Jon Alan Schmidt

Two different versions of the ending of the first additament to C. S. Peirce's 1908 article, "A Neglected Argument for the Reality of God," appear in the Collected Papers but were omitted from The Essential Peirce. In one, he linked the hypothesis of God's Reality to his entire theory of logic as semeiotic, claiming that proving the latter would also prove the former. In the other, he offered a final outline of his cosmology, in which the Reality of God as Ens necessarium is indispensable to both the origin and order of our existing universe of Signs. Exploring these passages, as well as the unpublished manuscript drafts of the article, provides important insights into the key concepts of instinct and continuity within Peirce's comprehensive system of thought.

Charles Peirce begins his best-known text about religious metaphysics by defining the proper name "God" as Ens necessarium. In two previously unpublished manuscripts, he advocates the hypothesis of such a "necessary being" as the only "rational explanation" that is "adequate to account for the sum total of reality," namely, "the three universes" that together encompass "all the phenomena there are." Combining key statements from those passages into a series of distinct steps yields a cosmological argumentation for this conclusion, one resembling that of Gottfried Leibniz. In conjunction with Peirce's other relevant writings, it has implications for the attributes of God, as well as for the relationship between God and the universe, while also raising questions that call for further study.

Charles Sanders Peirce is best known as the founder of pragmatism, but the name that he preferred for his overall system of thought was “synechism” because the principle of continuity was its central thesis. He considered time to be the paradigmatic example and often wrote about its various aspects while discussing other topics. This essay draws from many of those widely scattered texts to formulate a distinctively Peircean philosophy of time, incorporating extensive quotations into a comprehensive and coherent synthesis. Time is not an existential subject with past, present, and future as its incompatible predicates, but rather a real law enabling things to possess contrary qualities at its different determinations, and Peirce identifies four classes of such states based on when and how they are realized. Because time is continuous, it is not composed of instants, and even the present is an indefinite lapse during which we are directly aware of constant change. The accomplished past is perpetually growing as the possibilities and conditional necessities of the future are actualized at the present, and the entire universe evolves from being utterly indeterminate toward being absolutely determinate. Nevertheless, time must return into itself even if events are limited to only a portion of it, a paradox that is resolved with the aid of projective geometry. Temporal synechism thus touches on a broad spectrum of philosophical issues including mathematics, phenomenology, logic, and metaphysics.

Questions regarding the nature and acquisition of mathematical knowledge are perhaps as old as mathematical thinking itself, while fundamental issues of mathematical ontology and epistemology have direct bearing on mathematical cognition. Several original contributions to logic and mathematics made by the American polymath, Charles Sanders Peirce, are of direct relevance to these fundamental issues. This chapter explores scientific reasoning as it relates to abduction, a name that Peirce coined for educated “guessing” of hypotheses, which he took to be “the first step of scientific reasoning” and the only creative one. Yet he also argued that all deductive reasoning is mathematical and that all mathematical reasoning is diagrammatic. Representation, especially in the form of a diagrammatic system of logic that Peirce developed, is explored here along with his logic of inquiry, most notably in terms of its manifestation as the logic of ingenuity. Originating in the field of engineering, here the diagram of a problem serves as a heuristic substitute for evaluating the actual situation, an approach that can be extended to other forms of practical reasoning such as ethical deliberation. This chapter also touches upon such diverse but related subjects as non-Euclidean geometry and nonclassical logic, with additional examples that help to elucidate cognitive elements of mathematical knowledge.

Although modern modal logic came about largely after Peirce’s death, he anticipated some of its key aspects, including strict implication and possible worlds semantics. He developed the Gamma part of Existential Graphs with broken cuts signifying possible falsity, but later identified the need for a Delta part without ever spelling out exactly what he had in mind. An entry in his personal Logic Notebook is a plausible candidate, with heavy lines representing possible states of things where propositions denoted by attached letters would be true, rather than individual subjects to which predicates denoted by attached names are attributed as in the Beta part. New transformation rules implement various commonly employed formal systems of modal logic, which are readily interpreted by defining a possible world as one in which all the relevant laws for the actual world are facts, each world being partially but accurately and adequately described by a closed and consistent model set of propositions. In accordance with pragmaticism, the relevant laws for the actual world are represented as strict implications with real possibilities as their antecedents and conditional necessities as their consequents, corresponding to material implications in every possible world.

Charles Peirce developed Existential Graphs as a diagrammatic syntax for representing and reasoning about propositions, with three parts: Alpha for propositional logic, Beta for first-order predicate logic, and Gamma for aspects of modal logic, second-order logic, and metalanguage. He made several adjustments between 1909 and 1911 that merit further consideration: using heavy lines to denote possible states of things in which attached propositions would be true, drawing a red line just inside the edge of a page and writing postulates in the resulting margin, shading oddly enclosed areas instead of drawing thin lines as their boundaries, and using multiple sheets of paper to represent different subjects within the overall universe of discourse. These modifications can be combined to constitute a plausible candidate for Delta, a fourth part that Peirce intended to add but never spelled out. It implements modern formal systems of modal propositional logic in accordance with a version of possible worlds semantics in which the laws for the actual state of things are facts in every possible state of things.

Although he is best known as the founder of pragmatism, the name that Charles Sanders Peirce prefers to use for his comprehensive system of thought is "synechism" because the principle of continuity is its central thesis. This paper arranges and summarizes numerous quotations and citations from his voluminous writings to formalize and explicate his distinctive mathematical conceptions of hyperbolic and topical continuity, both of which are derived from the direct observation of time as their paradigmatic manifestation, and then apply them in normative science and metaphysics, especially logic as semeiotic and cosmology. The resulting conclusion is that the intelligibility of the universe is plausibly explained by conceiving it as one immense sign, a vast inferential process: a semiosic continuum whose connected constituent signs are indefinite until deliberately marked off, with God the Creator as its overall dynamical object in the infinite past and God completely revealed as its overall final interpretant in the infinite future.

In 1907, Charles Peirce attempted to write an article that would introduce his distinct variety of pragmatism to a general audience. He eventually produced more than five hundred handwritten sheets, culminating in five major variants. Peirce left the second unfinished, while extensive portions of the third through fifth have appeared in collections of his writings, including the beginning that is common to all five. This is the completed and signed first version, which has never been published before and offers fresh insights into the evolution of its author’s thinking about semeiotic and pragmatism.

Charles Peirce incorporates modality into his Existential Graphs by introducing the broken cut for possible falsity. Although it can be adapted to various modern modal logics, Zeman demonstrates that making no other changes results in a version that he calls Gamma-MR, an implementation of Jan Łukasiewicz's four-valued Ł-modal system. It disallows the assertion of necessity, reflecting a denial of determinism, and has theorems involving possibility that seem counterintuitive at first glance. However, the latter is a misconception that arises from overlooking the distinction between the intermediate truth values that are assigned to possibly true propositions as either X-contingent or Y-contingent. Any two propositions having the same ITV are possible together, while any two propositions having different ITVs, including those that are each other's negation, are possible individually yet not possible together. Porte shows that Ł-modal can be translated into classical logic by defining a constant for each ITV such that its implication of another proposition asserts the latter's possibility, while its conjunction with another proposition asserts the latter's necessity. These are expressed in the Alpha part of EG without broken cuts, simplifying derivations and shedding further light on Łukasiewicz's system, as long as graphs including either of the constants are properly interpreted. Ł-modal and Gamma-MR thus capture the two-sided nature of possibility as the limit between truth and falsity in Peirce's triadic conception.

The semeiotic of Charles Sanders Peirce is irreducibly triadic, positing that a sign mediates between the object that determines it and the interpretant that it determines. He eventually holds that each sign has two objects and three interpretants, standardizing quickly on immediate and dynamical (or real) for the objects but experimenting with a variety of names for the interpretants. The two most prominent terminologies are immediate/dynamical/final and emotional/energetic/logical, and scholars have long debated how they are related to each other. This paper seeks to shed new light on the matter by reviewing the numerous manuscript drafts where Peirce develops the latter nomenclature while attempting to introduce his pragmatism to a general audience. It then goes on to examine an additional set of interpretants, intentional/effectual/communicational, and shows that the three different trichotomies can be understood as complementary, rather than redundant or conflicting.

Peirce is best known as the founder of pragmatism, but his dissatisfaction with how others understood and appropriated it prompted him to rename his own doctrine “pragmaticism” and to compose several variants of his original maxim defining it, as well as numerous restatements and elaborations. This paper presents an extensive selection of such formulations, followed by analysis and commentary demonstrating that for Peirce the ultimate meaning of an intellectual concept is properly expressed as a conditional proposition about the deliberate, self-controlled conduct of its interpreters, not the law-governed behavior of its object.

Charles Sanders Peirce is best known as the founder of pragmatism, but the name that he preferred for his overall system of thought was ‘‘synechism’’ because the principle of continuity was its central thesis. He considered time to be the paradigmatic example and often wrote about its various aspects while discussing other topics. This essay draws from many of those widely scattered texts to formulate a distinctively Peircean philosophy of time, incorporating extensive quotations into a comprehensive and coherent synthesis. Time is not an existential subject with past, present, and future as its incompatible predicates, but rather a real law enabling things to possess contrary qualities at its different determinations, and Peirce identifies four classes of such states based on when and how they are realized. Because time is continuous, it is not composed of instants, and even the present is an indefinite lapse during which we are directly aware of constant change. The accomplished past is perpetually growing as the possibilities and conditional necessities of the future are actualized at the present, and the entire universe evolves from being utterly indeterminate toward being absolutely determinate. Nevertheless, time must return into itself even if events are limited to only a portion of it, a paradox that is resolved with the aid of projective geometry. Temporal synechism thus touches on a broad spectrum of philosophical issues including mathematics, phenomenology, logic, and metaphysics.

Although Peirce frequently insisted that continuity was a core component of his philosophical thought, his conception of it evolved considerably during his lifetime, culminating in a theory grounded primarily in topical geometry. Two manuscripts, one of which has never before been published, reveal that his formulation of this approach was both earlier and more thorough than most scholars seem to have realized. Combining these and other relevant texts with the better-known passages highlights a key ontological distinction: a collection is bottom-up, such that the parts are real and the whole is an ens rationis, while a continuum is top-down, such that the whole is real and the parts are entia rationis. Accordingly, five properties are jointly necessary and sufficient for Peirce’s topical continuum: rationality, divisibility, homogeneity, contiguity, and inexhaustibility.

Modern approaches to engineering ethics typically involve the systematic application of universal abstract principles, reflecting the culturally dominant paradigm of technical rationality (techne). By contrast, virtue ethics recognizes that sensitivity to context and practical judgment (phronesis) are indispensable in particular concrete situations, and therefore focuses on the person who acts, rather than the action itself. Virtues are identified within a specific social practice in accordance with its proper purpose, its societal role and associated responsibilities, and the internal goods that are unique to it. As a result, ethics is recognized as something integral to engineering, rather than supplemental to it. This is necessary and appropriate, since engineers are often the decision-makers in contexts where the potential beneficiaries and harm-bearers are not the same; even their routine technical choices have ethical ramifications. The reasoning process commonly employed by engineers is similar in structure to that of scientists as articulated by Charles Sanders Peirce, the founder of philosophical pragmatism. As a "logic of ingenuity," it requires retroductively creating a diagrammatic model of a problem and its proposed solution, and then deductively working out the consequences, such that this serves as an adequate substitute for inductively evaluating the actual situation, which does not yet exist. As with ethical deliberation more generally, the key to success is having the ability to discern the significant aspects of reality and consistently capture them, before definitively selecting a way forward from among multiple viable options. This requires a carefully cultivated habit of imagining possibilities, assessing alternatives, and selecting one of them to bring about.

Science is widely perceived as an especially systematic approach to knowing; engineering could be conceived as an especially systematic approach to willing. The transcendental precepts of Bernard Lonergan may be adapted to provide the backdrop for this assessment, which is manifest when the scientific and engineering methods are compared. In science, although the will is implicitly involved, the intellect is primary, because the goal is ideal—additional “objective” knowledge. In engineering, although the intellect is implicitly involved, the will is primary, because the goal is pragmatic—some “subjective” outcome, which is often selected by a manager or client, rather than the engineer. Furthermore, engineering problems are rarely well-defined; uncertainties and resource constraints dictate that they be conceptualized and solved heuristically. As a result, different engineers will follow different design procedures and develop different models, none of which is uniquely “correct.” Because tradeoffs are always necessary, engineering decision-making—and human behavior in general—is more intentional than rational. Recognizing this can help today’s society to overcome its traditional bias in favor of knowing over willing and to engage engineers more explicitly in addressing the many challenges that it faces, technological and otherwise.

Modern philosophy recognizes two major ethical theories: deontology, which encourages adherence to rules and fulfillment of duties or obligations; and consequentialism, which evaluates morally significant actions strictly on the basis of their actual or anticipated outcomes. Both involve the systematic application of universal abstract principles, reflecting the culturally dominant paradigm of technical rationality. Professional societies promulgate codes of ethics with which engineers are expected to comply, while courts and the public generally assign liability to engineers primarily in accordance with the results of their work, whether intended or unintended. A third option, prominent in ancient philosophy, has reemerged recently: virtue ethics, which recognizes that sensitivity to context and practical judgment are indispensable in particular concrete situations, and therefore rightly focuses on the person who acts, rather than the action itself. Beneficial character traits—i.e., virtues—are identified within a specific social practice in light of the internal goods that are unique to it. This paper proposes a comprehensive framework for implementing virtue ethics within engineering