 0 ⎞ ⎛ 1 0 ⎞
> ⎝ 1 0 ⎠ ⎝ 1 0 ⎠ ⎝ 1 1 ⎠ ⎝ 1 1 ⎠
> 
> ⎛ 0 1 ⎞ ⎛ 1 1 ⎞ ⎛ 0 1 ⎞ ⎛ 1 1 ⎞
> ⎝ 1 0 ⎠ ⎝ 1 0 ⎠ ⎝ 1 1 ⎠ ⎝ 1 1 ⎠
> 
> Relative to the universe {I, J}, the individual dual relatives of
> the form A:A are I:I and J:J while the individual dual relatives of
> the form A:B are I:J and J:I.
> 
> Peirce assigns the name ‘concurrents’ to dual relatives all whose
> individual aggregants are of the form A:A.  There are exactly 4 of
> these and their matrices are shown in the top row of the above display.
> All the rest are called ‘opponents’ and their matrices are listed in
> the bottom three rows.
> 
> Peirce gives the name ‘alio-relatives’ to dual relatives all whose
> individual aggregants are of the form A:B.  There are exactly 4 of
> these and their matrices are shown in the first column of the above
> display.  All the rest are called ‘self-relatives’ and their matrices
> are listed in the right hand three columns.
> 
> Notice that the relative 0, represented by a matrix with all 0 entries,
> falls under the definitions of both a concurrent and an alio-relative.
> 
> References
> 
> • Peirce, C.S. (1880), “On the Algebra of Logic”,
>American Journal of Mathematics 3, 15–57.
>Collected Papers (CP 3.154–251),
>Chronological Edition (CE 4, 163–209).
> 
> • Peirce, C.S., Collected Papers of Charles Sanders Peirce,
>vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),
>vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,
>Cambridge, MA, 1931–1935, 1958.  Volume 3 : Exact Logic, 1933.
> 
> • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition,
>Peirce Edition Project (eds.), Indiana University Press, Bloomington
>and Indianapolis, IN, 1981–.  Volume 4 (1879–1884), 1986.
> 
> Resources
> 
> • Peirce’s 1870 Logic Of Relatives
> http://intersci.ss.uci.edu/wiki/index.php/Peirce%27s_1870_Logic_Of_Relatives
> 
> -- 
> 
> academia: http://independent.academia.edu/JonAwbrey
> my word press blog: http://inquiryintoinquiry.com/
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[PEIRCE-L] Re: Triadic Philosophy

[Jon Awbrey]

Ah, but beauty and truth were always one.
Our blurred vision only sees them as two.
Making ontology purely a matter of focus.

Regards,

Jon

On 4/20/2015 12:42 PM, Stephen C. Rose wrote:
>
> Ontology consists of what is necessary for the
> achievement of the fusion of truth and beauty.
>
> Books http://buff.ly/15GfdqU
>

--

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[PEIRCE-L] Re: Triadic Philosophy

[Stephen C. Rose]

Whatever it is. it is the only thing that transcends
Reality - in the sense of defining its purpose or
the goal of continuity or whatever else you wish
to call it.



On Mon, Apr 20, 2015 at 12:54 PM, Jon Awbrey  wrote:

> Ah, but beauty and truth were always one.
> Our blurred vision only sees them as two.
> Making ontology purely a matter of focus.
>
> Regards,
>
> Jon
>
>
> On 4/20/2015 12:42 PM, Stephen C. Rose wrote:
> >
> > Ontology consists of what is necessary for the
> > achievement of the fusion of truth and beauty.
> >
> > Books http://buff.ly/15GfdqU
> >
>
> --
>
> academia: http://independent.academia.edu/JonAwbrey
> my word press blog: http://inquiryintoinquiry.com/
> inquiry list: http://stderr.org/pipermail/inquiry/
> isw: http://intersci.ss.uci.edu/wiki/index.php/JLA
> oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey
> facebook page: https://www.facebook.com/JonnyCache
>

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Re: [PEIRCE-L] Natural Propositions, Ch. 10: Corollarial and Theorematic Experiments with Diagrams

[Benjamin Udell]

Frederik, lists,

You wrote,

   My argument, which I may not have made sufficiently clear in the
   chapter, is that the small step from having spatiotemporal cell
   phone information represented in long lists of coordinates - and to
   synthesize that same information in one geographical map, is a
   corollarial step.

Yes, I agree that it's corollarial. I see that I didn't make my 
agreement clear, sorry about that. I saw it as a case where corollarial 
reasoning makes clear that which, as a practical matter, was quite 
obscure. I took it as a case of mere complication, as opposed to 
complexity in the sense of nontriviality.


You wrote,

   I admit it is more difficult, in general, to precisely extend the
   corollarial/theorematic distinction to applied cases - but as you
   can see I did the attempt picking map examples. The central problem
   for my pov seems to be that in applied cases you should not only
   include what is given in axiomatics (topographical maps largely
   respecting Euclidean geometry) but also in the more or less implicit
   ontological assumptions in the area of application - this is why i
   count Wegener's map experiment as theorematic. Taken as pure
   geometry, it is a trivial translation to move South America
   eastwards to compare its coastline with Africa's - but in terms of
   geology, it requires the addition of a "new idea" - namely that
   continents may move.

I think that the mathematical shifting of the South America map to 
compare its coastline with the Africa map's coastline is required, or at 
any rate helpful, in order to bring a surprising geological phenomenon 
to light - the good match. One has ignored geological assumptions in 
order to do this, and then, looking at it and bringing geological 
assumptions back into account, one is surprised. Then the idea of an 
actual geological movement of continents is considered and abduced as a 
simplifying explanation because it sheds some light how the good fit 
could have physically happened as a matter of course.


1. Here in the abduction, unlike in theorematic deduction, one has 
_/concluded/_ in the new element, as opposed to introducing it in order 
to conclude in something else.


2. Concluding abductively in the proposition of such geological 
movement, amounts to assuming it as a basis for deducing conceivable 
practical implications. Here in the predictive deduction, the new 
element (the hypothetical assumption), unlike the new element that makes 
a deduction theorematic, is asserted in the original conditions of the 
deductive problem, not introduced in some construction along the way.


3. The inductive tests of the deduced predictions will tend to support 
or overturn the hypothetical assumption; now the new element, the 
hypothetical assumption, is that which the reasoning would conclude by 
supporting or overturning, the reasoning's thesis, unlike in a 
theorematic deduction.


If we look at the above inquiry cycle as a whole, then the hypothetical 
assumption, although it is a new element, is that which one seeks to 
confirm or overturn, and that is not the role played by the new element 
in a theorematic deduction.


Yet, - a theorematic deduction's introduction of a new or outside idea 
(not part of the problem's explicit conditions or contemplated in the 
thesis that is to be proved) reminds one of an abductive inference's 
introduction of a new or outside idea to become the conclusion. And I 
agree that that's a phenomenon worth explaining. All I can think of at 
the moment is that it's as if the new element in the theorematic 
deduction were introduced by a higher-level or methodological abduction 
- 'if I introduce this idea, I might be able to deduce the thesis as a 
matter of course'.


Best, Ben

On 4/20/2015 11:31 AM, Frederik Stjernfelt wrote:

Dear Ben,  Franklin, lists,

Den 19/04/2015 kl. 20.05 skrev Benjamin Udell >:



Franklin, lists,

I agree with Jon, thanks for your excellent starting post.

You wrote,

[] Why can't corollarial reasoning, which involves
observation and experimentation, reveal unnoticed and hidden
relations? After all, on p.285-6, Frederik mentions the work of
police detective Jorn "Old Man" Holm and his computer program,
which Frederik describes as a "practical example of corollarial
map reasoning" (p.285). In this example, Holm uses the
corollarial reasoning to reveal information about the whereabouts
of suspects. Doesn't the comparison of the map reasoning with
suspects' testimony end up revealing unnoticed and hidden relations?




There's a distinction that some make between complexity and mere 
complication. Corollarial reasonings may accumulate mere 
complications until the result becomes hard to see, although it 
involves little if any complexity in, more or less, the sense of 
depth or nontriviality.


I don't know whether there's a theorematic approach to Jørn Holm's 
diagrammatizatio

[PEIRCE-L] The syllogism as a mathemtical category

[Sungchul Ji]

Hi,

A couple of days ago (while jogging, of course), a thought occurred to me
that the syllogism may fit the category diagram (also called the
'commutative triangle') I have been using so often on these lists.  I
checked  the idea just now by diagramming it on a piece of paper and found
that it indeed seems to work as expected:


  fg
Major Premise > Minor Premise >  Conclusion
|
   ^
|
   |
|__|
  h


Figure 1.  The syllogism as a category, with the structure-preserving
mappings defined as f = natural process, g = mental process, and h =
correspondence.
   These mappings are thought to satisfy the commutative
condition, f x g = h.


I am now wondering if this commutative triangle can be viewed as the
simplest unit of "reasoning" in human thought. If so, we may be justified
to state that:

"We think in categories."
  (05202-15-1)

which would be synonymous with

"We think in signs."
  (05202015-2)

since the Peirceasn sign is itself a commutative triangle, i.e., a category.


This leads me to ask whether it would be reasonable to divide all the signs
that we use on these lists into three classes -- (i) words (W) (used in
most of the posts, e.g., Ben, Edwina, Jeff, Jerry, Gary, Steven, etc.),
(ii) diagrams (D) (e.g., Jon, Howard, Edwina, me, etc.), and (iii)
mathematical formulas (M) (e.g., mostly me, e.g., see Table 1 below).

This WDM trichotomy is an observed fact on these lists and not a
theoretical construct.  For example, we can readily recognize these three
elements in Table 1:

W = at least 50% of the symbols appearing in the 6 x 4 table

D = the 6 x 4 table itself

M = the 8 equations appearing in the table


Table 1.  A possible relation among entropy, quanta, and information

1. Concept

*Entropy* (1)

*Quanta *(2)

*Information *(3)

2. Field of inquiry

Thermodynamics

Quantum mechanics

Informatics

3. Experiment/Measurement


S = ΔQ/T

Blackbody radiation spectra

Selecting m out of n possibilities

4. Statistical mechanical

formulation

S = - k∑ pi log pi



*Boltzmann-Gibbsentropy *(1866)

U(λ, T)  = (2πhc2/λ5)/(ehc/λkT – 1)

*Planck radiation equation*
(PRE) (1900) [1]

IP  = log2(AUC(P)/AUC(G))

where IP = Planckianinformation [2], AUC = area under the curve, P = PDE,
and G = *Gaussian-like equation* [3]

y = Ae–(x - µ)^2/(2*σ^2)

5. Mathematical formulation

H = - K∑ pi log pi


*Shannon entropy*(1948)

y = (a/(Ax+B)5)/(eb/(Ax + B)– 1)

*Planckian distribution equation* (PDE) (2008) [2]

I = A log2 (n/m)


*a unified theory of the amount of information*(UTAI) (2015) [4]

6. Emerging Concept

A measure of*DISORDER*

Quantization of action needed for*ORGANIZATION*

A measure of the *ORDER*of an organized system


It would be a challenge (and should be possible) to map the WDM trichotomy
to the three trichotomies of signs in Peircean semiotics.(
https://www.marxists.org/reference/subject/philosophy/works/us/peirce2.htm).

All the best.

Sung

-- 
Sungchul Ji, Ph.D.

Associate Professor of Pharmacology and Toxicology
Department of Pharmacology and Toxicology
Ernest Mario School of Pharmacy
Rutgers University
Piscataway, N.J. 08855
732-445-4701

www.conformon.net

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[PEIRCE-L] Re: Peirce's 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2

[Jon Awbrey]

Jim, List,

The form x:y is just Peirce's notation for the ordered pair (x, y).

A 2-point universe like {I, J} provides us with another example of formal 
degeneracy (loss of generality) since the number of “diagonal” terms (of the 
form A:A) is equal to the number of “off-diagonal” terms (of the form A:B) and 
so the case exhibits symmetries that will be broken as soon as one adds another 
element to the universe.  I am planning to take up a 3-point example in good 
time but I wanted to essay the graph-theoretic representation of dyadic 
relations first. 

Regards,

Jon

http://inquiryintoinquiry.com

> On Apr 20, 2015, at 12:46 PM, Jim Willgoose  wrote:
> 
> jon list.
>  
> Very nice work! I got stuck on the large number of objects that could be 
> attached to a relative and drifted off into prime numbers, factors, subgroups 
> and the 'conversion' formula(s). It is good to see a valuation for 
> interpreting some of these things.  Given the arrays of zeroes and ones, I 
> can begin to see how to replace the ":" sign with various operations that are 
> less general.
>  
> Jim W
>  
> > Date: Sun, 19 Apr 2015 14:40:33 -0400
> > From: jawb...@att.net
> > To: peirce-l@list.iupui.edu
> > Subject: [PEIRCE-L] Peirce's 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2
> > 
> > Post : Peirce's 1880 “Algebra Of Logic” Chapter 3 • Comment 7.2
> > http://inquiryintoinquiry.com/2015/04/19/peirces-1880-algebra-of-logic-chapter-3-%e2%80%a2-comment-7-2/
> > Date : April 19, 2015 at 1:00 pm
> > 
> > Peircers,
> > 
> > Note. This post has a lot of math formatting,
> > so please follow the link above for a more
> > readable text.
> > 
> > Because it can sometimes be difficult to reconnect abstractions with
> > their concrete instances, especially after the abstract types have
> > become autonomous and taken on a life of their own, let us resort
> > to a simple concrete case and examine the implications of what
> > Peirce is saying about the relation between general relatives
> > and individual relatives.
> > 
> > Suppose our initial universe of discourse has
> > exactly two individuals, I and J. Then there
> > are exactly four individual dual relatives or
> > ordered pairs of universe elements:
> > 
> > • I:I, I:J, J:I, J:J.
> > 
> > It is convenient arrange these in a square array:
> > 
> > ⎛ I:I I:J ⎞
> > ⎝ J:I J:J ⎠
> > 
> > There are 2^4 = 16 dual relatives in general over this universe of 
> > discourse,
> > since each one is formed by choosing a subset of the four ordered pairs and
> > then “aggregating” them, forming their logical sum, or simply regarding them
> > as a subset. Taking the square array of ordered pairs as a backdrop, any one
> > of the 16 dual relatives may be represented by a square matrix of binary 
> > values,
> > a value of 1 occupying the place of each ordered pair that belongs to the 
> > subset
> > and a value of 0 occupying the place of each ordered pair that does not 
> > belong
> > to the subset in question. The matrix representations of the 16 dual 
> > relatives
> > or dyadic relations over the universe {I, J} are displayed below:
> > 
> > ⎛ 0 0 ⎞ ⎛ 1 0 ⎞ ⎛ 0 0 ⎞ ⎛ 1 0 ⎞
> > ⎝ 0 0 ⎠ ⎝ 0 0 ⎠ ⎝ 0 1 ⎠ ⎝ 0 1 ⎠
> > 
> > ⎛ 0 1 ⎞ ⎛ 1 1 ⎞ ⎛ 0 1 ⎞ ⎛ 1 1 ⎞
> > ⎝ 0 0 ⎠ ⎝ 0 0 ⎠ ⎝ 0 1 ⎠ ⎝ 0 1 ⎠
> > 
> > ⎛ 0 0 ⎞ ⎛ 1 0 ⎞ ⎛ 0 0 ⎞ ⎛ 1 0 ⎞
> > ⎝ 1 0 ⎠ ⎝ 1 0 ⎠ ⎝ 1 1 ⎠ ⎝ 1 1 ⎠
> > 
> > ⎛ 0 1 ⎞ ⎛ 1 1 ⎞ ⎛ 0 1 ⎞ ⎛ 1 1 ⎞
> > ⎝ 1 0 ⎠ ⎝ 1 0 ⎠ ⎝ 1 1 ⎠ ⎝ 1 1 ⎠
> > 
> > Relative to the universe {I, J}, the individual dual relatives of
> > the form A:A are I:I and J:J while the individual dual relatives of
> > the form A:B are I:J and J:I.
> > 
> > Peirce assigns the name ‘concurrents’ to dual relatives all whose
> > individual aggregants are of the form A:A. There are exactly 4 of
> > these and their matrices are shown in the top row of the above display.
> > All the rest are called ‘opponents’ and their matrices are listed in
> > the bottom three rows.
> > 
> > Peirce gives the name ‘alio-relatives’ to dual relatives all whose
> > individual aggregants are of the form A:B. There are exactly 4 of
> > these and their matrices are shown in the first column of the above
> > display. All the rest are called ‘self-relatives’ and their matrices
> > are listed in the right hand three columns.
> > 
> > Notice that the relative 0, represented by a matrix with all 0 entries,
> > falls under the definitions of both a concurrent and an alio-relative.
> > 
> > References
> > 
> > • Peirce, C.S. (1880), “On the Algebra of Logic”,
> > American Journal of Mathematics 3, 15–57.
> > Collected Papers (CP 3.154–251),
> > Chronological Edition (CE 4, 163–209).
> > 
> > • Peirce, C.S., Collected Papers of Charles Sanders Peirce,
> > vols. 1–6, Charles Hartshorne and Paul Weiss (eds.),
> > vols. 7–8, Arthur W. Burks (ed.), Harvard University Press,
> > Cambridge, MA, 1931–1935, 1958. Volume 3 : Exact Logic, 1933.
> > 
> > • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition,
> > Peirce Edition Project (eds.), Indiana Univ

Re: Fwd: [biosemiotics:8342] Re: [PEIRCE-L] Natural Propositions, Ch. 10: Corollarial and Theorematic Experiments with Diagrams

[Benjamin Udell]

Franklin, lists,

I think that Frederik is largely assuming Peirce's terminology. Peirce 
uses the words 'schema' and 'diagram' pretty much interchangeably.


Here are some key quotes on which Frederik is basing his discussion of 
the theormatic-corollarial distinction. 
http://www.commens.org/dictionary/term/corollarial-reasoning


I once did a summary (footnoted with online links) of key points (at 
least as they seemed to me at the time); here it is with a few 
adjustments of the links:


   Peirce argued that, while finally all deduction depends in one way
   or another on mental experimentation on schemata or diagrams,^*[1]*
   still in corollarial deduction "it is only necessary to imagine any
   case in which the premisses are true in order to perceive
   immediately that the conclusion holds in that case", whereas
   theorematic deduction "is deduction in which it is necessary to
   experiment in the imagination upon the image of the premiss in order
   from the result of such experiment to make corollarial deductions to
   the truth of the conclusion."^*[2]* He held that corollarial
   deduction matches Aristotle's conception of direct demonstration,
   which Aristotle regarded as the only thoroughly satisfactory
   demonstration, while theorematic deduction (A) is the kind more
   prized by mathematicians, (B) is peculiar to mathematics,^*[1]* and
   (C) involves in its course the introduction of a lemma or at least a
   definition uncontemplated in the thesis (the proposition that is to
   be proved); in remarkable cases that definition is of an abstraction
   that "ought to be supported by a proper postulate."^*[3]*

   [1] Peirce, C. S., from section dated 1902 by editors in the "Minute
   Logic" manuscript, Collected Papers v. 4, paragraph 233, quoted only
   in part
   
http://www.commens.org/dictionary/entry/quote-minute-logic-chapter-iii-simplest-mathematics
   in "Corollarial Reasoning" in the Commens Dictionary of Peirce's
   Terms, 2003–present, Mats Bergman and Sami Paavola, editors,
   University of Helsinki. FULL QUOTE:
   
https://archive.org/stream/TheWorldOfMathematicsVolume3/Newman-TheWorldOfMathematicsVolume3#page/n366/mode/1up
   in The World of Mathematics, Vol. 3, p. 1776.
   [2] Peirce, C. S., the 1902 Carnegie Application, published in The
   New Elements of Mathematics, Carolyn Eisele, editor, quoted in
   "Corollarial Reasoning"
   
http://www.commens.org/dictionary/entry/quote-carnegie-institution-correspondence-4
   in the Commens Dictionary of Peirce's Terms, also transcribed by
   Joseph M. Ransdell, see "From Draft A - MS L75.35-39" in Memoir 19
   http://www.iupui.edu/~arisbe/menu/library/bycsp/l75/ver1/l75v1-06.htm#m19
   
   (once there, scroll down).
   [3] Peirce, C. S., 1901 manuscript "On the Logic of Drawing History
   from Ancient Documents, Especially from Testimonies', The Essential
   Peirce v. 2, see p. 96. See quote
   
http://www.commens.org/dictionary/entry/quote-logic-drawing-history-ancient-documents-especially-testimonies-logic-histor-5
   in "Corollarial Reasoning" in the Commens Dictionary of Peirce's Terms.

The introduction of an idea beyond the explicit conditions of a problem 
and not contemplated in the thesis to be proved is precisely a 
'complexifying' step.  One might think of it as a leveraging of 
imagination to deepen understanding, by which vague remark I'm trying to 
get at the idea that such complexity is very different from the tedious 
complication of hundreds or thousands of trivial computations, 
computations that need to be done sometimes even in pure mathematics, 
where it is known as 'brute force'. Tedious computation used to be done 
by people called 'computers' up until computing machines came into use; 
part of Peirce's burden at the Coast Survey was that there came a time 
when he had to do his own tedious, lengthy computations and, worse, he 
found that his computing power was no longer what it was when he was 
younger; errors crept in.


In CP 4.233 (again 
https://archive.org/stream/TheWorldOfMathematicsVolume3/Newman-TheWorldOfMathematicsVolume3#page/n366/mode/1up) 
in "The Essence of Mathematics", Peirce says,


   [] Just now, I wish to point out that after the schema has been
   constructed according to the precept virtually contained in the
   thesis, the assertion of the theorem is not evidently true, even for
   the individual schema; nor will any amount of hard thinking of the
   philosophers' corollarial kind ever render it evident. Thinking in
   general terms is not enough. It is necessary that something should
   be DONE. In geometry, subsidiary lines are drawn. In algebra
   permissible transformations are made. Thereupon, the faculty of
   observation is called into play. Some relation between the parts of
   the schema is remarked. But would this relation subsist in every
   possible case? Mere corollarial reasoning will so

Re: [PEIRCE-L] Natural Propositions, Ch. 10: Corollarial and Theorematic Experiments with Diagrams

[Benjamin Udell]

Frederik, lists,

I'm dissatisfied with my previous post in this thread, I feel like I've 
missed the forest for the trees. While I'm not convinced that there's a 
theorematic applied deduction in the Wegener example, still, the idea of 
continental drift is not merely a simplifying explanation of the fit 
between continental coastlines, it's also an idea that anybody would 
call nontrivial. It involves a complex new idea, and, if true (as it 
turned out to be), would foreseeably be a basis and foundation for much 
further discovery.  Its nontriviality doesn't give it intrinsic 
abductive merit in the way that its plausibility does, but said 
nontriviality still makes it something to be prized if it pans out (as 
it did). But so far, that's the nontriviality of prospective 
discoveries, what about a nontriviality of how one got to the abduction 
of continental drift? I'm trying to think of some parallelism between 
its abduction and theorematic deduction, so as to analogize the idea of 
abductive nontriviality to deductive theorematicity. Roughly, something 
involving nontrivial changes of standing beliefs about geology, changes 
equivalent to the idea of continental drift. Well, when even I think I'm 
talking too much, it's time I call it a day.


Best, Ben

On 4/20/2015 12:58 PM, Benjamin Udell wrote:


Frederik, lists,

You wrote,

My argument, which I may not have made sufficiently clear in the
chapter, is that the small step from having spatiotemporal cell
phone information represented in long lists of coordinates - and
to synthesize that same information in one geographical map, is a
corollarial step.

Yes, I agree that it's corollarial. I see that I didn't make my 
agreement clear, sorry about that. I saw it as a case where 
corollarial reasoning makes clear that which, as a practical matter, 
was quite obscure. I took it as a case of mere complication, as 
opposed to complexity in the sense of nontriviality.


You wrote,

I admit it is more difficult, in general, to precisely extend the
corollarial/theorematic distinction to applied cases - but as you
can see I did the attempt picking map examples. The central
problem for my pov seems to be that in applied cases you should
not only include what is given in axiomatics (topographical maps
largely respecting Euclidean geometry) but also in the more or
less implicit ontological assumptions in the area of application -
this is why i count Wegener's map experiment as theorematic. Taken
as pure geometry, it is a trivial translation to move South
America eastwards to compare its coastline with Africa's - but in
terms of geology, it requires the addition of a "new idea" -
namely that continents may move.

I think that the mathematical shifting of the South America map to 
compare its coastline with the Africa map's coastline is required, or 
at any rate helpful, in order to bring a surprising geological 
phenomenon to light - the good match. One has ignored geological 
assumptions in order to do this, and then, looking at it and bringing 
geological assumptions back into account, one is surprised. Then the 
idea of an actual geological movement of continents is considered and 
abduced as a simplifying explanation because it sheds some light how 
the good fit could have physically happened as a matter of course.


1. Here in the abduction, unlike in theorematic deduction, one has 
_/concluded/_ in the new element, as opposed to introducing it in 
order to conclude in something else.


2. Concluding abductively in the proposition of such geological 
movement, amounts to assuming it as a basis for deducing conceivable 
practical implications. Here in the predictive deduction, the new 
element (the hypothetical assumption), unlike the new element that 
makes a deduction theorematic, is asserted in the original conditions 
of the deductive problem, not introduced in some construction along 
the way.


3. The inductive tests of the deduced predictions will tend to support 
or overturn the hypothetical assumption; now the new element, the 
hypothetical assumption, is that which the reasoning would conclude by 
supporting or overturning, the reasoning's thesis, unlike in a 
theorematic deduction.


If we look at the above inquiry cycle as a whole, then the 
hypothetical assumption, although it is a new element, is that which 
one seeks to confirm or overturn, and that is not the role played by 
the new element in a theorematic deduction.


Yet, - a theorematic deduction's introduction of a new or outside idea 
(not part of the problem's explicit conditions or contemplated in the 
thesis that is to be proved) reminds one of an abductive inference's 
introduction of a new or outside idea to become the conclusion. And I 
agree that that's a phenomenon worth explaining. All I can think of at 
the moment is that it's as if the new element in the theorematic 
deduction were introduced by a higher-level 

Re: [biosemiotics:8342] Re: [PEIRCE-L] Natural Propositions, Ch. 10: Corollarial and Theorematic Experiments with Diagrams

[Frederik Stjernfelt]

Dear Ben, lists -

Thanks for two mails. The first largely resumes parts of my chapter and indeed 
Peirce's basic ideas of theorematicity - although it is not entirely correct 
that P saw his distinction as relative to intellect so that which is 
corollarial to a grownup will be theorematic to a child. Peirce insisted that 
theorematicity consists in the addition of something new to a problem - an 
additional object, manipulation, abstraction, perspective, etc. If once you 
know which such addition to add in the single case, the remaining problem 
becomes corollarial, but that has nothing to do with the intellect of the 
reasoner. A stupid but well-informed person may repeat Euclid's theorematic 
proof of the angular sum of the triangle, while an uninformed genius may be 
unable to find that proof - and still the proof requires the addition of 
auxiliary lines to the triangle no matter what.

But you address other important things. It seems as if, to some degree, Peirce 
without saying it assumes something like the discovery/justification 
distinction. When saying mathematical reasoning is deductive, this seems to be 
a justification claim merely, because in the actual procedure of searching for 
the proof of a theorem, Peirce realizes there may be an abductive 
trial-and-error phase, particularly in the theorematic cases where it is not 
evident which new element to add to your problem (is there also something akin 
to an inductive phase in mathematical proofmaking, e.g. when mathematicians 
compare and evaluate their result with respect to its potential effects in 
other areas of math?). So even if mathematics is the science that proceeds by 
deductive reasoning, there are non-deductive phases in it (discovery), even if 
the results are deductively valid (justification).

My idea with Wegener's map was, of course, to find a theorematic example from 
applied math. In such a case both the mathematical formalism (here, 
approximately Euclidean geometry) and the basic assumptions of the material 
field (geology) must be part of the status quo to which a new element, 
manipulation, principle etc. should be added. The transformation making the two 
continent coasts meet is trivial in the Euclidean sense, but the change in 
underlying geological ontology (from the axiom that continents are eternally 
stable to the axiom that they float on the surface of the earth) indeed 
requires the addition of a new idea. In some sense, the radicality of this new 
idea is eased by the triviality of the transformation in purely geometrical 
terms. What prompted the idea of generalizing the mathematical notions of 
corollarial/theorematic to the applied sciences, of course, is Peirce's 
classificaiton of the sciences where math is number one, implying that all 
other sciences wihtout exception use mathematical structures - but 
simultaneously that generalization cannot take place without introdcuding basic 
principles of those "lower" sciences, thereby modifying the corr/theor. 
distinction to some degree because it now has to involve ontological 
assumptions regarding positive knowledge. But still I think it makes good sense.

Best
F


Frederik, lists,

I'm dissatisfied with my previous post in this thread, I feel like I've missed 
the forest for the trees. While I'm not convinced that there's a theorematic 
applied deduction in the Wegener example, still, the idea of continental drift 
is not merely a simplifying explanation of the fit between continental 
coastlines, it's also an idea that anybody would call nontrivial. It involves a 
complex new idea, and, if true (as it turned out to be), would foreseeably be a 
basis and foundation for much further discovery.  Its nontriviality doesn't 
give it intrinsic abductive merit in the way that its plausibility does, but 
said nontriviality still makes it something to be prized if it pans out (as it 
did). But so far, that's the nontriviality of prospective discoveries, what 
about a nontriviality of how one got to the abduction of continental drift? I'm 
trying to think of some parallelism between its abduction and theorematic 
deduction, so as to analogize the idea of abductive nontriviality to deductive 
theorematicity. Roughly, something involving nontrivial changes of standing 
beliefs about geology, changes equivalent to the idea of continental drift. 
Well, when even I think I'm talking too much, it's time I call it a day.

Best, Ben

:


Franklin, lists,

I think that Frederik is largely assuming Peirce's terminology. Peirce uses the 
words 'schema' and 'diagram' pretty much interchangeably.

Here are some key quotes on which Frederik is basing his discussion of the 
theormatic-corollarial distinction. 
http://www.commens.org/dictionary/term/corollarial-reasoning

I once did a summary (footnoted with online links) of key points (at least as 
they seemed to me at the time); here it is with a few adjustments of the links:

Peirce argued that, while finally all deduction dep

Re: [PEIRCE-L] Stjernfelt: Chapter 9

[Franklin Ransom]

Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
counting qualities or characters doesn't seem to be helpful. Although it
should be possible to enumerate them, to a point, for the purpose of some
inquiry.

As I recall, Jon Awbrey in the last month or two referenced a text from
Peirce about the multiplication of breadth and depth using symbols like 1,
0, and the infinity loop, to distinguish cases such as essential depth and
breadth, substantial depth and breadth, the idea of nothing, the idea of
being, etc. If infinity was indeed used then, Peirce had certainly
contemplated infinite depth and infinite breadth, although perhaps not
simply in the sense of counting with no end, but in the direct sense of
being that which is without limit, so depth without limit or breadth
without limit.

-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
wrote:

>  Dear Franklin, Cathy, Lists -
>
> A small clarification: Peirce's *BxD=A* idea, I think, should not be
> taken a device for the arithmetic calculation of exact information size -
> it is rather the proposal of a general law relating Breadth and Depth. His
> idea comes from the simple idea that when intension is zero, there is no
> information, while when extension is zero, there is also no information -
> and that is the relation of the two factors in a product.  (It is a bit
> like his first Boole-inspired definition of universal quantification as a
> product - he defines truth as 1, falsity as 0,  then, in order to be true,
> each single case of a universal proposition should be true - if any single
> one of them is false, the total product of them all will be zero.)
> The BXD=A idea allows him to investigate what happens if intension or
> extension are in- or decreased, etc. - even if not being able to express
> that in precise numbers.
>
>  Best
> F
>
>
>  Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
> pragmaticist.lo...@gmail.com>:
>
>  Cathy, lists,
>
>  Well, look at this way: It is possible for there to be objects in the
> senses which are yet not perceived, because we do not yet have any idea of
> what it is to which we are looking. It takes a hypothesis to introduce a
> new idea to us to explain what it is, which hypothesis we can then put to
> the test. In order to do so, we must determine what kinds of characters to
> look for (deduction helps here) and then look for existent objects
> (induction) to learn whether the purported relations between characters
> obtain in fact, and in this way we come to understand the thing which we
> are experiencing. It is of course induction which gives us more
> information; abduction simply gives us the idea which needs to become
> informed, and deduction is merely explicative, based on relating the idea
> to other ideas and previously gathered information regarding those ideas.
>
>  Obviously, we cannot conduct induction without end, because that is a
> practical impossibility. Our 'sum', as you put it, far from being always an
> infinity, will very likely never be an infinity in practice, in whatever
> sense you mean to understand the application of infinity to a 'sum' of
> information. Of course, as an ideal, where science, the community of
> inquiry as such, continues to investigate, it is possible for the
> information of an idea to reach a much greater 'sum' than would otherwise
> be possible for individuals such as you or me. But it is a commonplace of
> science that ideas that work and continue to work are understood more
> thoroughly in their relations to other ideas over the course on inquiry.
> This means of course that not only the breadth, but also the depth of the
> idea continues to grow. As a result, typically, rather than tending to make
> comparisons moot, we start to see a hierarchy of ideas and related sciences
> appear.
>
>  Consider this passage: "The former [Cows] is a natural class, the latter
> [Red Cows] is not. Now one predicate more may be attached to Red Cows than
> to Cows; hence Mr. Mill's attempts to analyze the difference between
> natural and artificial classes is seen to be a failure. For, according to
> him, the difference is that a real kind is distinguished by unknown
> multitudes of properties while an artificial class has only a few
> determinate ones. Again there is an unusual degree of accordance among
> naturalists in making Vertebrates a natural class. Yet the number of
> predicates proper to it is comparatively small" (NP, p.238, quoting
> Peirce). We can see here that further simplifications are introduced, so
> taking what is learned about various vertebrates, a new idea, that of
> vertebrates, appears which simplifies the characters involved. Conversely,
> species under vertebrates will become much more determinate in terms of
> their characters, but be simplified with respect to their extension.
>
>  You said above: "Under synechism every real object has an infinite
> number of attributes, and every

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Jon Awbrey]

Franklin, List,

I think that was Ben Udell. 

Regards,

Jon

http://inquiryintoinquiry.com

> On Apr 20, 2015, at 7:30 PM, Franklin Ransom  
> wrote:
> 
> Cathy, Frederik, lists,
> 
> Yes, Frederik, that makes sense to me. As I mentioned in my previous post, 
> counting qualities or characters doesn't seem to be helpful. Although it 
> should be possible to enumerate them, to a point, for the purpose of some 
> inquiry.
> 
> As I recall, Jon Awbrey in the last month or two referenced a text from 
> Peirce about the multiplication of breadth and depth using symbols like 1, 0, 
> and the infinity loop, to distinguish cases such as essential depth and 
> breadth, substantial depth and breadth, the idea of nothing, the idea of 
> being, etc. If infinity was indeed used then, Peirce had certainly 
> contemplated infinite depth and infinite breadth, although perhaps not simply 
> in the sense of counting with no end, but in the direct sense of being that 
> which is without limit, so depth without limit or breadth without limit.
> 
> -- Franklin
> 
>> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt  
>> wrote:
>> Dear Franklin, Cathy, Lists - 
>> 
>> A small clarification: Peirce's BxD=A idea, I think, should not be taken a 
>> device for the arithmetic calculation of exact information size - it is 
>> rather the proposal of a general law relating Breadth and Depth. His idea 
>> comes from the simple idea that when intension is zero, there is no 
>> information, while when extension is zero, there is also no information - 
>> and that is the relation of the two factors in a product.  (It is a bit like 
>> his first Boole-inspired definition of universal quantification as a product 
>> - he defines truth as 1, falsity as 0,  then, in order to be true, each 
>> single case of a universal proposition should be true - if any single one of 
>> them is false, the total product of them all will be zero.) 
>> The BXD=A idea allows him to investigate what happens if intension or 
>> extension are in- or decreased, etc. - even if not being able to express 
>> that in precise numbers. 
>> 
>> Best
>> F
>> 
>> 
>>> Den 20/04/2015 kl. 01.14 skrev Franklin Ransom 
>>> :
>>> 
>>> Cathy, lists,
>>> 
>>> Well, look at this way: It is possible for there to be objects in the 
>>> senses which are yet not perceived, because we do not yet have any idea of 
>>> what it is to which we are looking. It takes a hypothesis to introduce a 
>>> new idea to us to explain what it is, which hypothesis we can then put to 
>>> the test. In order to do so, we must determine what kinds of characters to 
>>> look for (deduction helps here) and then look for existent objects 
>>> (induction) to learn whether the purported relations between characters 
>>> obtain in fact, and in this way we come to understand the thing which we 
>>> are experiencing. It is of course induction which gives us more 
>>> information; abduction simply gives us the idea which needs to become 
>>> informed, and deduction is merely explicative, based on relating the idea 
>>> to other ideas and previously gathered information regarding those ideas.
>>> 
>>> Obviously, we cannot conduct induction without end, because that is a 
>>> practical impossibility. Our 'sum', as you put it, far from being always an 
>>> infinity, will very likely never be an infinity in practice, in whatever 
>>> sense you mean to understand the application of infinity to a 'sum' of 
>>> information. Of course, as an ideal, where science, the community of 
>>> inquiry as such, continues to investigate, it is possible for the 
>>> information of an idea to reach a much greater 'sum' than would otherwise 
>>> be possible for individuals such as you or me. But it is a commonplace of 
>>> science that ideas that work and continue to work are understood more 
>>> thoroughly in their relations to other ideas over the course on inquiry. 
>>> This means of course that not only the breadth, but also the depth of the 
>>> idea continues to grow. As a result, typically, rather than tending to make 
>>> comparisons moot, we start to see a hierarchy of ideas and related sciences 
>>> appear.
>>> 
>>> Consider this passage: "The former [Cows] is a natural class, the latter 
>>> [Red Cows] is not. Now one predicate more may be attached to Red Cows than 
>>> to Cows; hence Mr. Mill's attempts to analyze the difference between 
>>> natural and artificial classes is seen to be a failure. For, according to 
>>> him, the difference is that a real kind is distinguished by unknown 
>>> multitudes of properties while an artificial class has only a few 
>>> determinate ones. Again there is an unusual degree of accordance among 
>>> naturalists in making Vertebrates a natural class. Yet the number of 
>>> predicates proper to it is comparatively small" (NP, p.238, quoting 
>>> Peirce). We can see here that further simplifications are introduced, so 
>>> taking what is learned about various vertebrates, a new idea, that

Re: [PEIRCE-L] Re: [biosemiotics:8363] Natural Propositions, Ch. 10:

[Howard Pattee]

At 12:22 PM 4/20/2015, Frederik Stjernfelt wrote:
Sorry for having rattled Franklin's empiricist 
sentiments with references to the a priori!
Empiricists seem to have an a priori fear of the 
a priori … but no philosophy of science has, as 
yet, been able to completely abolish the a priori . . .


This is clearly one philosopher's opinion, but to 
another rattled empiricist it sounds like 
anthropocentric question-begging. Does the 
information that distinguishes food from poison 
in the gene of E. coli or the nervous system of 
C. elegans depend on an a priori logic? Do I need 
an a priori logic to distinguish food from poison?


From what sources do you choose your logical a priori information?

Howard




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[PEIRCE-L] Re: [biosemiotics:8369] Re: Natural Propositions, Ch. 10:

[Franklin Ransom]

Frederik, lists,

I'm not sure, but this appears in my email as a separate thread, having
copied posts that I sent to the other thread. Since Frederik replied to my
posts on this one, I suppose I'll reply here for now. If this doesn't
appear as a new thread to anyone else, then please ignore my comment.

Just to be clear, I think that this will definitely be a case of "we will
just have to agree to disagree". Frederik, you are clearly professionally
committed to the a priori; I am constitutionally committed to radical
empiricism. Now that you are forewarned about that, I'll say a couple of
things about my point of view.

I'm not so sure that empiricists like myself have an "a priori fear of the
a priori". When I look at the philosophy of transcendentalism and its
results, the fear strikes me as quite experience-based. One can also think
about Peirce's remarks in "The Fixation of Belief" about the method of the
a priori.

I'm not, as an empiricist, particularly impressed with logical positivism
as a form of empiricism. I believe it a commonplace in classical pragmatism
that the theory of experience at play in pragmatism is not the atomistic
approach of the British empiricists or their inheritors in logical
positivism/empiricism. My understanding is that whether we are talking
about Peirce, James, or Dewey, experience is not conceived on the model of
a series of distinct, discrete sense impressions or sense-data. Instead,
experience is much more complex, in which conjunction and continuity are
just as much found in the experience as are disjunction and
discreteness--we do not require some outside source to make our experiences
appear connected for us in the first place. Certainly the mind works to
bring connection and continuity to its experiences. But it does not do this
ex nihilo; such connections and continuities work to extend in novel ways
connections and continuities already experienced--the mind generalizes what
it has been given to work with. So far as I see it, this is the empiricism
that classical pragmatism is based upon, and is part of what my take on
empiricism amounts to.

I'm not entirely sure what is meant by "dependence structures of
objectivity". I also find your ascription of fallibilism to a priori
knowledge as bizarre.

Rather than discuss what you have had to say further (this post would
become inordinately long), I think it would be best to simplify the matter.
Suppose I have a surprising experience, and then develop a hypothesis to
explain that experience. Once I have the idea in hand from the hypothesis,
I deduce consequences from this hypothesis to the point that I now know how
to put the hypothesis to inductive experimentation. Now, at this point, I
have not yet conducted any inductions. Is this process, from the gaining of
a hypothesis to the deduction of consequences, altogether a priori on your
account?

-- Franklin


On Mon, Apr 20, 2015 at 12:22 PM, Frederik Stjernfelt 
wrote:

>  Dear Franklin, lists -
>
>  Sorry for having rattled Franklin's empiricist sentiments with
> references to the a priori!
> Empiricists seem to have an a priori fear of the a priori … but no
> philosophy of science has, as yet, been able to completely abolish the a
> priori - even logical positvism had to admit logic as a remaining a priori
> field (reinterpreting that as tautologies, that is true).
> I should probably have given a note here to my own stance on the a priori
> - for the interested, I wrote a bit about it in ch. 8 of Diagrammatology
> (2007). My take on it there comes more from the early Husserl than from
> Peirce: the a priori has nothing to do with Kantian subjectivity, rather,
> it consists in dependence structures of objectivity - this makes it subject
> to fallibilism -  the a priori charts necessities - these come in two
> classes, formal ontology and material ontology - the former holds for all
> possible objects, the latter for special regions of reality (like physics,
> biology, society) - no discipline can function without more or less
> explicit conceptual networks defining their basic ideas - being
> fallibilist, a priori claims develop with the single scientific disciplines
> …
>
>  I happen to think this Husserlian picture (for a present-day version,
> see Barry Smith) is compatible with Peirce's classification of the sciences
> where, as it is well known, the upper echelon is taken to be a priori in
> the sense of not at all containing empirical knowledge while the lower,
> "positive" levels inherit structures from those higher ones, co-determining
> the way they organize and prioritize their empirical material.
> So, it is in this sense of "material ontology" that I speak of
> biogeographical ontology and and the ontology of human culture development
> involved in Diamond's argument. Given these assumptions, Diamond's
> argument, so I argue, is a priori. His conclusion that Eurasia privileges
> the spread of domesticated animals does not depend on the empirical
> investi

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Jon, Ben, lists,

Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of
thing to do, with the slow reads going on about Peirce's earlier logical
works. I apologize for the mistake!

-- Franklin

On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey  wrote:

> Franklin, List,
>
> I think that was Ben Udell.
>
> Regards,
>
> Jon
>
> http://inquiryintoinquiry.com
>
> On Apr 20, 2015, at 7:30 PM, Franklin Ransom 
> wrote:
>
> Cathy, Frederik, lists,
>
> Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
> counting qualities or characters doesn't seem to be helpful. Although it
> should be possible to enumerate them, to a point, for the purpose of some
> inquiry.
>
> As I recall, Jon Awbrey in the last month or two referenced a text from
> Peirce about the multiplication of breadth and depth using symbols like 1,
> 0, and the infinity loop, to distinguish cases such as essential depth and
> breadth, substantial depth and breadth, the idea of nothing, the idea of
> being, etc. If infinity was indeed used then, Peirce had certainly
> contemplated infinite depth and infinite breadth, although perhaps not
> simply in the sense of counting with no end, but in the direct sense of
> being that which is without limit, so depth without limit or breadth
> without limit.
>
> -- Franklin
>
> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
> wrote:
>
>>  Dear Franklin, Cathy, Lists -
>>
>> A small clarification: Peirce's *BxD=A* idea, I think, should not be
>> taken a device for the arithmetic calculation of exact information size -
>> it is rather the proposal of a general law relating Breadth and Depth. His
>> idea comes from the simple idea that when intension is zero, there is no
>> information, while when extension is zero, there is also no information -
>> and that is the relation of the two factors in a product.  (It is a bit
>> like his first Boole-inspired definition of universal quantification as a
>> product - he defines truth as 1, falsity as 0,  then, in order to be true,
>> each single case of a universal proposition should be true - if any single
>> one of them is false, the total product of them all will be zero.)
>> The BXD=A idea allows him to investigate what happens if intension or
>> extension are in- or decreased, etc. - even if not being able to express
>> that in precise numbers.
>>
>>  Best
>> F
>>
>>
>>  Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
>> pragmaticist.lo...@gmail.com>:
>>
>>  Cathy, lists,
>>
>>  Well, look at this way: It is possible for there to be objects in the
>> senses which are yet not perceived, because we do not yet have any idea of
>> what it is to which we are looking. It takes a hypothesis to introduce a
>> new idea to us to explain what it is, which hypothesis we can then put to
>> the test. In order to do so, we must determine what kinds of characters to
>> look for (deduction helps here) and then look for existent objects
>> (induction) to learn whether the purported relations between characters
>> obtain in fact, and in this way we come to understand the thing which we
>> are experiencing. It is of course induction which gives us more
>> information; abduction simply gives us the idea which needs to become
>> informed, and deduction is merely explicative, based on relating the idea
>> to other ideas and previously gathered information regarding those ideas.
>>
>>  Obviously, we cannot conduct induction without end, because that is a
>> practical impossibility. Our 'sum', as you put it, far from being always an
>> infinity, will very likely never be an infinity in practice, in whatever
>> sense you mean to understand the application of infinity to a 'sum' of
>> information. Of course, as an ideal, where science, the community of
>> inquiry as such, continues to investigate, it is possible for the
>> information of an idea to reach a much greater 'sum' than would otherwise
>> be possible for individuals such as you or me. But it is a commonplace of
>> science that ideas that work and continue to work are understood more
>> thoroughly in their relations to other ideas over the course on inquiry.
>> This means of course that not only the breadth, but also the depth of the
>> idea continues to grow. As a result, typically, rather than tending to make
>> comparisons moot, we start to see a hierarchy of ideas and related sciences
>> appear.
>>
>>  Consider this passage: "The former [Cows] is a natural class, the
>> latter [Red Cows] is not. Now one predicate more may be attached to Red
>> Cows than to Cows; hence Mr. Mill's attempts to analyze the difference
>> between natural and artificial classes is seen to be a failure. For,
>> according to him, the difference is that a real kind is distinguished by
>> unknown multitudes of properties while an artificial class has only a few
>> determinate ones. Again there is an unusual degree of accordance among
>> naturalists in making Vertebrates a natural class. Yet the number of
>> predicates

[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Jon Awbrey]

Franklin,

This looks like the post you had in mind:

BU:article.gmane.org/gmane.science.philosophy.peirce/15796/match=breadth+depth

BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/15796

Regards,

Jon

On 4/20/2015 8:21 PM, Franklin Ransom wrote:

Jon, Ben, lists,

Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of
thing to do, with the slow reads going on about Peirce's earlier logical
works. I apologize for the mistake!

-- Franklin

On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey  wrote:


Franklin, List,

I think that was Ben Udell.

Regards,

Jon

http://inquiryintoinquiry.com

On Apr 20, 2015, at 7:30 PM, Franklin Ransom 
wrote:

Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
counting qualities or characters doesn't seem to be helpful. Although it
should be possible to enumerate them, to a point, for the purpose of some
inquiry.

As I recall, Jon Awbrey in the last month or two referenced a text from
Peirce about the multiplication of breadth and depth using symbols like 1,
0, and the infinity loop, to distinguish cases such as essential depth and
breadth, substantial depth and breadth, the idea of nothing, the idea of
being, etc. If infinity was indeed used then, Peirce had certainly
contemplated infinite depth and infinite breadth, although perhaps not
simply in the sense of counting with no end, but in the direct sense of
being that which is without limit, so depth without limit or breadth
without limit.

-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
wrote:


  Dear Franklin, Cathy, Lists -

A small clarification: Peirce's *BxD=A* idea, I think, should not be
taken a device for the arithmetic calculation of exact information size -
it is rather the proposal of a general law relating Breadth and Depth. His
idea comes from the simple idea that when intension is zero, there is no
information, while when extension is zero, there is also no information -
and that is the relation of the two factors in a product.  (It is a bit
like his first Boole-inspired definition of universal quantification as a
product - he defines truth as 1, falsity as 0,  then, in order to be true,
each single case of a universal proposition should be true - if any single
one of them is false, the total product of them all will be zero.)
The BXD=A idea allows him to investigate what happens if intension or
extension are in- or decreased, etc. - even if not being able to express
that in precise numbers.

  Best
F


  Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
pragmaticist.lo...@gmail.com>:

  Cathy, lists,

  Well, look at this way: It is possible for there to be objects in the
senses which are yet not perceived, because we do not yet have any idea of
what it is to which we are looking. It takes a hypothesis to introduce a
new idea to us to explain what it is, which hypothesis we can then put to
the test. In order to do so, we must determine what kinds of characters to
look for (deduction helps here) and then look for existent objects
(induction) to learn whether the purported relations between characters
obtain in fact, and in this way we come to understand the thing which we
are experiencing. It is of course induction which gives us more
information; abduction simply gives us the idea which needs to become
informed, and deduction is merely explicative, based on relating the idea
to other ideas and previously gathered information regarding those ideas.

  Obviously, we cannot conduct induction without end, because that is a
practical impossibility. Our 'sum', as you put it, far from being always an
infinity, will very likely never be an infinity in practice, in whatever
sense you mean to understand the application of infinity to a 'sum' of
information. Of course, as an ideal, where science, the community of
inquiry as such, continues to investigate, it is possible for the
information of an idea to reach a much greater 'sum' than would otherwise
be possible for individuals such as you or me. But it is a commonplace of
science that ideas that work and continue to work are understood more
thoroughly in their relations to other ideas over the course on inquiry.
This means of course that not only the breadth, but also the depth of the
idea continues to grow. As a result, typically, rather than tending to make
comparisons moot, we start to see a hierarchy of ideas and related sciences
appear.

  Consider this passage: "The former [Cows] is a natural class, the
latter [Red Cows] is not. Now one predicate more may be attached to Red
Cows than to Cows; hence Mr. Mill's attempts to analyze the difference
between natural and artificial classes is seen to be a failure. For,
according to him, the difference is that a real kind is distinguished by
unknown multitudes of properties while an artificial class has only a few
determinate ones. Again there is an unusual degree of accordance among
naturalists in making Vertebrates a natura

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Benjamin Udell]

Franklin, Jon, lists,

Yep, that was me with Peirce's ∞'s and 0's of breadth and depth, March 
8, 2015, at the link:

https://www.mail-archive.com/peirce-l@list.iupui.edu/msg03282.html

- Best, Ben

On 4/20/2015 7:42 PM, Jon Awbrey wrote:


Franklin, List,

I think that was Ben Udell.

Regards,

Jon

http://inquiryintoinquiry.com

On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:


Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my previous 
post, counting qualities or characters doesn't seem to be helpful. 
Although it should be possible to enumerate them, to a point, for the 
purpose of some inquiry.


As I recall, Jon Awbrey in the last month or two referenced a text 
from Peirce about the multiplication of breadth and depth using 
symbols like 1, 0, and the infinity loop, to distinguish cases such 
as essential depth and breadth, substantial depth and breadth, the 
idea of nothing, the idea of being, etc. If infinity was indeed used 
then, Peirce had certainly contemplated infinite depth and infinite 
breadth, although perhaps not simply in the sense of counting with no 
end, but in the direct sense of being that which is without limit, so 
depth without limit or breadth without limit.


-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:


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[PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Jon,

Yes, that is exactly it, thank you so much!

-- Franklin

On Mon, Apr 20, 2015 at 8:30 PM, Jon Awbrey  wrote:

> Franklin,
>
> This looks like the post you had in mind:
>
> BU:
> article.gmane.org/gmane.science.philosophy.peirce/15796/match=breadth+depth
>
> BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/15796
>
> Regards,
>
> Jon
>
>
> On 4/20/2015 8:21 PM, Franklin Ransom wrote:
>
>> Jon, Ben, lists,
>>
>> Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of
>> thing to do, with the slow reads going on about Peirce's earlier logical
>> works. I apologize for the mistake!
>>
>> -- Franklin
>>
>> On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey  wrote:
>>
>>  Franklin, List,
>>>
>>> I think that was Ben Udell.
>>>
>>> Regards,
>>>
>>> Jon
>>>
>>> http://inquiryintoinquiry.com
>>>
>>> On Apr 20, 2015, at 7:30 PM, Franklin Ransom <
>>> pragmaticist.lo...@gmail.com>
>>> wrote:
>>>
>>> Cathy, Frederik, lists,
>>>
>>> Yes, Frederik, that makes sense to me. As I mentioned in my previous
>>> post,
>>> counting qualities or characters doesn't seem to be helpful. Although it
>>> should be possible to enumerate them, to a point, for the purpose of some
>>> inquiry.
>>>
>>> As I recall, Jon Awbrey in the last month or two referenced a text from
>>> Peirce about the multiplication of breadth and depth using symbols like
>>> 1,
>>> 0, and the infinity loop, to distinguish cases such as essential depth
>>> and
>>> breadth, substantial depth and breadth, the idea of nothing, the idea of
>>> being, etc. If infinity was indeed used then, Peirce had certainly
>>> contemplated infinite depth and infinite breadth, although perhaps not
>>> simply in the sense of counting with no end, but in the direct sense of
>>> being that which is without limit, so depth without limit or breadth
>>> without limit.
>>>
>>> -- Franklin
>>>
>>> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt 
>>> wrote:
>>>
>>>Dear Franklin, Cathy, Lists -

 A small clarification: Peirce's *BxD=A* idea, I think, should not be

 taken a device for the arithmetic calculation of exact information size
 -
 it is rather the proposal of a general law relating Breadth and Depth.
 His
 idea comes from the simple idea that when intension is zero, there is no
 information, while when extension is zero, there is also no information
 -
 and that is the relation of the two factors in a product.  (It is a bit
 like his first Boole-inspired definition of universal quantification as
 a
 product - he defines truth as 1, falsity as 0,  then, in order to be
 true,
 each single case of a universal proposition should be true - if any
 single
 one of them is false, the total product of them all will be zero.)
 The BXD=A idea allows him to investigate what happens if intension or
 extension are in- or decreased, etc. - even if not being able to express
 that in precise numbers.

   Best
 F


   Den 20/04/2015 kl. 01.14 skrev Franklin Ransom <
 pragmaticist.lo...@gmail.com>:

   Cathy, lists,

   Well, look at this way: It is possible for there to be objects in the
 senses which are yet not perceived, because we do not yet have any idea
 of
 what it is to which we are looking. It takes a hypothesis to introduce a
 new idea to us to explain what it is, which hypothesis we can then put
 to
 the test. In order to do so, we must determine what kinds of characters
 to
 look for (deduction helps here) and then look for existent objects
 (induction) to learn whether the purported relations between characters
 obtain in fact, and in this way we come to understand the thing which we
 are experiencing. It is of course induction which gives us more
 information; abduction simply gives us the idea which needs to become
 informed, and deduction is merely explicative, based on relating the
 idea
 to other ideas and previously gathered information regarding those
 ideas.

   Obviously, we cannot conduct induction without end, because that is a
 practical impossibility. Our 'sum', as you put it, far from being
 always an
 infinity, will very likely never be an infinity in practice, in whatever
 sense you mean to understand the application of infinity to a 'sum' of
 information. Of course, as an ideal, where science, the community of
 inquiry as such, continues to investigate, it is possible for the
 information of an idea to reach a much greater 'sum' than would
 otherwise
 be possible for individuals such as you or me. But it is a commonplace
 of
 science that ideas that work and continue to work are understood more
 thoroughly in their relations to other ideas over the course on inquiry.
 This means of course that not only the breadth, but also the depth of
 the
 idea continues to grow. As a result,

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

And thanks to you too, Ben!

On Mon, Apr 20, 2015 at 8:31 PM, Benjamin Udell  wrote:

>  Franklin, Jon, lists,
>
> Yep, that was me with Peirce's ∞'s and 0's of breadth and depth, March 8,
> 2015, at the link:
> https://www.mail-archive.com/peirce-l@list.iupui.edu/msg03282.html
>
> - Best, Ben
>
> On 4/20/2015 7:42 PM, Jon Awbrey wrote:
>
> Franklin, List,
>
>  I think that was Ben Udell.
>
> Regards,
>
> Jon
>
> http://inquiryintoinquiry.com
>
> On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:
>
> Cathy, Frederik, lists,
>
> Yes, Frederik, that makes sense to me. As I mentioned in my previous post,
> counting qualities or characters doesn't seem to be helpful. Although it
> should be possible to enumerate them, to a point, for the purpose of some
> inquiry.
>
> As I recall, Jon Awbrey in the last month or two referenced a text from
> Peirce about the multiplication of breadth and depth using symbols like 1,
> 0, and the infinity loop, to distinguish cases such as essential depth and
> breadth, substantial depth and breadth, the idea of nothing, the idea of
> being, etc. If infinity was indeed used then, Peirce had certainly
> contemplated infinite depth and infinite breadth, although perhaps not
> simply in the sense of counting with no end, but in the direct sense of
> being that which is without limit, so depth without limit or breadth
> without limit.
>
> -- Franklin
>
> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:
>
>
>
> -
> 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...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the
> BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm
> .
>
>
>
>
>
>

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Re: Fwd: [biosemiotics:8342] Re: [PEIRCE-L] Natural Propositions, Ch. 10: Corollarial and Theorematic Experiments with Diagrams

[Franklin Ransom]

Ben, lists,

It looks like Ben's post was sent to Peirce-L, but not the biosemiotics
list-serv. For biosemiotics list members, please see below for the post to
which I am responding.

"I think that Frederik is largely assuming Peirce's terminology. Peirce
uses the words 'schema' and 'diagram' pretty much interchangeably."

Yes, Ben, I would have guessed as much. In connection with this, I wonder
whether Peirce would have said Kant's schematization in the Critic of Pure
Reason is in fact a diagrammatization of some sort.

As to the rest of what you had to say, I don't find myself really in any
disagreement.

I see that Frederik mentioned that whether something is corollarial or
theorematic is not relative to a person's intelligence. I would suppose you
meant that a mathematician would have a much more advanced logic system
available to think about then the (average) schoolchild, in which case your
remark would make sense. While Frederik is right to point out that only
whether something new or foreign is introduced is what makes the reasoning
theorematic (I believe I mentioned in a previous post that this is what is
signficant for Frederik, and not so much the complexity of the schema), it
is also true that what logic system one is using will affect what counts as
corollarial reasoning and what as theorematic; that is, it will affect
whether the something "new" or "foreign" is really new or foreign to the
system, and the typical schoolchild probably has a much simpler logic
system to work with than the typical mathematician.

Actually, it just struck me that I mentioned that the complexity is not so
important for Frederik's account, and you have continued discussing
complexity to show how it is important. I'm sorry, I didn't mean to imply
that non-triviality is unimportant. It does get mentioned in the text at
some point, but does not play a prominent role, not nearly as much as the
point that something new or foreign must be introduced into the reasoning.
Though, I do wonder somewhat whether non-triviality is connected to a
theorem not being easily absorbed into a logic system that could turn what
was originally a theorematic reasoning into a purely corollarial reasoning.
Perhaps the newer or more foreign the idea, the more nontrivial and fecund
it may turn out to be?

-- Franklin

On Mon, Apr 20, 2015 at 4:18 PM, Benjamin Udell  wrote:

>  Franklin, lists,
>
> I think that Frederik is largely assuming Peirce's terminology. Peirce
> uses the words 'schema' and 'diagram' pretty much interchangeably.
>
> Here are some key quotes on which Frederik is basing his discussion of the
> theormatic-corollarial distinction.
> http://www.commens.org/dictionary/term/corollarial-reasoning
>
> I once did a summary (footnoted with online links) of key points (at least
> as they seemed to me at the time); here it is with a few adjustments of the
> links:
>
> Peirce argued that, while finally all deduction depends in one way or
> another on mental experimentation on schemata or diagrams,*[1]*  still in
> corollarial deduction "it is only necessary to imagine any case in which
> the premisses are true in order to perceive immediately that the conclusion
> holds in that case", whereas theorematic deduction "is deduction in which
> it is necessary to experiment in the imagination upon the image of the
> premiss in order from the result of such experiment to make corollarial
> deductions to the truth of the conclusion."*[2]*  He held that
> corollarial deduction matches Aristotle's conception of direct
> demonstration, which Aristotle regarded as the only thoroughly satisfactory
> demonstration, while theorematic deduction (A) is the kind more prized by
> mathematicians, (B) is peculiar to mathematics,*[1]*  and (C) involves in
> its course the introduction of a lemma or at least a definition
> uncontemplated in the thesis (the proposition that is to be proved); in
> remarkable cases that definition is of an abstraction that "ought to be
> supported by a proper postulate."*[3]*
>
> [1] Peirce, C. S., from section dated 1902 by editors in the "Minute
> Logic" manuscript, Collected Papers v. 4, paragraph 233, quoted only in
> part
> http://www.commens.org/dictionary/entry/quote-minute-logic-chapter-iii-simplest-mathematics
> in "Corollarial Reasoning" in the Commens Dictionary of Peirce's Terms,
> 2003–present, Mats Bergman and Sami Paavola, editors, University of
> Helsinki. FULL QUOTE:
> https://archive.org/stream/TheWorldOfMathematicsVolume3/Newman-TheWorldOfMathematicsVolume3#page/n366/mode/1up
> in The World of Mathematics, Vol. 3, p. 1776.
> [2] Peirce, C. S., the 1902 Carnegie Application, published in The New
> Elements of Mathematics, Carolyn Eisele, editor, quoted in "Corollarial
> Reasoning"
> http://www.commens.org/dictionary/entry/quote-carnegie-institution-correspondence-4
> in the Commens Dictionary of Peirce's Terms, also transcribed by Joseph
> M. Ransdell, see "From Draft A - MS L75.35-39" in Memoir 19
> http://w

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Benjamin Udell]

Franklin, Jon, Cathy, Frederik, lists,

You're welcome, Franklin.

Generally, before we get too stuck on the issue of infinite or zero 
breadth or depth, let's remember what Peirce is doing, actually using 
those extremes to show the implications of the ideas. How many people do 
that? Another way in which we don't have to get bogged down in exact 
finite-numerical determination of breadth and depth is to consider 
simply increases and decreases of breadth and depth and what, among 
logical acts, those changes in parts or total amount of information 
correspond to. An example of what Peirce _/does/_ with breadth and depth 
is in a paragraph in "Upon Logical Comprehension and Extension" (1867) 
http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm 
 . I have 
broken the paragraph up to help the pattern become even clearer. 
(Remember that Breadth a.k.a. Extension times Depth a.k.a. Comprehension 
equals Area a.k.a. Information.)


   It is only by confusing a movement which is accompanied with a
   change of information with one which is not so, that people can
   confound generalization, induction, and abstraction.
   /Generalization/ is an increase of breadth and a decrease of depth,
   without change of information. /Induction/ is a certain increase of
   breadth without a change of depth, by an increase of believed
   information.
   [Well, that's a neat distinction; it clarifies why Peirce speaks of
   verisimilar induction rather than inductive generalization, and
   implies that induction is not attenuative but instead has its
   premisses entailed by its conclusions, despite how Peirce's forms
   for induction look. - BU]
   /Abstraction/ is a decrease of depth without any change of breadth,
   by a decrease of conceived information.
   /Specification/ is commonly used (I should say unfortunately) for an
   increase of depth without any change of breadth, by an increase of
   asserted information.
   /Supposition/ is used for the same process when there is only a
   conceived increase of information.
   /Determination,/ for any increase of depth.
   /Restriction,/ for any decrease of breadth; but more particularly
   without change of depth, by a supposed decrease of information.
   /Descent,/ for a decrease of breadth and increase of depth, without
   change of information.
   [End quote]

When I first saw that years ago, I promptly made it into a table with 
fields, and was only a little disappointed to find that Peirce had not 
classified all possible combinations of increase / decrease of 
comprehension and of extension. He was using the ideas of comprehension 
and extension to classify logical acts already named in logical 
tradition, and I thought, I'll figure out what logic acts correspond to 
the remaining combinations, but I didn't soon figure it out and I 
drifted to other subjects. My point is that Peirce was remarkably 
productive at a philosophical-logic level with the ideas of breadth and 
depth. Okay, I don't know that nobody before him had attempted that sort 
of thing. But it's like walking into a room full of candy bars.


I'm not sure whether he stuck with that definition of determination.

Best, Ben

On 4/20/2015 8:38 PM, Franklin Ransom wrote:


And thanks to you too, Ben!

On Mon, Apr 20, 2015 at 8:31 PM, Benjamin Udell  > wrote:


Franklin, Jon, lists,

Yep, that was me with Peirce's ∞'s and 0's of breadth and depth,
March 8, 2015, at the link:
https://www.mail-archive.com/peirce-l@list.iupui.edu/msg03282.html

- Best, Ben

On 4/20/2015 7:42 PM, Jon Awbrey wrote:


Franklin, List,

I think that was Ben Udell.

Regards,

Jon

http://inquiryintoinquiry.com

On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:


Cathy, Frederik, lists,

Yes, Frederik, that makes sense to me. As I mentioned in my
previous post, counting qualities or characters doesn't seem to
be helpful. Although it should be possible to enumerate them, to
a point, for the purpose of some inquiry.

As I recall, Jon Awbrey in the last month or two referenced a
text from Peirce about the multiplication of breadth and depth
using symbols like 1, 0, and the infinity loop, to distinguish
cases such as essential depth and breadth, substantial depth and
breadth, the idea of nothing, the idea of being, etc. If
infinity was indeed used then, Peirce had certainly contemplated
infinite depth and infinite breadth, although perhaps not simply
in the sense of counting with no end, but in the direct sense of
being that which is without limit, so depth without limit or
breadth without limit.

-- Franklin

On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:


-
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L 
to this message. PEIRCE-L posts should go to pe

Re: [PEIRCE-L] Re: Stjernfelt: Chapter 9

[Franklin Ransom]

Ben, lists,

With respect to what you just noted about what he does with the breadth,
depth, and information work, I would like to point out that what you note
has to do with the work of inference upon a given state of information.
What I was referring to has to do with defining different states of
information as such. In fact, Peirce does some of that in the OLEC as
well--such as his logical treatment of the concepts of being and nothing,
substantial depth and breadth, etc.

"When I first saw that years ago, I promptly made it into a table with
fields, and was only a little disappointed to find that Peirce had not
classified all possible combinations of increase / decrease of
comprehension and of extension. He was using the ideas of comprehension and
extension to classify logical acts already named in logical tradition, and
I thought, I'll figure out what logic acts correspond to the remaining
combinations, but I didn't soon figure it out and I drifted to other
subjects. My point is that Peirce was remarkably productive at a
philosophical-logic level with the ideas of breadth and depth. Okay, I
don't know that nobody before him had attempted that sort of thing. But
it's like walking into a room full of candy bars."

Haha, yes, I agree with the sentiment that it's like walking into a room
full of candy bars (well, if I liked candy bars, anyway). That's why I find
it so frustrating to not see an updated account in the context of his
mature semiotic theory, a continuation of that remarkable productivity,
especially considering how productive he was otherwise in his mature
semiotic work. "Kaina Stocheia" does that a bit, but I would have hoped for
something more detailed and robust.

"I'm not sure whether he stuck with that definition of determination."

I had also been wondering that about the definition of determination.

-- Franklin


On Mon, Apr 20, 2015 at 9:15 PM, Benjamin Udell  wrote:

>  Franklin, Jon, Cathy, Frederik, lists,
>
> You're welcome, Franklin.
>
> Generally, before we get too stuck on the issue of infinite or zero
> breadth or depth, let's remember what Peirce is doing, actually using those
> extremes to show the implications of the ideas. How many people do that?
> Another way in which we don't have to get bogged down in exact
> finite-numerical determination of breadth and depth is to consider simply
> increases and decreases of breadth and depth and what, among logical acts,
> those changes in parts or total amount of information correspond to. An
> example of what Peirce _*does*_ with breadth and depth is in a paragraph
> in "Upon Logical Comprehension and Extension" (1867)
> http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm . I have
> broken the paragraph up to help the pattern become even clearer. (Remember
> that Breadth a.k.a. Extension times Depth a.k.a. Comprehension equals Area
> a.k.a. Information.)
>
> It is only by confusing a movement which is accompanied with a change of
> information with one which is not so, that people can confound
> generalization, induction, and abstraction.
> *Generalization* is an increase of breadth and a decrease of depth,
> without change of information. *Induction* is a certain increase of
> breadth without a change of depth, by an increase of believed information.
> [Well, that's a neat distinction; it clarifies why Peirce speaks of
> verisimilar induction rather than inductive generalization, and implies
> that induction is not attenuative but instead has its premisses entailed by
> its conclusions, despite how Peirce's forms for induction look. - BU]
> *Abstraction* is a decrease of depth without any change of breadth, by a
> decrease of conceived information.
> *Specification* is commonly used (I should say unfortunately) for an
> increase of depth without any change of breadth, by an increase of asserted
> information.
> *Supposition* is used for the same process when there is only a conceived
> increase of information.
> *Determination,* for any increase of depth.
> *Restriction,* for any decrease of breadth; but more particularly without
> change of depth, by a supposed decrease of information.
> *Descent,* for a decrease of breadth and increase of depth, without
> change of information.
> [End quote]
>
> When I first saw that years ago, I promptly made it into a table with
> fields, and was only a little disappointed to find that Peirce had not
> classified all possible combinations of increase / decrease of
> comprehension and of extension. He was using the ideas of comprehension and
> extension to classify logical acts already named in logical tradition, and
> I thought, I'll figure out what logic acts correspond to the remaining
> combinations, but I didn't soon figure it out and I drifted to other
> subjects. My point is that Peirce was remarkably productive at a
> philosophical-logic level with the ideas of breadth and depth. Okay, I
> don't know that nobody before him had attempted that sort of thing. But
> it's like walk