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.

There are experts in arithmetic, music, tennis, and fencing. But are there experts in morality? It is not surprising that there should be people like moral philosophers who are experts in moral theory, just as there are experts in tennis or music theory. But the question concerns whether there are analogues in morality of the expert tennis player or violinist. The unsophisticated answer might be that confessors, counselors, and perhaps even psychiatrists seem to qualify as moral experts in the relevant (...) sense. In turn, most conscientious confessors, counselors, and psychiatrists would deny that they themselves are experts in morality, even though they might claim expertise in divinity, marital advising, or treating emotional disorders. There are, moreover, persuasive philosophical arguments against the possibility of anyone’s being a moral expert, of which certain venerable reasonings of Socrates, Kant, and Ryle may be taken as representative. By examining several venerable arguments against the possibility of moral experts, we will, however, discover much to be said for the unsophisticated answer to the question. (shrink)

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)

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.

Writings of Charles S. Peirce: A chronological edition, volume 4, 1879?1884. Editor [in Chiefl, Christian J. W. Kloesel. Bloomington, Indianapolis: Indiana University Press, 1989. lxx + 698 pp. $57.50.