Let us begin with “Speculative Grammar”, the study of the elements of signs.
The more significant semeiotical papers Peirce wrote in his late years are those written for The Monist, and above all the one refused both from Atlantic Monthly and The Nation, that is “Pragmatism”, and the letters he sent to William James and Lady Welby. I will take passages from these papers and from the manuscripts. For the other two branches I will rely almost entirely upon manuscripts from the years 1908-1914.
a) The first vanishing point has to be found in Peirce’s description of the knowledge of the object. In EP 2:494, Peirce talks about a collateral observation but also about “an acquaintance with the system of signs”.
All that part of the understanding of the Sign which the Interpreting Mind has needed collateral observation for is outside the Interpretant. I do not mean by “collateral observation” acquaintance with the system of signs. What is so gathered is not COLLATERAL. It is on the contrary the prerequisite for getting any idea signified by the logic.
Now, we know that Peirce established the existence of two objects, the dynamical (or real) object and the immediate object. Here he explains that to understand the object of a sign we need not only a collateral observation but also “an acquaintance with the system of signs”. Collateral observation is easy to explain: in order to individuate a particular object as Napoleon (Peirce’s example, EP 2: 493) we need to have some acquaintance with that object that leads us to distinguish it/him from other possible objects falling under the same definition. In this sense also memory or previous knowledge of every kind falls under the head of collateral observation. And this kind of knowledge can be interpreted in a categorical sense as Secondness.
But Peirce here tells us that there is also another kind of knowledge, which is a “prerequisite” for knowing objects, signs and their interpretations. He defines it as the acquaintance with the system of signs. That is, there is also an experience of the order of the objects, which allows us to know that a particular object is to find in such and such position in a certain order of the class of signs. It means also that this system is already an object of our knowledge. Maybe it is at a different level (the level of familiarity) but it is not collateral, that means that it is not something beyond the realm of semiotic: it must be part of semiotic. This is a kind of Firstness in the Thirdness which a Sign is. So we have a general object known by familiarity, by acquaintance that is part of logic or semiotic. Here there is a huge difference with what Peirce sustained in his ’70s papers, where he considered familiarity and definition as pre-logical patterns of knowledge (W 3:257-275). The problem is: how can we know this general system? What is familiarity? Is that a direct intuition (which by the way would fall under the head of secondness)? If this is the case, it is difficult to avoid the nominalistic turn of this theory. Moreover, it would be in strong contrast with what Peirce wrote in the ’60s. If it is not a direct knowledge, how can we have it? Which is the faculty that allows us to know in such a way?
What is the problem of the recognition of this kind of knowledge? It implies a generality (very similar to that one of the universe of discourse) already present in the singular we are interested into. Even if we want this knowledge to coincide precisely with the Universe of Discourse as such, with Truth (MS. 138), we always have the trouble to have a singular universe that is general. And the problem is always the same that Peirce wrote many times in his mathematical writings on multitudes and collections (but also on the conception of Time): what allows a singular to be known as general (as part of a set) and what is general in a singular. In scotistic terms it is the problem of the relationship between natura communis and haecceitas. I think that this question, the relation between general and singular had always been a crucial one in Peirce’s thought, because it represents the link among categories and in a sense it is the heart of every kind of representation.
In this case, though, it seems to me that this kind of generality is even beyond the generality of the Universe of Discourse. In my view, but I will argue for this later, this acquaintance is relative to the dynamical object as the collateral observation is relative to the immediate object. In a sense, this acquaintance is beyond the immediacy of collections and multitudes that are always immediate objects or entia rationis. The general system of signs has the same charateristic of the hypothesis of the true continuum. It is always a kind of representation, but is far beyond every possible collection. We reach the hypothesis of continuum starting from the study of collections. In the same way we reach the system of signs beginning with the identification of the immediate object. But the latter and the former have a different nature. But this is, of course, just a hypothesis and it is not the point I want to make. What I want to point out now is only that there is a kind of general object and a kind of knowledge referred to it and that we need a theory to explain this presence. The question is: either this “acquaintance” means something like direct knowledge in William James (but we risk very much to follow a nominalistic kind of framework) or we have to find a realistic evolutionary account to explain it.
The second vanishing point is about the representamen. It is very well known and accepted what Parker said about Peirce’s need of a logic of icons and indices. I am not going to repeat his analysis but I want just to give you some further hints that work in favor of Parker’s thesis. First, I will quote the passage in which Peirce talks of these kinds of Logic.
The points I wish to make are particularly: 1st, that Breadth and Depth, which the logic books restrict to one class of signs, namely to terms, are equally applicable, by a legitimate and easy generalization of their meanings, not only to propositions and to arguments, but also to icons, indices and all kinds of signs. (MS. 200, 000049)
What I wish to do here is to cast a glance to the reasons, which urged this change. In MS. 659: 000038-39, speaking about the greatest mistake in logic, that according to him is what we call Pophirius Tree, Peirce says:
For this error is, with one exception the most fatal of all those into which great minds have ever fallen, for it is so prolific that it breeds other errors in almost every field of inquiry. It creates a dire fog of a false preconceptions that hang over every great question and shuts out the light of reason. This erroneous doctrine is that a sufficiency of general predicates added to the definition of any class will cut the class down so that it can no longer contain but a single individual.
What was wrong with the Porphirius Tree? U. Eco was right in saying that with the division made by definitions and specific differences we obtain either too many synonyms or too many homonyms. We never grasp the individual we are looking for. The big mistake in the history of philosophy is connected to the problem of the individual. For many years Peirce thought that the problem was in trying to individualize something that is general by nature and he had already shown in his Cambridge Conferences how to understand the very generality of continuum as the only possibility of knowledge for every single individual (RLT: 157-159). Still there was something that did not convince him so that he kept writing about this topic both in his mathematical and in his logical papers (or fragments of papers).
But why am I connecting the dilemma of individuality and continuity with the need of a new kind of logic? Because what is worthy in finding a new logic is that in this way it is possible to identify criteria according to which an object becomes a representation and, for analogy, a singular object can enter a collection as a part of it. I mean that there must be some criterion that allows the “emanation” (MS. 637, 000029) of the representamen. It is true that when we think an object we have already a sign. But it is also true that growing old Peirce felt more and more the importance of reality (as it is shown by the recognition of the role of the dynamical object) and the subtle difference between being and being represented. I say “subtle” because it seems to me that in Peirce’s late writings there is always a double move: on the one hand, he stresses the power of reality and its not reversible order; but, on the other hand, he tries to “ampliate” reasoning, so that the phenomenological and semeiotical patterns are even more bounded to each other than they used to be. I would describe this period as “the search for the true continuity between reality and thought”.
There are for sure many tools that realize this “emanation” of the representamen. When symbols are concerned, Peirce had already shown how to apply the two classical measures of breadth and depth, but when we are dealing with icons and indices, the matter becomes very obscure. Now, we know that Peirce was looking for a logic of icons and indices and I just suggested he needed it to overtake the mistake of the Porphirius Tree. As we saw, it does not grasp the real individual because it sticks to a conception of the individuality at the same time too weak and too strong. Too weak because it does not understand the Secondness of Individuality. Too strong because it does not understand the Thirdness of real continuity that can comprehend the individual without loosing its Secondness.
My theory is that at this point he felt the importance to inquire this field with the normative tools of Esthetics and Ethics. These sciences seem to be able to operate on reasoning and within reasoning (this is the change!) keeping in account breadth and depth of icons and indices. This is why Peirce stressed so much the terrific cognitive impact of these sciences on knowledge.
There is certainly a particular pleasure and a particular esthetic quality in fruitful reasonings; and the mathematicians, who seem to me, as a class, still, to be the champion reasoners of today […] have always attached great weight of importance to a certain esthetic quality of reasoning that they call “elegance”; and in view of this fact I do not see how any student of reasoning at all worthy of this twentieth century can leave unstudied the question of the logical value of this esthetic quality of reasoning at least. Moreover, in an age of the world in which excessive sentimentalism seems to many strong minds to be threatening the welfare, perhaps the perpetuation of the human race, it strikes me that it would be almost criminal for a student of reasoning to neglect the duty of inquiring just how far a reasoner ought to be influenced by the beauty or pleasurablenness of this or that opinion (MS. 681, 000008-9).
According to me, these two sciences allow us to deal with the “acquaintance with the system of signs” and with the pure indicality. In this way we can also understand the gnoseological meaning of Esthetics and Ethics, sciences that, according to Peirce, can be explained as the study on the admirable ends and deliberate application of reasoning. This theoretical position had been already held in the 1903 Harvard Lectures and it is precisely the acceptation of these two kinds of studies among sciences which makes one of the big differences between these lectures and the Cambridge Conferences held five years before. This is why for ethics we can quote a passage drawn from the fifth Harvard Lecture “The Three Normative Sciences”:
Ethics is the study of what ends of action we are deliberately prepared to adopt. That is right action which is in conformity to ends which we are prepared deliberately to adopt. That is all there can be in the notion of righteousness, as it seems to me (EP 2: 200).
For esthetics there is a significant passage in “A Sketch of Logical Critics”, one of the late articles that he was trying to write:
Meantime, instead of a silly science of Esthetics, that tries to bring us enjoyment of sensous Beauty, - by which I mean all beauty that appeals to our five senses, - that which ought to be fostered is meditation, ponderings, day-dreams (under due control), concerning ideals - oh no, no, no! “ideals” is far a too cold a word! I mean rather passionate admiring aspirations after an inward state that anybody may hope to attain or approach, but of whatever more specific complexion may enchant the dreamer. Our contemporary religious doubt will prove a terrible calamity indeed, if the sort of meditations I mean are to be weakened, lying as they do at the very bottom, the very lowest hold of the ship that carries all the hopes of humanity. One should be careful not to repress day-dreaming too absolutely. Govern it, - à la bonne heure! - I mean, see that self government is exercised; but be careful not to do violence to any part of the anatomy of the soul (EP 2:460).
From this point of view, in the late Peirce those two sciences seem to be really effective in the realm of logic. In particular, the first one seems necessary in order to understand the iconicity, while the second is probably devoted to indexicality. But how and where can they enter the realm of logic?
In order to answer this question, we have to consider Logical Critics, the second department of Peirce’s logic or semeiotic. Here we have the best clues and my vanishing points should find a possible interpretation. As everybody knows, Peirce spent many of his feeble forces writing more articulate descriptions of his retroductive guiding principle. Retroduction is the kind of reasoning that goes from consequent to antecedent. It had been since the ’60s one of the topics to which he devoted most of his analyses. In the Harvard Lectures held in 1903 he referred to it as the pragmatist paradigm as such: “Pragmatism intended as the logic of abduction” (former name for retroduction) was the title of his seventh lecture. As far as he continued his work on retroduction, he acknowledged the importance of instinct in this kind of reasoning. Generally speaking, instinct is “a way of voluntary acting prevalent almost universally among otherwise normal individuals of at least one sex or other unmistakable part of a race” (EP 2:464-465). Applied to humanity and taken in connection with rationality, it is something that has to do with the marvelous human capacity to guess the true hypothesis. Human beings, so far, have founded their theoretical way in a relative few number of attempts out of millions of possibilities.
At the very beginning he described this instinct as the anchor of science: as the anchor, it is important only insofar it is out of the boat of science. Instinct is just concerned with practical matters. Afterwards he painted it as irrational and practical hope (“On the logic of drawing history from ancient documents”, EP 2:107, 1898), reasonable insight (“The Nature of Meaning”, EP 2:217, 1903), conjecture (“What to make a reasoning sound”, EP 2:250, later in 1903), and finally, in 1908 he called it “rational instinct”. The last quotation has been drawn from “A Neglected Argument for the Reality of God” (EP: 446), the strange article that, in my opinion, is the beginning of the end, the starting point of his doubts. At the end, in the article “An Essay toward Improving Our Reasoning in Security and Uberty” (1913), he talks about an “intellectual instinct” (EP 2:464). He says here that reason is an intellectual instinct. So he passed from a conception that put instinct far apart from reason, to a one in which reason is part of instinct. And this is not surprisingly the same move operated by logic of mathematics toward logic of science (Fisch 1986, p. 336) and by logica docens toward logica utens. After the Neglected Argument they often coincide. Why did this change happen? I think that it was the study of retroduction and, in particular, of that very first step of retroduction which is well represented by Musement and its instinctive development in the Neglected Argument that made him think to a different role of that previous acquaintance with reality. Galileo called it il lume naturale. But let’s examine the development of retroduction and we will see how instinct works.
When something new has been proposed to our knowledge by experience, we formulate a hypothesis (there is no hypothesis if there is not something new and of a different level, order or continuum: otherwise we have got just a theorematical deduction). Peirce started thinking that this reasoning was just an inversion of the second figure of syllogism. This is his view also in the Cambridge Conferences held in 1898 (RLT: 131-142). But in the summary of retroduction Peirce gave in 1903 there are too many passages for a syllogism. Peirce himself says that the passage used to find out a new hypothesis does not belong to or come from any kind of syllogism.
The surprising fact, C is observed;
But if A were true, C would be a matter of course.
Hence, there is reason to suspect that A is true.
Thus, A cannot be abductively inferred, or if you prefer the expression, cannot be abductively conjectured, until is entire contents is already present in the premises, “If A were true, C would be a matter of course (EP 2:231).
There is no syllogism in here, in the moment in which we find out the hypothesis A. This is also the analysis proposed by T. Kapitan (1997, p. 477-496). At the beginning of retroduction something tells us that we can trust the working hypothesis, because it fits a certain order or modality of reality. Is that a direct knowledge, an infallible one? No, Peirce was sure about that. It is a fallible instinct. Infinitely more uberous than the rest of the development of reasoning, infinitely less secure, but necessary for reasoning. The passage that takes place here is the acceptance of instinct as a step of reasoning (and a very first one) or rather as the uberous ground of different kinds of reasoning. Hence, instinct somehow may share the nature of reasoning. Reasoning is something under control and after the Neglected Argument Peirce describes certain function of intellectual instinct in the same way. It is an action that we perform when we accept to inquire about something. The definition that he states in the Neglected Argument is:
Yes, it must be confessed that if we knew that the impulse to prefer one hypothesis to another really were analogous to the instincts of birds and wasps, it would be foolish not to give it play within the bound of reason; especially, since we must entertain some hypothesis or else forgo all further knowledge than that which we have already gained by that very means (EP2: 443-444).
What is this instinct useful for? According to the late Peirce, instinct is not only the irrational link between us and reality in evolution, something that guarantees on the presence of reality and its habit-taking changes, instinct is part of that reality, and insofar, it is evolutionary in itself, but, furthermore, instinct allows us to infer (!) the correctness of our hypothesis. Somehow it reads signs and makes hypotheses reasonable, that is, worth to be tried. It is Firstnes in Thirdness again.
What do I mean by saying that instinct “infers the correctness of our hypotheses”? I mean that when we have to understand a singular surprising fact, we must generalize it with a process that make it a subject: this is the hypostatic abstraction which presides over a particular kind of reasoning called theorematical deduction. It is the kind of reasoning by which we can formulate a mathematical hypothesis and draw its consequences. But after this first generalization we may still miss a satisfactory explanation because the order that we reached with our mathematical hypothesis is not significant for the point we must explain. It is what happens in the theory of numbers when we move from a certain set to a more multitudinous one. When we have a square root of 2 in the Q set or continuum or rational numbers, we face the lack of any possibility of explanation because in that set our surprising fact (the square root) it is not even a fact. So that we have to move to the more multitudinous set of the real numbers (R) in order to find a place for our square root of 2.
This passage from a level of continuity to another one is impossible to accomplish for theorematical deduction. This passage is covered by retroduction. And within it there is a particular “judgment” or “inference” which concerns the fitness of our surprising fact in the new continuum. This is what the “rational instinct” does. If we repeat the same operation of passing to a new continuum endlessly, we will arrive to an acquaintance with the general system of signs.
This is what happens in E. A. Poe’s Murderers de la Rue Morgue, quoted by Peirce as example of a good kind of retroduction supported by instinct. Here the surprising fact is the violence of the murder and the absence of hints that can make any sense (the absence means that at the level of order of signs/continuity they were searching into [which is humanity] they could not understand what was going on). But this absence leads Dupin, the detective, to move to another level (animality) and to feel/understand by instinct the perfect fitness of his hypothesis (the murder is an urang-utang) to the enigma of that particular murder.
My theory (and here my vanishing points find a unitary interpretation) is that instinct accomplishes that acquaintance with the general system of signs that we need in order to formulate a hypothesis, and the criteria according to which we can judge whether our hypothesis fits this continuum or this order must be somehow of an esthetic and ethic kind. And this would be an account of the elegance that mathematicians use. In this way we can understand that instinct has the role of accepting a retroductive hypothesis. All other kinds of hypothesis fall under the head of theorematical deduction.
Now we can also understand the distinction between “rational” and “intellectual”, the two words used by Peirce to describe instinct in his late writings. It is clear enough if we think to the Kantian sense of these words: rational could be something outside the judgment in itself, but not “intellectual”, where intellect is the faculty of judgment. For the late Peirce, instinct is where the judgment has its birth.
But, as the word says, instinct is just instinct and the fact that reason is part of it, does not mean they are just the same. Instinct is wider than reason. It can be used in the realm of reason (since the latter is part of the former) but it must have to do also with mind and consciousness, since they are the other levels of the organic development of human knowledge. I am not going trough these relations, but I want to point out the moment in which instinct may become reason. And of course this moment has to do with the one in which consciousness becomes reasoning, that is something under a certain control. Here we have again a hypothesis but it is the only one that makes sense following Peirce’s vague directions. Here I will quote a passage in which Peirce does not speaks of instinct but in which he is referring to a function that might be fulfilled by instinct, because it is once again firstness in thirdness. In this way we can try to describe the nature of this instinct and its organic relationship to judgment:
There is a celebrated passage in the second edition of the Critick der Reinen Vernunft and a very notable one, in which Kant says that the “I think” -Das Ich Denke - must be able to accompany all his ideas, “since otherwise they would not thoroughly belong to me”. A man less given to discoursing might remark on reading this: “For my part, I don’t hold my ideas as my ownty-downty; I had rather they were Nature’s and belonged to Nature’s author”. However, that would be to misinterpret Kant. In his first edition, he does not call the act “the I think” but “the object=x”. That which that act has to effect is the consecution of ideas; now, the need of consecution of ideas is a logical need and is due not, as Kant thinks, to their taking the form of the Urtheil, the assertion, but to their making an argument; and this is not “I think” that that always virtually accompanies an argument, but it is: “Don’t you think so?” (MS. 636, 000024-26).
From the point of view of faculties involved in knowledge, rational instinct has the role to accept the hypotheses of reality and in so far it is at the level in which mind becomes consciousness, a dialogue between two personalities within the self, and consciousness becomes reasoning, something that is somehow under control. In fact we can also answer to the questioning of reality saying: “I don’t care!”
The nucleus of the intellectual instinct is this kind of acceptation, the answer to the question “don’t you think so?” that reality brings to us. In this way intellectual instinct phenomenologically speaking is a firstness in thirdness, connected with esthetics (the general system of signs) and ethics (the indicality); logically speaking is the first step of reasoning; organically, it is an operation, which is referred to consciousness and its double personality in the moment in which it becomes reasoning.
As example we can take the mentioned Neglected Argument: musement, which is that kind of contemplation through which we can see the harmony among universes, is defended by the N.A.. The free contemplation and reading of signs (esthetical and ethical) is defended by the argument that “every heart will be ravished by its beauty” (EP2: 446). This “ravished”, according to my opinion, is an interpretation of signs made by the intellectual (well, rational at that time) instinct. So what we can say is that instinct is the very ground which allows us to judge reality. Its criterion is somehow difficult to identify, even though we can guess for analogy (it is firstness in thirdness) that it is related to esthetics and ethics. But what we know is that the function of instinct on judgment is to accept the suggestion of reality saying: “Yes, why not?”
Therefore, this is my view of Peirce’s late writings: studying the grammar and the principles on which retroduction is based; Peirce acknowledged that there was an uberous general ground, which is already part of reasoning but not mechanically necessary. There is a Firstness in Thirdness, that is part of reasoning, so that it can read signs and it is itself a sign, but that cannot be reduced to a logical necessary pattern and not even to a mathematical one.
It is surprising that among students of reasoning there should still be found some who incline to think that the processes of mathematics suffice to explain all sound inferences and who even assert positively that it is so. To be sure, if these gentlemen are mathematicians themselves, their opinion is comprehensible enough and quite in accordance with common opinion of mathematicians. But should they not belong to that class, one wonders how the easily observed predominant character of the non-mathematical views of mathematicians can have failed to cause them to examine the different types of reasoning more closely before pronouncing an opinion of so mathematical flavor (MS 678, 000005).
This is a huge difference for the thinker who just ten years before wrote:
Among these opinions which I have constantly maintained is this, that while abductive and inductive reasoning are utterly irreducible, either to the other or to deduction, or deduction to either of them, yet the only rationale of these methods is essentially deductive or necessary. If then we can state wherein the validity of deductive reasoning lies, we shall have defined the foundation of logical goodness of whatever kind.
Now all necessary reasoning, whether it be good or bad, is of the nature of mathematical reasoning (EP 2: 206).
What Peirce realized in his late days was that rationality is wider than logic and logic must include also instinct as the first level of reasoning. Moreover what we grasp with this kind of rational instinct is a wider evolutionary reality that is that true ordered continuum always implied in the knowledge of every kind of object (MS. 7), because it is relative to the dynamical object, it is the context of the dynamical object.
So, the change in Peirce’s mind lays in this feeling that truth and reality are not only teleological and eschatological, but they are also proleptical. Of course Peirce never stated propositions like the one that I have just mentioned (and probably he would not have like it), but he did many analyses on instinct and this is the only explanation (at least the only one I have found) which keeps them all together with a definite meaning.
At least, in this way we can understand Peirce’s doubts on pragmatism. It is probably useful to quote here the famous sentence that you can find in the article “An Essay toward Improving Our Reasoning in Security and Uberty”:
Yet the maxim of Pragmatism does not bestow a single smile upon beauty, upon moral virtue, or upon abstract truth; the three things that alone raise Humanity above Animality.
Pragmatism does not say anything about all those things, which are the glory of humanity and that are instead under the judgment of the intellectual instinct.
Just in order to confirm this change in Peirce’s mind we can also quote the late definitions of the relationship between Pragmatism and Methodeutics, the name chosen by Peirce after 1904 for the third department of logic. Methodeutics is “the theory of the advancement of knowledge of all kinds” (EP2: 256). I do not agree with M. Bergman (2000) and J.J. Liszka (1996), who think the study of the passage of meaning within the semeiotic triadic circle in every respect is to refer exclusively to this discipline. Meaning is already related to the grammar of object, representamen and interpretant, while Methodeutic is concerned with the organization among retroduction, deduction and induction and with all those themes connected to the method of inquiry, like ethics of terminology, social principle of research (the one defended in the Fixation of Belief) and freedom of research.
M. Fisch’s analysis is here the last word. He quoted the two passages of manuscripts 320 and 322. In the first Peirce says: “But Pragmatism is plainly, in the main, a part of Methodeutic” (MS. 320, 000024). And in the second: “Pragmatism is thus…a mere rule of methodeutic, or the doctrine of the logical method” (MS. 322, 000013).
If pragmatism belongs to Methodeutics we can understand why it cannot reach the peaks of humanity: beauty, morality and abstract truth. It is an important tool apt to verify something that has been discovered much before by instinct, which presides over retroduction. Pragmatism, intended as the logic of retroduction does not work when we have to formulate a true hypothesis. It just uses something already found among the signs by intellectual instinct.
Clues are not definitive and here I could quote just some of those you can find in Peirce’s late writings, but I think they are sufficient to put at stake Peirce’s doubts on Pragmatism. In this view Pragmatism is just a part of a much richer phenomenological and semeiotical conception of reality. Somehow Peirce had already understood this point when he accepted, in the late ’90s, the modalities of reality. But he still thought that pragmatism at least could explain the whole logical critics. In his late days he found that intellectual instinct, ankínoia (MS. 201), has the power to grasp, from a theoretical point of view, what pragmatism cannot grasp at all: beauty, goodness and abstract truth. Not only that, intellectual instinct is in this way part of retroduction and consequently, pragmatism has to be limited to Methodeutics. Pragmatism is no longer the logic of retroduction but only one of its consequences. From a theoretical point of view, what is more noticeable is that in this way Peirce indicated a realistic evolutionary link between the continuity of reality (represented in the system of signs) and reasoning. The relation between phenomenology and philosophy in this way would be even stronger than it was before.
I will conclude pointing out that the problems we touched have the same nature: they throw light on the difficult relationship between general and singular. There is no enigma from a phenomenological point of view: they are all firstness in thirdness. But Peirce needed an explanation also from a mathematical point of view (as he says in MS. 203). As we know, Peirce tried many times to solve the matter with the definition of continuity and it is not a case that just after 1908 he changed once again his mind on this topic.
The new path that Peirce tried to follow was a combination of the Cantorean system with his previous conception drawn by Kant and Aristotle (this definition as far as it goes is common both to Potter 1996, pp. 117-123 and Putnam 1995, p. 1-23). I do not want to go too far, because it is a field that needs to be carefully studied. But it seems to me that Peirce was starting once again from mathematical studies, deepening into the set theory and in the conception of ordinals that is behind it, trying in this way the fatidic link which would allow singulars to be understood in a general set and to generality to enter the real constitution of every individual. To put it in other terms, what he was trying to find out was a definition of continuum which would have allowed not only the generality that comes at the end of a transfinite induction (as Cantor’s hypothesis of continuum) but also the true proleptical generality different by nature from every set of denumerable series.
Continuity should have been a model rather than a result. But Peirce did not succeed in giving us a mathematical demonstration of this kind of continuum and he did not even show why we should try to find it, what should be the points that would be better to explain with a not cantorean hypothesis of continuity. What remains is the discourse about rational instinct, which seems to cover the same kind of proleptical pattern as far as semiotic is concerned. Future studies must verify if there is in the mathematical definition of continuum the same need of a firstness in thirdness that we found with the rational instinct and the critical and semeiotical insufficiency that it revealed.
Bergman, M. (2000). Reflections on the Role of the Commuincative Sign in Semeiotic. Transaction of the Charles S. Peirce Society
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Fisch, M. (1986). Peirce’s General Theory of Signs, In K.L. Ketner e C.J.W. Kloesel (Eds.), Peirce, Semeiotic, and Pragmatism (pp. 336). Bloomington Indiana University Press,.
Kapitan, T. (1997). Peirce and the Structure of Abductive Inference, in N. Houser, D. Roberts and J. Van Evra (Eds.), Studies in the Logic of Charles Sanders Peirce (pp. 477-496). Bloomington: Indiana University Press.
Liszka, J.J. (1996). A General Introduction to the Semeiotic of Charles Sanders Peirce, Indianapolis and Bloomington: Indiana University Press.
Potter, V. (1996). Peirce’s Philosophical Perspectives. New York: Fordham University Press.
Putnam, H. (1995). Peirce’s Continuum, In K. Ketner (Ed.), Peirce and Contemporary Thought, (pp. 1-23). New York: Fordham University Press.