Online research in philosophy

We characterise explicitly the decidable predicates on integers of Infinite Time Turing machines, in terms of admissibility theory and the constructible hierarchy. We do this by pinning down ζ, the least ordinal not the length of any eventual output of an Infinite Time Turing machine (halting or otherwise); using this the Infinite Time Turing Degrees are considered, and it is shown how the jump operator coincides with the production of mastercodes for the constructible hierarchy; further that the natural ordinals associated with the jump operator satisfy a Spector criterion, and correspond to the L ζ -stables. It also implies that the machines devised are "Σ 2 Complete" amongst all such other possible machines. It is shown that least upper bounds of an "eventual jump" hierarchy exist on an initial segment.

All around us the techno-memes are proliferating, and gearing up to take control; not that they realise it; they are just selfish replicators doing what selfish replicators do – getting copied whenever and wherever they can, regardless of the consequences. In this case they are using us human meme machines as their first stage copying machinery, until something better comes along. Artificial meme machines are improving all the time, and the step that will change everything is when these machines become self-replicating. Then they will no longer need us. Whether we live or die, or whether the planet is habitable for us or not, will be of no consequence for their further evolution.

Robert Casati and Achille C. Varzi, argue that time machines would be useless or have no practical applications on the grounds that travelling to the past would involve doing what has already been done. I argue that the sense in which travelling to the past involves doing what has already been done fails to support the claim that time machines would have no practical applications.

We discuss the possibility to build and operate a time machine, a device that produces closed timelike curves (CTCs). We specify the spacetime structure needed to implement a time machine and assess attempted no-go results against time machines in classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and in Euclidean quantum gravity. Such no-go theorems for time machines would show that, under physically reasonable conditions, CTCs cannot develop in spacetimes initially free of these pathologies. Our review indicates that an investigation of the prospects of achieving no-go results has not been entirely successful in establishing such generality. At the same time, the pursuit of chronology protection results has proved to be a fruitful way to probe the foundations of classical GTR and the interface between general relativity and quantum field theory.

The last few years have been good for time machines. Kip Thorne's renowned general relativity group at Caltech invented a new quantum gravitational approach to building a time gate, and, in an international collaboration, gave a plausible rebuttal of "grandfather paradox" arguments against time travel. Another respected group suggested time machines that exploit quantum mechanical time uncertainty. The technical requirements for these suggestions exceed our present capabilities, but each new approach seems less onerous than the last. There is hope yet that time travel will eventually become possible, even cheap.

Thinking about time travel is an entertaining way to explore how to understand time and its location in the broad conceptual landscape that includes causation, fate, action, possibility, experience, and reality. It is uncontroversial that time travel towards the future exists, and time travel to the past is generally recognized as permitted by Einstein’s general theory of relativity, though no one knows yet whether nature truly allows it. Coherent time travel stories have added flair to traditional debates over the metaphysical status of the past, the reality of temporal passage, and the existence of free will. Moreover, plausible models of time travel and time machines can be used to investigate the subtle relation between space-time structure and causality.

It surveys some philosophical issues concerning time travel and should serves as a quick introduction. It includes a new and improved way to define a time machine.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

Infinite time Turing machines extend the operation of ordinary Turing machines into transfinite ordinal time. By doing so, they provide a natural model of infinitary computability, a theoretical setting for the analysis of the power and limitations of supertask algorithms.

We present a counterexample to Krasnikov's (2002) much discussed time machine no-go result. In addition, we prove a positive statement: a time machine existence theorem under a modest "no holes" assumption.