Kelly suggested that it was useful to consider anyone as functioning as a scientist, in the business of applying theories, making hypotheses and predictions and testing them out in the practice of everyday life. One of Charles Peirce’s major contributions was to develop the disciplines of logic and the philosophy of science. We can deepen and enrich our understanding of Kelly’s vision by looking at what Peirce has to say about the process of science. For Peirce, the essence of science (...) was the application of the laws of inference. He developed a much broader concept of logic, elaborating the processes of deduction and induction and adding to these the logic of hypothetical inference, or ‘abduction’, even as Kelly broadened it further in his “departure from classical logic”. Examining the implications of these three forms of inference allows us to elaborate the dynamics involved in the process of construing, ordinacy and the cycles of experience, creativity and decision making. This is the second of a three part series examining the relationship between the work of Peirce and Kelly. The third will include a look at phenomenology, bipolarity, the self, dialogical process and sociological considerations. (shrink)

“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal (...) systems in the sense of Hilbert, Curry and the formalist school, (4) Symbolic logic, a science using symbols, such as Venn diagrams, (5) Mathematical logic, a mathematical approach to reasoning. We argue that these five meanings are independent and that the meaning (5) is the one which better characterized modern logic, which should therefore not be called “formal logic”. (shrink)

Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".

In this dissertation I provide a novel logic of the ordinary-language conditional. First, however, I endeavor to make clearer and more precise just what the objects of the study of the conditional are, as a lack of clarity as to what counts as an instance of a given category of conditional has resulted in deep and significant confusions in subsequent analysis. I motivate for a factual/counterfactual distinction, though not at the level of particular instances of the conditional. Instead, I argue (...) that each individual instance of the conditional may be interpreted either factually or counterfactually, rather than these instances dividing into distinct types. I examine the classic Oswald–Kennedy pair of sentences, typically taken to be the quintessential example of how conditionals must be split into two different categories, to show that they in fact do not demonstrate this. I then present my account of the logic underlying the ordinary-language conditional, the system C3, and a justification of the form it takes. This logic provides distinct interpretations of the conditional as it concerns what is factual or what is counterfactual, respectively. The factual interpretation is true when both antecedent and consequent are true at the actual world, false when the antecedent is true and consequent false, and not truth-apt otherwise. The counterfactual interpretation incorporates a ceteris paribus clause, ensuring that it is not falsified by extraordinary, unforeseeable occurrences, and is true when, at all worlds at which the antecedent is ceteris paribus true, the consequent too is true. It is false when, at any of these worlds the consequent is false; and not truth-apt otherwise. I go on to examine alternative theories of the conditional—from the suppositionalist approach to evaluating the putative indicative conditional, to Stalnaker’s combined indicative and counterfactual account, and Lewis’s analysis of the counterfactual; among a number of others—and offer comparison to my own theory. Finally, I look at various challenges to my account of the conditional. Being a strict conditional (albeit variably so), that of C3 is open to the objection that it fails to match ordinary speakers’ intuitions as regards its truth-value assignments to, for instance, conditionals with necessarily true consequents. I address these so- called paradoxes of the strict conditional, and also discussion the question of truth-preservation in the C3 system in the case of such inferences as those relying on transitivity and that of modus ponens. I maintain that these inferences are indeed truth-preserving under certain, specifiable, conditions, and I close by offering possible avenues for further research. (shrink)

The aim of this paper is to clarify the truth-functional interpretation of the logical connective of the material implication. The importance of such clarification lies in the fact that it allows avoiding the supposed paradoxes introduced by C. I. Lewis (1918). I argue that an adequate understanding of the history and purposes of logic is enough to dissolve them away. The defense is based on an exposition of propositional compositionalism. To compare, I also present Stalnaker’s (1968) alternative that seeks to (...) explain the implicit concept of conditionality of conditionals assertions. In order to reinforce my aim I expound the twelve different meanings of ‘implication’ stated by Corcoran (1993) in order to hold that a proper understanding of these meanings allows us to avoid ambiguities and confusions. Finally, I expect to show that despite the possible alternatives, compositionalism is still the best explanation for the truth-functionality account of logical connectives. (shrink)

Lewis' theory of meaning is barely touched by the contemporary trend to substitute a patient examination of the use of words for theorizing in the traditional manner. By way of contrast, some of his epistemological and ethical writings look as if Lewis had fulfilled the promise of linguistic analysis before it was made by Wittgenstein. Lewis' discussion of the good looks like an anticipation of the linguistic method. The question "what is good?" is answered as if it read "how is (...) the word 'good' used?" In comparison, his discussion of meaning has an anachronistic air about it. [...]. (shrink)

One of the least explored areas of C.S. Peirce's wide range of work is his contributions to psychology and the philosophy of mind. This dissertation examines the corpus of this work, especially as it relates to the subjects of mind, habit, instinct, sentiment, emotion, perception, consciousness, cognition, and community. The argument is that Peirce's contributions to these areas of investigation were both highly original and heavily influenced by the main intellectual currents of his time. An effort has been made to (...) present Peirce's philosophy without apology, within the conceptual framework and idiom of its time, and without appeal to a comprehensive view that Peirce never articulated. Nevertheless, as several noted interpreters have argued, much of this work can be viewed through the lens of Peirce's innovative theory of signs and the notion of the semiotic triad as its central unifying feature, despite the fact that the general theory was itself under continuous refinement and remained incomplete at the time of his death. Another hermeneutical device employed is William James' better known and more accessible work which, when juxtaposed with Peirce's ideas, serves to bring them into sharper relief. While general and historical in the presentation of material, this study seeks, at the same time, to engage the criticism of contemporary Peirce scholars in an attempt to account for several of the conundrums inherent in Peirce's work. Among the problems with implications for his philosophy of mind and theory of inquiry are the limitations of his theory of continuity, his negative view of the self, his somewhat ambiguous position on the relation of psychology to logic, and the metaethical puzzle arising from application of his theory of probable inference to truly fateful decisions. These problems provide an interesting perspective and lend balance to the truly insightful contributions Peirce made to the discovery of the mind. (shrink)

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...) is simply a logic that is both paraconsistent and paracomplete. -/- Despite being perfectly consistent and complete with respect to classical negation, nearly every normal modal logic, in its ordinary language and interpretation, admits to some latent paranormality: It is paracomplete with respect to a negation defined as an impossibility operator, and paraconsistent with respect to a negation defined as non-necessity. In fact, as it will be shown here, even in languages without a primitive classical negation, normal modal logics can often be alternatively characterized directly by way of their paranormal negations and related operators. So, instead of talking about ‘necessity’, ‘possibility’, and so on, modal logics could be seen just as devices tailored for the study of (modal) negation. This paper shows how and to what extent this alternative characterization of modal logics can be realized. (shrink)

t is often suggested that truth-preservation is insufficient for logical consequence, and that consequence needs to satisfy a further condition of relevance. Premises and conclusion in a valid consequence must be relevant to one another, and truth-preservation is too coarse-grained a notion to guarantee that. Thus logical consequence is the intersection of truth-preservation and relevance. This situation has the absurd consequence that one might concede that the conclusion of an argument was true (since the argument had true premises and was (...) truth-preserving); yet should refuse to infer the conclusion from the premises, in the absence of demonstration of the relevance of the premises to the conclusion. The error lies in giving insufficient attention to the notion of truth-preservation. Relevance is no separable ingredient in the analysis of logical consequence, but a necessary condition of it. What we show is that if an argument really is truth-preserving, then that in itself is enough to show that the premises are (logically) relevant to the conclusion. (shrink)

The aim of this article is to describe in some detail the actual relationship between Charles S. Peirce and Alfred N. Whitehead, paying particular attention to the Peircean notions of science and metaphysics, with the conviction that this contrast can help to understand better the scope and depth of C. S. Peirce’s thought.