Drawing on recently published correspondence as well as on a survey of Polish and international philosophical activity published in 1937 and details concerning the publisher and bookseller Aleksander Mazzucato, I provide evidence that, contrary to some recent assertions (but in line with older bibliographical entries), Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ was not published in journal form until 1936, although preprints, lacking two corrections and a small addendum, were likely available in the late months of 1935.

This paper responds to Rancière’s reading of Lyotard’s analysis of the sublime by attempting to articulate what Lyotard would call a “differend” between the two. Sketching out Rancière’s criticisms, I show that Lyotard’s analysis of the Kantian sublime is more defensible than Rancière claims. I then provide an alternative reading, one that frees Lyotard’s sublime from Rancière’s central accusation that it signals nothing more than the mind’s perpetual enslavement to the law of the Other. Reading the sublime through the figure (...) of the “event,” I end by suggesting that it may even have certain affinities with what Rancière calls “politics.”. (shrink)

This takes a little-known reading of Kafka’s “In the Penal Colony” by Lyotard as the starting point for an examination of the relation between body and law. Lyotard’s late notion of the intractable serves as a frame for this examination: explicitly claimed to be an absolute condition of morals, I argue it also has political implications, which are here drawn out through the link between the intractable and the body. In Lyotard’s later writings, the body is usually associated with an (...) originary affectivity, which is sometimes equated with sexual difference but sometimes appears to come “before” and exceed this law of bodily differences. It is the latter case, I argue, that allows for a path to be opened beyond the bodily violence of the law to be found in Kafka, especially if this is framed in terms of a certain “politics of incommensurability.”. (shrink)

Hans Kelsen and Max Weber are conventionally understood as initiators not only of two distinct and opposing processes of concept formation, but also of two discrete and contrasting theoretical frameworks for the study of law. _The Foundation of the Juridical-Political: Concept Formation in Hans Kelsen and Max Weber _places the conventional understanding of the theoretical relationship between the work of Kelsen and Weber into question. Focusing on the theoretical foundations of Kelsen’s legal positivism and Weber’s sociology of law, and guided (...) by the conceptual frame of the juridico-political, the contributors to this interdisciplinary volume explore convergences and divergences in the approach and stance of Kelsen and Weber to law, the State, political science, modernity, legal rationality, legal theory, sociology of law, authority, legitimacy and legality. The chapters comprising _The Foundation of the Juridical-Political _uncover complexities within as well as between the theoretical and methodological principles of Kelsen and Weber and, thereby, challenge the enduring division between legal positivism and the sociology of law in contemporary discourse. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:“Out of the Order of Number”: Benjamin and Irigaray Toward a Politics of Pure MeansPeter Fenves* (bio)At the heart of the legal orders that arose in conjunction with the Enlightenment idea of law as rules of conduct universally applicable to all those who belong to a properly instituted political body lies a formula for the justification of the violence on which the law depends in order for it to (...) be an actual, effective, and therefore “living” law—and not merely an idea: violence is justified insofar as it is a means for the control of those violent acts that are not themselves means for the control of immediate threats of violence. As Walter Benjamin indicates in the opening paragraphs of his most explicit exposition of legal and political theory, “Toward the Critique of Violence” (1921), the justification of violence as a means is the point of contention around which arguments over the origin, nature, and purpose of the modern state endlessly circle. Justified violence is supposed to be of a different order than unjustified violence, and so in the context of legal reasoning it is no longer called “violence” but “coercion” or “punishment.” Yet as the formula for the justification of violence indicates, the violence of the legal order is not in general sanctioned for the purpose of subduing immediate threats to one’s own life—this is the justification for the extralegal violence of “private persons”—but for the purpose of preserving the law itself: the law is inviolable. As long as the legal order makes the law effective and thus gives it life, it, too, is inviolable, and all violence other than its own can henceforth be interpreted as an immediate threat not to life itself—however this may be understood—but to the legal order. The end of legally sanctioned violence, its purpose and function, is not to put an end to violence as such but, instead, to thwart all threats to the law in the name of which violence can be sanctioned. Everything that enters into the space over which the legal order imposes its sentence is therefore implicated in the disquieting—or, as Benjamin says, “rotten” [GS 2: 188; SW 242]—ambiguity of legal violence understood as a means whose justification lies in the application of the law: the legal order can justify its own violence only insofar as this violence is a means to an end, but the end it serves can never be separated from itself as means, for the law, by virtue of its universality, is at bottom unconcerned with the life of those upon whom the violence it justifies is exercised or with the life of those whom this violence is supposed to protect. The violence of the legal order is concerned solely with itself, with its own majesty—without, however, ceasing to present itself as a means and reverting to what all legal violence once was: immediate manifestation.Nothing that enters into the space of the legal order can escape the ambiguity of the violence through which the law comes to life. Or at least nothing can escape this ambiguity as long as the space on which the legal order founds itself runs counter to the sole space that accords with the strict universality of the law: a universally accessible, indivisible, and undivided space that is nevertheless capable of the greatest degree of discreteness, differentiation, and individuation. In place of this space the legal orders that arose in Europe over the course of the last five centuries set out something like its parody: [End Page 43] homogeneous and yet fully divided domains whose divisions from one another are momenta of the extralegal violence to which each legal order owes its origin. At least one species of being has always been seen to move outside the space of the legal order—a species whose specificity, speciesness, and spatiality have thus given rise to interminable analysis: the angels. The space that angels traverse—and, in particular, the ones who enter into Luce Irigaray’s writings—does not suffer division into homogeneous domains but does not therefore amount to an undifferentiated expanse, a yawning abyss, or a formless chaos; it is... (shrink)

In making assertions one takes on commitments to the consistency of what one asserts and to the logical consequences of what one asserts. Although there is no quick link between belief and assertion, the dialectical requirements on assertion feed back into normative constraints on those beliefs that constitute one's evidence. But if we are not certain of many of our beliefs and that uncertainty is modelled in terms of probabilities, then there is at least prima facie incoherence between the normative (...) constraints on belief and the probability-like structure of degrees of belief. I suggest that the norm-governed practice relating to degrees of belief is the evaluation of betting odds. (shrink)

The relationship between human rights and civil rights is twofold: on the one hand these rights can be viewed as forming a unity, and on the other there is a significant difference between them. The unity of human and civil rights is based upon the widely shared view that both are fundamental and universal rights, inherent to all human beings without regard to any contingent factors. This unity, however, is weakened by the division of our world into a plurality (...) of separate and independent states. It thus becomes plausible to assume that the citizens of a particular state are endowed with certain fundamental rights towards each other and their state, which are stronger than the rights existing between human beings in general. In this respect, human and civil rights are significantly different.However positive law may draw the line between human and civil rights, any such delimitation needs moral justification and is questionable from an ethical point of view. Moreover, there is reason to doubt that traditional approaches are still suitable in a world in which different societies are merging in their economic, political and ecological affairs. This article considers the ethical foundation for human and civil rights in an attempt to determine whether the traditional delimitation between them is in need of revision. An argument is made that human and civil rights differ in their moral justification. While human rights can be justified by the basic principle of a universal morality, namely the principle of universalization, civil rights are based on our conception of social justice. The justification for civil rights, however, proceeds from the assumption that any given society is a self-sufficient and independent community. Since this assumption no longer corresponds to the conditions of our modern world, the article concludes that a new understanding of basic rights is imperative. (shrink)

Dealing with the metaphysical foundations of modern physical science, this book demonstrates that not only is classical metaphysics not in conflict with the principles of modern experimental science but that, when analogously transferred to the different divisions of modern science, the metaphysical principle of unity makes intelligible all the laws of modern science. This revolutionary book provides the means for reestablishing the unity of science by interpreting the whole of modern experimental science from the perspective of an analogous transfer of (...) the metaphysical principle of unity rather than in terms of efficient causality. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Slaves and the Generals of ArginusaePeter HuntIn the second half of 406 B.C. the Athenians made two shocking decisions. They freed the slaves who had fought in the battle of Arginusae and gave them citizenship, and they condemned to death their victorious generals. I suggest that these two events were related. Specifically, I would like to argue, first, that the competition for rowers to man the huge navies (...) of this period had extended even to slaves. The promise of freedom was intended to motivate the slaves: the grant of Athenian citizenship was an attempt to keep them rowing for Athens rather than deserting and ending up in the enemy's navy. Second, I would like to consider the trial of the generals in the context of this costly, divisive, and controversial policy. A priori considerations, historical parallels, and a few admittedly tenuous pieces of direct evidence suggest that their policy of rewarding the slaves contributed to the generals' unpopularity that made them so vulnerable to prosecution.Slaves to CitizensPassages in Aristophanes' Frogs and a scholiast's quotation of Hellanicus tell us that the slaves who fought in the battle of Arginusae were given freedom and citizenship. Most historians believe that the Athenians freed these slaves,1 but, given Athenian exclusiveness-manifest in Pericles' citizenship law-some doubt that they would have allowed a large group [End Page 359] of slaves to become citizens.2 The evidence, however, indicates that this was exactly what happened.Frogs won first prize at the Lenaean festival of 405-406, about six months after the Athenian naval victory at Arginusae. Early in the play, Dionysus and his slave Xanthias are traveling to Hades. When Dionysus mocks Xanthias for complaining about the load he is carrying, Xanthias exclaims:Dash it all, why wasn't I in that naval battle? Then I could really and truly tell you to go to blazes!(Ar. Ran. 33)3Fighting in the naval battle would have freed Xanthias from carrying Dionysus' baggage and allowed him to tell his master off. A bit later, Charon refuses to ferry Xanthias to Hades:I don't take slaves, unless they fought in the life-or-death naval battle.(190-91)4Again, slaves who have fought in a naval battle are treated differently from other slaves. From these passages alone, one might guess that the slaves who fought in some naval battle-Arginusae being the most recent and probable one-were given their freedom: they did not have to serve their masters and could ride with Charon rather than walking around the lake to get to Hades.Ian Worthington argues against this, the traditional reading of these lines. Xanthias' regret at not serving in the naval battle (33) is not that he would be then be free, but rather that then he would be dead and not forced to serve Dionysus.5 Aristophanes, however, was addressing an [End Page 360] audience many of whom had either fought at Arginusae or had relatives who had. We may associate Arginusae primarily with the deaths of the unrescued crews, but in 405 Arginusae was considered a successful relief mission and a great victory. Aristophanes was addressing the living victors, for whom "to fight at the naval battle" could not serve as shorthand for "to die." Worthington's reading of lines 190-91 is also less convincing than the traditional interpretation. He claims that those who "fought in the life-or-death naval battle" are the men whose drowning after the battle gave rise to the trial of the generals. The text gives no hint or suggestion that Charon is talking about this subset of the sailors who fought in the battle. Rather, Charon refers to another subset of those who fought in the battle, the slaves: "I don't take slaves, unless...." So we should stay with the traditional interpretation and the scholia to Frogs 33, which, although not an independent source, accords with our reading of Aristophanes: ("[I]n the previous year, in the archonship of Antigenes, the Athenians... won a naval battle around Arginusae and freed the slaves who had fought along with them").6Our first evidence for... (shrink)

"Paternalism" comes from the Latin pater, meaning to act like a father, or to treat another person like a child. In modern philosophy and jurisprudence, it is to act for the good of another person without that person's consent, as parents do for children. It is controversial because its end is benevolent, and its means coercive. Paternalists advance people's interests at the expense of their liberty. In this, paternalists suppose that they can make wiser decisions than the people for whom (...) they act. Sometimes this is based on presumptions about their own wisdom or the foolishness of other people, and can be dismissed as presumptuous. But sometimes it is not. It can be based on relatively good knowledge, as in the case of paternalism over young children or incompetent adults. Sometimes the role of paternalist is thrust upon the unwilling, as when we find ourselves the custodian and proxy for an unconscious or severely retarded relative. Paternalism is a temptation in every arena of life where people hold power over others: in childrearing, education, therapy, and medicine. But it is perhaps nowhere as divisive as in criminal law. Whenever the state acts to protect people from themselves, it seeks their good; but by doing so through criminal law, it does so coercively, often against their will. (shrink)

This is the second volume of Oxford Studies in Political Philosophy. Since its revival in the 1970s political philosophy has been a vibrant field in philosophy, one that intersects with jurisprudence, normative economics, political theory in political science departments, and just war theory. OSPP aims to publish some of the best contemporary work in political philosophy and these closely related subfields. The papers in this volume address a range of central topics and represent cutting edge work in the field. They (...) are grouped into three main themes: ideal theory, the moral assessment of states, and issues in social reliations. (shrink)

This paper is the report of a meetingthat gathered many of the UK's most senioranimal scientists with representatives of thefarming industry, consumer groups, animalwelfare groups, and environmentalists. Therewas strong consensus that the current economicstructure of agriculture cannot adequatelyaddress major issues of concern to society:farm incomes, food security and safety, theneeds of developing countries, animal welfare,and the environment. This economic structure isbased primarily on competition betweenproducers and between retailers, driving foodprices down, combined with externalization ofmany costs. These issues must be addressed (...) by acombination of legislation, restructuring ofthe market, and use of public funds. Themeeting included workshops that made otherrecommendations for research and education. Themost urgent requirement is recognition thatchange is needed and development of a visionfor what that change must achieve. (shrink)

In natural deduction classical logic is commonly formulated by adding a rule such as Double Negation Elimination (DNE) or Classical Reductio ad Absurdum (CRA) to a set of introduction and elimination rules sufficient for intuitionist first-order logic with conjunction, disjunction, implication, negation and the universal and existential quantifiers all taken as primitive. The natural deduction formulation of intuitionist logic, coming from Gentzen, has nice properties:— (i) the separation property: an intuitionistically valid inference is derivable using only the introduction and elimination (...) rules governing the connectives and/or quantifiers that occur in the premises (if any) and conclusion; (ii) the (strict) subformula property: more narrowly, there is a derivation of any intuitionistically valid inference that employs only subformulas of the formulas occurring in premises (if any) and conclusion. (Every formula is, of course, a subformula of itself.). (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Beyond the Abortion Wars: A Way Forward for a New Generation by Charles C. CamosyRebecca Todd PetersBeyond the Abortion Wars: A Way Forward for a New Generation Charles C. Camosy Grand Rapids, MI: Eerdmans, 2015. 207Pp. $22.00As the title Beyond the Abortion Wars suggests, Camosy seeks a new way to address abortion in the United States that moves past the binary divisions of “pro-life” and “pro-choice.” Based on (...) his read of shifting public opinion, demographics, and interpretations of constitutional law, Camosy bypasses the question of whether our national abortion policy will change (he thinks it will) in order to focus on the question of what the new public policy ought to be (3).Camosy, a Catholic theologian, acknowledges early on that the argument he is putting forth is consistent with defined Catholic doctrine (6). Placing him solidly in the “pro-life” camp, many of the positions he seeks to defend and promote (life begins at conception, women are coerced into abortion, abortion is “tragic,” and most women seek abortion for “convenience”) are hardly new. In fact, his whole framing of the argument falls in line with the increasingly strident “pro-life” approach to abortion, which argues that abortion “hurts” women (112). This strategy developed in the 1990s after the Planned Parenthood vs. Casey decision opened up the possibility for state regulation of abortion and is the predominant rationale behind the recent spate of state regulations following the 2010 midterm elections that swept Republicans into state houses across the country (288 regulations between 2010–15 compared to 292 between 1995–2010). Camosy’s most controversial claim for the pro-life side is likely to be that the use of “indirect abortion” is morally acceptable for “proportionately serious reason(s),” which he identifies as rape and saving the life of the pregnant woman (83). The bill he proposes, the Mother and Prenatal Child Protection Act, allows for “indirect abortion” after a three-day waiting period and with submission of a signed affidavit claiming that the pregnancy is the result of nonconsensual sex. But it also establishes “equal protection of the law for prenatal children” and criminalizes abortion under most circumstances.It is unlikely that many on the pro-choice side will see these concessions as acceptable compromises. It’s a shame that Camosy seeks such an unlikely compromise rather than developing a common ground legislative proposal incorporating the many long-term feminist goals that are actually included in his bill: equal pay for equal work; addressing discrimination against parents (especially women), pregnant women, and new mothers; protection against domestic [End Page 210] violence; parental leave; universal prekindergarten and subsidized child care; and increased measures to collect child support, among others. These could serve as a basis for important legislation that would support pregnant women and their families and might indeed create circumstances in which some would decide to continue their pregnancies. Tellingly, his legislation completely ignores comprehensive sex education and free and unhindered access to all forms of contraception—the two strategies that have historically proven most effective in reducing abortion rates.As a Christian ethicist who is also working on the issue of abortion, I can appreciate that Camosy’s work is informed by his own beliefs and commitments on this issue. I share his desire to find a way forward on the issue of abortion and move beyond the abortion wars. However, I was unsatisfied with Camosy’s paternalistic approach to the issue of abortion and the women who terminate their pregnancies. His repeated assertions that women are coerced into abortion do not reflect the majority of social-scientific studies on the issue; his belief that criminalizing abortion would function to teach people (including these coerced women) that abortion is morally wrong is positively patriarchal; and his judgmental accusation that most women seek abortions for reasons of convenience betrays a deep disregard for women’s safety, economic well-being, and concern for their families, not to mention their health. We clearly have very different definitions of convenience.Rebecca Todd PetersElon UniversityCopyright © 2016 The Society of Christian Ethics... (shrink)

Various natural deduction formulations of classical, minimal, intuitionist, and intermediate propositional and first-order logics are presented and investigated with respect to satisfaction of the separation and subformula properties. The technique employed is, for the most part, semantic, based on general versions of the Lindenbaum and Lindenbaum–Henkin constructions. Careful attention is paid to which properties of theories result in the presence of which rules of inference, and to restrictions on the sets of formulas to which the rules may be employed, restrictions (...) determined by the formulas occurring as premises and conclusion of the invalid inference for which a counterexample is to be constructed. We obtain an elegant formulation of classical propositional logic with the subformula property and a singularly inelegant formulation of classical first-order logic with the subformula property, the latter, unfortunately, not a product of the strategy otherwise used throughout the article. Along the way, we arrive at an optimal strengthening of the subformula results for classical first-order logic obtained as consequences of normalization theorems by Dag Prawitz and Gunnar Stålmarck. (shrink)

Drawing on recently published correspondence as well as on a survey of Polish and international philosophical activity published in 1937 and details concerning the publisher and bookseller Aleksander Mazzucato, I provide evidence that, contrary to some recent assertions (but in line with older bibliographical entries), Tarski's ‘Der Wahrheitsbegriff in den formalisierten Sprachen’ was not published in journal form until 1936, although preprints, lacking two corrections and a small addendum, were likely available in the late months of 1935.

This article begins by outlining some of the history—beginning with brief remarks of Quine's—of work on conditional assertions and conditional events. The upshot of the historical narrative is that diverse works from various starting points have circled around a nexus of ideas without convincingly tying them together. Section 3 shows how ideas contained in a neglected article of de Finetti's lead to a unified treatment of the topics based on the identification of conditional events as the objects of conditional bets. (...) The penultimate section explores some of the consequences of the resulting logic of conditional events while the last defends it. (shrink)

Of his numerous investigations ... Tarski was most proud of two: his work on truth and his design of an algorithm in 1930 to decide the truth or falsity of any sentence of the elementary theory of the high school Euclidean geometry. [...] His mathematical treatment of the semantics of languages and the concept of truth has had revolutionary consequences for mathematics, linguistics, and philosophy, and Tarski is widely thought of as the man who "defined truth". The seeming simplicity of (...) his famous example that the sentence "Snow is white" is true just in case snow is white belies the depth and complexity of the consequences which can be drawn from the possibility of giving a general treatment of the concept of truth in formal mathematical languages in a rigorous mathematical way. (J.W. Addison). (shrink)

The majority of formal accounts attribute to Stoic logicians the classical truth-functional understanding of the material conditional and exclusive disjunction.These interpretations were disputed,...

The thesis that, in a system of natural deduction, the meaning of a logical constant is given by some or all of its introduction and elimination rules has been developed recently in the work of Dummett, Prawitz, Tennant, and others, by the addition of harmony constraints. Introduction and elimination rules for a logical constant must be in harmony. By deploying harmony constraints, these authors have arrived at logics no stronger than intuitionist propositional logic. Classical logic, they maintain, cannot be justified (...) from this proof-theoretic perspective. This paper argues that, while classical logic can be formulated so as to satisfy a number of harmony constraints, the meanings of the standard logical constants cannot all be given by their introduction and/or elimination rules; negation, in particular, comes under close scrutiny. (shrink)

This article begins by exploring a lost topic in the philosophy of science:the properties of the relations evidence confirming h confirmsh'' and, more generally, evidence confirming each ofh1, h2, ..., hm confirms at least one of h1, h2,ldots;, hn''.The Bayesian understanding of confirmation as positive evidential relevanceis employed throughout. The resulting formal system is, to say the least, oddlybehaved. Some aspects of this odd behaviour the system has in common withsome of the non-classical logics developed in the twentieth century. Oneaspect (...) – its ``parasitism'''' on classical logic – it does not, and it is this featurethat makes the system an interesting focus for discussion of questions in thephilosophy of logic. We gain some purchase on an answer to a recently prominentquestion, namely, what is a logical system? More exactly, we ask whether satisfaction of formal constraints is sufficient for a relation to be considered a (logical) consequence relation. The question whether confirmation transfer yields a logical system is answered in the negative, despite confirmation transfer having the standard properties of a consequence relation, on the grounds that validity of sequents in the system is not determined by the meanings of the connectives that occur in formulas. Developing the system in a different direction, we find it bears on the project of ``proof-theoretic semantics'''': conferring meaning on connectives by means of introduction (and possibly elimination) rules is not an autonomous activity, rather it presupposes a prior, non-formal,notion of consequence. Some historical ramifications are alsoaddressed briefly. (shrink)

From the point of view of proof-theoretic semantics, we examine the logical background invoked by Neil Tennant's abstractionist realist account of mathematical existence. To prepare the way, we must first look closely at the rule of existential elimination familiar from classical and intuitionist logics and at rules governing identity. We then examine how well free logics meet the harmony and uniqueness constraints familiar from the proof-theoretic semantics project. Tennant assigns a special role to atomic formulas containing singular terms. This, we (...) find, secures harmony and uniqueness but militates against the putative realism. (shrink)

First paragraph: Truthmaker theory maintains that for every truth there is something, some thing, some entity, that makes it true. Balking at the prospect that logical truths are made true by any particular thing, a consequence that may in fact be hard to avoid (see Restall 1996, Read 2000), this principle of truthmaking is sometimes restricted to (logically) contingent truths. I aim to show that even in its restricted form, the principle is provably false.

Proofs of Gödel's First Incompleteness Theorem are often accompanied by claims such as that the gödel sentence constructed in the course of the proof says of itself that it is unprovable and that it is true. The validity of such claims depends closely on how the sentence is constructed. Only by tightly constraining the means of construction can one obtain gödel sentences of which it is correct, without further ado, to say that they say of themselves that they are unprovable (...) and that they are true; otherwise a false theory can yield false gödel sentences. (shrink)

Plausibly, when we adopt a probabilistic standpoint any measure Cb of the degree to which evidence e confirms hypothesis h relative to background knowledge b should meet these five desiderata: Cb > 0 when P > P < 0 when P < P; Cb = 0 when P = P. Cb is some function of the values P and P assume on the at most sixteen truth-functional combinations of e and h. If P < P and P = P then (...) Cb ≤ Cb; if P = P and P < P then Cb ≥ Cb. Cb – Cb is fully determined by Cb and Cbe – Cbe; if Cb = 0 then Cb + Cbe = 0. If P = P then Cb = Cb. (shrink)

Starting from John MacFarlane's recent survey of answers to the question ‘What is assertion?’, I defend an account of assertion that draws on elements of MacFarlane's and Robert Brandom's commitment accounts, Timothy Williamson's knowledge norm account, and my own previous work on the normative status of logic. I defend the knowledge norm from recent attacks. Indicative conditionals, however, pose a problem when read along the lines of Ernest Adams' account, an account supported by much work in the psychology of reasoning. (...) Furthermore, there seems to be no place for degrees of belief in the accounts of belief and assertion given here. Degrees of belief do have a role in decision‐making, but, again, there is much evidence that the orthodox theory of subjective utility maximization is not a good description of what we do in decision‐making and, arguably, neither is it a good normative guide to how we ought to make decisions. (shrink)

Some propositions add more information to bodies of propositions than do others. We start with intuitive considerations on qualitative comparisons of information added . Central to these are considerations bearing on conjunctions and on negations. We find that we can discern two distinct, incompatible, notions of information added. From the comparative notions we pass to quantitative measurement of information added. In this we borrow heavily from the literature on quantitative representations of qualitative, comparative conditional probability. We look at two ways (...) to obtain a quantitative conception of information added. One, the most direct, mirrors Bernard Koopman’s construction of conditional probability: by making a strong structural assumption, it leads to a measure that is, transparently, some function of a function P which is, formally, an assignment of conditional probability (in fact, a Popper function). P reverses the information added order and mislocates the natural zero of the scale so some transformation of this scale is needed but the derivation of P falls out so readily that no particular transformation suggests itself. The Cox–Good–Aczél method assumes the existence of a quantitative measure matching the qualitative relation, and builds on the structural constraints to obtain a measure of information that can be rescaled as, formally, an assignment of conditional probability. A classical result of Cantor’s, subsequently strengthened by Debreu, goes some way towards justifying the assumption of the existence of a quantitative scale. What the two approaches give us is a pointer towards a novel interpretation of probability as a rescaling of a measure of information added. (shrink)

In his penetrating and thought-provoking article “What Is Logic?” Ian Hacking flags an issue that he leaves undiscussed.

While there is now considerable experimental evidence that, on the one hand, participants assign to the indicative conditional as probability the conditional probability of consequent given antecedent and, on the other, they assign to the indicative conditional the “defective truth-table” in which a conditional with false antecedent is deemed neither true nor false, these findings do not in themselves establish which multi-premise inferences involving conditionals participants endorse. A natural extension of the truth-table semantics pronounces as valid numerous inference patterns that (...) do seem to be part of ordinary usage. However, coupled with something the probability account gives us—namely that when conditional-free ϕ entails conditional-free ψ, “if ϕ then ψ” is a trivial, uninformative truth—we have enough logic to derive the paradoxes of material implication. It thus becomes a matter of some urgency to determine which inference patterns involving indicative conditionals participants do endorse. Only thus will we be able to arrive at a realistic, systematic semantics for the indicative conditional. (shrink)

Peter Milne; VII*—Tarski, Truth and Model Theory, Proceedings of the Aristotelian Society, Volume 99, Issue 1, 1 June 1999, Pages 141–168, https://doi.org/10.11.

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic (...) completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, Łukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates. (shrink)

From Introduction: In a 1968 article, ‘Probability Measures of Fuzzy Events’, Lotfi Zadeh pro-posed accounts of absolute and conditional probability for fuzzy sets (Zadeh, 1968).

The visual arts operated as a touchstone for French philosopher Jean-François Lyotard, influencing his thinking on everything from epistemology to politics. Building on the recent publication of a bilingual, six-volume edition of his writings on contemporary art and artists, this special issue of_ Cultural Politics_ provides a focus on Lyotard’s aesthetics. The issue includes a review of Lyotard’s writings on art, a discussion of his early figural aesthetics, and an essay on Lyotard’s little-known work, _Pacific Wall_, as well as two (...) essays on Lyotard and music. Two previously untranslated works by Lyotard himself are also featured: the influential article “Argumentation and Presentation: The Crisis of Foundations” and the interview “What to Paint?,” given at the time of the publication of the book of the same name. Painter Leon Phillips, whose work embodies many of the attributes of painting that were most important to Lyotard, is the featured artist for the issue. Throughout, the contributors argue for the primary importance of aesthetics in understanding Lyotard’s thought. Peter W. Milne is Assistant Professor in the Department of Aesthetics at Seoul National University. (shrink)

본고는 반성에 대한 리오타르의 후기 저작 두 가지를 논한다. 리오타르는 그의 칸트 독해에서 반성 개념에 대해 논한 바 있다. 본고는 그 중 칸트의 숭고미에 대하여 를 리오타르의 보다 이전의 저술인 비인간 에 포함된 에세이, “Si l’on peut penser sans corps” 와 관련하여 논한다. 이는 칸트의 반성에 대한 리오타르의 보다 자세한 논의인 칸트의 숭고미에 대하여 를 보다 넓은 차원에서 이해하고자 하는 시도이다. 이를 위해 본고는 후기 리오타르 사상에서 주요하게 등장하는, 사유와 신체 모두와 연관을 맺는 정념 개념에 주목한다.

A proof employing no semantic terms is offered in support of the claim that there can be truths without truthmakers. The logical resources used in the proof are weak but do include the structural rule Contraction.