Craig Warmke

In the bitcoin whitepaper, Satoshi Nakamoto (2008: 2) defines an electronic coin as a chain of digital signatures. Many have since defined a bitcoin as a chain of digital signatures. This latter definition continues to appear in reports from central banks, advocacy centers, and governments, as well as in academic papers across the disciplines of law, economics, computer science, cryptography, management, and philosophy. Some have even used it to argue that what we now call bitcoin is not the real bitcoin. The definition fails, however. This is important because the Chain Definition obscures Satoshi’s solution to a dilemma in the design of electronic cash, as well as the truth about bitcoin’s privacy and fungibility. In this article, I explain why the Chain Definition fails and what Satoshi likely endorsed instead. Along the way, I untangle some issues around bitcoin fungibility and clarify some others around the ontology of digital assets.

Over the last half century, possible worlds have bled into almost every area of philosophy. In the metaphysics of modality, for example, philosophers have used possible worlds almost exclusively to illuminate discourse about metaphysical necessity and possibility. But recently, some have grown dissatisfied with possible worlds. Why are horses necessarily mammals? Because the property of being a horse bears a special relationship to the property of being a mammal, they say. Not because every horse is a mammal in every possible world. Some have recently begun to use properties to develop rivals to possible worlds semantics which may someday compare in formal power and capture the different systems of modal logic. In this paper, I do two things. I first offer a quick primer on possible worlds semantics. Then I discuss three rivals and the work they have left to do.

Many want to know what bitcoin is and how it works. But bitcoin is as complex as it is controversial, and relatively few have the technical background to understand it. In this paper, I offer an accessible on-ramp for understanding bitcoin in the form of a model. My model reveals both what bitcoin is and how it works. More specifically, it reveals that bitcoin is a fictional substance in a massively coauthored story on a network that automates and distributes jobs normally entrusted to centralized publishing institutions. My model therefore falsifies a popular view according to which each bitcoin is a chunk of code.

Leibniz's conceptual containment theory says that singular propositions of the form a is F are true when the complete concept of being a contains the concept of being F. In this paper, I provide a new semantics for first-order logic built around this idea. The semantics resolves longstanding problems for Leibniz's theory and can represent, without possible worlds, both hyperintensional distinctions among properties and a certain kind of presumably impossible situation that standard approaches cannot represent. The semantics also captures the strong soundness and completeness of classical first-order logic.