Infinite time Turing machines with only one tape are in many respects fully as powerful as their multi-tape cousins. In particular, the two models of machine give rise to the same class of decidable sets, the same degree structure and, at least for partial functions f : ℝ → ℕ, the same class of computable functions. Nevertheless, there are infinite time computable functions f : ℝ → ℝ that are not one-tape computable, and so the two models of infinitary computation (...) are not equivalent. Surprisingly, the class of one-tape computable functions is not closed under composition; but closing it under composition yields the full class of all infinite time computable functions. Finally, every ordinal that is clockable by an infinite time Turing machine is clockable by a one-tape machine, except certain isolated ordinals that end gaps in the clockable ordinals. (shrink)

D E Cooper; Is Language Learned?1, Journal of Philosophy of Education, Volume 9, Issue 1, 30 May 2006, Pages 93–104, https://doi.org/10.1111/j.1467-9752.1975.tb.

Editors and commentators ancient and modern have not responded very well to the challenge of the two riddles which round off the contest between Damoetas and Menalcas at the end of Eclogue 3 . The first is generally regarded as impossibly difficult; the second as impossibly easy. Critics take refuge in quoting Servius' despairing statement: sciendum aenigmata haec sicuti pleraque carere aperta solutione. Yet it is most unlikely that Virgil would introduce insoluble or meaningless riddles into the Bucolica. If there (...) is no solution the lines become pointless, even tasteless; and these are not epithets to be applied lightly to Virgil's poetry. (shrink)

The real history of the covey of attention-artists who call themselves "The Birds." A great deal of uncertainty--and even some genuine confusion--surrounds the origin, evolution, and activities of the so-called Avis Tertia or "Order of the Third Bird." Sensational accounts of this "attentional cult" emphasize histrionic rituals, tragic trance-addictions, and the covert dissemination of obscurantist ontologies of the art object. Hieratic, ecstatic, and endlessly evasive, the Order attracts sensual misfits and cabalistic aesthetes--both to its ranks, and to its scholarship. In (...) recent years, however, the revisionist work of the research collective ESTAR(SER) has done much to clear the air, bringing archival precision to the history of this covey of attention-artists who call themselves "The Birds." Gathering the best articles of the last twenty years of The Proceedings of ESTAR(SER), this volume represents a landmark in the history of aesthetic practices, and will be a point of departure for future work wading the muddy marshes at the limits of historicism."--Publisher description. (shrink)

The editors of the new fragment of Gallus draw attention to line 6, ‘fecerunt carmina Musae’. They say ‘“fecerunt” is unusual in such a context, and to a Roman reader would inevitably suggest ; the Muses of Gallus provided craftsmanship as well as inspiration’. It is possible to be more precise: cf. Euphorion fr. 118 Powell.

These books entertain as well as teach philosophical wisdom by looking closely at entertainment icons.

"Essays examine philosophical aspects of the iPod portable audio player, focusing on its status as a cultural icon and object with many meanings"--Provided by ...

Inside What Would Plato Do?, you'll find the basics of philosophy, written in an easy, digestible way we can all understand, along with questions to help you apply these important theories to your own life. So, after you've learned about a philosophical concept, you'll then be challenged to test yourself and see how the results can impact your daily life. For instance, after learning about Kant's theory of morality and the importance of intention you're challenged with questions like: Can good (...) people do bad things? Was there a time when you intended to do something helpful that ended up being hurtful? Does that make you a good person (because you intended to do good) or a bad person (because the results were bad)? What Would Plato Do? will not only help you better understand some of the greatest thinkers ever but will also help you think of the world around you in a whole new way! (shrink)

This book proposes a theory of reference--answering the question of whether Jewish, Christian, and Muslim scriptures refer to the same God--within a semantic framework acceptable to atheists and fideists.

Although the Neo-Darwin Theory of Evolution is one of the most celebrated theories in science, nonetheless it has received many criticisms. These criticisms are documented and a new transdisciplinary theory of origin is introduced. Darwin's original argument was that natural selection, through heritable changes, changed simple organisms over time. These heritable changes are responsible for the complex plethora of life seen around us today. Darwin's original theory, however, was deconstructed after the fact into a mutation-based theory. This mutation-based theory in (...) its current form is an insufficient and indeed unnecessary transdisciplinary explanation. A subsequent statistical comparison between the six extant scientifically based primary theories of origin was undertaken and based on current biological knowledge a statistically significantly best fit phenotypic model emerged. (shrink)

Causal theories of content, a popular family of approaches to defining the content of mental states, commonly run afoul of two related and serious problems that prevent them from providing an adequate theory of mental content—the misrepresentation problem and the disjunction problem. In this paper, I present a causal theory of content, built on information theoretic tools, that solves these problems and provides a viable model of mental content. This is the greatest surprise reduction theory of content, which identifies the (...) content of a signal as the event the surprisal of which is most reduced by that signal. Conceptually, this amounts to the claim that the content of a signal is the event the probability of which has increased by the largest proportion, or the event that the signal makes the most less surprising to us. I develop the greatest surprise reduction theory of content in four stages. First, I introduce the general project of causal theories of content, and the challenges presented to this project by the misrepresentation and disjunction problems. Next, I review two recent and prominent causal theories of content and demonstrate the serious challenges faced by these approaches, both clarifying the need for a solution to the misrepresentation and disjunction problems and providing a conceptual background for the greatest surprise reduction theory. Then, I develop the greatest surprise reduction theory of content, demonstrate its ability to resolve the misrepresentation and disjunction problems, and explore some additional applications it may have. Finally, I conclude with a discussion of a particularly difficult challenge that remains to be addressed—the partition problem—and sketch a path to a potential solution. (shrink)