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...     

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.     

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.     

Andrew Robinson. God and the World of Signs: Trinity,Evolution and the Metaphysical Semiotics of C.S. Peirce

ABSTRACT

Christian theologians have considered the significance of life elsewhere in the cosmos since the fifteenth century, but the brevity of these discussions calls for greater theological precision: the notion of multiple incarnations, for example, is often explored without reference to the detail of Christological formulations. Attention to the logical mode in which such work is set out is also fruitful, where the scholastic category of suitability or fittingness holds particular promise. As suitable, God’s actions are free and yet congruent, being consistent with the divine nature, with creaturely natures, and with the ends of God’s dealings with creatures.     

Diagrammatic Reasoning: Some Notes on Charles S. Peirce and Friedrich A. Lange

According to the received view, Charles S. Peirce's theory of diagrammatic reasoning is derived from Kant's philosophy of mathematics. For Kant, only mathematics is constructive/synthetic, logic being instead discursive/analytic, while for Peirce, the entire domain of necessary reasoning, comprising mathematics and deductive logic, is diagrammatic, i.e. constructive in the Kantian sense. This shift was stimulated, as Peirce himself acknowledged, by the doctrines contained in Friedrich Albert Lange's Logische Studien (1877 Lange, F.A. 1877. Logische Studien: Ein Beitrag zur Neubegründung der formalen Logik und der Erkenntnisstheorie, H. Cohen, ed., Iserlohn: Verlag von J. Baedeker (LS). [Google Scholar]). The present paper reconstructs Peirce's reading of Lange's book, and illustrates what, according to Peirce, was right and what was problematic in Lange's account of reasoning. It further seeks to explain how Peirce's theory of deductive reasoning was a combination of Kant's philosophy of mathematics and Lange's philosophy of logic.     

Peirce: Underdetermination,Agnosticism, and Related Mistakes

There are two ways that we might respond to the underdetermination of theory by data. One response, which we can call the agnostic response, is to suspend judgment: “Where scientific standards cannot guide us, we should believe nothing”. Another response, which we can call the fideist response, is to believe whatever we would like to believe: “If science cannot speak to the question, then we may believe anything without science ever contradicting us”. C.S. Peirce recognized these options and suggested evading the dilemma. It is a Logical Maxim, he suggests, that there could be no genuine underdetermination. This is no longer a viable option in the wake of developments in modern physics, so we must face the dilemma head on. The agnostic and fideist responses to underdetermination represent fundamentally different epistemic viewpoints. Nevertheless, the choice between them is not an unresolvable struggle between incommensurable worldviews. There are legitimate considerations tugging in each direction. Given the balance of these considerations, there should be a modest presumption of agnosticism. This may conflict with Peirce's Logical Maxim, but it preserves all that we can preserve of the Peircean motivation.     

Death,Myth and Reality in C.S. Lewis

C.S. Lewis's life and writings were profoundly shaped by his childhood experience of his mother's death. It is significant that the young hero's dying mother is mentioned at the very beginning of the first book of the Narnia sequence (seeThe Magician's Nephew.)., which in more general terms offers a mythopoeic version of the Christian interpretation of death. Lewis had a keen awareness of the power of myth (he would not have denied that the Christian gospel is myth). However, it was in the experience of the death of his wife (recounted inA Grief Observed) that he felt confronted by reality in a way that shook his faith to its foundations. This article will explore the tension between myth and reality in Lewis's attempts to write, as a Christian, of the experience of death.     

Indian students' perceptions of the ideal self, the ideal leader, the ideal teacher, Indira Gandhi and the business executive.

The Activity Vector Analysis (AVA) was administered to three samples drawn from a population of graduate students at an Indian university. Results indicated a high positive relationship among the perceptions of the ideal self, ideal teacher, and ideal leader. Likewise, the consensual profile of Indira Gandhi was found to be quite similar to the ideal self cluster (r = .96). The collective perception of the business executive, however, was only remotely similar to the other two character profiles.     

Modality,Quantification, and Many Vlach-Operators

Consider two standard quantified modal languages \(\textbf{\textsf{A}}\) and \(\textbf{\textsf{P}}\) whose vocabularies comprise the identity predicate and the existence predicate, each endowed with a standard S5 Kripke semantics where the models have a distinguished actual world, which differ only in that the quantifiers of \(\textbf{\textsf{A}}\) are actualist while those of \(\textbf{\textsf{P}}\) are possibilist. Is it possible to enrich these languages in the same manner, in a non-trivial way, so that the two resulting languages are equally expressive—i.e., so that for each sentence of one language there is a sentence of the other language such that given any model, the former sentence is true at the actual world of the model iff the latter is? Forbes (1989) shows that this can be done by adding to both languages a pair of sentential operators called Vlach-operators, and imposing a syntactic restriction on their occurrences in formulas. As Forbes himself recognizes, this restriction is somewhat artificial. The first result I establish in this paper is that one gets sameness of expressivity by introducing infinitely many distinct pairs of indexed Vlach-operators. I then study the effect of adding to our enriched modal languages a rigid actuality operator. Finally, I discuss another means of enriching both languages which makes them expressively equivalent, one that exploits devices introduced in Peacocke (1978). Forbes himself mentions that option but does not prove that the resulting languages are equally expressive. I do, and I also compare the Peacockian and the Vlachian methods. In due course, I introduce an alternative notion of expressivity and I compare the Peacockian and the Vlachian languages in terms of that other notion.     

Form symbolism, analogy, and metaphor

Simple forms, such as a square and a circle, can be symbolic; for example, a square can be deemed to behard and a circle to besoft. The relation between form symbolism and the comprehension of metaphors and analogies was studied in three experiments. Subjects were asked to rate matches between terms such assoft andhard andcircle andsquare as symbols (Experiment 1), metaphors (Experiment 2), and analogies (Experiment 3). The results show that a highly rated symbolic relation could be a poorly rated metaphorical relation. Ratings of analogies were similar to ratings of symbols. We argue that apt metaphors, analogies, and symbolic forms claim that the vehicle and the topic of the comparisons have common features, but that metaphoric representation entails more common features than does either symbolism or analogy, because metaphor requires that the vehicle be an especially apt example of a superordinate class. Thus, metaphor is a particularly strong claim about common features shared by the topic and the vehicle.