In 1910, only four years before his death, Peirce began an adumbration of a life's worth of major results concerning nondeductive logic—results that he had reached after more than forty-five years of extremely careful and detailed investigations2—as follows: "I must premiss that we, all of us, use this word ["probability"] with a degree of laxity which corrupts and rots our reasoning to a degree that very few of us are at all awake to."3 Peirce continued the adumbration by outlining his (...) mature theory, according to which, contrary to what is generally supposed, there is not just one measure of "falling short of certainty,"4 viz. probability. Rather, there are three utterly distinct and mutually incommensurable .. (shrink)
Royce’s sustained interest in technical logic is beyond doubt. One of his first publications, which appeared while he was still teaching at the University of California at Berkeley, was a logic primer, and many of the productions of his later career were articles on logic. Indeed, it can well seem that Royce spent at least ten or eleven years working almost exclusively on logic following his attendance at Peirce’s 1898 Cambridge Conference Lectures, entitled Reasoning and the Logic of Things. During (...) this period he filled dozens of notebooks with minute explorations of Boolean functions and relations, investigating them mostly by using fourcircle Venn diagrams. Less obvious than Royce’s devotion to logic .. (shrink)
In this paper, a game-theoretical semantics is developed for the so-called alpha part of Charles S. Peirce's System of Existential Graphs of 1896. This alpha part is that portion of Peirce's graphs that corresponds to propositional logic. The paper both expounds a game-theoretical semantics for the graphs that seems close to Peirce's own intentions and proves for the alpha part of the graphs that this semantics is adequate.
Lines of identity in Peirce's existential graphs are logically complex structures that comprise both identity and existential quantification. Yet geometrically they are simple: linear continua that cannot have “furcations” or cross “cuts.” By contrast Peirce's “ligatures” are geometrically complex: they can both have furcations and cross cuts. Logically they involve not only identity and existential quantification but also negation. Moreover, Peirce makes clear that ligatures are composed of lines of identity by virtue of the fact that such lines can be (...) “connected” with one another and can “abut upon” one another at a cut. This paper shows in logical detail how ligatures are composed and how they relate to identity, existential quantification, and negation. In so doing, it makes use of Peirce's non-standard account of the linear continuum, according to which, when a linear continuum is separated into two parts, the parts are symmetric rather than asymmetric, and the one point at which separation occurs actually becomes two points, each of which is a Doppelgänger of the other. (shrink)
The inaugural collection in an exciting new exchange between philosophers and geographers, this volume provides interdisciplinary approaches to the environment as space, place, and idea. Never before have philosophers and geographers approached each other's subjects in such a strong spirit of mutual understanding. The result is a concrete exploration of the human-nature relationship that embraces strong normative approaches to environmental problems.
This paper argues that several important tenets of the so-called "new theory of reference"--also known as the "historical-explanation theory" and as the "causal theory" of reference--were developed by william james as early as 1885 and that by 1895 they were elaborated by him in no less detail than contemporary theorists have so far done. these tenets include the central doctrine that reference is dependent on a causal or historical-explanatory chain connecting the act of referring with the entity referred to. james' (...) theory of reference is argued to be an aspect of his theory of truth. reference in james is argued to be an aspect of his pragmatic conception of the "workings" of true ideas. (shrink)
From three simple Peircean semeiotic principles, the general formula is derived for the number of definable sign-types from the number of semeiotic trichotomies to be used in defining the sign-types. If k is the number of such trichotomies, then [ ]/2 is the number of sign-types definable by appealing to them. The significance of the derivation lies in its setting constraints on particular detailed theories of sign-types.