A yet innominate mode of inference has become so frequent in certain quarters that the time has come to fashion a suitable name for it. The scheme of thought in question goes a bit like this:
If A, then B.
Not B.
──────────────────
But A simply has to be ❢❢❢
I know some scholars will insist that it ought to be called “modus dolendo dolens” or something like that, but let’s not be pedantic.
Re: Peirce List • On Peirce Preservation
Cf: Inquiry List • What Peirce Preserves
Looking back from this moment, I think I see things a little differently. The critical question is whether our theoretical description of inquiry gives us a picture that is true to life, preserving the life of inquiry and serving to guide us on its way, or whether it “murders to dissect”, leaving us with nothing but a Humpty Dumpty hodge-podge of false idols and torn and twisted bits of maps that mislead the quest at every turn.
There is a natural semantics that informs mathematical inquiry. It permeates the actual practice even of those who declare for some variety of nominal faith in their idle off‑hours. Peirce is unique in his ability to articulate the full dimensionality of mathematical meaning but echoes of his soundings keep this core sense reverberating, however muted, throughout pragmatism.
If I sift the traditions of theoretical reflection on mathematics according to how well their theoretical images manage to preserve this natural stance on mathematical meaning, I would tend to sort Frege more in a class with Boole, De Morgan, Peirce, and Schröder, since I have the sense when I read them they are all talking like mathematicians, not like people who are alien to mathematics.
It was so windy today, 30 mph gusts at times, that I had to take a chair out on the deck and wait for moments when the tree held still for half a second.
Our Enlightenment Forerunners had the insight to see the critical flaw in all historical failures at democratic government, to wit, or not — If the People are to Rule then the People must become Wise.
The consequence is that equally distributed education and information are not just commodities you buy so you and yours can get ahead of them and theirs — they are essential to the intelligent functioning of government and the public interest.
That is why we are supposed to have universal free public education. That is why we are meant to have a government operated postal service to enable the free‑flow of information at a nominal fee, not whatever price the market will bear.
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.
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 —
cc: Peirce List
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.
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.
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.
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.
Inquiry Into Inquiry 