Rewording the Rules on Disjunctive Probability

Logic is a central and highly useful part of philosophy. Its value is particularly evident when it comes to keeping our thinking about disjunctive probabilities clear. Because of the two meanings of “or” (“just one of these statements is true,” “at least one of these statements is true”), logic can show how the likelihood of a disjunction being true can be determined quite easily. To gauge the chance that one of two or more exclusive alternatives is true, one need only sum up their respective likelihoods. And to know the chance that at least one of two or more compatible alternatives is true, one simply has to figure the chance that it is false that all of them are false!     

KAGAWA TOYOHIKO (1888–1960): WITNESS TO THE COSMIC DRAMA

At home and abroad, Kagawa Toyohiko was probably the best‐known Japanese Christian evangelist, social reformer, writer, and public intellectual of the twentieth century, nominated for the Nobel Prize in Literature twice (1947, 1948) and the Nobel Peace Prize three times (1954, 1955, 1956). Appealing to the masses with little knowledge of Christian faith, Kagawa believed that a positive, religio‐aesthetic interpretation of nature and science was a key missiological concern in Japan. He reasoned that a faith rooted in the kenotic movement of incarnation and self‐giving must strongly support the scientific quest. A voracious reader of science and especially biology, he argues for “directionality,” or what he calls “initial purpose” in the long, painful, cosmic journey from matter to life to mind (or consciousness). Through an antireductionistic, a posteriori methodological pluralism that sought to “see all things whole,” this “scientific mystic” employed Christian, Buddhist, Neo‐Confucian, personalist, and vitalist ideas to envision complementary roles for science and religion in modern society.     

Arrow Logic and Infinite Counting

We consider arrow logics (i.e., propositional multi-modal logics having three -- a dyadic, a monadic, and a constant -- modal operators) augmented with various kinds of infinite counting modalities, such as 'much more', 'of good quantity', 'many times'. It is shown that the addition of these modal operators to weakly associative arrow logic results in finitely axiomatizable and decidable logics, which fail to have the finite base property.     

Quantified Propositional Logic and the Number of Lines of Tree-Like Proofs

There is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over Substitution Frege Systems, if one considers proofs as trees. Whether this is true also for the number of symbols, is still an open problem. This revised version was published online in June 2006 with corrections to the Cover Date.     

A Note on Graded Modal Logic

We introduce a notion of bisimulation for graded modal logic. Using this notion, the model theory of graded modal logic can be developed in a uniform manner. We illustrate this by establishing the finite model property and proving invariance and definability results.     

Skepticism and Epistemic Logic

This essay attempts to implement epistemic logic through a non-classical inference relation. Given that relation, an account of '(the individual) a knows that A' is constructed as an unfamiliar non-normal modal logic. One advantage to this approach is a new analysis of the skeptical argument.     

Intuitionistic Propositional Logic without 'Contraction' but with 'Reductio'

Routley-Meyer type relational complete semantics are constructed for intuitionistic contractionless logic with reductio. Different negation completions of positive intuitionistic logic without contraction are treated in a systematical, unified and semantically complete setting.     

Hack or Die: How Humanity Steers Into Its Post-Digital Future

This article introduces stories as a link between culture and evolution. It elaborates how the decline of interhuman communication leads to a loss of perception, capability for cooperation, and human intelligence and contributes to the current ecocide. It shows how cybernetics hacked the relationship between evolution and machine development, which brought forth the outlines of man’s current digital transformation and future. It suggests that Lucas Pawlik is still working on a possible sustainable future for humanity that Heinz von Foerster tried to initiate.     

On Becoming a Cybernetician: Highlights and Milestones

In this article, I describe how I encountered cybernetics and how it became an important part of my life. I begin with an account of my time at Brunel University and also describe how I came to work with Gordon Pask, one of the few intellectuals and researchers in the UK who styled themselves as cyberneticians. To enrich my story, I include an overview of the story of cybernetics as I perceive it. Given the importance I attach to cybernetics as an intellectual tool, I end with a plea for it to be included in all educational curricula.