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PAP [ed.]

Let us now consider non-necessary reasoning. This divides itself, according to the different ways in which it may be valid, into three classes: probable deduction; experimental reasoning, which I now call Induction; and processes of thought capable of producing no conclusion more definite than a conjecture, which I now call Abduction.
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Abduction is no more nor less than guessing, a faculty attributed to Yankees. [—] Such validity as this has consists in the generalization that no new truth is ever otherwise reached while some new truths are thus reached. This is a result of Induction; and therefore in a remote way Abduction rests upon diagrammatic reasoning.

If I were to attach a definite meaning to “anthropomorphism,” I should think it stood to reason that a man could not have any idea that was not anthropomorphic, and that it was simply to repeat the error of Kant to attempt to escape anthropomorphism. At the same time, I am confident a man can pretty well understand the thoughts of his horse, his jocose parrot, and his canary-bird, so full of espièglerie; and though his representation of those thoughts must, I suppose, be more or less falsified by anthropomorphism, yet that there is a good deal more truth than falsity in them, – and more than if he were to attempt the impossible task of eliminating the anthropomorphism I am for the present sufficiently convinced.

A Diagram, in my sense, is in the first place a Token, or singular Object used as a Sign; for it is essential that it should be capable of being perceived and observed. It is, however, what is called a General sign; that is, it denotes a general Object. It is, indeed, constructed with that intention, and thus represents the Object of that intention. Now the Object of an intention, purpose, or desire is always General. The Diagram represents a definite Form of Relation. This Relation is usually one which actually exists, as in a map, or is intended to exist, as in a Plan. But this is so far from being essential to the Diagram as such, that if details are added to represented existential or experiential peculiarities, such additions are distinctly of an undiagrammatic nature. The pure Diagram is designed to represent and to render intelligible, the Form of Relation merely. Consequently, Diagrams are restricted to the representation of a certain class of relations; namely, those that are intelligible.

…a Diagram is an Icon of a set of rationally related objects. By rationally related, I mean that there is between them, not merely one of those relations which we know by experience, but know not how to comprehend, but one of those relations which anybody who reasons at all must have an inward acquintance with. This is not a sufficient definition, but just now I will go no further, except that I will say that the Diagram not only represents the related correlates, but also, and much more definitely represents the relations between them, as so many objects of the Icon.

Which is the more primitive (or fundamental, or simple) form of relation, that of an Equiparance (i.e. a reciprocal relation), or that of a Disquiparance? I say that it is the Disquiparance, or rather, it is the Opponency, or relation of which a specialization may be a Disquiparance.

Which is the more primitive (or fundamental, or simple) form of relation, that of an Equiparance (i.e. a reciprocal relation), or that of a Disquiparance? I say that it is the Disquiparance, or rather, it is the Opponency, or relation of which a specialization may be a Disquiparance.

Let us now consider non-necessary reasoning. This divides itself, according to the different ways in which it may be valid, into three classes: probable deduction; experimental reasoning, which I now call Induction; and processes of thought capable of producing no conclusion more definite than a conjecture, which I now call Abduction. [—] The general principle of the validity of Induction is correctly stated in the Johns Hopkins Essay, but is too narrowly defined. All the forms of reasoning there principally considered come under the class of Inductions, as I now define it. Much could now be added to the Essay. The validity of Induction consists in the fact that it proceeds according to a method which though it may give provisional results that are incorrect will yet, if steadily pursued, eventually correct any such error. The two propositions that all Induction possesses this kind of validity, and that no Induction possesses any other kind that is more than a further determination of this kind, are both susceptible of demonstration by necessary reasoning.

‘Thinking’ is a fabled ‘operation of the mind’ by which an imaginary object is brought before one’s gaze. If that object is a Sign upon which an argument may turn, we call it a Thought. All that we know of the ‘Thinking’ is that we afterwards remember that our attention was actively on the stretch, and that we seemed to be creating Objects or transformations of Objects while noting their analogy to something supposed to be real. We choose to call ‘an operation of the mind’; and we are, of course, quite justified in doing so, provided it be well understood that its being so consists merely in our so regarding it, just as Alexander, Hannibal, Caesar, and Napoleon constitute a single quaternion, or plural of four, as long as we put them together in thought. The ‘operation of the mind’ is an ens rationis. That is my insufficient excuse for speaking of it as ‘fabled’.

‘Thinking’ is a fabled ‘operation of the mind’ by which an imaginary object is brought before one’s gaze. If that object is a Sign upon which an argument may turn, we call it a Thought. All that we know of the ‘Thinking’ is that we afterwards remember that our attention was actively on the stretch, and that we seemed to be creating Objects or transformations of Objects while noting their analogy to something supposed to be real. We choose to call ‘an operation of the mind’; and we are, of course, quite justified in doing so, provided it be well understood that its being so consists merely in our so regarding it, just as Alexander, Hannibal, Caesar, and Napoleon constitute a single quaternion, or plural of four, as long as we put them together in thought. The ‘operation of the mind’ is an ens rationis. That is my insufficient excuse for speaking of it as ‘fabled’.