Patrick Grim

This paper surveys our inescapable limits as cognitive agents with regard to a full world of fact: the well-known metamathematical limits of axiomatic systems, limitations of explanation that doom a principle of sufficient reason, limitations of expression across all possible languages, and a simple but powerful argument regarding the limits of conceivability. In ways demonstrable even from within our limits, the full world of fact is inescapably beyond us. Here we propose that there must nonetheless be a totality of fact, and that despite our limits we can know something of its general character. The world as the totality of fact must form a plenum, with a radically unfamiliar formal structure that contains distinct elements corresponding to each element of its own power set.

Most current modeling for evolution of communication still underplays or ignores the role of local action in spatialized environments: the fact that it is immediate neighbors with which one tends to communicate, and from whom one learns strategies or conventions of communication. Only now are the lessons of spatialization being learned in a related field: game-theoretic models for cooperation. In work on altruism, on the other hand, the role of spatial organization has long been recognized under the term ‘viscosity’.Here we offer some simple simulations that dramatize the importance of spatialization for studies of both cooperation and communication, in each case contrasting a model dynamics in which strategy change proceeds globally, and a spatialized model dynamics in which interaction and strategy change both operate purely locally. Local action in a spatialized model clearly favors the emergence of cooperation. In the case of communication, spatialized models allow communication to arise and flourish where the global dynamics more typical in the literature make it impossible.Simulations make a dramatic case for spatialized modeling, but analysis proves difficult. In a final section we outline some of the surprises of spatial dynamics but also some of the complexity facing attempts at deeper analysis.

In the spatialized Prisoner's Dilemma, players compete against their immediate neighbors and adopt a neighbor's strategy should it prove locally superior. Fields of strategies evolve in the manner of cellular automata (Nowak and May, 1993; Mar and St. Denis, 1993a,b; Grim 1995, 1996). Often a question arises as to what the eventual outcome of an initial spatial configuration of strategies will be: Will a single strategy prove triumphant in the sense of progressively conquering more and more territory without opposition, or will an equilibrium of some small number of strategies emerge? Here it is shown, for finite configurations of Prisoner's Dilemma strategies embedded in a given infinite background, that such questions are formally undecidable: there is no algorithm or effective procedure which, given a specification of a finite configuration, will in all cases tell us whether that configuration will or will not result in progressive conquest by a single strategy when embedded in the given field. The proof introduces undecidability into decision theory in three steps: by (1) outlining a class of abstract machines with familiar undecidability results, by (2) modelling these machines within a particular family of cellular automata, carrying over undecidability results for these, and finally by (3) showing that spatial configurations of Prisoner's Dilemma strategies will take the form of such cellular automata

Philosophy of Science and the Occult has two aims: to introduce the philosophy of science through an examination of the occult, and to examine the occult rigorously enough to raise central issues in philosophy of science. Patrick Grim has compiled selections by authors with divergent views on astrology, parapsychology, and UFO’s to emphasize topics standard to the philosophy of science. He discusses issues such as confirmation and selection for testing, possibility and a priori probabilities, causality and time, explanation and the nature of scientific laws, the status of theoretical entities, the problem of demarcation, theory and observation, and science and values. A sketch of where these arise in the collection accompanies the table of contents. The context of the occult serves to make the initial introduction of these issues immediately understandable and forcefully compelling

Predicates are term-to-sentence devices, and operators are sentence-to-sentence devices. What Kaplan and Montague's Paradox of the Knower demonstrates is that necessity and other modalities cannot be treated as predicates, consistent with arithmetic; they must be treated as operators instead. Such is the current wisdom.A number of previous pieces have challenged such a view by showing that a predicative treatment of modalities neednot raise the Paradox of the Knower. This paper attempts to challenge the current wisdom in another way as well: to show that mere appeal to modal operators in the sense of sentence-to-sentence devices is insufficient toescape the Paradox of the Knower. A family of systems is outlined in which closed formulae can encode other formulae and in which the diagonal lemma and Paradox of the Knower are thereby demonstrable for operators in this sense.

We extend previous work by modeling evolution of communication using a spatialized genetic algorithm which recombines strategies purely locally. Here cellular automata are used as a spatialized environment in which individuals gain points by capturing drifting food items and are 'harmed' if they fail to hide from migrating predators. Our individuals are capable of making one of two arbitrary sounds, heard only locally by their immediate neighbors. They can respond to sounds from their neighbors by opening their mouths or by hiding. By opening their mouths in the presence of food they maximize gains; by hiding when a predator is present they minimize losses. We consider the result a 'natural' template for benefits from communication; unlike a range of other studies, it is here only the recipient of communicated information that immediately benefits.

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic.

This is an exploration of a cluster of related logical results. Taken together these seem to have something philosophically important to teach us: something about knowledge and truth and something about the logical impossibility of totalities of knowledge and truth. The book includes explorations of new forms of the ancient and venerable paradox of the :Liar, applications and extensions of Kaplan and Montague's paradox of the Knower, generalizations of Godel's work on incompleteness, and new uses of Cantorian diagonalization. Throughout, the concern is with metaphysical and epistemological implications of these results: what such results may have to teach us about knowledge, truth, and possibility.

Philosophical modeling has a long and distinguished history, but the computer offers new and powerful prospects for the creation and manipulation of models. It seems inevitable that the computer will become a major tool in future philosophical research. Here I offer an overview of explorations in philosophical computer modeling that we in the Group for Logic and Formal Semantics at SUNY Stony Brook have undertaken: explorations regarding (1) the potential emergence of cooperation in a society of egoists, (2) self‐reference and paradox in fuzzy logic, (3) a fractal approach to formal systems, and (4) on‐going explorations with models for the emergence of communication. The attempt is not to give a detailed report on any of these but to give a bird s‐eye view of them all, emphasizing the general form that the models take, the philosophical motivations behind them, and the kinds of philosophical results that they may have to offer.

‘The problem with simulations is that they are doomed to succeed.’ So runs a common criticism of simulations—that they can be used to ‘prove’ anything and are thus of little or no scientific value. While this particular objection represents a minority view, especially among those who work with simulations in a scientific context, it raises a difficult question: what standards should we use to differentiate a simulation that fails from one that succeeds? In this paper we build on a structural analysis of simulation developed in previous work to provide an evaluative account of the variety of ways in which simulations do fail. We expand the structural analysis in terms of the relationship between a simulation and its real-world target emphasizing the important role of aspects intended to correspond and also those specifically intended not to correspond to reality. The result is an outline both of the ways in which simulations can fail and the scientific importance of those various forms of failure.

'Post-critical,' as Echeverria rightly notes, "is one of those catchy, yet slippery phrases which seem to crop up in so many places that they take on a power of their own." But for the purposes of this study, at least, he manages to circumscribe the topic with remarkable clarity: "... the traditional meaning of a critique of knowledge excluded reflection on one's own historical context as an essential trait of philosophical theories, and relegated that context to psychology. 'Post-critical' philosophy wants to reinstate that historical context as one that must itself necessarily be included in the very idea of theory or, as the case may be, of philosophical criticism."