We consider various classes of algebras obtained by expanding idempotent semirings with meet, residuals and Kleene-*. An investigation of congruence properties (e-permutability, e-regularity, congruence distributivity) is followed by a section on algebraic Gentzen systems for proving inequalities in idempotent semirings, in residuated lattices, and in (residuated) Kleene lattices (with cut). Finally we define (one-sorted) residuated Kleene lattices with tests to complement two-sorted Kleene algebras with tests.

It is shown that the Boolean center of complemented elements in a bounded integral residuated lattice characterizes direct decompositions. Generalizing both Boolean products and poset sums of residuated lattices, the concepts of poset product, Priestley product and Esakia product of algebras are defined and used to prove decomposition theorems for various ordered algebras. In particular, we show that FLw-algebras decompose as a poset product over any finite set of join irreducible strongly central elements, and that bounded n-potent GBL-algebras are represented (...) as Esakia products of simple n-potent MV-algebras. (shrink)

This is also where we begin investigating lattices of logics and varieties, rather than particular examples.

We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. (...) Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17]. (shrink)

For an infinite cardinal K a stronger version of K-distributivity for Boolean algebras, called k-partition completeness, is defined and investigated . It is shown that every k-partition complete Boolean algebra is K-weakly representable, and for strongly inaccessible K these concepts coincide. For regular K ≥ u, it is proved that an atomless K-partition complete Boolean algebra is an updirected union of basic K-tree algebras. Using K-partition completeness, the concept of γ-almost compactness is introduced for γ ≥ K. For strongly inaccessible (...) K we show that K is K-almost compact iff K is weakly compact, and if K is 2K-almost compact, then K is measurable. Further K is strongly compact iff it is γ-almost compact for all γ ≥ K. (shrink)

It is shown that Tarski’s set of ten axioms for the calculus of relations is independent in the sense that no axiom can be derived from the remaining axioms. It is also shown that by modifying one of Tarski’s axioms slightly, and in fact by replacing the right-hand distributive law for relative multiplication with its left-hand version, we arrive at an equivalent set of axioms which is redundant in the sense that one of the axioms, namely the second involution law, (...) is derivable from the other axioms. The set of remaining axioms is independent. Finally, it is shown that if both the left-hand and right-hand distributive laws for relative multiplication are included in the set of axioms, then two of Tarski’s other axioms become redundant, namely the second involution law and the distributive law for converse. The set of remaining axioms is independent and equivalent to Tarski’s axiom system. (shrink)

This reissue of his collection of early essays, Logico-Linguistic Papers, is published with a brand new introduction by Professor Strawson but, apart from minor ...

A complete system of classical Aristotelian logic intended for honors high school and college.

Ohne Rücksicht auf disziplinäre Schranken bringt dieses Buch verschiedene nicht-reduktionistische Lerntheorien miteinander ins Gespräch. In einem offenen Diskurs, der die Konzepte zueinander in Beziehung setzt, werden die unterschiedlichen Perspektiven kritisch abgewogen und hinsichtlich ihrer Stärken und Schwächen diskutiert.

Delo se loteva vprašanja aktualnosti pojma subjekta v filozofiji in politiki skozi analizo tistih avtorjev, ki so ga domnevno najbolj radikalno pokopali: pokaže, da vznik radikalno novega in problematika subjekta zavzema osrednje mesto v Deleuzovi filozofiji, kakor tudi v Lyotardovi pozni misli posvečeni praznini, v Foucaultovi obravnavi biopolitike in biooblasti, v delu Negrija in Hardta o Imperiju, ter nazadnje v Badioujevi predelavi temeljnih filozofskih kategorij biti, resnice in subjekta, na osnovi katerih je dandanes znova možna renesansa filozofije. Ta ima po (...) Badiouju štiri razsežnosti, ki se v delu Vznik subjekta nenehno prepletajo: »V osnovi želja filozofije implicira razsežnost upora: ni filozofije brez nezadovoljstva mišljenja v njegovem soočenju s svetom, kakršen je. Pa vendar želja filozofije vključuje tudi logiko: to je, prepričanje v moč argumenta in uma.«. (shrink)

The relationship of part to whole is one of the most fundamental there is; this is the first and only full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. 'Parts could easily be the standard book on mereology for the next (...) twenty or thirty years.' Timothy Williamson, Grazer Philosophische Studien. (shrink)

In this short but meaty book, Peter Unger questions the objective answers that have been given to central problems in philosophy. As Unger hypothesizes, many of these problems are unanswerable, including the problems of knowledge and scepticism, the problems of free will, and problems of causation and explanation. In each case, he argues, we arrive at one answer only relative to an assumption about the meaning of key terms, terms like "know" and like "cause," even while we arrive at (...) an opposite answer relative to quite different assumptions, but equally arbitrary assumptions, about what the key terms mean. (shrink)

Narrative thinking -- Narrative thinking about one's past -- Grief : a case study -- Narrative thinking about one's future -- Self-forgiveness : a case study -- The narrative sense of self -- Narrative, truth, life, and fiction.

While Hermann Levin Goldschmidt didn’t read Yiddish anarchists, there seems to have been a convergent evolution in their thinking. Goldschmidt’s looking up to Jewish lore as a source of liberating creativity is commonly encountered in Yiddish anarchist texts. His view of action as a constant response to internal and external challenges in the struggle for an open future is developed by Isaac Nachman Steinberg on the basis of nineteenth-century vitalism. Goldschmidt’s theory of anarchist individualism as willed self-limiting solidarity has a (...) compelling parallel in Hillel Solotaroff’s view of history. His use of impressionism and photography to eternalize the immediacy of human actuality is akin to Rudolf Rocker’s championing of decadent literature. In both cases, the goal of anarchism is not a dictatorship of the former downtrodden, but a continuous and contradictory evolution of freedom in ever-changing contexts. (shrink)

The Rudin-Keisler ordering of ultrafilters is extended to complete Boolean algebras and characterised in terms of elementary embeddings of Boolean ultrapowers. The result is applied to show that the Rudin-Keisler poset of some atomless complete Boolean algebras is nontrivial.

The norm of assertion, to be in force, is a social norm. What is the content of our social norm of assertion? Various linguistic arguments purport to show that to assert is to represent oneself as knowing. But to represent oneself as knowing does not entail that assertion is governed by a knowledge norm. At best these linguistic arguments provide indirect support for a knowledge norm. Furthermore, there are alternative, non-normative explanations for the linguistic data (as in recent work from (...) Van Elswyk). Direct arguments would rely on normative judgments about the permissibility or impermissibility of assertions with and without the speaker knowing the content asserted. John Turri's work experimental results purport to show that our norm of assertion is factive, and probably knowledge. But as a number of recent experimentalists (Kneer, Reuter and Broessel, Marsili and Wiegmann) have shown, Turri's results rely on the problemmatic use of 'should' as in 'Maria should assert that she owns a 1990 watch.' Correcting for this, these experimentalists provide strong evidence that our norm of assertion is not factive. The standard reply to evidence like this from the assertion of unlucky falsehoods is the excuse maneuver. But Marsili and Wiegmann, following Turri's protocol for testing for excuse validation, show that participants who judge that assertions unlucky falsehoods are permissible are not guilty of excuse validation. Given our current understanding of the experimental evidence, knowledge is not our norm of assertion. (shrink)

Metz holds that we can use African communal ethics to constitute global economic practices such as appropriation, production, distribution and consumption in such a way that promotes harmonious relations. In this article, I will show that Metz’s reformist approach to constituting the global economic practices is problematic as it fails to deal with the fundamental problem that pertains to a racialised world order that is structurally configured by coloniality of being. I will show that reformist approaches such as Metz’s use (...) of African communal ethics to constitute global economic practices in a way that promotes harmonious relations are undesirable attempts that are opposed and curtailed by a structural racialised logic/ontology of the world that governs and supervises the evolution of the world economic structures and practices in a way which undermines harmonious relations and in a way which causes economic marginalisation and impoverishment of historically disadvantaged indigenous Africans. (shrink)

Philosophy of music has flourished in the last thirty years, with great advances made in the understanding of the nature of music and its aesthetics. Peter Kivy has been at the center of this flourishing, and now offers his personal introduction to philosophy of music, a clear and lively explanation of how he sees the most important and interesting philosophical issues relating to music. Anyone interested in music will find this a stimulating introduction to some fascinating questions and ideas.

Abstractabstract:Karl Marx’s acerbic observation in the opening lines of The Eighteenth Brumaire that “all facts and personages of great importance in world history occur the first time as tragedy, the second as farce” may be profitably applied to a reconsideration of literary farce sui generis, a genre represented in this article by a long-neglected work of utopian fiction, Archibald Marshall’s Upsidonia (1915). Although Upsidonia’s current disregard is arguably undeserved, the article’s chief interest is not to reclaim the novel on aesthetic (...) grounds but to illuminate the mechanics of what Marx would call its “serious buffoonery.” In its persistent reversal of capitalist principles and relations, Upsidonia naturally invites readers to revisit Marx, whose mordant gambit may serve as a key to Marshall’s own farcical plot and praxis, rooted in return and repetition, the essential maneuvers of farce itself. (shrink)

This introduction by leading scholar Peter Trawny is the first to tackle the Black Notebooks, whose recent publication revealed the extent of Heidegger's anti-Semitism. Trawny directly confronts the most problematic aspects of Heidegger's thought, also fully surveying his work, from early writings to his magnum opus, Being and Time.

The so-called "Theology of Aristotle" is a translation of the Enneads of Plotinus, the most important representative of late ancient Platonism. It was produced in the 9th century CE within the circle of al-Kindī, one of the most important groups for the early reception of Greek thought in Arabic. In part because the "Theology" was erroneously transmitted under Aristotle's authorship, it became the single most important conduit by which Neoplatonism reached the Islamic world. It is referred to by such thinkers (...) as al-Fārābī, in an attempt to demonstrate the agreement between Platonism and Aristotelianism, Avicenna, who wrote a set of comments on the text, and later on thinkers of Safavid Persia including Mullā Ṣadrā. Yet the "Theology" is not just a translation. It may in fact more accurately be described as a creative paraphrase, which takes frequent liberties with the source text and even includes whole paragraphs' worth of new material. Adamson's book offers a philosophical interpretation of the changes introduced in the Arabic version. It is argued that these changes were in part intended to show the relevance of Plotinus' thought for contemporary Islamic culture, for instance by connecting the Neoplatonist theory of the First Principle to theological disputes within Islam over the status of God's attributes. At the same time the paraphrase reflects a tendency to harmonize the various strands of Greek thought, so that a critique by Plotinus of Aristotle's theory of the soul is subtly changed into a defense of Aristotle's theory against a possible misinterpretation. The upshot, or so Adamson argues, is that the "Theology" needs to be read as an original philosophical work in its own right, and understood within the context of the ʿAbbāsid era. (shrink)

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs (...) of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification. (shrink)

Morality and economic rationality: integrative economic ethics as the rational ethics of economic activity; Part II. Reflections on the Foundations of Economic ...

Peter Anstey presents a thorough and innovative study of John Locke's views on the method and content of natural philosophy. Focusing on Locke's Essay concerning Human Understanding, but also drawing extensively from his other writings and manuscript remains, Anstey argues that Locke was an advocate of the Experimental Philosophy: the new approach to natural philosophy championed by Robert Boyle and the early Royal Society who were opposed to speculative philosophy. On the question of method, Anstey shows how Locke's pessimism (...) about the prospects for a demonstrative science of nature led him, in the Essay, to promote Francis Bacon's method of natural history, and to downplay the value of hypotheses and analogical reasoning in science. But, according to Anstey, Locke never abandoned the ideal of a demonstrative natural philosophy, for he believed that if we could discover the primary qualities of the tiny corpuscles that constitute material bodies, we could then establish a kind of corpuscular metric that would allow us a genuine science of nature. It was only after the publication of the Essay, however, that Locke came to realize that Newton's Principia provided a model for the role of demonstrative reasoning in science based on principles established upon observation, and this led him to make significant revisions to his views in the 1690s. On the content of Locke's natural philosophy, it is argued that even though Locke adhered to the Experimental Philosophy, he was not averse to speculation about the corpuscular nature of matter. Anstey takes us into new terrain and new interpretations of Locke's thought in his explorations of his mercurialist transmutational chymistry, his theory of generation by seminal principles, and his conventionalism about species. (shrink)

A historical investigation of the exclusion of Africa and Asia from modern histories of philosophy.

Paulo Freire : the educator, his oeuvre, and changing contexts -- Holistic interpretations of Freire's work : a critical review -- Critical literacy, praxis, and emancipatory politics -- "Remaining on the same side of the river" : neo-liberalism, party movements, and the struggle for greater coherence -- Reinventing Freire in a Southern context : the Mediterranean -- Engaging with practice : a Freirean reflection on different pedagogical sites.

What is ethics? Where do moral standards come from? Are they based on emotions, reason, or some innate sense of right and wrong? For many scientists, the key lies entirely in biology---especially in Darwinian theories of evolution and self-preservation. But if evolution is a struggle for survival, why are we still capable of altruism? In his classic study The Expanding Circle, Peter Singer argues that altruism began as a genetically based drive to protect one's kin and community members but (...) has developed into a consciously chosen ethic with an expanding circle of moral concern. Drawing on philosophy and evolutionary psychology, he demonstrates that human ethics cannot be explained by biology alone. Rather, it is our capacity for reasoning that makes moral progress possible. In a new afterword, Singer takes stock of his argument in light or recent research on the evolution of morality.--Publisher's description. (shrink)

Children from various countries have been acknowledged and studied for their ability to philosophize, while, unfortunately, Filipino children have not received similar recognition. In this paper, I make a rather unpopular claim that Filipino children can and already are doing philosophy in their efforts to make sense of their existential conditions. “Doing philosophy” here refers to the act of being perplexed by one's own or other people's experiences and making an effort to comprehend them. Filipino children, are a vast and (...) diverse group, coming from various backgrounds, speaking different or even multiple languages, and representing rich cultures and unique circumstances. This diversity adds richness to the wide array of experiences from which existential questions can emerge. However, to truly comprehend the philosophical thinking of Filipino children, they need opportunities and guidance to explore their existential questions and solutions, regardless of how tentative or rudimentary these may seem to adults. Without such opportunities, it remains unclear to what extent their thinking engages with philosophical themes and issues. This not only offers Filipino adults a view of children’s inner worlds but also brings fresh perspectives to commonly held assumptions. (shrink)

"Divination and Human Nature" casts a new perspective on the rich tradition of ancient divination--the reading of divine signs in oracles, omens, and dreams. Popular attitudes during classical antiquity saw these readings as signs from the gods while modern scholars have treated such beliefs as primitive superstitions. In this book, Peter Struck reveals instead that such phenomena provoked an entirely different accounting from the ancient philosophers. These philosophers produced subtle studies into what was an odd but observable fact--that humans (...) could sometimes have uncanny insights--and their work signifies an early chapter in the cognitive history of intuition. Examining the writings of Plato, Aristotle, the Stoics, and the Neoplatonists, Struck demonstrates that they all observed how, setting aside the charlatans and swindlers, some people had premonitions defying the typical bounds of rationality. Given the wide differences among these ancient thinkers, Struck notes that they converged on seeing this surplus insight as an artifact of human nature, projections produced under specific conditions by our physiology. For the philosophers, such unexplained insights invited a speculative search for an alternative and more naturalistic system of cognition. Recovering a lost piece of an ancient tradition, "Divination and Human Nature" illustrates how philosophers of the classical era interpreted the phenomena of divination as a practice closer to intuition and instinct than magic. (shrink)

Von Peter Sloterdijk kann man zu Recht sagen, daß jeder seiner Aufsätze, jeder seiner Vorträge auch ein ungeschriebenes Buch ist.

The relationship of part to whole is one of the most fundamental there is, yet until now there has been no full-length study of this concept. This book shows that mereology, the formal theory of part and whole, is essential to ontology. Peter Simons surveys and criticizes previous theories, especially the standard extensional view, and proposes a more adequate account which encompasses both temporal and modal considerations in detail. This has far-reaching consequences for our understanding of such classical philosophical (...) concepts as identity, individual, class, substance and accident, matter, form, essence, dependence, and integral whole. It also enables the author to offer new solutions to long-standing problems surrounding these concepts, such as the Ship of Theseus Problem and the issue of mereological essentialism. The author shows by his use of formal techniques that classical philosophical problems are amenable to rigorous treatment, and the book represents a synthesis of issues and methods from the analytical tradition and from the older continental realist tradition of Brentano and the early Husserl. (shrink)

Peter S. Fosl offers a radical interpretation of Hume as a thoroughgoing sceptic on epistemological, metaphysical and doxastic grounds. He first contextualises Hume's thought in the sceptical tradition and goes on to interpret the conceptual apparatus of his work - including the Treatise, Enquiries, Essays, History, Dialogues and letters.

Timothy Williamson has argued that in the debate on modal ontology, the familiar distinction between actualism and possibilism should be replaced by a distinction between positions he calls contingentism and necessitism. He has also argued in favor of necessitism, using results on quantified modal logic with plurally interpreted second-order quantifiers showing that necessitists can draw distinctions contingentists cannot draw. Some of these results are similar to well-known results on the relative expressivity of quantified modal logics with so-called inner and outer (...) quantifiers. The present paper deals with these issues in the context of quantified modal logics with generalized quantifiers. Its main aim is to establish two results for such a logic: Firstly, contingentists can draw the distinctions necessitists can draw if and only if the logic with inner quantifiers is at least as expressive as the logic with outer quantifiers, and necessitists can draw the distinctions contingentists can draw if and only if the logic with outer quantifiers is at least as expressive as the logic with inner quantifiers. Secondly, the former two items are the case if and only if all of the generalized quantifiers are first-order definable, and the latter two items are the case if and only if first-order logic with these generalized quantifiers relativizes. (shrink)

Since its original publication in 1975, this groundbreaking work has awakened millions of people to the existence of "speciesism"—our systematic disregard of nonhuman animals—inspiring a worldwide movement to transform our attitudes to animals and eliminate the cruelty we inflict on them. In Animal Liberation, author Peter Singer exposes the chilling realities of today’s "factory farms" and product-testing procedures—destroying the spurious justifications behind them, and offering alternatives to what has become a profound environmental and social as well as moral issue. (...) An important and persuasive appeal to conscience, fairness, decency, and justice, it is essential reading for the supporter and the skeptic alike. (shrink)

Do we think in natural language? Or is language only for communication? Much recent work in philosophy and cognitive science assumes the latter. In contrast, Peter Carruthers argues that much of human conscious thinking is conducted in the medium of natural language sentences. However, this does not commit him to any sort of Whorfian linguistic relativism, and the view is developed within a framework that is broadly nativist and modularist. His study will be essential reading for all those interested (...) in the nature and significance of natural language, whether they come from philosophy, psychology or linguistics. (shrink)

This text provides a unique and compelling account of Wittgenstein's impact upon twentieth century analytic philosophy, from its inception at the turn of the ...

In recent years, interest in desert-based theories of justice has increased, and this seems to represent a challenge to equality-based theories of justice.[i] The best distribution of outcomeadvantage with respect to desert, after all, need not be the most equal distribution of outcomeadvantage. Some individuals may deserve more than others. Outcome egalitarianism is, however, implausible, and so the conflict of outcome desert with outcome equality is of little significance.[ii] Most contemporary versions of egalitarianism are concerned with neutralizing the differential effects (...) of brute luck and not with equality of outcome. I shall argue that, in order to be plausible, a desert-based theory of justice can and must be compatible with this form of egalitarianism. There is, however, a stronger form of brute luck egalitarianism, which, as I shall explain, is concerned with equalizing the advantages from brute luck—and not merely with neutralizing the differential effects thereof. Under idealized conditions in which agents have perfect information about the outcomes that their choices generate, even this stronger form of egalitarianism, I shall show, is compatible with pure desert theory. Under conditions of incomplete information, however, strong brute luck egalitarianism is incompatible with a pure desert theory that appeals, as I shall explain, to moral, rather than prudential, desert. (shrink)

First published in 1987. Routledge is an imprint of Taylor & Francis, an informa company.

"How do we go about weighing evidence, testing hypotheses and making inferences? According to the model of 'inference to the Best explanation', we work out what to inter from the evidence by thinking about what would actually explain that evidence, and we take the ability of a hypothesis to explain the evidence as a sign that the hypothesis is correct. In inference to the Best Explanation, Peter Lipton gives this important and influential idea the development and assessment it deserves." (...) "The second edition has been substantially enlarged and reworked, with a new chapter on the relationship between explanation and Bayesianism, and an extension and defence of the account of contractive explanation. It also includes an expanded defence of the claims that our inferences really are guided by diverse explanatory considerations, and that this pattern of inference can take us towards the truth. This edition of Inference to the Best Explanation has also been updated throughout and incudes a new bibliography."--BOOK JACKET. (shrink)