C.S. Peirce on Mathematical Practice: Objectivity and the Community of Inquirers

Topoi - What understanding of mathematical objectivity is promoted by Peirce’s pragmatism? Can Peirce’s theory help us to further comprehend the role of intersubjectivity in...     

Autopoietic enactivism: action and representation re-examined under Peirce’s light

The purpose of this article is to start a dialogue between the so-called autopoietic enactivism and the semiotic pragmatism of C. S. Peirce, in order to re-examine both action and representation under a Peircean light. The focus lays on autopoietic enactivism because this approach offers a wider theoretical scope to cognition based on the continuity of life and mind, embodiment, dynamic and non-linear interaction between a system and its environment which are compatible ideas with Peirce’s semiotic pragmatism. The term ‘pragmatic’ has been introduced in cognitive science to reinforce the idea that cognition is a form of practice and to help action-oriented viewpoints to escape representationalism. In this paper, I shall try to demonstrate that Peirce’s semiotic pragmatism can be a meaningful methodological path to guide a reconciliation between not only anti-Cartesianism and representation but also representation and action. In order to accomplish this purpose, Peirce’s account to action, habit, thought and mind will be addressed through some of the guiding principles of his semiotic—sign and sign action. What follows is the re-examining of the problem of representation—as refuted by autopoietic enactivism—under the light of Peirce’s semiotic pragmatism.

     

Charles S. Peirce and the Medieval Doctrine of consequentiae

In 1898 C. S. Peirce declares that the medieval doctrine of consequences had been the starting point of his logical investigations in the 1860s. This paper shows that Peirce studied the scholastic theory of consequentiae as early as 1866–67, that he adopted the scholastics’ terminology, and that that theory constituted a source of logical doctrine that sustained Peirce for a lifetime of creative and original work.     

Peirce’s ‘Prescision’ as a Transcendental Method

Abstract

In this Paper I interpret Charles S. Peirce’s method of prescision as a transcendental method. In order to do so, I argue that Peirce’s pragmatism can be interpreted in a transcendental light only if we use a non‐justificatory understanding of transcendental philosophy. I show how Peirce’s prescision is similar to some abstracting procedure that Immanuel Kant used in his Critique of Pure Reason. Prescision abstracts from experience and thought in general those elements without which such experience and thought would be unaccountable. Similarly, in the Aesthetics, Kant isolated the a priori forms of intuition by showing how they could be abstracted from experience in general, while experience in general cannot be thought without them. However, if Peirce’s and Kant’s methods are similar in this respect, they reached very different conclusions.     

Kidnapping an ugly child: is William James a pragmaticist?

Since the term ‘pragmatism’ was first coined, there have been debates about who is or is not a ‘real’ pragmatist, and what that might mean. The division most often drawn in contemporary pragmatist scholarship is between William James and Charles Peirce. Peirce is said to present a version of pragmatism which is scientific, logical and objective about truth, whereas James presents a version which is nominalistic, subjectivistic and leads to relativism. The first person to set out this division was in fact Peirce himself, when he distinguished his own ‘pragmaticism’ from the broad pragmatism of James and others. Peirce sets out six criteria which defines ‘pragmaticism’: the pragmatic maxim; a number of ‘preliminary propositions’; prope-positivism; metaphysical inquiry; critical common-sensism; and scholastic realism. This paper sets out to argue that in fact James meets each of these criteria, and should be seen as a ‘pragmaticist’ by Peirce’s own lights.     

Why Peirce’s Anti-Intuitionism is not Anti-Cartesian: The Diagnosis of a Pragmatist Dogma

A close reading of Descartes’ works, particularly his Regulae ad Directionem Ingenii, calls into question the common interpretation of Peirce’s ‘Questions Concerning Certain Faculties Claimed for Man’ and ‘Some Consequences of Four Incapacities’ as being anti-Cartesian. In particular, Descartes’ conception of intuition differs from Peirce’s, and on one plausible reading of Descartes his intuitionism actually mirrors Peirce’s inferentialism in key respects. Given these similarities between Descartes and Peirce, the dogmatic status of the anti-Cartesian interpretation of Peirce becomes evident.     

Explaining dubious assertions

David Sosa argues that the knowledge account of assertion is unsatisfactory, because it cannot explain the oddness of what he calls dubious assertions. One such dubious assertion is of the form ‘P but I do not know whether I know that p.’ Matthew Benton has attempted to show how proponents of the knowledge account can explain what’s wrong this assertion. I show that Benton’s explanation is inadequate, and propose my own explanation of the oddness of this dubious assertion. I also explain what’s wrong with other dubious assertions mentioned by Sosa.     

The Cube,the Square and the Problem of Existential Import

One of the claims made for C. S. Peirce's existential graphs has been that they are a deductively complete formulation of first-order logic with identity. As Peirce presented them, this is true only for certain versions of first-order logic :those which do not include terms for individuals. I amend Peirce's rules here, showing, in particular, how they are capable of demonstrating that, for instance, ‘Jack is in the kitchen’ contradicts ‘Jack is not in the kitchen’     

Assertion,Complexity, and Sincerity

The target of this paper is the ‘simple’ knowledge account of assertion, according to which assertion is constituted by a single epistemic rule of the form ‘One must: assert p only if one knows p’ (where p is a proposition). My aim is to argue that those who are attracted to a knowledge account of assertion should prefer what I call the ‘complex’ knowledge account, according to which assertion is constituted by a system of rules all of which are, taken together, constitutive of assertion. One of those rules—which, following John Searle, I call the ‘preparatory condition’—is of the form ‘One must: assert p only if one knows p.’ All else being equal, simple accounts are preferable to complex accounts. I argue in this paper that all else isn't equal. While the simple knowledge account provides an elegant explanation of certain data, it is hard to see how to integrate the simple knowledge account into a more general theory of illocutionary acts. Because the complex knowledge account avoids this objection while explaining the same data as the simple knowledge account does, I conclude that the complex knowledge account is superior to the simple knowledge account.     

Peirce on Truth as the Predestinate Opinion

Abstract: In 1878's ‘How to Make Our Ideas Clear’, Peirce states that truth is the predestinate opinion, or that which is fated to be ultimately agreed to by all who investigate. Later in his life, though, he would claim both (i) that truth is what would be believed if we could figure out the right method of inquiry and (ii) that, instead of affirming that truth is the predestinate opinion in 1878, he ought to have affirmed that truth is what would be believed if inquiry were carried sufficiently far. The aim of this paper is to provide an account of why the early Peirce endorses the claim that truth is the predestinate opinion and why the late Peirce is compelled to modify that position. I argue that Peirce's early statement that truth is the predestinate opinion is motivated by his theory that all mental action is of the nature of a valid inference and that the later modification of his view is partly motivated by his rejection of that theory.     

Toward an objective phenomenological vocabulary: how seeing a scarlet red is like hearing a trumpet’s blare

Nagel’s challenge is to devise an objective phenomenological vocabulary that can describe the objective structural similarities between aural and visual perception. My contention is that Charles Sanders Peirce’s little studied and less understood phenomenological vocabulary makes a significant contribution to meeting this challenge. I employ Peirce’s phenomenology to identify the structural isomorphism between seeing a scarlet red and hearing a trumpet’s blare. I begin by distinguishing between the vividness of an experience and the intensity of a quality. I proceed to identify further points of structural isomorphism (a) between the experience of seeing a scarlet red and of hearing a trumpet blare and (b) between the qualities of those experiences. Lastly, I gesture towards how these distinctions can be an aid in describing what it is like to be a bat.     

Peirce on Education: Discussion of Peirce’s Definition of a University

I write this short essay in response to Peirce, as a feminist, pragmatist, and cultural studies scholar, in the hope that it will help to bring feminism and pragmatism together. I suggest that Peirce offers marginalized and colonized people a way to argue for the importance of their input, with his theory of fallibilism, even if he still claims a position of privilege. He also offers assistance through his concept of “a community of inquirers.” It is curious that Peirce’s definition of a university argues for a split between theory and practice that his earlier work sought to heal. Peirce opened a door to help diverse scholars be able to enter the university, and find a way to address issues of power, with his youthful connecting of theory to practice, that his more senior position draws our attention away from and seeks to hold off. Fortunately, it is too late. Peirce’s youthful pragmatism has been developed in important ways by other scholars and now serves as an example of a way to do philosophy that does connect theory to practice and does seek to address real problems in diverse peoples lives, and help to find solutions that effect change.     

Peirce on facts and true propositions

Peirce maintains that facts and propositions are structurally isomorphic. When we understand how Peirce thinks they are isomorphic, we find that a common objection raised against epistemic conceptions of truth – that there are facts beyond the ken of discovery – holds no water against Peirce’s claim that truth is what would be believed after a sufficiently long and rigorous course of inquiry.     

Heidegger on Assertion,Method and Metaphysics

In Sein und Zeit Heidegger makes several claims about the nature of ‘assertion’ [Aussage]. These claims are of particular philosophical interest: they illustrate, for example, important points of contact and divergence between Heidegger's work and philosophical movements including Kantianism, the early Analytic tradition and contemporary pragmatism. This article provides a new assessment of one of these claims: that assertion is connected to a ‘present‐at‐hand’ ontology. I also indicate how my analysis sets the stage for a new reading of Heidegger's further claim that assertion is an explanatorily derivative phenomenon. I begin with a loose overview of Heidegger's position and then develop a sharper formulation of the key premises. I go on to argue that existing treatments of the supposed link between assertion and the ‘present‐at‐hand’ are unsatisfactory, and advance a new, ‘methodological’, interpretation of that link. Finally, I sketch the implications of my interpretation for the further claim that assertion is explanatorily derivative.     

Assertion and grounding: a theory of assertion for constructive type theory

Taking Per Martin-Löf’s constructive type theory as a starting-point a theory of assertion is developed, which is able to account for the epistemic aspects of the speech act of assertion, and in which it is shown that assertion is not a wide genus. From a constructivist point of view, one is entitled to assert, for example, that a proposition A is true, only if one has constructed a proof object a for A in an act of demonstration. One thereby has grounded the assertion by an act of demonstration, and a grounding account of assertion therefore suits constructive type theory. Because the act of demonstration in which such a proof object is constructed results in knowledge that A is true, the constructivist account of assertion has to ward off some of the criticism directed against knowledge accounts of assertion. It is especially the internal relation between a judgement being grounded and its being known that makes it possible to do so. The grounding account of assertion can be considered as a justification account of assertion, but it also differs from justification accounts recently proposed, namely in the treatment of selfless assertions, that is, assertions which are grounded, but are not accompanied by belief.     

How unexpected observations lead to new beliefs: A Peircean pathway

People acquire new beliefs in various ways. One of the most important of these is that new beliefs are acquired as a response to experiencing events that one did not expect. This involves a form of inference distinct from both deductive and inductive inference: abductive inference. The concept of abduction is due to the American pragmatist philosopher C. S. Peirce. Davies and Coltheart (in press) elucidated what Peirce meant by abduction, and identified two problems in his otherwise promising account requiring solution if that account were to become fully workable. Here we propose solutions to these problems and offer an explicit cognitive model of how people derive new beliefs from observations of unexpected events, based on Peirce’s work and Sokolov’s ideas about prediction error triggering new beliefs. We consider that this model casts light not only upon normal processes of belief formation but also upon the formation of delusional beliefs.     

“心为太极”说在朱子学中的诠释

朱子在《易学启蒙》中曾引用邵雍“心为太极”之说。此说与朱子学的固有观念似乎相矛盾。但“心为太极”说在朱子学的框架内至少曾出现如下三种理解:朱子本人以“心”为易图的中心方位来解释“太极虚中之象”的“环中说”;在朱子后学中具有广泛影响的禀赋说;现代学者所揭示出的“境界说”。三种说法并不矛盾,“环中说”背后所体现的是“太极不离阴阳”的活动性原则,它与“禀赋说”所代表的实体性原则相辅相成,二者的统一就是“境界说”。此外,“心为太极”还有一层工夫的含义,对于提示学者在自家身上体贴太极观念具有重要的意义。     

Continuity, Naturalism, and Contingency: A Theology of Evolution Drawing on the Semiotics of C. S. Peirce and Trinitarian Thought

The starting point for this article is the question of the relationship between Darwinism and Christian theology. I suggest that evolutionary theory presents three broad issues of relevance to theology: the phenomena of continuity, naturalism, and contingency. In order to formulate a theological response to these issues I draw on the semiotics (theory of signs) and cosmology of the American philosopher Charles Sanders Peirce. Peirce developed a triadic theory of signs, underpinned by a threefold system of metaphysical categories. I propose a semiotic model of the Trinity based on Peirce's semiotics and categories. According to this model the sign‐processes (such as the genetic “code”) that are fundamental to life may be understood as vestiges of the Trinity in creation. I use the semiotic model to develop a theology of nature that addresses the issues raised by evolutionary theory. The semiotic model amounts to a proposal for a new metaphysical framework within which to understand the relationship between God and creation and between theology and science.     

Neat,Swine, Sheep,and Deer: Mill and Peirce on Natural Kinds

In the earliest phase of his logical investigations (1865–1870), Peirce adopts Mill's doctrine of real Kinds as discussed in the System of Logic and adapts it to the logical conceptions he was then developing. In Peirce's definition of natural class, a crucial role is played by the notion of information: a natural class is a class of which some non-analytical proposition is true. In Peirce's hands, Mill's distinction between connotative and non-connotative terms becomes a distinction between symbolic and informative and pseudo-symbolic and non-informative forms of representation. A symbol is for Peirce a representation which has information. Just as for Mill all names of Kind connote their being such, so for Peirce all symbols profess to correspond to a natural class.