[...]... precisely this tradition of philosophical model building and thought experiments All that is new are the astounding computational resources now available for philosophical modeling As our subtitle indicates, we conceive of the chapters that follow as explorations in philosophical computer modeling In no case are they intended as the final word on the topics addressed; we hope rather that they offer some suggestive... research in the context of computer modeling Our ultimate hope is that others will find an environment of computer modeling as philosophically promising as we have We offer a handful of sample explorations with operating software and accessible source code in the hope that some of our readers will not only enjoy some of these initial explorations but will find tools useful in carrying the exploration further... attempt to open the semantical dynamics of selfreference and self-referential reasoning for investigation in their own right Here we use computer modeling in order to extend the tradition into infinite-valued logic Unlike many previous investigators, we will not be trying to find simple patterns of semantic stability Our concern will rather be with the infinitely intricate patterns of semantic instability... same information on a time-series graph and on the corresponding web diagram Here we start with an initial estimated value XQ—0.1, in this case—indicated by the arrow in the time-series graph at the left On the web diagram to the right we plot this value on the x-axis of the Cartesian plane, again using an arrow to indicate our starting point In the web diagram we now move vertically until we reach the. .. first point of intersection, we move horizontally to the right until we hit the x = y line The point of intersection here has an x-coordinate corresponding to what was our y-coordinate a minute ago—an x coordinate that therefore represents our value xi With that new x-coordinate in hand, we can move vertically to our function line again—down this time—intersecting our function line at a point with... models of social interaction using game theory within cellular automata (akin to the "Game of Life').10 The basic question is the same: How might social cooperation emerge within a society of self-serving egoists? Interestingly, the modeltheoretic answers that seem to emerge often echo Hobbes's second principle The most studied model of social interaction in game theory is undoubtedly the Prisoner's... the Divided Line to models of social contracts and John Rawls's original position If one is looking for philosophical models, one can find them in Heraclitus's river, in Plato's charioteer model of the tripartite soul, in Aristotle's squares of opposition, in the levels of Dante's Inferno, Purgatorio, and Paradiso, in Locke's impressions on the mind and in Descartes's captained soul in the sixth meditation... seemingly unexceptional notion of truth, and this seemed to doom the hope of formulating the laws of logic in full generality.2 The study of the paradoxes or insolubilia continued into the medieval period in work by Paul of Venice, Occam, Buridan, and others The Liar lies at the core of Cantor's diagonal argument and the "paradise" of transfinite infinities it gives us Russell's paradox, discovered in. .. between 0 and 1 The behaviors of the two sentences diverge sharply in an infinite-valued context, however Within a continuum of values, as we have seen, the Liar oscillates between any initial value x and 1 — x Perhaps unexpectedly, it is the Minimalist rather than the simple Liar that converges on the infinite classical oscillation between 0 and 1 The Simple liar, the Half-Sayer, and the Minimalist offer... we get the oscillation between 2/3 and 1 /3 shown in the second frame In the infinitevalued case, any initial value v generates a periodic alternation between the values v and (1 - v) The one fixed point for the infinite-valued Liar is 1/2, which returns at each step an identical revised value of 1/2 Were we to graph continued iteration using time-series graphs we would have to extend them indefinitely . for philosophical modeling. As our subtitle indicates, we conceive of the chapters that follow as explorations in philosophical computer modeling. In no case are they intended as the final. within the context of infinite-valued logic. Philosophical interest in the concept of chaos is ancient, apparent already in Hesiod's Theogeny of the eighth century B.C. Chaos theory in the. reasoning for investigation in their own right. Here we use computer modeling in order to extend the tradition into infinite-valued logic. Unlike many previous investigators, we will not be trying