Seminario del Grupo de Estudios Peirceanos
Universidad de Navarra, 22 de junio 2006
ABSTRACT: From a peircean viewpoint, any attempt to provide a scientific account of a given subject begins with the adoption of an explanatory hypothesis. Granted that Peirce’s own philosophy is in large extent an attempt to explain human reasoning through scientific means, it is not surprising that he had adopted his own ones. This paper intends to examine the hypothesis which lies behind Peirce’s early writings about scientific inquiry: namely, the convergence of reality and truth. In first place, we should consider that there are two kinds of convergence involved here. Ontologic convergence is asserted of reality: it supposes that there will be an assignable distribution of characters. On the other hand, epistemic convergence is asserted of inquirers' beliefs: it suggests that a self-correcting procedure of inquiry would constrain each investigator towards agreement. Nevertheless, it is important to discern that the general idea of convergence itself is a hypothesis: it is an insight on the modus operandi of nature and of mind. The hypothesis of convergence leads us, in short, to the notion of necessity in the long run (or knowledge a ulteriori), and it could explain why investigators are expected to attain sound agreement about reality. In fact, Peirce himself abandoned such a view around 1880-90s. But convergence was a very attractive hypothesis, and Peirce would hardly abandon it without some sensation that something important was missed. Incidentally, an appeal to a type of contingent convergence returned years later in the conceptions of habit and agapastic evolution. Now, Peirce was not committed to the idea of necessity in the long run, particularly because necessity in the long run dismisses an important characteristic of nature: its endless development. At any rate, regarding abduction, the claim that humans can have insights about the general habits of nature due to the continuity between mind and matter, it still consists in a hypothesis of convergence made in order to explain why investigators are allowed to divine the secrets of nature by abductive means. Peirce's early notion of convergence as necessity in the long run and the consequent commitment to an absolute conception of truth were anancastic; while Peirce's later view was agapastic. But the hypothesis of convergence itself, grasped by abductive means, was never abandoned: it was transformed.
KEYWORDS: Convergence, long run frequencies, habit, abduction, C. S. Peirce.
Pragmatism can be roughly described as a type of empiricism concerned with the future, so much so that "habit" and "experience" are evaluated by their consequents rather than by their antecedents. John Dewey expressed such characterization in his paper "The Development of American Pragmatism". According to Dewey: "Pragmatism, thus, presents itself as an extension of historical empiricism, but with this fundamental difference, that it does not insist upon antecedent phenomena but upon consequent phenomena; not upon the precedents but upon the possibilities of action" (1981, p. 50). This change of perspective fully appeared around 1878, in the Peirce's well-known pragmatic maxim: to consider the sensible effects of intellectual concepts. We must confess that the future is an elusive subject and most discussions sounds speculative. But there is a particular instance that deserves careful attention: namely, the role of the long run in probability. At first sight, probability makes the future uncertain and unpredictable. However, this claim is not completely true. In probabilistic matters we are not able to predict singular cases, but we can have accurate knowledge about frequencies in the long run.
According to Ian Hacking (1965; 1975), probability has always suggested two distinct meanings historically interlaced. In first place, there is a mathematical sense concerning chance and distributions of characters, properties, etc, which can be expressed by relative numbers, accordingly cases favorable divided by the total of cases. This mathematical probability is brought upon analysis of oddities, and it is considered objective. As Peirce once noted in "The doctrine of chance", unique events do not have degrees of probability — either it occurs or it fails to occur. Probability, objectively speaking, is asserted of indefinite series: when it is said that the probability of throwing a "five" with a dice is 1/6, it is understood that, in the long run, one sixth of throws will turn up five. With each throwing, however, either a "five" turns up or it does not, and we are unable to anticipate what will be. But, at same time, we can be sure that the distribution will converge to a stable ratio when the number of throwings increases. In other words, mathematical probability supports the appearance of some stable frequency in the long run (Bernoulli's Weak Law of Large Numbers). Note that we are not defending the gambler's fallacy, that is: "the fallacy of supposing, of a sequence of independent events, that the probabilities of later outcomes must increase or decrease to compensate for earlier outcomes" (Audi, 1999, p. 339). We are just highlighting that we can expect some kind of objective convergence of random designs. Indeed, random designs provide a curious kind of knowledge about the whole, but it does not provide any information about the characteristics of the parts.
On the other hand, probability has also an epistemic sense concerning an evaluation of belief making process: for instance, which degree of reliability is provided by a particular experimental design. In this second sense, degrees of probability are attributed to our statements, propositions, predictions, etc., as a way of evaluating the "weight" of beliefs. If inquirers could obtain more and more empirical data, under adequate statistical standards, it would increase the probability attributed to their statements, propositions and predictions. But inquirers hardly could obtain enough data, in view of the fact that they always deal with their individual and finite amount of experience. Based on this analysis, Peirce (1992b) concludes that science should not rely on finite individual experience, but on the endless experiences of an unlimited community of inquirers. It could be argued that, in fact, there can be no such community. Nevertheless, in some cases, "extrapolation" from limited available data is mathematically legitimate — it is as if we had unlimited experience.
Although these distinct meanings can be seen as covering different domains, if, in the long run, distributions of characters converged towards a stable state, and the reliability of beliefs converged asymptotically towards its maximum, then those distributions could be known, and with large degree of certainty. That is what supports Peirce's claim that: "the opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by truth, and the object represented in this opinion is the real" (Peirce, 1992a, p. 139). Here appears Peirce's notion of necessity in the long run in the realm of reality as well as in the realm of beliefs: there would be one reality fated to be known by all inquirers. (Hans Reichenbach (1939, p. 189) once noted that peircean approach to probability anticipates his own formulation).
Nevertheless, Peirce's view does not fit in the Kantian traditional classification of knowledge as a priori and a posteriori. Knowledge a priori has an important role in rationalistic schools: it is a way of establishing truth at the outset in order to justify a system of correlated ideas. On the other hand, empiricists usually are occupied with a posteriori judgments, for experience itself concerns what we have known from the past: which sensations impressed our minds, which ideas were associated to those impressions, and which habits we have acquired during our lives. But pragmatism intends to be a philosophical method occupied with the future of experience; thus, although considering that a posteriori knowledge deserves close attention, pragmatists tend to stress that any action has a component which is not completely implied in the past.
For sure, mere statistical accounts can be appropriately described as synthetic a posteriori. And necessity is not required here: for instance, that one fifth of world population is Chinese does not involve any a priori law. Thus probability, as Peirce understood it, surely is not synthetic a posteriori because implies necessity —so, perhaps they should be seen as a priori. But probabilistic statements cannot be synthetic a priori since their necessity only applies to large series, but not to the next case. Here, our central concern is that there is no clear place for the necessity implied by probabilistic statements in the Kantian framework. In fact, Kant usually thought of probability as something secondary. For instance, there is an emphatic passage of Prolegomena (1783) that states:
Nothing can be more absurd, than in metaphysics, a philosophy from pure reason to think of grounding our judgments upon probability and conjecture. Everything that is to be known a priori, is thereby announced as apodictically certain, and must therefore be proved in this way. We might as well think of grounding geometry or arithmetic upon conjectures. As to the doctrine of chances in the latter, it does not contain probable, but perfectly certain, judgments concerning the degree of the probability of certain cases, under given uniform conditions, which, in the sum of all possible cases, infallibly happen according to the rule, though it is not sufficiently determined in respect to every single chance2.
In others words, Kant himself discerned that probability involves necessity in the long run, "though it is not sufficiently determined in respect to every single chance". Here we do not pretend to make a case against Kant. Our goal is only to show that, in probabilistic statements, we always have to stress that they do not constrain single events, but constrain the whole class in the long run. We are highlighting that there is necessity implied in probabilistic statements, but it is not exactly a priori: so much so that it is always required the qualification "in the long run". We defend that such a deficit can be overcome by the introduction of a new class — namely, synthetic knowledge a ulteriori, defined as "what is known about an indefinite number of cases, but not about isolated instances". And knowledge a ulteriori consists in a category that could embrace the notion of necessity in the long run (Kinouchi, 2006).
In fact, necessity in the long run is implied when we discuss theories based on probabilistic determinism. For instance, thermodynamics takes advantage of probability in order to predict the whole behavior of a collection in the long run, although does not provide any particular information about a single molecule. In other domain, quantum mechanics, the wave-function prescribes the probability of distribution of results. Also in statistical mechanics, this procedure of calculation of probability in the long run is practically essential in the analysis of dynamical systems (particularly regarding the notion of dynamical attractors). But all these forms scientific knowledge do not involve a priori knowledge, because there is no constitutive necessity, from the out-set, but a collective necessity in the long run. And there is large amount of literature about Peirce’s expertise on probabilistic matters.
Peirce held that, in the long run, we are fated to discover true and justified beliefs (if scientific inquiry were pursued indefinitely). Such type of certainty is what I mean by knowledge a ulteriori. It is a third category of synthetic knowlege: but it is neither a priori nor a posteriori. And the notion of necessity in the long run, when applied on the development of science itself, explains how scientific inquiry constrains different minds towards a common and sound opinion. At any rate, it does continue not fitting in the categorization of knowledge either as a priori or a posteriori, since it is not necessary at the outset — thus it is not a priori— but, at same time, it is not merely a posteriori, because it involves necessity in the long run. In summary, it is not "knowledge which results contingently from the past" but "knowledge which embodies necessity in the future". That is why we affirm that Peirce's early ideas concerns knowledge a ulteriori, or knowledge necessary in the long run.
From a peircean viewpoint, any attempt to provide a scientific account of a given subject begins with the adoption of an explanatory hypothesis. Granted that Peirce's own philosophy is in large extent an attempt to explain human reasoning through scientific means (Santaella, 2004), so it is not surprising that he had adopted his own ones. For sure, his characterization of truth and reality depends upon the hypothesis of convergence of scientific beliefs and facts. If, in the long run, distributions converged towards a stable state, and the reliability of belief making process converged asymptotically towards its maximum, then the opinion fated to be ultimately agreed would truly represent the distribution of characters, properties, etc. So, the hypothesis of convergence entails necessity in the long run in the realm of reality as well as in the realm of beliefs. In short, there would be one reality fated to be known by all inquirers. In this respect, some contemporary philosophers sympathetic to pragmatism consider that James (1975 ) and Dewey (1938) were more convincing than Peirce. For the critics, such an absolute conception of reality and truth was the weak point of Peirce's pragmatism.
"Truth, Reality and Convergence" is a recent paper by Christopher Hookway (2004) that examines the development of Peirce's view about convergence of beliefs and facts. Hookway emphasizes the fact that Peirce's early absolute conception of reality suffered considerable weakening after 1880. Thus, to say that Peirce always defended an absolute conception of reality is an incomplete account of his philosophy. In Hookway's words:
In the 1860 and 1870s, Peirce's approach to question about reality was to pick out a distinctive set of signs or sentences, those that are fated to accept if we inquire sufficiently well, and then to define reality as the objects of these sentences. This, he thought, was the only way to give pragmatic sense to the concept of reality. By the 1880s, he was already embarked upon a journey that would offer him an independent empirical handle on the idea of a reality that is external to us and independent of our thought. And there is no reason to think that this way of articulating his realism would commit him to any version of the absolute conception of reality (p. 146).
We also do not pretend to make a case against Hookway. It is matter of fact that Peirce abandoned his early conceptions about truth and reality. But there is a commentary that deserves attention. According to Hookway: "Transforming the commitment to convergence into a hope, a regulative ideal, is a pervasive feature of his later writings" (p. 134). Now, I wonder whether Peirce was really committed to the idea of convergence. For sure convergence was an attractive hypothesis: it could explain why we should expect agreement about reality in the long run. But, in my view, in Peirce's later works convergence main value is heuristic rather than regulative. Convergence is not a maxim that should be dogmatically followed: it is just an attractive hypothesis that explains the process by which "the opinion which is fated to be ultimately agreed to by all who investigate is what we mean by truth, and the object represented in this opinion is the real" (Peirce, 1992 , p. 139). Without convergence, it would be hard to see why different researchers, starting from different opinions at the outset, would come to agreement about reality. But it does not require that we commit ourselves to agreement: its value is heuristic rather than regulative or normative.
Moreover, it is important to discern that the hypothesis of convergence consists in an insight achieved by abductive means. It was neither deduced from first principles attributed to human nature, nor induced by examining particular cases (indeed, human beings, including scientists and philosophers, look prone to diverge rather than converge). It was conjectured in order to explain how scientific inquiry constrains different minds towards a common and sound opinion. And it is a so attractive conjecture that one hardly abandons it without the sensation that something important was lost. Incidentally, an appeal to a soft kind of convergence returned years later in Peirce's conception of agapastic evolution.
In this new context, the idea of necessity in the long run appears rather as an obstacle than as a solution. Necessity in the long run pertains to the domain of secondness: in short, it is anancastic. It supposes that development and growing of nature will reach some fixed limit in the future. For instance, that classical thermodynamics (in accordance with Boltzmann) entails the heat-death of Universe. This heat-death does not mean annihilation; only that temperature will be the same at different places, so we will not be able to obtain "work" from thermodynamic processes. Peirce (1992 ) himself called attention to such vision, in "Design and Chance". But for the mature Peirce, the main character of universe is its endless development. Here, the concept of habit is central. Habit is a tendency, but it does not lead towards an ultimate stable state. Habit has as goal its own tendency of growing. Habit is agapastic. As said by Peirce: "A physical law is absolute. On the other hand, no exact conformity is required by the mental law (…) since it would instantly crystallize thought and prevent all further formation of habit. The law of mind only makes a given feeling more likely to arise" (1992 , p. 292). At any rate, there is some type of converge in the air, for habit tends to reinforce its own activity. In other words, habit is neither erratic as chance, nor destined in the sense of a necessary convergence in the long run, but habit tends towards its own endless development.
Thus, in order to fully apprehend the role of habit in the evolution of nature and of mind, we have to adopt an agapastic framework. In Peirce's words (1993 ): "The agapastic development of thought is the adoption of certain mental tendencies, not altogether heedlessly, as in tychasm, nor quite blindly by the mere force of circumstances or of logic, as in anancasm, but by an immediate attraction for the idea itself, whose nature is divined before the mind possesses it, by the power of sympathy, that is, by the virtue of continuity of mind" (p. 364).
With regard to abduction, the claim that we can have insights about the general habits of nature "by the virtue of continuity of mind" consists in a type of agapastic convergence that allows insights on nature. So, agapastic convergence is involved in the idea of habit itself. The abduction of convergence is the insight that mind and nature partakes habits whose development approximates each other. According to Antônio Rosa (2003): "A Razão, na sua totalidade, envolve, por um lado, uma evolução da natureza para a inteligibilidade e, por outro, o postulado afirmando a afinidade entre natureza e conhecimento (...) Mas trata-se efectivamente de um ideal, uma esperança, não de uma realidade efectiva. As nossas teorias estão ainda demasiadas fragmentadas e, a existir, a afinidade é uma presunção indirecta" (p. 365). In fact, the hypothesis of convergence itself was not discarded. That "presunção indirecta" of affinity between reality and our beliefs is still a form of convergence, but, now, it is agapastic and it is central for the claim that humans can divine the modus operandi of nature by abductive means.
Peirce's early notion of convergence as necessity in the long run and the consequent
commitment to an absolute conception of truth were anancastic; while his mature
conception of convergence became agapastic. In any case, the hypothesis of convergence
itself was never abandoned completely: and it does continue providing an explanation
of why inquirers sometimes divine the secrets of nature. And this insight, that
reality and mind converges agapastically, is abductive: the abduction of convergence.
1. The author aknowledges to Prof. Jaime Nubiola for the opportunity of presenting this paper at the Grupo de Estudios Peirceanos of Universidad de Navarra, and also to Sara Barrena and Izaskun Martínez for their kind and helpfull attention during our wonderful days at Pamplona and San Sebastián.
2. Kant, 1783, section "Solution Of The General Question Of The Prolegomena:
'How Is Metaphysics Possible As A Science?'". Accessed in 03/05/2006, at
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Fecha del documento: 20 julio 2006
Ultima actualización: 20 julio 2006