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
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.
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”
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 - -
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
Forgive me, Author, for I have signed
A sign that forges your original sign —
How I miss the indelible mark of thine!
It looks like the Annotum developers are following the fashion of the day in rolling out their platform first and testing it later. There doesn’t appear to be any way to edit the articles ported over from Knol to Annotum without reducing them to utter hash, so I copied my Knol articles to another blog, archiving them under the Annotum theme until such time as the Annotum developers get the bugs out of their system. In the meantime I will continue working on those and other articles here.
A Curious Truth of Classical Logic
Peirce’s law is a propositional calculus formula which states a non‑obvious truth of classical logic and affords a novel way of defining classical propositional calculus.
Peirce’s law is commonly expressed in the following form.
Peirce’s law holds in classical propositional calculus, but not in intuitionistic propositional calculus. The precise axiom system one chooses for classical propositional calculus determines whether Peirce’s law is taken as an axiom or proven as a theorem.
Here is Peirce’s own statement and proof of the law:
A fifth icon is required for the principle of excluded middle and other propositions connected with it. One of the simplest formulae of this kind is:
This is hardly axiomatical. That it is true appears as follows. It can only be false by the final consequent 
Peirce goes on to point out an immediate application of the law:
From the formula just given, we at once get:
where the 
Note. Peirce uses the sign of illation 
Representing propositions in the language of logical graphs, and operating under the existential interpretation, Peirce’s law is expressed by means of the following formal equivalence or logical equation.
Using the axiom set given in the articles on logical graphs, Peirce’s law may be proved in the following manner.
The following animation replays the steps of the proof.
A stronger form of Peirce’s law also holds, in which the final implication is observed to be reversible, resulting in the following equivalence.
The converse implication 
Representing propositions as logical graphs under the existential interpretation, the strong form of Peirce’s law is expressed by the following equation.
Using the axioms and theorems listed in the entries on logical graphs, the equational form of Peirce’s law may be proved in the following manner.
The following animation replays the steps of the proof.
cc: FB | Logical Graphs • Laws of Form • Mathstodon • Academia.edu
cc: Conceptual Graphs • Cybernetics • Structural Modeling • Systems Science
Inquiry Into Inquiry 
Knowledge Workers of the World, Unite❢
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:
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:
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 —
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.
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