A structure A = (A; E₀, E₁ , . . . , ${E_{n - 2}}$) is an n-grid if each E i is an equivalence relation on A and whenver X and Y are equivalence classes of, repectively, distinct E i and E j , then X ∩ Y is finite. A coloring χ : A → n is acceptable if whenver X is an equivalence class of E i , then {ϰ Є X: χ(ϰ) = i} is finite. If (...) B is any set, then the n-cube B n = (B n ; E₀ E₁ , . . . , ${E_{n - 2}}$) is considinate axis. Kuratowski [9], generalizing the n = 3 case proved by Sierpiński [17], proved that ℝ n has an acceptable coloring iff ${2^{{N_0}}}$ ≤ ${N_{n - 2}}$. The main result is: of A is a semialgebraic (i.e., first-order definable in the field of reals) n-grid, then the following are equivalent: (1) if A embeds all finite n-cubes, then ${2^{{N_0}}}$ ≤ ${N_{n - 2}}$; if A embeds ℝ n , then ${2^{{N_0}}}$ ≤ ${N_{n - 2}}$; (3) A has an acceptable coloring. (shrink)

An apparent paradox is obtained in all previous treatments of the Trouton–Noble experiment; there is a three-dimensional (3D) torque T in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque T′ in S′, the rest frame of the capacitor. Different explanations are offered for the existence of another 3D torque, which is equal in magnitude but of opposite direction giving that the total 3D torque is zero. In this paper, it is (...) considered that 4D geometric quantities and not the usual 3D quantities are well-defined both theoretically and experimentally in the 4D spacetime. In analogy with the decomposition of the electromagnetic field F (bivector) into two 1-vectors E and B we introduce decomposition of the 4D torque N (bivector) into 1-vectors N s , N t . It is shown that in the frame of “fiducial” observers, in which the observers who measure N s and N t are at rest, and in the standard basis, only the spatial components $N_{s}^{i}$ and $N_{t}^{i}$ remain, which can be associated with components of two 3D torques T and T t . In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in complete agreement with the principle of relativity and with the Trouton–Noble experiment without the introduction of any additional torque. (shrink)

We give examples of (i) a simple theory with a formula (with parameters) which does not fork over [Formula: see text] but has [Formula: see text]-measure 0 for every automorphism invariant Keisler measure [Formula: see text] and (ii) a definable group [Formula: see text] in a simple theory such that [Formula: see text] is not definably amenable, i.e. there is no translation invariant Keisler measure on [Formula: see text]. We also discuss paradoxical decompositions both in the setting of discrete (...) groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups. (shrink)

Consider the regularity thesis that each possible event has non-zero probability. Hájek challenges this in two ways: there can be nonmeasurable events that have no probability at all and on a large enough sample space, some probabilities will have to be zero. But arguments for the existence of nonmeasurable events depend on the axiom of choice. We shall show that the existence of anything like regular probabilities is by itself enough to imply a weak version of AC sufficient to prove (...) the Banach–Tarski Paradox on the decomposition of a ball into two equally sized balls, and hence to show the existence of nonmeasurable events. This provides a powerful argument against unrestricted orthodox Bayesianism that works even without AC. A corollary of our formal result is that if every partial order extends to a total preorder while maintaining strict comparisons, then the Banach–Tarski Paradox holds. This yields an argument that incommensurability cannot be avoided in ambitious versions of decision theory. (shrink)

In this paper we present definitions of different four-dimensional (4D) geometric quantities (Clifford multivectors). New decompositions of the torque N and the angular momentum M (bivectors) into 1-vectors Ns, Nt and Ms, Mt, respectively, are given. The torques Ns, Nt (the angular momentums Ms, Mt), taken together, contain the same physical information as the bivector N (the bivector M). The usual approaches that deal with the 3D quantities $\varvec{E,\,B,\,F,\,L,\,N}$ etc. and their transformations are objected from the viewpoint of the invariant (...) special relativity (ISR). In the ISR, it is considered that 4D geometric quantities are well-defined both theoretically and experimentally in the 4D spacetime. This is not the case with the usual 3D quantities. It is shown that there is no apparent electrodynamic paradox with the torque, and that the principle of relativity is naturally satisfied, when the 4D geometric quantities are used instead of the 3D quantities. (shrink)

Hausdorff's paradoxical decomposition of a sphere with countably many points removed actually produced a partition of this set into three pieces A,B,C such that A is congruent to B, B is congruent to C, and A is congruent to B ∪ C. While refining the Banach–Tarski paradox, R. Robinson characterized the systems of congruences like this which could be realized by partitions of the sphere with rotations witnessing the congruences: the only nontrivial restriction is that the system should (...) not require any set to be congruent to its complement. Later, J. F. Adams showed that this restriction can be removed if one allows arbitrary isometries of the sphere to witness the congruences. The purpose of this paper is to characterize those systems of congruences which can be satisfied by partitions of the sphere or related spaces into sets with the property of Baire. A paper of Dougherty and Foreman gives a proof that the Banach–Tarski paradox can be achieved using such sets, and gives versions of this result using open sets and related results about partitions of spaces into congruent sets. The same method is used here; it turns out that only one additional restriction on a system of congruences is needed to make it solvable using subsets of the sphere with the property of Baire with free rotations witnessing the congruences. Actually, the result applies to any complete metric space acted on in a sufficiently free way by a free group of homeomorphisms. We also characterize the systems solvable on the sphere using sets with the property of Baire but allowing all isometries. (shrink)

Alfred Tarski was one of the greatest logicians of the twentieth century. His influence comes not merely through his own work but from the legion of students who pursued his projects, both in Poland and Berkeley. This chapter focuses on three key areas of Tarski's research, beginning with his groundbreaking studies of the concept of truth. Tarski's work led to the creation of the area of mathematical logic known as model theory and prefigured semantic approaches in the philosophy of language (...) and philosophical logic, such as Kripke's possible worlds semantics for modal logic. We also examine the paradoxical decomposition of the sphere known as the Banach–Tarski paradox. Finally we examine Tarski's work on decidable and undecidable theories, which he carried out in collaboration with students such as Mostowski, Presburger, Robinson and others. (shrink)

We explore a general method based on trees of elementary submodels in order to present highly simplified proofs to numerous results in infinite combinatorics. While countable elementary submodels have been employed in such settings already, we significantly broaden this framework by developing the corresponding technique for countably closed models of size continuum. The applications range from various theorems on paradoxical decompositions of the plane, to coloring sparse set systems, results on graph chromatic number and constructions from point-set topology. Our (...) main purpose is to demonstrate the ease and wide applicability of this method in a form accessible to anyone with a basic background in set theory and logic. (shrink)

Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid three-dimensional objects, (iii) in the theory of effective computability (Church-Turing thesis) related to the possible “solution of supertasks,” and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for physical applications are (...) discussed: Canlorian “naive” (i.e., nonaxiomatic) set theory, contructivism, and operationalism. In the author's opinion, an attitude of “suspended attention” (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same time, physicists should be open to “bizarre” or “mindboggling” new formalisms, which need not be operationalizable or testable at the lime of their creation, but which may successfully lead to novel fields of phenomenology and technology. (shrink)

This article investigates the paradoxical nature of cameraless photography. Born after the invention of early photography, the camera apparatus is clearly a precondition of the idea and practice of cameraless photography (photography made without a camera). Yet, at the same time, cameraless photography is situated as a form of pure photography, giving rise to the idea that the spirit of photography lies somewhere beyond the mediation of the camera. This article approaches the paradoxical nature of cameraless photography in (...) an indirect manner by considering the spectrality of photography: from conceptions of early photography as itself spectral, to the manifestation of spectres in spirit photography, to the decomposition of the spectres by X-rays and radioactivity. Cameraless photography plays a twofold role in this genealogy of photographic spectres: first, it goes against a certain understanding of the spirit of photography as conditioned by the manipulating force of the camera apparatus; second, it proves the existence of spectres by uncovering the ontological convulsions of the world. (shrink)

The book reconstructs the history of Western ethics. The approach chosen focuses the endless dialectic of moral codes, or different kinds of ethos, moral doctrines that are preached in order to bring about a reform of existing ethos, and ethical theories that have taken shape in the context of controversies about the ethos and moral doctrines as means of justifying or reforming moral doctrines. Such dialectic is what is meant here by the phrase ‘moral traditions’, taken as a name for (...) threads of moral discourse, made in turn of other interwoven threads, including transmission of shared codes, appeals to reform of prevailing custom, rational argument about the justification of some precept on the basis of some shared general teaching or principle, and rational argument about the ultimate basis for principles and justification of authoritative teaching. That is, the approach adopted to the reading of ethical texts depends on a firm belief in the fact that philosophers hardly created any ethical doctrine out of nothing. The main point this book tries to highlight is how different philosophical theories emerged and followed each other as a result of attempts at accounting for what was going on in the world of moral traditions. Changes were propelled by controversies between different schools, and highly abstract arguments were the unintended effects of moves made by controversialists forced to transform (and occasionally to turn upside down) their own doctrines in order to face the challenge posed by other arguments. This is the reason why the book examines not only texts that already enjoy pride of place in the history of philosophy (Aristotle, Kant, Hegel), but also other texts usually treated in the histories of religions (the Bible, the Talmud, the Quran), and others considered to be much less philosophical (Plutarchus, Pufendorf). -/- 1. Plato and a response to ethical scepticism. Two different traditions of morality in VI-V century Greece are described. The birth of philosophical questioning of traditional morality and temporal and spatial variation of custom is described within the context of the v century crisis, the demise of traditional aristocratic and tyrannical rule and the birth of democracy. Two conflicting answers to the challenge are reconstructed, namely conventionalist or immoralist theories formulated by the Sophists and the eudemonist and intellectualist Socratic theory. Plato’s own reformulation of Socrates answer to the Sophists is reconstructed. His psychological views, his classification of the four cardinal virtues and his political theory are described as parts of a unitary system, culminating in an extremely realist moral ontology identifying the idea of the good with the essence of the (moral and extra-moral) world itself. -/- 2. Aristotle and the invention of practical philosophy. Aristotle’s invention of practical philosophy as a field separated from first philosophy is shown to be an implication of his break with Plato moral ultra-realism. Aristotle’s agenda in his moral works is arguably dependent on a polemical intention, namely dismantling Socratic intellectualism. The semi-inductive or virtuously circular method of practical philosophy is illustrated, starting with the received opinions of the better and wiser individuals and trying dialectically to sift what is left of mistake and inconsistence in such opinions, finally trying to correct mistakes and make the overall practical science more consistent. The chapter illustrates then the relationship of individual ethics, or ‘monastics’, with the art and the science of the pater familias, or ‘economics’, and the science of the ruler and citizen, or politics. The nature of virtues, or better, excellences of character, is discussed, highlighting the basic role of hexis, or ‘disposition’. Prudence, or better practical wisdom, is the focus of the chapter. Its relationship with bouleusis or deliberation is examined, and its autonomous status vis-à-vis theoretical knowledge is stressed. -/- 3. Diogenes and philosophy as a way of life. The chapter provides an overview of Hellenistic ethics, which almost amounts to Hellenistic schools of philosophy, in so far as ‘philosophy’ became in these centuries primarily the name for a way of life. The typical character of the Cynical movement is highlighted, that of a school of life, not a school aimed at providing any kind of intellectual training was to be provided. -/- 4. Epicurus and ethics as self-care. The peculiar character of the Epicurean school is described, a combination of a science of well-being aiming, more than at pleasure as in the popular view, at reduction of useless suffering, of unnecessary needs, and at a balanced selection of pleasures of the best and most durable kind. -/- 5. Epictetus and ethics as therapy of the passions. The various phases of Stoicism are described, and the shifting place given to ethics in the Stoic system of idea, culminating in the paradoxical view of ethics, its impossibility in principle notwithstanding, as the only truly significant and necessary part of philosophy. Cicero is treated, showing how his own synthesis of various Hellenistic trends is as a truly philosophical enterprise, deserving serious consideration after one or two centuries when he was confined to the role of literate. Epictetus is chosen as the best example of what the Stoic tradition could yield, an art of living based on sophisticated introspection, in turn aimed at making a kind of cognitive therapy possible, dismantling obnoxious passions at their root by systematically correcting false representations. -/- 6. Philo and the reconciliation of Torah and Platonism. A reconstruction of basic ideas from a few books of the Hebrew Bible is provided, starting with the Prophetic tradition and the focus on God’s mercy as the source of motivation and standard for human behaviour. Then a comparative analysis is undertaken of a parallel tradition, namely the three codifications of the Torā (Law or, better, Instruction), highlighting how a core of moral ideas may be recognized as a basis and preamble of codification of civil law, cultural practice, and regulation of ritual purity. The importance of Leviticus is stressed as the turning point when emphasis mercy, typical of the Prophetic tradition, is combined with the legal tradition, yielding the change in sensibility of the Second Temple time. Philo of Alexandria is described as one of the three leading figures – together with Rabbi Hillel and Rabbi Yeshua – at the apex the emergence of the mentioned new sensibility, gradually including mercy as an essential part of justice and establishing the starting point of both the Rabbinic and the Christian tradition. This consists precisely in the precept of one’s neighbour’s love or of the golden rule, two eventually identical precepts whose meaning is arguably more sober and sensible than the long-lasting Christian tradition deriving from John and Augustine has made us believe and no novelty vis-à-vis so-called Ancient-Testament teachings. -/- 7. Augustine and Christianity as Neo-Platonism. The first section examines the moral doctrines of so-called 'ethical Treaties' from the Talmud, a group of treaties, among which the best known is Pirqé Avot, that were left out of the six "orders" of the canon as they did not fit in any of the six groups of issues ritual or legal on which the division was based. According to Maimonides, their peculiar theme is provided by the Deòt, 'opinions', i.e., mental dispositions, that is, the translation of the Greek term hexeis and Arab akhlak (in turn providing in this language the name for ethics as such). The three topics I reconstruct are: i) the notion of Torah: The Torah is understood as the world order itself, or as the ‘Wisdom’ that existed even before creation and was ‘the tool by which the world was built’; however, the Torah is an earthly and human entity, as it was "received" by humans, and from that very moment belongs to them; ii) the relationship between love of God and love of neighbour; the treaties require us to study and practice the Torah ‘for its own sake’, that is, require us to act out of love, not out of fear or hope of reward; iii) the idea of sanctification of daily life: having disappeared with the destruction of the Temple the possibility of any conflict between liturgical service and everyday life, the latter is assumed to be in itself divine service: to give food to the poor has the same value as sacrifices in the Temple, and as an implication, the insistence become recurrent on the goodness of created things in themselves along with a polemic against ascetic currents. The conclusions drawn are: i) the moral teachings of the Talmud and those of Yeshua are, rather than similar, virtually identical; one may safely say that the precept of love and the golden rule are central ones for all Talmudic rabbis, that mercy plays an indispensable role alongside with justice, and the latter is not a different thing from one’s neighbour’s love; ii) a peculiarity of Talmud rabbis facing Yeshua is the idea of study as worship, and knowledge as a source of justice; but this is an idea of Judaism after the Temple's destruction that cannot be attributed to the Pharisees of Yeshua’s time; iii) the relation of study and practice in the Talmud parallels that between faith and deeds in Paul's epistles, that is, respectively faith or learning are a necessary and sufficient condition to be recognized as righteous , but deeds are the inevitable effect of either faith or learning. The sayings ascribed to Yeshua are examined first, yielding the conclusion that a close equivalent may be found for every saying in Talmudic literature and yet the whole is ascribed to one rabbi, with rather consistent stress on God’s mercy and unconditional forgiving as the mark of true imitation of God. Thus, Yeshua’s teaching is pure Judaism. The third section describes briefly the galaxy of Gnostic currents and Manichaeism, trying to sketch the profile of moral teachings resulting from an encounter of Asian spiritual traditions, Hellenistic lore and sparks of teachings from apocalyptic Jewish currents. The last section summarizes the turbulent history of several encounters between Christian currents and Hellenistic philosophical schools. The first one was with late Cynicism. Recent, rather controversial, literature discovered the jargon and a few topics from the Stoic-Cynical popular philosophy in a few books from the New Testament itself. This, far from proving that Rabbi Yeshua had been influenced by cynic preachers, is a proof of the necessity felt by Christian preachers to translate the original ‘Christian’ teaching into a Greek lexicon deeply impregnated with cynic terminology. The second was with Platonism, yielding the mild and temperate moral teaching of Clemens of Alexandria, teaching the sanctity of nature and the human body, the joy of moderate fruition of ‘natural’ kinds of pleasures, and the beauty of the marital life – in short, the opposite of the standard picture of Medieval Christianity. Ambrose of Milan brings about a different kind of synthesis, namely with Middle Platonism, where Stoic themes prevail. The most shocking case is Augustine, where an early Manichean education is overcome in a former phase by a synthesis of Plotinian Neo-Platonism and Christian preaching, yielding a sustained polemic with the Manicheans and rather optimistic views on life and Creation, the body and sexuality, and Hebrew-Judaic tradition not far from Clemens of Alexandria. In a later phase, occasioned by controversy on the opposite front, with such Christian currents as the Pelagians and Donatists, Augustine comes back to heavily anti-Judaic and world-denying ascetic attitudes where is earlier Manichean upbringing seems to emerge again. The tragedy of medieval Christianity will be the later Augustine’s overwhelming influence. A final section is dedicated to the monastic tradition where a curious mixture of world-denying asceticism with an astonishingly penetrating ‘science’ of introspection emerges. -/- 8. Al Farabi and the reconciliation of Islam and Platonism. The Qurān and the qadit, that is, collections of sayings ascribed to the prophet Muhammad contain a wealth of precepts and catalogues of virtues mirroring moral contents from the Jewish and the Christian traditions, among them the basic notion of imitation of the Deity, where mercy is assumed to be its basic trait. An important tradition within Islam, namely Sufism, stressed to the utmost degree the role of mercy, turning Islam into a mystic doctrine centred on retreat from the world, abandonment to God’s will, and a peaceful and fraternal attitude to our fellow-beings. A secular literary tradition originating in the Sassanid Empire, the literature of advice to the Prince had for a time a widespread influence in the newly constituted Arabic-Islamic commonwealth. In a later phase, the legacy of Hellenic philosophy made its way into the intellectual elite of the Islamic world. The first important legacy was Platonic, and the Republic became the main text for Islamic Platonism. Al-Farabi wrote an enjoyable remake of the Platonic Republic, arguing that the citizen’s virtues were the basis on which the political building needs to rest. The secular lawgiver is enlightened by the light of reason in his everyday practice of governance, but room is made for the Prophet as the voice of revealed truth that confirms and completes the rational truth that philosophy may afford. In a second phase also Aristotelian and Stoic influence were assimilated. Miskawayh’s treatise was the masterwork at the time Arabic philosophy reached its Zenith. It is a treatment of the soul’s diseases and their remedies, combining the Aristotelian doctrine of the golden mean with the Stoic doctrine of the passions and elements of Galenic medicine. Towards the eleventh-twelve centuries a war raged among theologians and philosophers, finally won by the former with disappearance of philosophy as such. The newly established mainstream, yet, was no kind of intolerant fanaticism. It drew from the work of mystic theologian Al-Ghazālī, the best heir of Sufism, teaching a tolerant and peaceful attitude to our fellow-beings and a passive attitude to destiny as an expression of the Divine will. -/- 9. Moshe ben Maimon and the reconciliation of Torah and Aristotelian ethics. The encounter between the Talmudic tradition and Hellenic philosophy had taken place a first time in Alexandria at the time of Philo but the two traditions had parted way again. In fact, the kind of Platonic Judaism founded by Philo survived only within Christianity, in the fourth Gospel and then in writings by Clemens of Alexandria. The Talmudic literature had absorbed just less striking traits from the Hellenic Philosophy, namely an idea of ethics as care of the self and a role for the education of character as propaedeutic to theoretical knowledge. In the Arabic-Islamic world, a second round started when Jewish authors writing in Arabic undertook the task to prove the full compatibility of the tradition deriving from Torah and Platonic philosophy. The culmination of this attempt is provided by Moshe ben Maimon who tried to use Aristotelian ethics as a language into which the teaching from the Pirké Avot could be translated. -/- 10. Thomas Aquinas and the reconciliation of Christian morality and Aristotelian ethics. In the first section the fresh start is described of philosophical ethics in Latin Europe at the turn of the Millennium. In a first phase, Anselm and Peter Abelard built on a Platonic and Augustinian legacy. In this phase. remarkable innovations are introduced, including Abelard’s claim of the obliging character of erring consciousness. In a second phase, the rediscovery of Nicomachean Ethics thanks to Latin translation of Arabic versions gives birth to a new wave of ethical studies, recovering the very idea of Aristotelian practical philosophy, with the potential implication of full legitimization of natural morality, i.e. ethics without Revelation. Aquinas’s ethics is a theological ethics out of which it would be vain to try to extract a self-contained philosophical ethics. His treatment of topics in philosophical ethics, yet, does not boil down to repetition of Aristotelian arguments but is rather a creative reshaping of such arguments. For example, he introduces also in the practical philosophy a first principle parallel to the principle of non-contradiction; and he also carries out a synthesis of Aristotelianism, Stoicism, and neo-Platonism. Even though it is essentially moral theology, Aquinas’s doctrine - unlike Augustine – grants full citizenship to "natural" morality, firstly by rejecting the claim that the corruption of human nature due to the original sin is so radical as to leave "pure nature" incapable of moral goodness. The doctrine is presented in a more sophisticated formulation in a few of the Quaestiones, such as De Malo and De Veritate, in the Summa contra Gentes and in the commentaries to Aristotle than in the famous Summa Theologica, but the latter work includes the only or the largest exposition of some decisive part of the theory. Thus, the Summa Theologica should be read for what it is more than criticized for not being what it was not meant to be. It was not meant to be the brilliant synthesis of all that Reason he had been able to produce with what Revelation had added about which the Neo-Thomists used to dream, but rather a manual for the training of preachers and confessors, where theoretical claims are not too demanding and a few serious tensions are left. Besides a jump between the Prima Secundae and the Secunda Secundae, being the former an essay in virtue theory and the latter a handbook for confessors, the most serious tension is perhaps the one between the ethics of right reason presented in most of Ia-IIae and the eudemonistic ethics developed in quaestiones 1-5 of the same part; the alternative ethical theory which also may be found in Augustine, the Stoic view of a cosmic reason eventually coincident with the moral law, was believed by Anselm (followed by John Duns Scotus and William of Ockham) to be incompatible with eudemonism. It is questionable whether Thomas could reduce the tension proving that it is just an apparent tension, in so far as the right reason and bliss derived from knowledge of God tend to coincide, but this is just a conjecture. Thomas’s ethics is a virtue ethic, not a law-based one, and moral judgment focuses on the virtues, particularly charity, not on the commandments and even less on absolute prohibitions; Thomas, however, would not have considered a drastic alternative between law and the virtues such as the one which has been advanced in late twentieth-century philosophy to be justified. Nonetheless, when it discusses ‘special’ virtues, it ceases to be an ethics of virtue and becomes a disappointing and often contradictory discussion of legal and illegal acts. Such a discussion takes most of the time ‘reasonable’ middle positions on controversial issues but not the alternative approach that Aristotelianism would have made possible; even when some occasional Aristotelian claim shows up, such as money’s barrenness as a reason against usury, this seems to be made by an author who apparently ignores the Aristotelian Thomas of the Prima Secundae. It is an ethic of human autonomy which recognizes the binding character of the individual conscience and, potentially, even a duty to disobey unjust laws. It is true that what Thomas writes in his discussion of death penalty and persecution of heretics is simply disgusting, and yet we should blame Thomas the man, not Thomist ethical theory. Finally, Thomas’s ethics is not ethical ‘absolutism’, as both traditionalist Catholic theologians and secularist enemies of dogmatic morality tend to believe. It is instead an ethic of prudential judgment. Exceptions to this approach – or better results of logical fallacies – are such claims as the absolute character of negative precepts and of the existence of "intrinsically evil acts", claims that simply cease to make sense in the light of Thomas’s own distinction between human act and natural act, carrying consequences Thomas did not live long enough to draw or was not consistent enough to dare to draw. -/- 11. Francisco de Vitoria and casuistry. The first topic illustrated is the discussion about the notion of pura natura, namely the human condition after the original sin and before divine revelation. The core notion was already there in Aquinas but was later developed by Caietanus (Thomas de Vio) with a number of interesting implications: firstly a view of human nature as such much more positive than Augustine’s and his followers’ view, including both Calvinists and Jansenists; secondly, the implication that the philosopher’s morality, as opposed to the Christian’s morality, is a quite respectable kind of morality; thirdly, that theocracy and prosecution of the unfaithful lacked justification, with more far-fetching consequences than Aquinas himself had dared to draw. The second topic is casuistry, a new name for a comparatively older way of thinking, which was already there in late Stoicism and Cicero as well as in the Talmudic literature. This is an approach aimed at yielding probable enough solutions for doubtful cases even in absence of completely safe staring points. The genre developed from medieval reference books for confessors and became by the sixteenth-century a sophisticated tool-box for dealing with various fields of applied ethics. Francisco Vitoria, the main authority of Baroque Scholasticism, was a controversial figure, among the proponents of the new discipline of casuistry and a consistent proponent of more separation between the religious and the civil authority, stricter limits to the legitimacy of war, innate rights of non-Christian nations in the New World based on the notion of pura natura, providing a standard of ‘natural’ goodness, previous to revelation, on which the Indian nations were judged to live in a naturally good condition, provided with the institutions of family, justice, and religion had accordingly a right to full respect by Christian sovereigns. Bartolomé de Las Casas, arguing along similar lines, was the leader of a historical battle in defence of the rights of the Indios. -/- 12. Michel de Montaigne and the art of living. A short description of one of the Renaissance Phyrronism, one of the classical philosophies revived in the fifteenth and sixteenth century. Montaigne combines the sceptical epistemology with an understanding of ethics – indeed of philosophy as a whole – in terms of an art of living inspired by two basic ideas, sagesse, that is, practical wisdom as the only kind of rationality available after theology, science, and tradition have declared bankrupt, and an aesthetic ideal of self-transformation through the art of writing and introspection. -/- 13. Pierre Nicole and neo-Augustinianism. The chapter illustrates first the vicissitudes of Augustinianism newly born after the late medieval triumph of Thomist Aristotelianism in the alternative Protestant and Catholic versions processed by the Calvinists and the Jansenists. Then it illustrates the doctrines of Pierre Nicole, Blaise Pascal’s best disciple, on the impossibility of introspection, on the ubiquity of self-deception, on the incurably evil character of the passion of love, and on the two moralities, the one of the man of the world, the morality of honesty which is indispensable for granting peace and order but devoid of any true value for eternal salvation, since the same external behaviour may be prompted by opposite motivations, and the morality of charity, the only true one but also useless to society. The third topic is Pierre Malebranche’s view of self-deception as a ubiquitous phenomenon accounting for human action and responsibility and his reformulated theory of self-love, no less ubiquitous than for Nicole and yet not as incurably evil, given the distinction between morally indifferent and even necessary amour de soi and vicious amour proper, a distinction on which the whole of Rousseau’s moral and political theory rests. -/- 14. Samuel von Pufendorf and the new science of morality. The chapter is dedicated to the discovery of the idea of a ‘new moral science’. Hugo Grotius is discussed first highlighting the real character of his project, much closer to the Thomist idea of a natural law accessible to non-corrupted human reason when human beings are living in a state of pura natura. Then Hobbes’s combination of scepticism, voluntarism, and conventionalism is described and both the continuity with Grotius’s new science, in the search for non-revealed rational morality, and the break with him, in the adoption of voluntarism and refusal of an intellectualist view of natural law, are illustrated. Pufendorf’s work is illustrated as a synthesis of the two previous attempts and the – up to Schneewind underestimated – paradigmatic example of the new science of morality. -/- 15. Richard Cumberland and consequentialist voluntarism. The chapter gives an overview of eighteenth-century Anglican ethics, noticing how the Cambridge tradition gave special weight to natural theology as opposed to positive or revealed theology – and how two Cambridge fellows, John Gay and Thomas Brown, elaborated on Cumberland’s (and Malebranche’s, as well as Leibniz’s) strategy for finding a third way between intellectualist view and voluntarist view of the laws of nature. The result of their elaboration was a kind of a rational-choice account of the origins of natural laws, where a law-giver God chooses among a number possible sets of laws on a maximizing criterion, and God’s maximandum is happiness for his creatures. The chapter notices also how such a solution aimed at solving at once the problem of evil and that of the foundation of moral obligation by proving how God’s choice was justified as far as it was the one minimising the amount of suffering in the world. 16. Richard Price and intuitionism. The chapter describes first the doctrines of the Cambridge Platonists, an example of hyper-rationalist reaction to Calvinism. Secondly it describes the sophisticated and universally ignored – from Sidgwick to Anscombe –version of what was later labelled ‘ethical intuitionism’ – showing how it escapes familiar objections and misrepresentations of intuitionism – from Mill to Rawls – in grounding its argument on transcendental arguments while carefully avoiding recourse to introspection and psychological evidence, which has been taken as a too easy target by critics of intuitionism. Thirdly, the chapter discusses Whewell’s ‘philosophy of morality’, as opposed to ‘systematic morality’, not unlike Kant’s distinction between a pure and an empirical moral philosophy. Whewell worked out a systematization of traditional normative ethics as a first step before its rational justification; he believed that the point in the philosophy of morality is justifying a few rational truths about the structure of morality such as to rule hedonism, eudemonism, and consequentialism; yet a system of positive morality cannot be derived solely from such rational truths but requires consideration of the ongoing dialectics between idea and fact in historically given moralities. Whewell’s intuitionism turns out closer to Kantian ethics than commentators have made us believe until now, and quite different from what Sidgwick meant by intuitionism. -/- 17. Adam Smith and the morality of role-switch. The chapter describes first, Hutcheson’s attempt at basing the ‘new science’ of natural law on different bedrock than Pufendorf and the English Platonists, namely a moral sense, a faculty whose existence is assumed to be proved on an empirical basis. The second step is a reconstruction of Hume’s rejoinder in terms of a new science of man including morality on an ‘experimental’ basis, that is, a ‘Newtonian’ hypothetical-deductive approach, distinguished from Hutcheson’s allegedly uncritical descriptive approach to human nature. The third step is a reconstruction of Adam Smith theory of morality understood as emerging from a spontaneous interplay of exchanges of situations (the most basic meaning of the word ‘sympathy’ as construed by this author). -/- 18. Jeremy Bentham and utilitarianism. The bulk of the chapter is dedicated to the doctrines of Jeremy Bentham. The Enlightenment spirit that suggested the idea of a new morality, free from religion, is illustrated. The notion of utility is illustrated as well as the subsequent formulations of the principle of utility. The idea of felicific calculus is discussed, showing how its inner difficulties prompted several reformulations of the principle of utility in order to avoid undesirable implications of proposed formulations. The role of the thesis of spontaneous convergence between interest and duty is discussed, showing how it left numberless questions open, and the distinction between the virtues of prudence, justice and beneficence is described as a way out of the deadlocks of classical utilitarianism. After Bentham, Mill’s reformed utilitarianism is reconstructed, showing how it is a kind of mixed system – as closer to common sense as it gives up Bentham’s claims to consistency and simplicity – resulting as unintended consequences from the controversies in which Mill was too keen to engage. The hidden agenda of the controversy between Utilitarianism and Intuitionism, going beyond the image of the battle between Prejudice and Reason, is described, showing how both competing philosophical outlooks turn out to be more research programs than self-contained doctrinal bodies, and such programs appear to be implemented, and indeed radically transformed while in progress thanks to their enemies no less than to their supporters. -/- 19. Immanuel Kant, practical reason and judgment. The chapter argues that Kant took from Moses Mendelssohn the idea of a distinction between geometry of morals and a practical ethic. He was drastically misunderstood by his followers precisely on this point. He had learned from the sceptics and the Jansenists the lesson that men are prompted to act by deceptive ends, and he was aware that human actions are also empirical phenomena, where laws like the laws of Nature may be detected. His practical ethics made room for judgment as a holistic procedure for assessing the saliency of relevant moral qualities in one given situation; this procedure yields the same results as the geometry of morals does for abstract cases but does so immediately and without balancing conflicting duties with each other, since what makes for the salient quality of a situation is perceived from the very beginning. Kant's practical philosophy is richer than the received image, making room for an ‘empirical moral philosophy’ or moral anthropology including treatment of commerce, needs, value and price, happiness and well-being; the overall social theory and philosophy of history is less different from Adam Smith's than the received image makes believe; the paradox of happiness is central to Kant's philosophy; a distinction between happiness and well-being is clearly drawn; the distinction plays a basic role in establishing a link between the economic and the moral life. -/- 20. Georg Wilhelm Friedrich Hegel and the critique of abstract universalism. The chapter describes first the Romantic movement and the implications some of its concerns, rescuing passions, community, tradition, the individual as the bearer of a unique destiny, and the longing for organic unity between the individual, mankind and nature. Hegel’s contribution is discussed then, highlighting how, on the one hand, he shared a number of these concerns and on the other he had more rationalist leanings. The notion of morality is the pivotal point of the reconstruction, highlighting how Hegel construes this notion as a key to his own diagnosis of the malaise of modernity – the separation of individual and Gemeinschaft – and how his attack on Kant turns around this very idea. -/- 21. Friedrich Nietzsche against Christianity and the Enlightenment. The chapter illustrates first the idea of deconstruction of the back-world of values. Nietzsche claims to be legitimate heir of the French moralists, Leibniz, Kant and Hegel, in so far as he allegedly carries out to its deepest implications their discovery of what lies behind traditional naïve belief in the existence of an objective realm of values just waiting for description by the philosopher. The two exemplars form which genealogy draws inspiration are the classical philologist’s historical reconstructions of lost meanings and the chemist’s decomposition of elements. Then the genealogy of the notions of good and evil carried out in the first dissertation of Genealogy of morals is illustrated with its paradoxical conclusion that will to power is in fact the only ‘genuine’ kind of goodness. The third point illustrated is the dialectic of ascetism and self-realization with its ambiguous outcome. The suggested interpretation of such outcome is that Nietzsche’s normative ethics is a kind of virtue ethics taking an aesthetic ideal as a normative standard -/- 22. George Edward Moore and ideal utilitarianism. The chapter discusses the ideas of common sense and common-sense morality in Sidgwick. I argue that, far from aiming at overcoming common-sense morality, Sidgwick aimed purposely at grounding a consist code of morality by methods allegedly taken from the natural sciences to reach, also in ethics, the same kind of “mature” knowledge as in the natural sciences. His whole polemics with intuitionism was vitiated by the a priori assumption that the widespread ethos of the educated part of humankind, not the theories of the intuitionist philosophers, was what was worth considering as the expression of intuitionist ethics. In spite of a naïve positivist starting-point, Sidgwick was encouraged by his own approach in exploring the fruitfulness of coherentist methods for normative ethics. Thus, Sidgwick left an ambivalent legacy to twentieth-century ethics: the dogmatic idea of a “new” morality of a consequentialist kind, and the fruitful idea that we can argue rationally in normative ethics albeit without shared foundations. Then it reconstructs the background of ideas, concerns and intentions out of which Moore’s early essays, the preliminary version, and then the final version of Principia Ethica originated. I stress the role of religious concerns, as well as that of the Idealist legacy. I argue that PE is more a patchwork of rather diverging contributions than a unitary work, not to say the paradigm of a new school in Ethics. I add a comparison with Rashdall’s almost contemporary ethical work, suggesting that the latter defends the same general claims in a different way, one that manages to pave decisive objections in a more plausible way. I end by suggesting that the emergence of Analytic Ethics was a more ambiguous phenomenon than the received view would make us believe, and that the wheat (or some other gluten-free grain) of this tradition, that is, what logic can do for philosophy, should be separated from the chaff, that is, the confused and mutually incompatible legacies of Utilitarianism and Idealism. -/- 23. Edmund Husserl and the a-priori of action. The chapter illustrates first the idea of phenomenology and the Husserl’s project of a phenomenological ethic as illustrated in his 1908-1914 lectures. The key idea is dismissing psychology and trying to ground a new science of the a priori of action, within which a more restricted field of inquiry will be the science of right actions. Then the chapter illustrates the criticism of modern moral philosophy carried out in the 1920 lectures, where the main target is naturalism, understood in the Kantian meaning of primacy of common sense. The third point illustrate is Adolph Reinach’s theory of social acts as a key the grounding of norms, a view that basically sketches the very ideas ‘discovered’ later by Clarence I. Lewis, John Searle, Karl-Otto Apel and Jürgen Habermas. A final section is dedicated to Nicolai Hartman, who always refused to define himself a phenomenologist and yet developed a more articulated and detailed theory of ‘values’ – with surprising affinities with George E. Moore - than philosophers such as Max Scheler who claimed to Husserl’s legitimate heirs. -/- 24. Bertrand Russell and non-cognitivism. The chapter reconstructs first the discussion after Moore. The naturalistic-fallacy argument was widely accepted but twisted to prove instead that the intuitive character of the definition of ‘good’, its non-cognitive meaning, in a first phase identified with ‘emotive’ meaning. Alfred Julius Ayer is indicated as a typical proponent of such non-cognitivist meta-ethics. More detailed discussion is dedicated to Bertrand Russell’s ethics, a more nuanced and sophisticated doctrine, arguing that non-cognitivism does not condemn morality to arbitrariness and that the project of a rational normative ethics is still possible, heading finally to the justification of a kind of non-hedonist utilitarianism. Stevenson’s theory, another moderate version of emotivism is discussed at some length, showing how the author comes close to the discovery of the role of a pragmatic dimension of language as a basis for ethical argument. Last of all, the discussion from the Forties about Hume’s law is described, mentioning Karl Popper’s argument and Richard Hare’s early non-cognitivist but non-emotivist doctrine named prescriptivism. -/- 25. Elizabeth Anscombe and the revival of virtue ethics. The chapter discusses the three theses defended by Anscombe in 'Modern Moral Philosophy'. I argue that: a) her answer to the question "why should I be moral?" requires a solution of the problem of theodicy, and ignores any attempts to save the moral point of view without recourse to divine retribution; b) her notion of divine law is an odd one more neo-Augustinian than Biblical or Scholastic; c) her image of Kantian ethics and intuitionism is the impoverished image manufactured by consequentialist opponents for polemical purposes and that she seems strangely accept it; d) the difficulty of identifying the "relevant descriptions" of acts is not an argument in favour of an ethics of virtue and against consequentialism or Kantian ethics, and indeed the role of judgment in the latter is a response to the difficulties raised by the case of judgment concerning future action. A short look at further developments in the neo-naturalist current is given trough a reconstruction of Philippa Foot’s and Peter Geach’s critiques to the naturalist-fallacy argument and Alasdair MacIntyre’s grand reconstruction of the origins and allegedly unavoidable failure of the Enlightenment project of an autonomous ethic. -/- 26. Richard Hare and neo-Utilitarianism. The chapter addresses the issue of the complex process of self-transformation Utilitarianism underwent after Sidgwick’s and Moore’s fatal criticism and the unexpected Phoenix-like process of rebirth of a doctrine definitely refuted. A glimpse at this uproarious process is given through two examples. The first is Roy Harrod Wittgensteinian transformation of Utilitarianism in pure normative ethics depurated from hedonism as well as from whatsoever theory of the good. This results in preference utilitarianism combined with a ‘Kantian’ version of rule utilitarianism. The second is Richard Hare’s two-level preference utilitarianism where act utilitarianism plays the function of eventual rational justification of moral judgments and rule-utilitarianism that of action-guiding practical device. -/- 27. Hans-Georg Gadamer and rehabilitation of practical philosophy. The post-war rediscovery of ethics by many German thinkers and its culmination in the Sixties in the movement named ‘Rehabilitation of practical philosophy’ is described. Among the actors of such rehabilitation there were a few of Heidegger’s most brilliant disciples, and Hans-Georg Gadamer is chosen as a paradigmatic example. His reading of Aristotle’s lesson I reconstructed, starting with Heidegger’s lesson but then subtly subverting its outcome thanks to the recovery of the central role of the notion of phronesis. -/- 28. Karl-Otto Apel and the revival of Kantian ethics. Parallel to the neo-Aristotelian trend, there was in the Rehabilitation of practical philosophy a Kantian current. This started, instead than the rehabilitation of prudence, with the discovery of the pragmatic dimension of language carried out by Charles Peirce and the Oxford linguistic philosophy. On this basis, Karl-Otto Apel singled out as the decisive proponent of the linguistic and Kantian turn in German-speaking ethics, worked out the performative-contradiction argument while claiming that this was able to provide a new rational and universal basis for normative ethics. An examination of his argument is some detail is offered, followed by a more cursory reconstruction of Jürgen Habermas’s elaboration on Apel’s theory. -/- 29. John Rawls and public ethics as applied ethics. Rawls’s distinction between a “political” and a “metaphysical” approach to one central part of ethical theory, namely the theory of justice, is interpreted as a formulation of the same basic idea at the root of both the principles approach and neo-casuistry, both discussed in the following chapter, namely that it is possible to reach an agreement concerning positive moral judgments even though the discussion is still open – and in Rawls’ view never will be close – on the basic criteria for judgment. -/- 30. Beauchamp and Childress and bioethics as applied ethics. The chapter presents the revolution of applied ethics while stressing its methodological novelty, exemplified primarily by Beauchamp and Childress principles approach and then by Jonsen and Toulmin’s new casuistry. -/- . (shrink)

This paper examines an insoluble Cartesian problem for classical AI, namely, how linguistic understanding involves knowledge and awareness of u’s meaning, a cognitive process that is irreducible to algorithms. As analyzed, Descartes’ view about reason and intelligence has paradoxically encouraged certain classical AI researchers to suppose that linguistic understanding suffices for machine intelligence. Several advocates of the Turing Test, for example, assume that linguistic understanding only comprises computational processes which can be recursively decomposed into algorithmic mechanisms. Against this background, in (...) the first section, I explain Descartes’ view about language and mind. To show that Turing bites the bullet with his imitation game, in the second section I analyze this method to assess intelligence. Then, in the third section, I elaborate on Schank and Abelsons’ Script Applier Mechanism (SAM, hereby), which supposedly casts doubt on Descartes’ denial that machines can think. Finally, in the fourth section, I explore a challenge that any algorithmic decomposition of linguistic understanding faces. This challenge, I argue, is the core of the Cartesian problem: knowledge and awareness of meaning require a first-person viewpoint which is irreducible to the decomposition of algorithmic mechanisms. (shrink)

The role played by the symmetric structure of a group of finite Morley rank without involutions in the proof by contradiction of Frécon 2018 was put in evidence in Poizat 2018; indeed, this proof consists in the construction of a symmetric space of dimension two (“a plane”), and then in showing that such a plane cannot exist.To a definable symmetric subset of such a group are associated symmetries and transvections, that we undertake here to study in the abstract, without mentioning (...) a group envelopping them. This leads us to consider axiomatically defined structures that we callsymmetrons(preferably todyadic symmetric setsas was done in Lawson & Lim 2004).Glauberman's$Z^*$-Theorem allows to elucidate completely the structure of the finite symmetrons: each of them is isomorphic to the set of symmetries associated to a symmetric subspace of a finite group without involutions, which is far from being uniquely determined. In fact, there exist non-isomorphic finite groups which have the same symmetries, and also finite symmetrons which are not isomorphic to the symmetries of a group.The situation is not so clear in the case of symmetrons of finite Morley rank, or even algebraic, which are the main objects of study of this paper. But in spite of the fact that a symmetron be a structure much weaker that a group, we can extend to symmetrons some well-known results concerning groups of finite Morley rank: chain condition, decomposition into connected components, characterisation of the generic definable subsets, elliptic generation, etc. These properties are new even in the case of a symmetric subspace of a group, and allow to bypass the computations made by Frécon during the construction of his paradoxical plane.Moreover, assuming the Algebricity Conjecture, we generalize Glauberman's Theorem to the finite Morley rank context. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Diacritics 29.4 (1999) 84-115 [Access article in PDF] Be-longing and Bi-lingual States Doris Sommer "How sad that people don't keep commitments any more. Even marriages last only about five years.""Yes, but long-distance marriages can stretch those five years out over weekends and vacations to make relationships last a lifetime."Benedict Anderson's provocative new book, The Spectre of Comparisons: Nationalism, Southeast Asia and the World, raises questions about political relationships over (...) time and over space. Like precarious modern marriages and their corollary "political" kinships (in-laws in Spanish are one's familia política), national sentiment today strains with the movements of transnational communities from home to distant enclaves. Over time, ties can unravel as modern subjects choose, or not, to identify with adopted political relatives. Is one's country the bastion of a people reluctant to receive more immigrants? Is it the sender of surplus people who will, in turn, send money home? (Heads of state in El Salvador, Guatemala, and Mexico typically object to US restrictions on immigration.) Or is it the harbor for many peoples? Does belonging even to a recently invented country anchor an existential need, a be-longing, because being a "man"--as Hannah Arendt still called the subject of politics--means striving for recognition among equals? Or, do many citizens today feel like resident aliens (to themselves or to others), belonging rather to ethnic minorities and perhaps--long-distance--to other nations of origin or of choice? Anderson is right to worry about precarious belongings and optional obligations.In the end though, he finds solace from the threats of egotism and despair, and from the social decomposition of too much movement (what Arjun Appadurai calls "modernity at large") in the resilient promise of the "goodness of nations." Confidence in the extrapersonal goals and pride in national belonging appears, almost miraculously, in the last of seventeen chapters. Each of these brilliant and erudite essays will reconfirm our admiration for Anderson. My own personal debt includes his extraordinary generosity and the good counsel that encourages me to follow him, sometimes with a swerve, as will be evident when my appreciation for be-longing plays bi-lingual games.The opening pages of The Spectre of Comparisons theorize a paradox in the postcolonial condition: the inescapable folly of comparing one's nation to another, or to a mother country. Concepts like nation or culture, after all, take on meaning in their particular contexts and by contrast with others. The core chapters chronicle aborted beginnings and abusive conflations of the nation and the state. But hope has the last word, thanks to three guarantees of national imaginings: the promising and innocent unborn generations; the nation's dead (war heroes); and the living who are ever willing to give the nation another chance, and yet another. Feelings of pride and shame come together in the end, because citizens invest, often against the evidence, in "the goodness [End Page 84] of nations" [364]. This resilience shows up right after the trouble in chapter 16, where shame was the connection between nation and narrator in Mario Vargas Llosa's 1987 novel about Peru. Unfounded but unrelenting, Anderson's hope follows on shame rather abruptly and suggests that shame itself is a sign of our care for our countries. 1 The narrator of El hablador had tried to escape from his ill-fated country, his "malhadado país," only to be haunted by it.My question is whether Anderson's coda to this Peruvian novel is inspired by the same indomitable demon of comparisons that he has been exposing throughout the essays. José Rizal had named the meddling devil to blame it for distracting the Filipino from the lovely garden he saw in Manila, assailing him with memories of a European original or model [2]. This double vision raises a specter of possible inauthenticity; it undermines meaning as models slip from centers to peripheries. Local concepts lose their particularities in global vocabularies. Anderson calls the movement a "logic of seriality." I prefer to call it trans-latio, literally a carrying from one place to another... (shrink)

The aim of this article is to describe the change of the Korean society after the neoliberal crisis in 1997. The economic crisis in Korea resulted from the militant struggles of working class between 1987-1997. But it had been used as a moment for deepening the neoliberal reformation and the recomposition of capital. This paradoxical process had been accomplished by a wide and violent lay-off as in any other countries. In this process the first notable factor is the appearance (...) of cooperative attitude in the Korean progressive labor movement. The author described the context of decomposition of militant working class in factories, and groped for the new recomposition of working class and the formation of autonomous multitudes in the whole range of Korean society. (shrink)

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering (...) and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics. (shrink)

An analysis of two heuristic strategies for the development of mechanistic models, illustrated with historical examples from the life sciences. In Discovering Complexity, William Bechtel and Robert Richardson examine two heuristics that guided the development of mechanistic models in the life sciences: decomposition and localization. Drawing on historical cases from disciplines including cell biology, cognitive neuroscience, and genetics, they identify a number of "choice points" that life scientists confront in developing mechanistic explanations and show how different choices result in (...) divergent explanatory models. Describing decomposition as the attempt to differentiate functional and structural components of a system and localization as the assignment of responsibility for specific functions to specific structures, Bechtel and Richardson examine the usefulness of these heuristics as well as their fallibility—the sometimes false assumption underlying them that nature is significantly decomposable and hierarchically organized. When Discovering Complexity was originally published in 1993, few philosophers of science perceived the centrality of seeking mechanisms to explain phenomena in biology, relying instead on the model of nomological explanation advanced by the logical positivists (a model Bechtel and Richardson found to be utterly inapplicable to the examples from the life sciences in their study). Since then, mechanism and mechanistic explanation have become widely discussed. In a substantive new introduction to this MIT Press edition of their book, Bechtel and Richardson examine both philosophical and scientific developments in research on mechanistic models since 1993. (shrink)

Decomposition is a bracing, revisionary, and provocative inquiry into music—from Beethoven to Duke Ellington, from Conlon Nancarrow to Evelyn Glennie—as a personal and cultural experience: how it is composed, how it is idiosyncratically perceived by critics and reviewers, and why we listen to it the way we do. Andrew Durkin, best known as the leader of the West Coast–based Industrial Jazz Group, is singular for his insistence on asking tough questions about the complexity of our presumptions about music and (...) about listening, especially in the digital age. In this winning and lucid study he explodes the age-old concept of musical composition as the work of individual genius, arguing instead that in both its composition and reception music is fundamentally a collaborative enterprise that comes into being only through mediation. Drawing on a rich variety of examples—Big Jay McNeely’s “Deacon’s Hop,” Biz Markie’s “Alone Again,” George Antheil’s Ballet Mécanique, Frank Zappa’s “While You Were Art,” and Pauline Oliveros’s “Tuning Meditation,” to name only a few—Durkin makes clear that our appreciation of any piece of music is always informed by neuroscientific, psychological, technological, and cultural factors. How we listen to music, he maintains, might have as much power to change it as music might have to change how we listen. (shrink)

In [12], P. Scowcroft and L. van den Dries proved a cell decomposition theorem for p-adically closed fields. We work here with the notion of P-minimal fields defined by D. Haskell and D. Macpherson in [6]. We prove that a P-minimal field K admits cell decomposition if and only if K has definable selection. A preprint version in French of this result appeared as a prepublication [8].

This paper defends an interpretation of Gottlob Frege’s views on the structure of thought. I argue that Frege did not think that a thought has a unique decomposition into its component senses, but rather the same thought can be decomposed into senses in multiple, distinct ways. These multiple decompositions will often have distinct logical forms. I also argue against Michael Dummett and others that Frege was committed to the sense of a predicate being a function from the sense of (...) a name (or names) to a complete thought. I defend my Frege interpretation against a puzzle often discussed in the Frege literature; namely, that the Multiple Decompositions Thesis is incompatible with Frege’s stated view that a thought is built up out of its component senses as parts. I provide textual evidence and argument that Frege thought of the part/whole relation in such a way that a whole can be analyzed into (or built up out of) parts in multiple, distinct ways, thus dissolving the puzzle. I conclude with discussion of every sort of example of multiple decompositions that can be found in Frege's work. (shrink)

Paradoxes are many things. Artificial intelligence views them as viruses of the brain, strange replicators that unexpectedly exploit design possibilities. For the child, they are intellectual cartwheels, an everyday delight. For mathematicians and logicians, they reveal skeletons in the closet of reason. For philosophers and dramatists, they capture the contradictions of experience. The historian of ideas sees that they come in successive waves, surging through Classical Greece, the Renaissance and the twentieth century. Professor Leiber's user-'friendly guide to paradoxes provides an (...) up-to-date survey of an ancient and perennial source of puzzlement. Book jacket. (shrink)

A synaptic algebra is a generalization of the self-adjoint part of a von Neumann algebra. In this article we extend to synaptic algebras the type-I/II/III decomposition of von Neumann algebras, AW∗-algebras, and JW-algebras.

We develop a notion of cell decomposition suitable for studying weak p-adic structures definable). As an example, we consider a structure with restricted addition.

Functional decomposition is an important goal in the life sciences, and is central to mechanistic explanation and explanatory reduction. A growing literature in philosophy of science, however, has challenged decomposition-based notions of explanation. ‘Holists’ posit that complex systems exhibit context-sensitivity, dynamic interaction, and network dependence, and that these properties undermine decomposition. They then infer from the failure of decomposition to the failure of mechanistic explanation and reduction. I argue that complexity, so construed, is only incompatible with (...) one notion of decomposition, which I call ‘atomism’, and not with decomposition writ large. Atomism posits that function ascriptions must be made to parts with minimal reference to the surrounding system. Complexity does indeed falsify atomism, but I contend that there is a weaker, ‘contextualist’ notion of decomposition that is fully compatible with the properties that holists cite. Contextualism suggests that the function of parts can shift with external context, and that interactions with other parts might help determine their context-appropriate functions. This still admits of functional decomposition within a given context. I will give examples based on the notion of oscillatory multiplexing in systems neuroscience. If contextualism is feasible, then holist inferences are faulty—one cannot infer from the presence of complexity to the failure of decomposition, mechanism, and reductionism. (shrink)

We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic cells. (...) From this we can derive quantifier-elimination, and give a characterization of definable functions. In particular, we conclude that multiplication can only be defined on bounded sets, and we consider the existence of definable Skolem functions. (shrink)

C-minimality is a variant of o-minimality in which structures carry, instead of a linear ordering, a ternary relation interpretable in a natural way on set of maximal chains of a tree. This notion is discussed, a cell-decomposition theorem for C-minimal structures is proved, and a notion of dimension is introduced. It is shown that C-minimal fields are precisely valued algebraically closed fields. It is also shown that, if certain specific ‘bad’ functions are not definable, then algebraic closure has the (...) exchange property, and for definable sets dimension coincides with the rank obtained from algebraic closure. (shrink)

Decompositional equivalence is the principle that there is no preferred decomposition of the universe into subsystems. It is shown here, by using a simple thought experiment, that quantum theory follows from decompositional equivalence together with Landauer’s principle. This demonstration raises within physics a question previously left to psychology: how do human—or any—observers identify or agree about what constitutes a “system of interest”?

I argue, through appeal to the distinction between analysis and decomposition described by Dummett, that Wittgenstein employs both of those notions in the Tractatus. I then bring this interpretation to bear upon the issue of propositional unity, where I formulate an objection to the views of both Leonard Linksy and José Zalabardo. I show that both Linsky and Zalabardo fail to acknowledge the distinction between analysis and decomposition present in the Tractatus, and that they consequently mischaracterise Wittgenstein’s position (...) with respect to propositional unity. (shrink)

In this paper we develop a differential analogue of o-minimal cell decomposition for the theory CODF of closed ordered differential fields. Thanks to this differential cell decomposition we define a well-behaving dimension function on the class of definable sets in CODF. We conclude this paper by proving that this dimension is closely related to both the usual differential transcendence degree and the topological dimension associated, in this case, with a natural differential topology on ordered differential fields.

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

Recently, decomposition-based multiobjective evolutionary algorithms have good performances in the field of multiobjective optimization problems and have been paid attention by many scholars. Generally, a MOP is decomposed into a number of subproblems through a set of weight vectors with good uniformly and aggregate functions. The main role of weight vectors is to ensure the diversity and convergence of obtained solutions. However, these algorithms with uniformity of weight vectors cannot obtain a set of solutions with good diversity on some (...) MOPs with complex Pareto optimal fronts. To deal with this problem, an improved decomposition-based multiobjective evolutionary algorithm with adaptive weight adjustment is proposed. Firstly, a new method based on uniform design and crowding distance is used to generate a set of weight vectors with good uniformly. Secondly, according to the distances of obtained nondominated solutions, an adaptive weight vector adjustment strategy is proposed to redistribute the weight vectors of subobjective spaces. Thirdly, a selection strategy is used to help each subobjective space to obtain a nondominated solution. Comparing with six efficient state-of-the-art algorithms, for example, NSGAII, MOEA/D, MOEA/D-AWA, EMOSA, RVEA, and KnEA on some benchmark functions, the proposed algorithm is able to find a set of solutions with better diversity and convergence. (shrink)

In the empirical logic approach to quantum mechanics, the physical system under consideration is given in terms of a manual of sample spaces. The resulting propositional structure has been shown to form an orthoalgebra, generalizing the structure of an orthomodular poset. An orthoalgebra satisfies the unique Mackey decomposition (UMD) property if, given two commuting propositions a and b, there is a unique jointly orthogonal triple (e, f, c) such that a=e⊕c and b=f⊕c. In a manual, E is refined by (...) F if E is logically equivalent to some partition of F, making results from F at least as informative as those from E. The main result is a characterization of the UMD property in terms of the refinement structure of an underlying manual, provided the manual is event saturated and orthogonally additive. (shrink)

"The book presents in accessible fashion recent important work on the self and self-consciousness and also moves the issues forward with interesting new ideas. It provides a notably crisp and clear treatment of some extremely intriguing topics." -- Jane Heal, Department of Philosophy, University of Cambridge In this book, José Luis Bermú dez addesses two fundamental problems in the philosophy and psychology of self-consciousness: (1) Can we provide a noncircular account of fully fledged self-conscious thought and language in terms of (...) more fundamental capacities? (2) Can we explain how fully fledged self-conscious thought and language can arise in the normal course of human development? Bermú dez argues that a paradox (the paradox of self-consciousness) arises from the apparent strict interdependence between self-conscious thought and linguistic self-reference. The paradox renders circular all theories that define self-consciousness in terms of linguistic mastery of the first-person pronoun. It seems to follow from the paradox of self-consciousness that no such account or explanation can be given. Drawing on recent work in empirical psychology and philosophy, the author argues that any explanation of fully fledged self-consciousness that answers these two questions requires attention to primitive forms of self-consciousness that are prelinguistic and preconceptual. Such primitive forms of self-consciousness are to be found in somatic proprioception, the structure of exteroceptive perception, and prelinguistic forms of social interaction. The author uses these primitive forms of self-consciousness to dissolve the paradox ofself-consciousness and to show how the two questions can be given an affirmative answer. (shrink)

Frege seems to hold two incompatible theses:(i) that sentences differing in structure can yet express the same sense; and (ii) that the senses of the meaningful parts of a complex term are determinate parts of the sense of the term. Dummett offered a solution, distinguishing analysis from decomposition. The present paper offers an embellishment of Dummett?s distinction by providing a way of depicting the internal structures of complex senses?determinate structures that yield distinct decompositions. Decomposition is then shown to (...) be adequate as a foundation for the informativity and analyticity of logic. (shrink)

This dissertation formulates, defends, and exemplifies a semantic approach that I call Cognitive Decompositionism. Cognitive Decompositionism is one version of lexical decompositionism, which holds that the meaning of lexical items are decomposable into component parts. Decompositionism comes in different varieties that can be characterized in terms of four binary parameters. First, Natural Decompositionism contrasts with Artful Decompositionism. The former views components as word-like, the latter views components more abstractly. Second, Convenient Decompositionism claims that components are merely convenient fictions, while Real (...) Decompositionism claims that components are psychologically real. Third, Truth-conditional Decompositionism contrasts with various non-truth-conditional theories, in particular with Quantum Semantics. And fourth, Holistic Decompositionism assumes that decompositions are circular, as opposed to Atomistic Decompositionism, which assumes that some primitive basis ultimately underlies semantic components. Cognitive Decompositionism is the conjunction of the following theses: decomposition is Artful , Psychologically Real , Quantum , and Atomistic . As I substantiate these claims, I will be responding to the anti-decompositionist theories of Fodor, Davidson, and Quine. (shrink)

We prove that forp-optimal fields a cell decomposition theorem follows from methods going back to Denef’s paper [7]. We derive from it the existence of definable Skolem functions and strongp-minimality. Then we turn to stronglyp-minimal fields satisfying the Extreme Value Property—a property which in particular holds in fields which are elementarily equivalent to ap-adic one. For such fieldsK, we prove that every definable subset ofK×Kdwhose fibers overKare inverse images by the valuation of subsets of the value group is semialgebraic. (...) Combining the two we get a preparation theorem for definable functions onp-optimal fields satisfying the Extreme Value Property, from which it follows that infinite sets definable over such fields are in definable bijection iff they have the same dimension. (shrink)

The paradox of pain refers to the idea that the folk concept of pain is paradoxical, treating pains as simultaneously mental states and bodily states. By taking a close look at our pain terms, this paper argues that there is no paradox of pain. The air of paradox dissolves once we recognize that pain terms are polysemous and that there are two separate but related concepts of pain rather than one.

We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition is based on the properties of the congruence lattices of algebras. We consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.

This paper presents decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. All necessary and sufficient conditions for the decomposition are deployed to investigate the commutativity, sensitivity, and the effect of disturbance on the fourth-order LTVS. Some systems are commutative, and some are not commutative, while some are commutative under certain conditions. Based on this fact, the commutativity of fourth-order Euler-type LTVS is investigated by introducing the commutative requirements, theories, and (...) conditions. The fourth-order Euler-type LTVSs are investigated into commutative pairs of twice Euler-type second-order linear time-varying systems. The decomposition theories and conditions are derived, proved, and solved to simplify the use of commutativity for practical and industrial uses. Some fourth-order systems are sensitive toward change in initial conditions or parameters while others are not, and the effect due to disturbance also varies within systems. Furthermore, the stability and robustness of systems have so many issues. But we consider fourth-order Euler-type LTVS to observe, investigate, and tackle these issues. Lastly, the realization of fourth-order LTVS from cascaded two second-order systems can be laboratory experimented which is an open problem for future engineers to investigate. However, the theoretical results show a good agreement with the simulation results is considered in this work. Perhaps it might have unlimited physical applications in science and engineering as well as theoretical contribution. But beyond any reasonable doubt, the novelty is guaranteed because this study is the first of its kind that introduces the decomposition of the fourth-order Euler-type linear time-varying system as a commutative pair of two second-order Euler-type systems. Illustrative examples are presented to support the results. (shrink)

This article proposes three new decompositions of inequality measures, drawn from the framework of cooperative game theory. It allows the impact of players’ interactions, rather than players’ contributions to inequality, to be taken into consideration. These innovative approaches are especially suited for the study of income inequality when the income has a hierarchical structure: the income is composed of several primary sources, with the particularity that each of them is also composed of secondary sources. We revisit the Shapley–Owen value that (...) quantifies the importance of each of these secondary sources in the overall income inequality. Our main contribution is to decompose this importance into two parts: the pure marginal contribution of the considered source and a weighted sum of pairwise interactions. We then provide an axiomatic characterization of each additive interaction decomposable (AID) coalitional value considered in this paper. We give an application of these decompositions in the context of inequality theory. (shrink)