Paradisaical Logic and the After Math

Posted on April 9, 2012 by Jon Awbrey

Re: Peter Cameron • Cultures, Tribes, or Just an Illusion?
Re: Peirce List • (1) (2) (3) (4)

Not too coincidentally with the mention of Peirce’s existential graphs, a tangent of discussion elsewhere brought to mind an old favorite passage from Peirce, where he is using his entitative graphs to expound the logic of relatives.  Here is the observation I was led to make.

Paradisaical Logic

Negative operations (NOs), if not more important than positive operations (POs), are at least more powerful or generative, because the right NOs can generate all POs, but the reverse is not so.

Which brings us to Peirce’s amphecks, NAND and NNOR, either of which is a sole sufficient operator for all boolean operations.

In one of his developments of a graphical syntax for logic, that described in passing an application of the Neither-Nor operator, Peirce referred to the stage of reasoning before the encounter with falsehood as “paradisaical logic, because it represents the state of Man’s cognition before the Fall.”

Here’s a bit of what he wrote there —

Resources

cc: Peirce List

Posted in Amphecks, C.S. Peirce, Critical Thinking, Inquiry, Logic, Logic of Relatives, Logical Graphs, Logical Reflexion, Mathematics, Peirce, Relation Theory, Second Intentions, Semiotics, Sign Relations, Truth Theory, Visualization | Tagged , , , , , , , , , , , , , , , | 2 Comments

C.S. Peirce • Relatives of Second Intention

Posted on April 7, 2012 by Jon Awbrey

Selections from C.S. Peirce, “The Logic of Relatives”, CP 3.456–552

488.   The general method of graphical representation of propositions has now been given in all its essential elements, except, of course, that we have not, as yet, studied any truths concerning special relatives;  for to do so would seem, at first, to be “extralogical”.

Logic in this stage of its development may be called paradisaical logic, because it represents the state of Man’s cognition before the Fall.  For although, with this apparatus, it is easy to write propositions necessarily true, it is absolutely impossible to write any which is necessarily false, or, in any way which that stage of logic affords, to find out that anything is false.  The mind has not as yet eaten of the fruit of the Tree of Knowledge of Truth and Falsity.

Probably it will not be doubted that every child in its mental development necessarily passes through a stage in which he has some ideas, but yet has never recognised that an idea may be erroneous;  and a stage that every child necessarily passes through must have been formerly passed through by the race in its adult development.  It may be doubted whether many of the lower animals have any clear and steady conception of falsehood;  for their instincts work so unerringly that there is little to force it upon their attention.  Yet plainly without a knowledge of falsehood no development of discursive reason can take place.

489.   This paradisaical logic appears in the study of non‑relative formal logic.  But there no possible avenue appears by which the knowledge of falsehood could be brought into this Garden of Eden except by the arbitrary and inexplicable introduction of the Serpent in the guise of a proposition necessarily false.  The logic of relatives affords such an avenue, and that, the very avenue by which in actual development, this stage of logic supervenes.  It is the avenue of experience and logical reflexion.

490.   By logical reflexion, I mean the observation of thoughts in their expressions.  Aquinas remarked that this sort of reflexion is requisite to furnish us with those ideas which, from lack of contrast, ordinary external experience fails to bring into prominence.  He called such ideas second intentions.  Is is by means of relatives of second intention that the general method of logical representation is to find completion.

Reference

  • Charles S. Peirce, “The Logic of Relatives”, The Monist, vol. 7, 161–217, (1897).  Reprinted, CP 3.456–552.
Posted in Abstraction, Amphecks, C.S. Peirce, Cognition, Experience, Inquiry, Logic, Logic of Relatives, Logical Graphs, Logical Reflexion, Mathematics, Peirce, Relation Theory, Second Intentions, Semiotics, Sign Relations, Truth Theory | Tagged , , , , , , , , , , , , , , , , | 7 Comments

C.S. Peirce • A Guess at the Riddle

Posted on March 21, 2012 by Jon Awbrey

Selections from C.S. Peirce, “A Guess at the Riddle”, CP 1.354–416

359.   First and Second, Agent and Patient, Yes and No, are categories which enable us roughly to describe the facts of experience, and they satisfy the mind for a very long time.  But at last they are found inadequate, and the Third is the conception which is then called for.  The Third is that which bridges over the chasm between the absolute first and last, and brings them into relationship.

We are told that every science has its Qualitative and its Quantitative stage;  now its qualitative stage is when dual distinctions,—whether a given subject has a given predicate or not,—suffice;  the quantitative stage comes when, no longer content with such rough distinctions, we require to insert a possible half-way between every two possible conditions of the subject in regard to its possession of the quality indicated by the predicate.

Ancient mechanics recognized forces as causes which produced motions as their immediate effects, looking no further than the essentially dual relation of cause and effect.  That is why it could make no progress with dynamics.  The work of Galileo and his successors lay in showing that forces are accelerations by which a state of velocity is gradually brought about.  The words cause and effect still linger, but the old conceptions have been dropped from mechanical philosophy;  for the fact now known is that in certain relative positions bodies undergo certain accelerations.

Now an acceleration, instead of being like a velocity a relation between two successive positions, is a relation between three;  so that the new doctrine has consisted in the suitable introduction of the conception of Threeness.  On this idea, the whole of modern physics is built.

The superiority of modern geometry, too, has certainly been due to nothing so much as to the bridging over of the innumerable distinct cases with which the ancient science was encumbered;  and we may go so far as to say that all the great steps in the method of science in every department have consisted in bringing into relation cases previously discrete.

  • Charles S. Peirce, “A Guess at the Riddle”, MS 909 (1887–88).
    First published in CP 1.354–416.  Reprinted in EP1, 245–279.
Posted in C.S. Peirce, Dynamics, Geometry, Inquiry, Peirce, Physics, Triadic Relations, Triadicity | Tagged , , , , , , , | 10 Comments

C.S. Peirce • The Reality of Thirdness

Posted on March 16, 2012 by Jon Awbrey

Selections from C.S. Peirce, “Lowell Lectures of 1903”, CP 1.343–349

343.   We may say that the bulk of what is actually done consists of Secondness — or better, Secondness is the predominant character of what has been done.  The immediate present, could we seize it, would have no character but its Firstness.  Not that I mean to say that immediate consciousness (a pure fiction, by the way), would be Firstness, but that the quality of what we are immediately conscious of, which is no fiction, is Firstness.

But we constantly predict what is to be.  Now what is to be, according to our conception of it, can never become wholly past.  In general, we may say that meanings are inexhaustible.  We are too apt to think that what one means to do and the meaning of a word are quite unrelated meanings of the word “meaning”, or that they are only connected by both referring to some actual operation of the mind.  Professor Royce especially in his great work The World and the Individual has done much to break up this mistake.

In truth the only difference is that when a person means to do anything he is in some state in consequence of which the brute reactions between things will be moulded to conformity to the form to which the man’s mind is itself moulded, while the meaning of a word really lies in the way in which it might, in a proper position in a proposition believed, tend to mould the conduct of a person into conformity to that to which it is itself moulded.

Not only will meaning always, more or less, in the long run, mould reactions to itself, but it is only in doing so that its own being consists.  For this reason I call this element of the phenomenon or object of thought the element of Thirdness.  It is that which is what it is by virtue of imparting a quality to reactions in the future.

Reference

  • Charles S. Peirce, “Lowell Lectures of 1903”, III, vol. 1, 3rd Draught.  (CP 1.343)
Posted in C.S. Peirce, Comprehension, Inquiry, Intension, Intention, Intentionality, Logic, Meaning, Peirce, Peirce's Categories, Pragmatic Cosmos, Purpose, Reality, References, Semiotics, Sign Relations, Sources, Thirdness, Triadic Relations | Tagged , , , , , , , , , , , , , , , , , , | Leave a comment

☆ships of yore

Posted on March 11, 2012 by Jon Awbrey

Signs of Spring

on the trailing edge of an icy winged age,
semele lies enleved in the foils of hades.
when shall we see her depart the departed?
when will i mark my recue from the shades?
not till signs of spring charge the skies,
not till summer gives voice to the air --
a dove outside my window this morning?
if only it were that kind of year!

jon awbrey,
in honor of his father, 11 march 2002
Posted in In Memoriam | Tagged | 2 Comments

C.S. Peirce • Objective Logic

Posted on March 9, 2012 by Jon Awbrey

Selections from C.S. Peirce, “Minute Logic” (1902), CP 2.111–118

111.   With Speculative Rhetoric, Logic, in the sense of Normative Semeotic, is brought to a close.  But now we have to examine whether there be a doctrine of signs corresponding to Hegel’s objective logic;  that is to say, whether there be a life in Signs, so that — the requisite vehicle being present — they will go through a certain order of development, and if so, whether this development be merely of such a nature that the same round of changes of form is described over and over again whatever be the matter of the thought or whether, in addition to such a repetitive order, there be also a greater life-history that every symbol furnished with a vehicle of life goes through, and what is the nature of it.

⁂

112.   The first question, then, which I have to ask is:  Supposing such a thing to be true, what is the kind of proof which I ought to demand to satisfy me of its truth?  Am I simply to go through the actual process of development of symbols with my own thoughts, which are symbols, and am I to find in the sense of necessity and evidence of the following of one thought upon another an adequate assurance that the course followed is the necessary line of thought’s development?  That is the way the question has usually been put, hitherto, both by Hegelians and by Anti-Hegelians.

But even if I were to find that the sequence of conceptions in Hegel’s logic carried my mind irresistibly along its current, that would not suffice to convince me of its universal validity.  Nor, on the other hand, does the mere fact that I do not find a single step of Hegel’s logic, or any substitute for it that I have met with, either convincing or persuasive, give me any assurance whatever that there is no such life-history.  It seems to me natural to suppose that it would be far easier satisfactorily to answer the question of whether there is such a thing than to find out what particular form that life-history would take if it were a reality;  and not only natural to suppose so, but made as certain by solid reasons as any such anticipation in regard to proofs could well be.

⁂

114.   But whatever be the kind and degree of our logical assurance that there is any real world, external or internal, that same kind and degree of assurance we certainly have that there not only may be a living symbol, realizing the full idea of a symbol, but even that there actually is one.

115.   I examine the question from this point of view.  It certainly seems as if the mere hypothesis of such a thing as a symbol sufficed to demonstrate such a life-history.  Still, a fallacy is to be suspected.  How can a mere hypothesis prove so much as this seems to prove, if it proves anything?  I call in the data of experience, not exactly the every-minute experience which has hitherto been enough, but the experience of most men, together with the history of thought.  The conclusion seems the same.  Yet still, the evidence is unsatisfactory.  The truth is that the hypothesis involves the idea of a different mode of being from that of existential fact.  This mode of being seems to claim immediate recognition as evident in the mere idea of it.  One asks whether there is not a fallacy in using the ordinary processes of logic either to support it or to refute it.

116.   Aristotelianism admitted two modes of being.  This position was attacked by William Ockham, on the ground that one kind sufficed to account for all the phenomena.  The hosts of modern philosophers, to the very Hegels, have sided with Ockham in this matter.  But now the question comes before us for reëxamination:  What are the modes of being?

One might antecedently expect that the cenopythagorean categories would require three modes of being.  But a little examination will show us that they could be brought into fairly presentable accordance with the theory that there were only two, or even only one.  The question cannot be decided in that way.  Besides, it would be illogical to rely upon the categories to decide so fundamental a question.  The only safe way is to make an entirely fresh investigation.

But by what method are we to pursue it?  In such abstract questions, as we shall have already found, the first step, often more than half the battle, is to ascertain what we mean by the question — what we possibly can mean by it.  We know already how we must proceed in order to determine what the meaning of the question is.  Our sole guide must be the consideration of the use to which the answer is to be put — not necessarily the practical application, but in what way it is to subserve the summum bonum.  Within this principle is wrapped up the answer to the question, what being is, and what, therefore, its modes must be.

It is absolutely impossible that the word “Being” should bear any meaning whatever except with reference to the summum bonum.  This is true of any word.  But that which is true of one word in one respect, of another in another, of every word in some or another respect, that is precisely what the word “being” aims to express.  There are other ways of conceiving Being — that it is that which manifests itself, that it is that which produces effects — which have to be considered, and their relations ascertained.

117.   Having thus worked out a tolerable conception of Being, we turn to modes of being.  But these are metaphysical conceptions.  Let us first inquire how the validity of any metaphysical conception is to be determined.  For this purpose we have only to apply the principles of Speculative Rhetoric.  We sketch out the method and apply it to a few metaphysical conceptions, such as Reality, Necessity, etc.  In process of this, we discover that all such metaphysical conceptions are but determinations of the categories, and consequently form a regular system.  We also find that they can be held as valid only in approximative and imperfect senses.

118.   But this seems to be in conflict with our conception of Being, particularly as derived from the notion of symbol;  which, however, is solidly founded, too.  We now begin to see the sense of talking of modes of being.  They are elements of coöperation toward the summum bonum.  The categories now come in to aid us materially, and we clearly make out three modes or factors of being, which we proceed to make clear to ourselves.  Arrived at this point, we can construct a Weltanschauung.  From this platform, ethics acquires a new significance, as will be shown.  Logic, too, shines forth with all its native nobility.  Common men carry this Weltanschauung in their breasts;  and perhaps the pimp, the looting missionary, the Jay Gould, may, through the shadows of their degradation, catch now and then a purer glimpse of it, than the most earnest of citizens, the Cartises, the Emersons, the Bishop Myriels.  It is beautifully universal;  and one must acknowledge that there is something healthy in the philosophy of faith, with its resentment at logic as an impertinence.  Only it is very infantile.  Our final view of logic will exhibit it (on one side of it) as faith come to years of discretion.

Posted in C.S. Peirce, Inquiry, Peirce, References, Sources | Tagged , , , , | 14 Comments

Ouch❢

Posted on February 22, 2012 by Jon Awbrey

A child hears it said that the stove is hot.  But it is not, he says; and, indeed, that central body is not touching it, and only what that touches is hot or cold.  But he touches it, and finds the testimony confirmed in a striking way.  Thus, he becomes aware of ignorance, and it is necessary to suppose a self in which this ignorance can inhere.  …

In short, error appears, and it can be explained only by supposing a self which is fallible.

Ignorance and error are all that distinguish our private selves from the absolute ego of pure apperception.

🙞 C.S. Peirce • “Questions Concerning Certain Faculties Claimed For Man”

Posted in C.S. Peirce, Ego, Error, Ignorance, Inquiry, References, Selfhood, Semiotics, Sources | Tagged , , , , , , , , | 7 Comments

i wax impressionistic

Posted on February 20, 2012 by Jon Awbrey 
would that i could be starting something new ~~~
but there is all of this unfinished business - -
and so many threads spin out from this point - -
the endeavor toward a functional integration
of logic and information within a reasonable
account of inquiry, the obstacles to inquiry
that rise up to block any way forward, as if
in the very moment that we derive a positive
momentum in any direction at all.  and still ~ ~
i look for an organized way to begin and see
nothing at all of that organic kind to start ---
or maybe i mistake the nature of the organon - -

— jon awbrey • 01 jan 2002

Posted in Verse | Tagged | Leave a comment

The Big Picture

Posted on February 18, 2012 by Jon Awbrey

Scientific knowledge will not save the world if it remains in the brains and blogs and journals of scientists and makes no impression on people in general, policymakers, and the powers that be.

Reflections on recent discussions too numerous to enumerate, but including these:

I plan to talk about many things on this blog: from math to physics to earth science and biology, computer science and the technologies of today and tomorrow — but in general, centered around the theme of what scientists can do to help save a planet in crisis.

— John Baez

Listen! For no more the presage of my soul,
Bride-like, shall peer from its secluding veil;
But as the morning wind blows clear the east,
More bright shall blow the wind of prophecy.

— Words of Cassandra in Aeschylus’ Agamemnon

Posted in Inquiry, The Big Picture | Tagged , | Leave a comment

Knowledge Workers of the World, Unite❢

Posted on February 2, 2012 by Jon Awbrey

Comments on Gowers’s Weblog

Post 1. What’s wrong with electronic journals?

Comment 1.1

Having spent a good part of the 1990s writing about what the New Millennium would bring to our intellectual endeavours, it is only fair that I should have spent the last dozen years wondering why the New Millennium is so late in arriving. With all due reflection I think it is time to face the fact that the fault, Dear Gowers, is not in our technology, but in ourselves.

Here is one of my last, best attempts to get at the root of the matter:

Journal Version
Awbrey, S.M., and Awbrey, J.L. (2001), “Conceptual Barriers to Creating Integrative Universities”, Organization : The Interdisciplinary Journal of Organization, Theory, and Society 8(2), Sage Publications, London, UK, 269–284.  Abstract.  Online.
Conference Version
Awbrey, S.M., and Awbrey, J.L. (1999), “Organizations of Learning or Learning Organizations : The Challenge of Creating Integrative Universities for the Next Century”, Second International Conference of the Journal ‘Organization’, Re‑Organizing Knowledge, Trans‑Forming Institutions : Knowing, Knowledge, and the University in the 21st Century, University of Massachusetts, Amherst, MA.  Online.

Comment 1.2

Prestige = Prestidigitation

Comment 1.3

There are indeed Big Picture questions that open up here — the future of knowledge and inquiry, the extent to which their progress will be catalyzed or inhibited by collaborative versus corporate-controlled information technologies, the stance of knowledge workers, vigilant or acquiescent, against the ongoing march of global corporate feudalism — and maybe this is not the place or time to pursue these questions, but in my experience discussion, like love and gold, is where you find it. Being questions of this magnitude, they will of course arise again. The question is — who will settle them, and to whose satisfaction?

Post 2. Abstract thoughts about online review systems

Comment 2.1

What is inquiry? And how can we tell if a potential contribution makes an actual contribution to it? Questions like these often arise, as far as mathematical inquiry goes, in trying to build heuristic problem solvers, theorem-provers, and other sorts of mathematical amanuenses.

Charles S. Peirce, who pursued the ways of inquiry more doggedly than any thinker I have ever read, sifted the methods of “fixing belief” into four main types — Tenacity, Authority, Plausibility (à priori pleasingness), and full-fledged Scientific Inquiry.

I posed the question — “What part do arguments from authority play in mathematical reasoning?” — on MathOverFlow some time ago and received a number of interesting answers.

Comment 2.2

The late Joseph Ransdell (1931–2010), who did more to keep C.S. Peirce’s thought alive on the Web than anyone else I know, had a particular interest in the issues surrounding open peerage and publication. Synchronicity being what it is, the members of the Peirce List have been conducting a slow reading of one of Joe’s papers on the subject, where he examined the work of Paul Ginsparg on open access and Peter Skagestad on intelligence augmentation in the light of Peirce’s theory of signs, a.k.a. semiotic. Here is the paper:

Comment 2.3

Re: Eric Zaslow

In order to have an error-correcting system, or be capable of changing the mission statement in other than a random way, one has to have an independent sense of the objective. In practice, this usually means a number of independent but converging operations that tell you when and how far your system has gone off course.

Comment 2.4

Re: Edward Cree

There is a very instructive post about the difference between measures and targets (means and ends) on Peter Cameron’s Blog —

Goodhart’s law asserts:

When a measure becomes a target, it ceases to be a good measure.

Comment 2.5

Re: Edward Cree

This enters on a wide-ranging subject — one that tears me between rushing in and fearing to tread …

I didn’t get around to finishing this comment, but I think I meant to introduce a few extra readings by way of establishing the scope of this wide-ranging subject.

Readings —

Post 3. Elsevier’s open letter point by point, and some further arguments

Comment 3.1

As I said before, the problem is not Elsevier, but Elsewhere.

Participants in a particular paradigm of publishing or perishing are currently feeling the pinch of a proprietary system that served them in the past, feeling they have become its serfs not its lords. Will these angelic doctors look homeward, to the prisons of prestige and priority they have served to build around themselves? — Ay, there’s the rub.

On jugera …

Post 4. Elsevier Withdraws Support for Research Works Act

Comment 4.1

Re: “This deserves a post to itself, despite my intention to reclaim this blog for its core purpose.”

On the other hand, we could try thinking like mathematicians about the problem before us. What are the elements of the problem, and what does it mean to think like a mathematician, anyway?

Experience tells me that private interests like publishers, and those who increasingly serve private interests on the public’s payroll, will continue to define the problem to their satisfaction and keep trying to enforce solutions that suit those interests, but we may find matter that touches our core purpose by standing back and taking a fresh look at the whole system involved.

A good start has been made —

Since I’m trying to discuss the fundamentals here, let me briefly address the question of whether the notion of the “quality” of a piece of mathematics makes sense. We certainly talk as though it makes sense, but is there something objective that underlies the seemingly subjective judgments that we make the whole time?

— Timothy Gowers • Abstract thoughts about online review systems

But it’s only a start …

Comments on John Baez’s “Azimuth”

Post 5. The Education of a Scientist

Comment 5.1

I think that all of the world’s citizens need to start paying more attention to the push by private interests to private-profitize the entire public sector, including control over education, research, and the social media. The stakes for society and the planet cannot be overestimated.

Comments on Peter Cameron’s Blog

Post 6. Open Access Publishing

Comment 6.1

By nature and training a whole systems thinker, I tend to view the architecture of commerce, the architecture of government, and the architecture of inquiry as participants in a larger system.

When it comes to the desiderata of inquiry, I find myself constantly returning to the guidance of Charles S. Peirce, so elegantly maximized in the following words:

My last best expression of how I saw the problem of sustaining the soul of inquiry within the body of the post*modern millennial university is contained in the following paper:

One out of three is all I can do today …

* Yes, that’s a Kleene star. You do the math.

Comment 6.2

As far as the interaction between the dynamics of commerce and the dynamics of inquiry goes, there may always be a tension between the two value systems, the one that is coming to value short-term monetary profit above all else, and the one that orients itself toward sustainable truth over the long haul.

But I think we are passing a critical point, where the party of gold is now insisting on a right to control the whole, or else crush the party of green out of existence.

Back when this discussion starting hitting the air webs, I collected a few of my impressions on this blog page:

Comment 6.3

Re: Dratman

Peer review as a measure of quality can be replaced — and in these times there is no austerity of forces pushing to replace it with something far worse. Wherever you find a measure of quality that is too one-dimensional and simple-minded to be true, you will find that someone is getting filthy rich selling the custodians of quality a clockwork broom.

Comment 6.4

Re: James Street

We may continue to criticize establishment ways of doing everything, as I, for one, have always done, but my point is that far worse ways are now in the offing, and being pushed by forces that are resolutely alien to the common ideals of our many-splintered communities of inquiry.

Comment 6.5

Re: James Street

Strictly speaking, “peer” means “equal”. When a question cannot be settled among equals, “an umpire”, whose name derives by false division from “a non-peer“, must be called into play. However imperfect a given peer system may be in practice, nothing destroys the community and its ideals so much as umpires who insinuate themselves in the process of inquiry when there is no call for them to do so.

Comment 6.6

Re: James Street

Having said a little about the dynamics of inquiry in its own right and the impact of commerce and inquiry on each other, it was my intention to make at least tangential remarks on the other sides of the tri-umpirate: {Commerce, Government, Inquiry}.

We have quite naturally come to the lambda point of all three, but there very little but chaos reigns, so let me back up and offshore a fraction of the excess tension to a brant on my own blog —

Post 7. Student Questionnaires

Comment 7.1

The difference between the devil and the divinity may lie in the details, but it’s not unusual for the devil to decoy us with detail after detail, when the unexamined premiss is the screen behind which the real deil lies.

Comment 7.2

The tests themselves — good, bad, but mostly ugly — are a diversionary maneuver. The end-run we should be watching is the sneaking shift in the locus of evaluation and therefore control.

A couple of articles pertaining to the Great Education Deformation on the U.S. scene —

Naturally, Neyman blames Pearson.

Comments on Bridging Differences

Post 8. The Pearsonizing of the American Mind

Comment 8.1

The difference between the devil and the divinity may lie in the details, but it’s not unusual for the devil to decoy us with detail after detail, when the unexamined premiss is the screen behind which the real deil lies.

A bit more prosaically —

The tests themselves — good, bad, but mostly ugly — are a diversionary maneuver. The end-run we should be watching is the sneaking shift in the locus of evaluation and therefore control.

Comment 8.2

Yes, it’s all about the Locusts of Control —

Being by nature and training a whole systems thinker, I tend to view the War on Democracy, the War on Education, and the War on Science as just three fronts in a full-scale war on the ability of free societies to chart their own ships of state with information, knowledge, and wisdom about all aspects of the realities that face them.

So I think there is a lot at stake, to say the least.

Posted in Comments Elsewhere, Inquiry, Open Access Research, Social Media, The Big Picture | Tagged , , , , | 4 Comments