In 1885 Peirce, working together at Johns Hopkins University with his then student O.H. Mitchell, discovered quantification theory[44], and this led him to begin a further revision of his basic categories, especially in relation to the notion of Secondness. The discovery of quantification theory raised some rather fundamental problems concerning the actual nature of the object. Basically, quantification theory allows for the introduction of indices into the algebra of logic. These indexical terms, which Mitchell and Peirce introduced initially as F1 (the universal quantifier) to mean that "proposition F is true for every object in the universe" [CP 3.363], and Fu (the existential quantifier) which means that "the same is true of some object" [CP 3.363], Peirce then went on to develop into the notations II iFi and …iFi respectively, which became the standard symbolism of Boole-Schröder algebra.[45] Peirce's previous logics had not contained any concept of the individual, and this meant that the notion of Secondness had to be revised accordingly. The index merely denotes things, it "asserts nothing; it only says `There!'" [CP 3.361]. In doing so, the relation of sign to object seen as "a correspondence in fact" of the earlier version of Secondness from the "New List", which did not refer directly to an individual, which Peirce had up til then considered ideal entities, had to be changed.
Around this time, too, Peirce began to look again at the issue of the final opinion, for which had received some criticism, amongst others Monist editor Paul Carus, and which, as we remember, had caused some problems for his theory of reality. From this time on, Peirce mainly considered the coming of an ultimate agreement as purely a regulative principle, with the result that the Real, although its existence cannot be a priori proved, can be affirmed as a likely postulate well supported by present evidence. The Real then, in this view, depends on the coherence of observations, and thus the convergence of agreement of different observations made by different interpreters in the long run.
In about 1880, in a paper entitled "One, Two, Three: Fundamental Categories of Thought and of Nature" [CP 1.369-372; 1.376-378], Peirce first presented his new categories as three sorts of logical relations, monadic, dyadic and triadic. All possible logical relations, including the sign relation, are presumed to belong to these three classes, which are general. Every predicate of a proposition is classified by the schema, so the categories hold good for all possible cognitions. Here I follow closely Murphey's (1993, p. 304) clear explication of this system of classification: Monadic relations include absolute terms [CP 1.370]. Dyadic relations can be genuine or degenerate; being degenerate if the relative properties derived from the relation would belong to those subjects even if the other correlate of the relation be eliminated. Triadic relations can be genuine, singly or doubly degenerate. Singly degenerate if dyadic relations between members of pairs continue to hold if the third is absent, and doubly degenerate if the subjects retain their relative properties independently of the other correlates. In a genuine triad neither the relative character of the correlates, nor the dyadic relations among pairs of correlates would exist if any of the correlates were eliminated [CP 1.366f; 1.370-372]
Genuine dyadic and triadic relations can thus be considered irreducible, with all genuine triadic relations being combinatorial, and all combinatorial relations being triadic. The relation which holds between any two elements could not exist with out the third, of which the sign relation is Peirce's best available example. The relation between sign and object is made by the interpretant (as third); the relation between the interpretant and object is made by the sign which brings the interpretant into that relation; and the relation between the sign and the interpretant exists only through the object as the common value in the extensional domain [CP 1.480; 6.32] Since all combinatorial relations are triadic, the categories are both irreducible and complete. With the above being seen specifically in relation to signs, doubly degenerate signs are icons since the characters derived from the relation would be possessed by it in any case, as would its object. If the relation is simply degenerate, the sign is an index, with a real relation to its object independent of any third. If the relation is genuine, the sign is a symbol [CP 2.247f]
In accordance with Kant's doctrine, which Peirce had come to accept, that the conception of the logical form of knowledge is to be considered a priori, while its content must come though sensory experience, the categories in the revised list now receive a double aspect: a formal aspect having to do with the logical classification of relations, while their material aspect has to do with the classification of experience.[CP 1.452]
With regard to Firstness, Firsts in their material aspect are not percepts (images with structures and combining a number of sense qualities), but simple and without structure. Every percept has a First which is the single impression created by the total ensemble of its elements. If a single sense quality is abstracted from a percept and considered alone, this quality is a First, not a concept, since it cannot be analysed or explained. They are "irrational", merely "modifications of consciousness" produced by the act of perception of the thing.
With regard to Secondness, Seconds in their material sense possess "thisness", the characteristic of being unambiguously designated by "this" - from which Peirce derives his principle of individuation.[3.434; 3.460] "Thisness" is associated with, and probably derived from[46], the Scotian concept of "haecceity", which is a kind of experience involving "resistance", "brute reaction", "compulsion", "interruption", "intrusion" - a kind of shock. It is also "irrational", in that it cannot be known by reason, but only by means of its inherent "insistency" [6.318]. The possession of "thisness" gives existence to the object. This brings Peirce back to the Kantian position that existence can only be given in intuition, not in concepts [A50-52; B74-76] Thisness can be real, but reality is not thisness, thus the externality of an object can only be inferred from the experience of thisness, rather than proved.
Thirdnesss is not (insofar as we can speak of its material aspect)[47], as opposed to Firstness and Secondness, "irrational", rather it is the category associated with rationality or intelligibility. The third aspect of the sign is the interpretant which has to do with the meaning of signs, but which is nonetheless not its meaning. The relation of a sign to its meaning exists only because the sign is interpreted as having that meaning by an interpretant, requiring that there is an infinite series of interpretant signs. The infinite series of interpretants does not actually constitute the meaning of the sign, but is a necessary condition if the sign is to have a meaning. Meaning itself lies outside of the series. By an extension of the Pragmatic Maxim the meaning of a concept is the possible future effects that its being lawful would necessarily determine - i.e. its "habits" cf. one of Peirce's earlier formulations that "what a thing means is simply what habits it involves" [CP 5.491] Peirce regards every instance of lawfulness as a sign, since whatever is subject to law is a necessarily a sign of the law it is subject to. Thirdness is thus both the category of law or regularity, and of rationality or intelligibility.
Peirce had, as mentioned previously, come to regard Thirdness as associated with continuity, in the sense that relations constitute continuous connections among their correlates, and relations cannot be created except as specifications of already existing relations (Murphey 1993, p. 318). New relations are therefore only possible as specifications of existing continuous connections. This is one of the basic assumptions of the notion of Synechism, which together with Tychism and Agapism, forms the conceptual basis for Peirce's cosmology.
If we again return to the issue of the terminological changes with regard to Peirce's three divisions of logic, it seems clear that the revision of the categories, coupled as it was with the discovery of quantification theory in some way lies behind Peirce's terminological shift to the triad of "Pure Grammar", "Logic Proper" and "Pure Rhetoric", documented by Fisch as having appeared around 1897. Especially the division of the three basic categories Firstness, Secondness and Thirdness into their formal and material senses carries with it the notions of purity or genuineness and impurity or degeneracy, which (and here I am of course merely speculating freely without recourse to any more substantial documentation than is provided in this present article), may well have given rise to the shift to terms involving concepts associated with purity and genuineness (cf. "Pure" and "Proper" in the triad above). Interestingly, Murphey notes at the end of his section on the first major revision of the categories that:
"It is obvious that the revision of 1885 led to very substantial changes in the definitions of the categories. Indeed these changes are so great that Peirce ought to have adopted new names for them to prevent confusion with his other papers. It is a striking example of Peirce's method of work that he did not do so. He evidently thought of these revisions as merely a correcting and developing of his system within the overall architectonic plan: the plan itself, including the terminology, remains unchanged. And nowhere in Peirce's writing is there any explicit statement which would indicate that beneath this shell of changeless terminology major alterations have been made. The result is a confusion which one who regarded himself as an expert on the ethics of terminology ought to have spared his readers." (Murphey 1993, p. 319-20)
Here, I would tend to be more sympathetic to Peirce's considerable labours and say that although the definitions of the categories certainly changed considerably in terms of their inherent content, the basic triadic nature of Peirce's ontology would have been rather difficult to convey by the use of other categorial terms than First, Second and Third. Also, as Murphey too points out in a footnote to the above citation, the division into formal and material aspects is at the heart of the revision, and the formal nature of the categories is not in fact changed in any significant way Additionally, I believe it is important to emphasize that at this stage, Peirce's normative theory of inquiry, which the Carnegie application of 1902 represents a reasonably clear presentation of, albeit in a rather schematic form, was at this time beginning to take shape, and the prominence given there to presentation of the logic and the three associated sciences of semeiotic, which in the Carnegie application are actually termed "Stechiologic", "Critic" and "Methodeutic", illustrate clearly that it was the development of this normative theory of inquiry that stood foremost in Peirce's mind around this time.
Murphey (1993, p. 358f) attributes to a certain extent the commencement of serious work by Peirce at the beginning of the twentieth century on this normative theory of inquiry to James' aggressive marketing of the term "Pragmatism" in his lecture at the University of California in 1898 (see also footnote 34 above). Peirce, as we have seen, came to disagree with what he considered James' far too utilitarian interpretation of the notion of Pragmatism, and since it had now become a highly public affair, he now felt obliged to try and qualify it in a way that would be more in accordance with his own conception of the term. Murphey (1993, p. 359) notes in this connection that:
"The sudden, almost spectacular, reformulation of Peirce's philosophy which occurred in 1901-02 cannot be laid wholly at James' door. As I have tried to show, many of the problems underlying it were in Peirce's mind before 1898 and would doubtless have reached solution in due time. What James did was to force the issue. Peirce was compelled to decide where he stood on a wide range of associated questions. The results were a sweeping revision of the architectonic, the introduction of phenomenology and normative science, and extension of the theology, and a complete revision of the theory of cognition."
In his cosmology, which he began to develop around 1890[48], and which we shall unfortunately not be able go into in much detail here, Peirce expounded the view that in evolution there is in the cosmos a general teleological tendency towards what he called the "growth of concrete reasonableness", which is basically grounded in the idea of the gradual evolution of rationality or lawfulness which is actualised by being embodied in action. Peirce's teleology does not, however, involve a completely determinist view of evolution towards some previously determined end, but rather what Carl Hausman (1993) in his brilliantly readable book "Charles S. Peirce's Evolutionary Philosophy" has characterised as a "developmental teleology", where spontaneity or "chance" plays an important role. In the first of his Monist papers, Peirce argued on the basis of his concept of "critical common sensism", which in turn was built upon his adaptation of Bain's doubt-belief theory in the evolutionary oriented theory of inquiry he had formulated in the 1870's, that the mind is naturally adapted through natural selection to the interpretation and understanding of nature, and that it is this adaptation that has led us to our present level of knowledge. We have, however, no certain way of being sure that our present sets of adaptations always will be functional, since the inherent element of chance in the evolutionary process makes it impossible to predict exactly how things will develop in the future. There is therefore a need for a comprehensive theory of cosmic evolution which will give us at least some idea of what kinds of laws, if any, we may expect nature to follow, and to provide us with methods of coping with whatever kinds of situations that might possibly arise.
Peirce's cosmology explores the relationship between mind and nature and postulates that there is a continuity between the two, that universe itself is mind, and that natural processes cannot therefore be radically different from those of our thought as we attempt to fix our beliefs. The logical patterns of hypothesis (abduction), induction and deduction are consequently equivalent to those which the universe uses to create order from pure chance. The indeterminacy of pure chance, of which the developing universe is the most positive example of, correlates with the vividness of feeling that is associated with human consciousness, with the degree of consciousness being inversely correlated with the degree to which mind is ruled by habit. The real world is the world of mind, and real objects are no more than portions of mind which have taken habits and assumed specific forms. The universe is evolving slowly towards concrete reasonableness out of a continuum of pure feeling, which is in itself completely indeterminate, through initially spontaneous breaks in this continuity which constitute instances of a generalising tendency. This generalising tendency has a tendency to repeat, even though it is merely a result of the unlimited, arbitrary variation of the primal feeling. Once the tendency to repeat (i.e. to take habits) had appeared, there would be an increasing tendency for it to perpetuate itself. Hence there would be a general evolution of the cosmos from Firstness (pure feeling) through Secondness (actualities which repeat themselves) to Thirdness (lawfulness).
The universal mind is not, as are human beings and animals, subject to evolutionary selection and the struggle for survival, so that there must be some further purpose directing the evolutionary process. This is the "agapistic development of thought [..] distinguished by its purposive character, this purpose being the development of an idea" [CP 6.315] To explain agapé, Peirce invokes St John's statement "God is love", and takes the example of an idea that he himself is interested in. He writes:
"It is my creation. It is my creature; for as I have shown in last July's Monist, it is a little person. I love it; and I will sink myself in perfecting it. It is not by dealing out cold justice to the circle of ideas that I can make them grow, but by cherishing them and tending them as I would the flowers in my garden. The philosophy that we draw from St. John's gospel is that this is the way the mind develops; and as for the cosmos, only so far as it yet is mind, and so has life, it is capable of further evolution. Love, recognizing germs of loveliness in the hateful, gradually warms it into life, and makes it lovely. That is the sort of evolution which every student of my essay "The Law of Mind" must see that synechism calls for." [CP 6.289]
The living of the idea, through the concrete acts necessary for its "cherishing" is the governing idea for action and thought which constitutes the personality of the individual. Two persons are thus merely two ideas, and can become subsumed in a supraindividual personality, such as is manifested in the idea of the nation or the community in general. The evolving universe, then, since it is mind, and which individuals are an integral part of, in fact actually comprises the community of investigators. To the extent that individuals can, by constantly working to develop their methods of making their ideas clear, overcome ignorance and error, which in the long run is all that differentiates man from the universal mind, then they will come to converge with this community of mind. This represents a choice of free will; any man can if he wishes take part in the development of the universal mind through allowing himself to adopt this path on the basis of "an immediate attraction for the idea itself, whose nature is divined before the mind possesses it, by the power of sympathy, that is, by virtue of the continuity of mind..." [CP 6.037]
To this end, it is necessary to develop a methodical and normative theory of inquiry. Peirce believed that the fundamental ideas of the special sciences are all classifiable by the categories, and thus that the categories are the basis of all special knowledge. The aim of his architectonic was to prove certain fundamental and general theorems with regard to all possible human knowledge. A systematic science of logic that is both grounded in the categories and which applies the necessary methods of mathematical reasoning to establish the truths of the logic so derived seemed to him the only way to achieve this. If the growth of concrete reasonableness is considered as an end in itself, and so as something inherently admirable, the characterisation of this reasonableness must be informed by aesthetics, the study of ends [CP 1615; 1.612]. Ethics then depends on aesthetics, and logic upon ethics. In the final draft of Memoir 9 of his Carnegie application "On The Bearing Of Esthetics And Ethics Upon Logic", Peirce writes:
"I begin by explaining the nature of the normative sciences. They have often been mistaken for practical sciences, or arts. I show that they are at the opposite pole of the sphere of science, and are so closely allied to mathematics that it would be a much smaller error to say that, like mathematics, they were simply occupied in deducing the consequences of initial hypotheses. Their peculiar dualism, which appears in the distinctions of the beautiful and the ugly, right and wrong, truth and falsity, and which is one cause of their being mistaken for arts, is really due to their being on the border between mathematics and positive science; and to this, together with their great abstractness, is due their applicability to so many subjects, which also helps to cause their being taken for arts. Having analyzed the nature of the precise problems of the three, and given some considerations generally overlooked, I show that ethics depends essentially upon esthetics and logic upon ethics. [...] But the methods of reasoning by which the truths of logic are established must be mathematical, such reasoning alone being evident independently of any logical doctrine."
He then goes on to explain how these methods might be refined through his division of logic in general into the three disciplines of stechiologic, critical logic and methodeutic. In a draft of Memoir 13 "On The Division Of Logic", Peirce writes:
"Logic is primarily divided into stechiologic, critic, and methodeutic, which are defined in terms of the categories. Logic relates to terms, propositions, and arguments. Stechiologic treats of every variety. Critic has no direct bearing upon terms, upon analytic, or explicatory, propositions, nor upon necessary reasoning as such. It does, however, treat of meaningless and absurd terms, of irrelevant definitions, of fallacious demonstrations and of probable deductions. Methodeutic has no direct bearing upon any terms or propositions or upon any kind of reasoning except that which starts hypotheses. After critical logic has pronounced a hypothesis to be justifiable (being a verifiable hypothesis which explains the surprising fact), it remains to submit the hypothesis to methodeutic in order to determine whether it should be the first among the justifiable hypotheses to be considered. No such supplementary inquiry is called for in the case of a deductive or an inductive conclusion. Indirectly, however, methodeutic treats of all kinds of signs." [MS L75, Memoir 13, Draft E (164-165)]
Murphey chose to end the 1961 edition of his excellent work on the development of Peirce's philosophy on a seemingly somewhat melancholy note, concluding that:
"As one reads through the thousands of pages of manuscript which is all that remains from Peirce's life's labor, one cannot escape the feeling that these are the ruins of a once great structure. Every paragraph and doctrine seem to be fragmentary parts of some larger whole. [...] But this is an illusion - Peirce's illusion: the grand design was never fulfilled. The reason was that Peirce was never able to find a way to utilize the continuum concept effectively. The magnificent synthesis which the theory of continuity seemed to promise somehow always eluded him, and the shining vision of the great system always remained a castle in the air." (Murphey 1993, p. 407)
In his brief preface to the 1993 edition he however takes pains to explain that he never meant with this reflection to demean Peirce's standing as "the greatest American philosopher and philosopher, [...] a philosopher of the first rank - the equal if not the superior of any other thinker of the nineteenth century" (Murphey 1993, p. vi). And indeed, in another work published subsequently to the first edition of his book together with Elizabeth Flower (Flower & Murphey 1977), he goes on to describe how he believed Peirce actually did succeed in bringing his final system together.
What seems increasingly clear today is that Charles Sanders Peirce, one of our few true scientist philosophers, who until the day he died never gave up on the monumental task upon which he began with his first readings of Kant in 1855, the building of a comprehensive architectonic of theories, and who in his thinking predated many developments now at the forefront of modern science in innovative fields of mathematics and computer science such as chaos and catastrophe theory, complexity theory, dynamic systems theory, artificial intelligence and artificial life, to name but a few, actually did succeed, as Ransdell has consistently maintained previously, as well as one might expect any human being to do so in the course of a lifetime in realising what he set out to do, and all this in spite of a personally tragic life story which no one could possibly envy him.
If we go even further consider the extent to which various aspects of Peirce's thinking, and especially perhaps his fundamental triadic system of categories and the associated concept of the triadic sign relation, have permeated into and influenced, often in fundamental ways, modern thinking in fields so diverse as semiotics, sociology, psychology and cognitive science, art, music, literature and film studies, mathematics, linguistics, semantics, pragmatics, philosophy of language, mathematics, communication studies and the history and philosophy of science, it seems clear that even though, as Murphey points out above, Peirce was in his own lifetime never really able to utilise optimally the theory of continuity that he had painstakingly developed with the tools he then had at his disposal, his principles of the continuity of the mind, and of the community of investigators, seem still to be very much at work in favour of this particular philosophical project coming to some kind of fruition embodied in the "growth of concrete reasonableness", at least in "the long run".