The first collection of Leibniz's key writings on the binary system, newly translated, with many previously unpublished in any language. -/- The polymath Gottfried Wilhelm Leibniz (1646–1716) is known for his independent invention of the calculus in 1675. Another major—although less studied—mathematical contribution by Leibniz is his invention of binary arithmetic, the representational basis for today's digital computing. This book offers the first collection of Leibniz's most important writings on the binary system, all newly translated by the authors with many (...) previously unpublished in any language. Taken together, these thirty-two texts tell the story of binary as Leibniz conceived it, from his first youthful writings on the subject to the mature development and publication of the binary system. -/- As befits a scholarly edition, Strickland and Lewis have not only returned to Leibniz's original manuscripts in preparing their translations, but also provided full critical apparatus. In addition to extensive annotations, each text is accompanied by a detailed introductory “headnote” that explains the context and content. Additional mathematical commentaries offer readers deep dives into Leibniz's mathematical thinking. The texts are prefaced by a lengthy and detailed introductory essay, in which Strickland and Lewis trace Leibniz's development of binary, place it in its historical context, and chart its posthumous influence, most notably on shaping our own computer age. (shrink)

Offering an introduction to algorithms, this work considers automata in the context of their applications, NP-completeness, Turing machine notation and Chomsky normal form.

By theword problemfor some class of algebraic structures we mean the problem of determining, given a finite setEof equations between words and an additional equationx=y, whetherx=ymust hold in all structures satisfying each member ofE. In 1947 Post [P] showed the word problem for semigroups to be undecidable. This result was strengthened in 1950 by Turing, who showed the word problem to be undecidable forcancellation semigroups,i.e. semigroups satisfying thecancellation propertyNovikov [N] eventually showed the word problem for groups to be undecidable.In 1966 (...) Gurevich [G] showed the word problem to be undecidable forfinitesemigroups. However, this result on finite structures has not been extended to cancellation semigroups or groups; indeed it is easy to see that a finite cancellation semigroup is a group, so both questions are the same. We do not here settle the word problem for finite groups, but we do show that the word problem is undecidable for finite semigroups with zero satisfying an approximation to the cancellation property. (shrink)

A Krom formula of pure quantification theory is a formula in conjunctive normal form such that each conjunct is a disjunction of at most two atomic formulas or negations of atomic formulas. Every class of Krom formulas that is determined by the form of their quantifier prefixes and which is known to have an unsolvable decision problem for satisfiability is here shown to be a conservative reduction class. Therefore both the general satisfiability problem, and the problem of satisfiability in finite (...) models, can be effectively reduced from arbitrary formulas to Krom formulas of these several prefix types. (shrink)

This book taps the best American thinkers to answer the essential American question: How do we sustain our experiment in government of, by, and for the people? Authored by an extraordinary and politically diverse roster of public officials, scholars, and educators, these chapters describe our nation's civic education problem, assess its causes, offer an agenda for reform, and explain the high stakes at risk if we fail.

Philosophical discussions of gentrification have tended to focus on residential displacement. However, the prevalence of residential displacement is fiercely contested, with many urban geographers regarding it as quite uncommon. This lends some urgency to the underexplored question of how one should evaluate other forms of gentrification. In this paper, I argue that one of the most important harms suffered by victims of displacement gentrification is loss of access to the goods conferred by membership in a thriving local community. Leveraging the (...) social scientific literature, I go on to argue that non-displacement gentrification also often damages local communities. One can hence extend existing philosophical critiques of displacement gentrification to argue that non-displacement gentrification likewise poses a threat to relational equality, and often violates certain basic occupancy rights. Focusing on the value that inheres in thriving local communities also suggests some new possibilities for critiquing gentrification. For instance, existing occupancy rights critiques focus on incumbent land users’ interests in stability. However, one can also argue in a Lockean mode that incumbent land users’ occupancy rights are at least partially grounded in their community having laboured together to create objects of value. An extension of Michael Walzer’s theory of justice to incorporate community goods as a separate ‘sphere’ might also have widespread appeal. Taken together, these arguments constitute a sustained and theoretically ecumenical case for the pro tanto moral objectionability of gentrification. (shrink)

This paper defends the claim that mere temporal proximity always and without exception strengthens certain moral duties, including the duty to save – call this view Robust Temporalism. Although almost all other moral philosophers dismiss Robust Temporalism out of hand, I argue that it is prima facie intuitively plausible, and that it is analogous to a view about special obligations that many philosophers already accept. I also defend Robust Temporalism against several common objections, and I highlight its relevance to a (...) number of practical policy debates, including longtermism. My conclusion is that Robust Temporalism is a moral live option, that deserves to be taken much more seriously in the future. (shrink)

We might begin a search for the possibility of translation with a search for a common moral foundation for both the Eastasian world and the Western world. Answers come easily with a qualified yes or no; for example, we might make a list or table comparing how East and West think about adultery. This is unsatisfying; we ourselves are often unclear what we think and feel about these issues. So, a few of the more circumspect might ask where our own (...) sense of the moral arises. Perhaps we will seek the source of the OUGHT. Our friends from the Orient might ask us what these words moral or OUGHT mean. I do not think the West can as easily convey to the East what it means by sense of obligation as the West imparts technology. Try to translate our word obligation by the Japanese word giri; this translation is suspect since for the West, obligations are obligations only if they grate against the well ingrained inclinations of our being. The Kantian necessary test of authenticity of the true moral act will be if we act against the grain of our inclinations. (shrink)

Moral latitude is only ever a matter of coincidence on the most popular decision procedure in the literature on moral uncertainty. In all possible choice situations other than those in which two or more options happen to be tied for maximal expected choiceworthiness, Maximize Expected Choiceworthiness implies that only one possible option is uniquely appropriate. A better theory of appropriateness would be more sensitive to the decision maker’s credence in theories that endorse agent-centred prerogatives. In this paper, we will develop (...) and defend a modified version of this view that allows for agent-centred prerogatives and supererogation as part of its verdicts about appropriateness. (shrink)

The article examines one quodlibet of thomas of sutton (c. 1287 a. d.) and compares it with a quodlibet of william of ockham (d. 1349 a. d.). both attack the position of henry of ghent on the distinction between essence and existence. and both reach opposite conclusions. thomas of sutton argued that the distinction is a real one, while ockham saw it only as nominal and connotative. the opposing views stem from different epistemologies and different metaphysics.

Efficient causality -- Final causality -- Knowledge of the self and God -- The divine ideas -- The via moderna.

Nucleosomes are the basic elements of chromatin structure. Polyamines, such as spermine and spermidine, are small ubiquitous molecules absolutely required for cell growth. Photoaffinity polyamines bind to specific locations in nucleosomes and can change the helical twist of DNA in nucleosomes. Acetylation of polyamines reduces their affinity for DNA and nucleosomes, thus the helical twist of DNA in nucleosomes could be regulated by cells through acetylation. I suggest that histone and polyamine acetylation act synergistically to modulate chromatin structure. On naked (...) DNA, the photoaffinity spermine bound preferentially to a specific ‘TATA’ sequence element, suggesting that polyamines may be involved in the unusual chromatin structure in this region. Further work is needed to test whether the specificities shown by photoaffinity polyamines are also shown by cellular polyamines; such experiments are now feasible. (shrink)