Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak (...) admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study. (shrink)

The Visser rules form a basis of admissibility for the intuitionistic propositional calculus. We show how one can characterize the existence of covers in certain models by means of formulae. Through this characterization, we provide a new proof of the admissibility of a weak form of the Visser rules. Finally, we use this observation, coupled with a description of a generalization of the disjunction property, to provide a basis of admissibility for the intermediate logics BD2 and (...) GSc. (shrink)

In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of type-2 theory of effectivity. This gives rise to a natural representation of the set of Borel probability measures on X. We compare this representation to a canonically constructed representation which encodes a Borel probability measure as a lower semicontinuous function from the open sets to the unit interval. We show that this canonical representation (...) is admissible with respect to the weak topology on Borel probability measures. Moreover, we prove that for countably-based topological spaces the representation via probabilistic processes is equivalent to the canonical representation and thus admissible with respect to the weak topology. (shrink)

The property of admissibility of representations plays an important role in Type–2 Theory of Effectivity . TTE defines computability on sets with continuum cardinality via representations. Admissibility is known to be indispensable for guaranteeing reasonable effectivity properties of the used representations.The question arises whether every function that is computable with respect to arbritrary representations is also computable with respect to closely related admissible ones. We define three operators which transform representations into admissible ones in such a way that (...) relative computability of functions is preserved. Thus the use of admissible representations rather than of non–admissible ones does not decrease the class of relatively computable functions. (shrink)

In recent years much effort has gone into the study of languages which strengthen the classical first-order predicate calculus in various ways. This effort has been motivated by the desire to find a language which is(I) strong enough to express interesting properties not expressible by the classical language, but(II) still simple enough to yield interesting general results. Languages investigated include second-order logic, weak second-order logic, ω-logic, languages with generalized quantifiers, and infinitary logic.

The notion of a weakly scattered theory T is defined. T need not be scattered. For each a model of T, let sr() be the Scott rank of . Assume sr() ≤ ω\sp A \sb 1 for all a model of T. Let σ\sp T \sb 2 be the least Σ₂ admissible ordinal relative to T. If T admits effective k-splitting as defined in this paper, then θσ\cal Aθ\cal A$ a model of T.

This paper presents a sound and complete five-sided sequent calculus for first-order weak Kleene valuations which permits not only elegant representations of four logics definable on first-order weak Kleene valuations, but also admissibility of five cut rules by proof analysis.

In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...) semantics can meet that challenge by allowing for each interpretation to be composed of multiple scenarios. Using that idea, a logic with a complex semantic behavior can be understood as an appropriate combination of ingredient logics with simpler semantic behaviors into which the original logic is given a collection of translations preserving its soundness. Completeness is then achieved through the judicious choice of the admissible translating mappings. The present note provides interpretation by way of possible-translations semantics for a group of fundamental paraconsistent logics extending the positive fragment of classical propositional logic. The logics PI, Cmin, mbC, bC, mCi and Ci, among others, are all initially presented through their non-truth-functional bivaluation semantics and sequent versions and then split by way of possible-translations semantics based on 3-valued ingredients. (shrink)

The paper studies the logic TL(NBox+-wC) – logic of discrete linear time with current time point clusters. Its language uses modalities Diamond+ (possible in future) and Diamond- (possible in past) and special temporal operations, – Box+w (weakly necessary in future) and Box-w (weakly necessary in past). We proceed by developing an algorithm recognizing theorems of TL(NBox+-wC), so we prove that TL(NBox+-wC) is decidable. The algorithm is based on reduction of formulas to inference rules and converting the rules in special reduced (...) normal form, and, then, on checking validity of such rules in models of singleexponential size in the rules. Also we consider the admissibility problem for TL(NBox+-wC) and show how to reduce the problem for admissibility to the decidability of TL(NBox+-wC) itself using definable universal modalities. (shrink)

We study game formulas the truth of which is determined by a semantical game of uncountable length. The main theme is the study of principles stating reflection of these formulas in various admissible sets. This investigation leads to two weak forms of strict-II11 reflection . We show that admissible sets such as H and Lω2 which fail to have strict-II11 reflection, may or may not, depending on set-theoretic hypotheses satisfy one or both of these weaker forms.

I argue that on very weak assumptions about truth (in particular, that there are coherent norms governing the use of "true"), there is a proposition absolutely inexpressible with conventional language, or something very close. I argue for this claim "constructively": I use a variant of the Berry Paradox to reveal a particular thought for my readership to entertain that very strongly resists conventional expression. I gauge the severity of this expressive limitation within a taxonomy of expressive failures, and argue (...) that despite its strength there is nothing incoherent about admitting its existence. The argument forms part of a project of clarifying precisely what trade-offs are required to secure the kinds of expressive power truth theorists typically want, in the process showing that the admission of very strong expressive limitations may ultimately prove to be the lesser of two evils. (shrink)

Let A be an admissible set. A sentence of the form ∀R̄φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence if φ ∈ A (φ is $\bigvee\Phi$ , where Φ is an A-r.e. set of sentences from A; φ ∈ Lω1ω). A sentence of the form ∃R̄φ is an ∃2(A) (∃s 2(A),∃2(Lω1ω)) sentence if φ is a ∀1(A) (∀s 1(A),∀1(Lω1ω)) sentence. A class of structures is, for example, a ∀1(A) class if it is the class of models of a ∀1(A) sentence. Thus (...) ∀1(A) is a class of classes of structures, and so forth. Let Mi be the structure $\langle i, 0$. Let Γ be a class of classes of structures. We say that a sequence $J_1,\ldots,J_i,\ldots, i < \omega$, of classes of structures is a Γ sequence if $J_i \in \Gamma, i < \omega$, and there is I ∈ Γ such that M ∈ Ji if and only if [M, Mi] ∈ I, where [,] is the disjoint sum. A class Γ of classes of structures has the easy uniformization property if for every Γ sequence $J_1,\ldots,J_i, \ldots, i < \omega$, there is a Γ sequence $J'_1,\ldots,J'_i,\ldots, i < \omega$, such that $J'_i \subseteq J_i, i < \omega, \bigcup J'_i = \bigcup J_i$, and the J'i are pairwise disjoint. The easy uniformization property is an effective version of Kuratowski's generalized reduction property that is closely related to Moschovakis's (topological) easy uniformization property. We show over countable structures that ∀1(A) and ∃2(A) have the easy uniformization property if A is a countable admissible set with an infinite member, that ∀s 1(Lα) and ∃s 2(Lα) have the easy uniformization property if α is countable, admissible, and not weakly stable, and that ∀1(Lω1ω) and ∃2(Lω1ω) have the easy uniformization property. The results proved are more general. The result for ∀s 1(Lα) answers a question of Vaught (1980). (shrink)

Many classically valid meta-inferences fail in a standard supervaluationist framework. This allegedly prevents supervaluationism from offering an account of good deductive reasoning. We provide a proof system for supervaluationist logic which includes supervaluationistically acceptable versions of the classical meta-inferences. The proof system emerges naturally by thinking of truth as licensing assertion, falsity as licensing negative assertion and lack of truth-value as licensing rejection and weak assertion. Moreover, the proof system respects well-known criteria for the admissibility of inference rules. (...) Thus, supervaluationists can provide an account of good deductive reasoning. Our proof system moreover brings to light how one can revise the standard supervaluationist framework to make room for higher-order vagueness. We prove that the resulting logic is sound and complete with respect to the consequence relation that preserves truth in a model of the non-normal modal logic _NT_. Finally, we extend our approach to a first-order setting and show that supervaluationism can treat vagueness in the same way at every order. The failure of conditional proof and other meta-inferences is a crucial ingredient in this treatment and hence should be embraced, not lamented. (shrink)

For Savage (1954) as for de Finetti (1974), the existence of subjective (personal) probability is a consequence of the normative theory of preference. (De Finetti achieves the reduction of belief to desire with his generalized Dutch-Book argument for Previsions.) Both Savage and de Finetti rebel against legislating countable additivity for subjective probability. They require merely that probability be finitely additive. Simultaneously, they insist that their theories of preference are weak, accommodating all but self-defeating desires. In this paper we dispute (...) these claims by showing that the following three cannot simultaneously hold: (i) Coherent belief is reducible to rational preference, i.e. the generalized Dutch-Book argument fixes standards of coherence. (ii) Finitely additive probability is coherent. (iii) Admissible preference structures may be free of consequences, i.e. they may lack prizes whose values are robust against all contingencies. (shrink)

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are (...) connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. (shrink)

The subsystem S of Parry's AI [10] (obtained by omitting modus ponens for the material conditional) is axiomatized and shown to be strongly complete for a class of three valued Kripke style models. It is proved that S is weakly complete for the class of consistent models, and therefore that Ackermann's rule is admissible in S. It also happens that S is decidable and contains the Lewis system S4 on translation — though these results are not presented here. S is (...) arguably the most relevant relevant logic known at this time to be decidable. (shrink)

The statements traditionally labelled “necessary,” among them the valid theorems of mathematics and logic, are identified as “those whose truth is independent of experience.” The “truth” of a necessary statement has to be independent of the truth or falsity of experiential statements; a necessary statement can be neither confirmed nor refuted by empirical tests.The admission of genuinely necessary statements presents the empiricist with a troublesome problem. For an empiricist may be defined, in terms of the current idiom, as one who (...) adheres to some version, however “weak,” of a principle of verifiability. One, that is, who claims that no statement can have cognitive meaning unless its truth depends, however indirectly, upon the truth of experiential statements; unless it can be provisionally confirrned or refuted by empirical tests. Allowing that some necessary statements have cognitive meaning, then, would be to provide a prima facie case against the validity of the principle of verifiability. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reply to Stephen PhillipsArindam ChakrabartiMuch as I am honored by Stephen Phillips' detailed defense, in the face of my methodological "refutation," of the Nyāya thesis that a raw perception of the qualifier is a necessary causal factor for some (not all) determinate perception of an entity as qualified, I am not fully convinced that my deeper qualms about the very idea of immaculate perception unimpregnated by predicative structure have (...) all been adequately addressed. Instead of a detailed response, which I intend to undertake elsewhere, I wish to underscore the central worry behind my fifth (which Phillips calls "good") and seventh (which Phillips calls "weak") objections.When I claimed that perception is introduced, taxonomically, as a variety of veridical awareness, I had in mind the opening line of Gaṅgeśa's section on the definition of perception:sā ca pramā caturvidhā, pratyakṣānumityupamitiśābdā-bhedātAnd such veridical awareness is of four kinds: perception, inferential knowledge, knowledge from similarity, and knowledge from words.1This seems to be flatly incompatible with the admission of a subclass of perceptions that are not veridical awarenesses!Why does Phillips say that I am simply mistaken? True, taxonomic difficulties cannot overturn empirical evidence. But recall that there is no direct apperceptive evidence for "raw perception." The sole evidence is a generalization from a whole series of mediate (parokṣa) awarenesses that can happily afford to be instrumentally and crucially caused by other awarenesses. On the other hand, immediacy, which is the hallmark of a perception, consists of not having another awareness in its causal nexus. My seeing of a wall as white is direct, rather than inferential, analogical, or testimonial, to the extent that I did not have to go through any other awareness first in order to arrive at this visual perception. An inductive generalization from other mediate (cognition-generated) cognitions should not have such inexorable probative power over our account of immediate sensory cognition as to force us into admitting a neither-true-nor-false third kind of raw awareness!Phillips seems to have overlooked the metaphor of "spelling" that I used in this context while giving my second objection. If the step-by-step picture of building up the content of perception that Gaṅgeśa assumes is correct, then each element of the perceptual content of the predicative perception that this is a flower—the universal flowerhood, the actual physical object identified as "this," and qualification as a cementing relation, in this case inherence—would first have to be cognized in the unconnected "raw" manner! Now, even if we somehow swallow the idea of seeing a universal barely and not in relation to any one of its instances, it simply makes no [End Page 114] sense to talk about a bare, raw, unstructured perceptual acquaintance with qualification or inherence! Logically and structurally one could argue that unless you have "got" a, b, and R first, you cannot have the complex aRb. But this is admittedly a process of logical postmortem dissection of a whole piece of direct qualificative perception. And the point of my metaphorical warning—"You need to have 'L' and 'O' and 'D' and 'N' to spell 'London,' but you do not need to spell 'L' or 'O' or 'D' or 'N' first. Single letters simply cannot be spelled!"—was this: there are all sorts of different ways of "getting." You need to "get" the qualifying feature somehow in order to see or hear or taste something as qualified by that feature, but you do not therefore need to see or hear or taste that feature alone first in a bare, raw, unqualified manner! I do believe, like a good Naiyāyika, that high-pitchedness (or fifthness, in the octave) can be heard although it is a sound-universal. But I refuse to admit that before I can hear a sung note as high-pitched or (the fifth) I must somehow hear that universal directly without hearing it in any note!The central point, once again, is this: all awareness is intentional, according to Nyāya. There are only three kinds of intentional roles that our awarenesses assign to their objects: the role of... (shrink)

I respond to six objections, raised by Selim Berker and Karl Schafer, against the theory offered in my Empiricism and Experience: (1) that the theory needs a problematic notion of subjective character of experience; (2) that the transition from the hypothetical to the categorical fails because of a logical difficulty; (3) that the constraints imposed on admissible views are too weak; (4) that the theory does not deserve the label 'empiricism'; (5) that the motivations provided for the Reliability constraint (...) are insufficient; and (6) that convergence is bound to fail since epistemic entitlements are permissions. (shrink)

Primary objective: This study represents the first large-scale research on high school philosophy in a public education curriculum in North America. Our objective was to identify the impacts of high school philosophy, as well as the challenges of teaching it in its current format in Ontario high schools. Research design: The qualitative research design captured the perspectives of students and teachers with respect to philosophy at the high school level. All data collection was structured around central questions to provide insight (...) into the dynamics of their shared process of teaching/learning. Methods and procedures: We conducted semi-structured with interviews philosophy teachers (n = 9), classroom observations (n = 142), and student focus groups at 16 diverse high schools. Transcripts were coded according to themes. Results: Our findings reflect the complicated nature of philosophy as a discipline characterized by abstract thinking. Participants found it mind-opening, yet challenging, providing educational opportunities that are largely absent in conventional schooling. They saw multiple connections between philosophy and other subjects, but also appreciated its distinctive benefits. Teachers relied primarily on textbooks and contemporary media to deliver the curriculum. We found that a teacher’s background in philosophy may influence what is taught in philosophy courses and how, especially given the flexibility of the provincial curriculum. Conclusions: The findings suggest that philosophy is a unique, beneficial subject that teachers enjoy teaching and students greatly value, characterizing it as both difficult and rewarding. Our study revealed that considerable differences exist in how philosophy is taught and learned around the province. The flexibility of the provincial curriculum appears to be an invitation for creative and responsive teaching; however, philosophy teachers’ weak preparation can, by their own admission, be a hindrance to effective curriculum delivery. Studying philosophy enhances students’ thinking about other academic areas of study and in some cases opens them up to new ways of thinking. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Augustine's Intellectual Conversion: The Journey from Platonism to ChristianityTravis E. AblesBrian Dobell. Augustine's Intellectual Conversion: The Journey from Platonism to Christianity. Cambridge-New York: Cambridge University Press, 2010. Pp. xvii + 250. Cloth, $82.00.The question of Augustine's Platonism is famously vexed. Since Peter Brown, the standard reading holds that Augustine did not move beyond the Neoplatonism of his early dialogues until he studied the writings of the apostle Paul (...) in the mid-390s CE, after which his distinctive theology begins to emerge. In this book, Brian Dobell's basic claim is that, whatever the validity of the "volitional conversion" of book 8, Augustine is not truly converted to orthodox Christianity until he discards the Photinian (adoptionist) Christology he admits to in Confessions [hereafter conf.] 7.19.25, and discards the Platonic ascent as a means to contemplative union with God, both of which take place with the reading of Paul. But the book is equally motivated by a concern to defend the historicity of conf.; Dobell claims it is perfectly reliable, once we understand the latter half of book 7 not as a few months in 386, but as a compressed narrative spanning Augustine's entire development until his true conversion to Christianity around 395. [End Page 137]Dobell develops this argument by isolating Augustine's twofold way of salvation in the writings of the late 380s. First is the "way of authority," in which Augustine's putative Photinian Christology portrays Christ as a kind of "poor man's Plato, sent to provide a path to salvation for the uneducated masses" (96). The human Jesus is "assumed" by God and is as "a man of outstanding wisdom" (73) but is not the incarnate Son. Dobell analyzes the homo assumptus/susceptus language of the early writings, arguing that Augustine does not truly hold an orthodox Christology until 396, concordant with the development of his theology of operative grace. The second, much longer section of the book concerns the "way of reason," the intellectualist path of salvation expressed in Augustine's early obsession with the liberal disciplines. Dobell dissects the Platonic ascents of conf. 7, adducing verbal and conceptual parallels from texts ca. 387–390 (De immortalitate animae, De ordine, De libero arbitrio, De vera religione) showing how Augustine's métaphysique des degrés d'être, a concept Dobell borrows from Olivier Du Roy, provides both a means of articulating these ascents and an answer to the problem of evil. But by De doctrina christiana, Augustine has decisively rejected the Platonic ascent and the liberal disciplines, and it simply remains for his Christology to come in line for the "intellectual conversion" to be complete.Dobell's book is a significant addition to the current debate. His knowledge of the first decade or so of Augustine's literary output is impressive, and his familiarity with the secondary literature is considerable, though not encyclopedic—he misses the work of J. Patout Burns, which complicates the Pauline thesis through consideration of the anti-Donatist literature. Dobell offers magisterial and invaluable discussions of famously fraught topics such as Augustine's indecisiveness about the preexistence of the soul, or the volitional solution to the problem of evil. There are some problems with Dobell's argument, though. While his main thesis that conf. 7.9.13ff. is a kind of précis of almost a decade of intellectual development deserves serious consideration, and is an elegant solution to debates about the historicity of Augustine's narrative in conf., the supporting arguments Dobell employs are less persuasive. A major portion of his book revolves around the contention that Augustine's early, heretical Photinian Christology extends much longer than modern scholarship has realized, that Augustine rectifies this Christology in conjunction with a Pauline soteriology of grace, and that all of this has to happen before Augustine's conversion is complete. If we suspend the question of normativity inherent in deciding Augustine's "orthodoxy" (particularly prior to Chalcedon), Dobell still does not succeed in showing that the early "pedagogical" homo assumptus Christology is, in fact, adoptionist; indeed, his evidence is often rather weak (for a tacit admission, see 73). On the flip... (shrink)

This paper aims to study the organizational excellence and the extent of its clarity in the Palestinian universities from the perspective of students. Researchers have used the descriptive and analytical approach and used the questionnaire for data collection and distributed to students in universities. The researchers used a sample stratified random method by the university. The total number of students was (381) and (235) were distributed to identify the study population. (166) questionnaires were recovered with rate of (96.3%). We used (...) statistical analysis (SPSS) program for data entry, processing and analysis. The study reached the following conclusions: that (62.8%) of the study population believe that the availability of "faculty staff" somewhat weak, showed that the number of Academic staff is appropriate to the number of students. The results confirmed that (66.4%) of the study population believe that the suitability "admission policies" is average, showed that the admission policies declared for the students, it is also transparent, the university administration provides orientation programs for newley admitted students. The results showed that (55.4%) of the study population believe that the "Student support" is low in the universities, and (52.8%) of the study population believe that "student activities" in the universities is low. The study found a set of recommendations, including: the establishment of university centers for gifted and talented students, follow their growth and their creations after graduating from college and while working in the sectors of production, and provide college library modern references in all disciplines. (shrink)

Let κ be a cardinal, and let H κ be the class of sets of hereditary cardinality less than κ ; let τ (κ) > κ be the height of the smallest transitive admissible set containing every element of {κ}∪H κ . We show that a ZFC-definable notion of long unfoldability, a generalisation of weak compactness, implies in the core model K, that the mouse order restricted to H κ is as long as τ. (It is known that some (...) weak large cardinal property is necessary for the latter to hold.) In other terms we delimit its strength as follows: Theorem Con(ZFC+ω2-Π 1 1-Determinacy) ⇒ ⇒Con(ZFC+V=K+∃ a long unfoldable cardinal ⇒ ⇒Con(ZFC+∀X(X # exists) + ‘‘ $\forall D \subseteq \omega_1 D$ is universally Baire ⇔ ∃r∈R(D∈L(r)))’’, and this is set-generically absolute). We isolate a notion of ω-closed cardinal which is weaker than an ω1-Erd\ os cardinal, and show that this bounds the first long unfoldable: Theorem Let κ be ω -closed. Then there is a long unfoldable ł<κ. (shrink)

Persons concerned with medical education sometimes argued that medical students need no formal education in ethics. They contended that if admissions were restricted to persons of good character and those students were exposed to good role models, the ethics of medicine would take care of itself. However, no one seems to give much philosophic attention to the ideas of model or role model. In this essay, I undertake such an analysis and add an analysis of role. I show the weakness (...) in relying on role models exclusively and draw implications from these for appeals to virtue theory. Furthermore, I indicate some of the problems about how virtue theory is invoked as the ethical theory that would most closely be associated to the role model rhetoric and consider some of the problems with virtue theory. Although Socrates was interested in the character of the (young) persons with whom he spoke, Socratic education is much more than what role modeling and virtue theory endorse. It -- that is, philosophy -- is invaluable for ethics education. (shrink)

In this article I propose a view which explains how it is possible that the disagreement concerning clear cases of a given vague predicate is genuine, whereas that concerning borderline cases is faultless. I take the possibility of faultless disagreement concerning borderline cases to be an important characteristic of vague predicates and in my view any adequate theory of vagueness should account for it. My proposal might be called “contextual supervaluationism” and it is inspired by Kölbel's relativist view from his (...) paper “Vagueness as Semantic”. Following Kölbel I claim that the range of admissible sharpenings assumed by supervaluationism is context‐dependent, but contrary to him I maintain that we need supertruth as well as truth at a sharpening. Moreover – again unlike Kölbel – I argue that utterances concerning borderline cases are permissible. I claim, however, that such utterances should be assertives rather than assertions, since they express only a weak belief of the speaker. It is the different illocutionary forces of utterances concerning clear cases and borderline cases that make it possible to explain the distinct nature of disagreements over such cases. (shrink)

The author gentzenizes the positive fragmentsT + andR + of relevantT andR using formulas with, prefixes (subscripts). There are three main Gentzen formulations ofS +{T+,R +} calledW 1 S +,W 2 S + andG 2 S +. The first two have the rule of modus ponens. All of them have a weak rule DL for disjunction introduction on the left. DL is not admissible inS + but it is needed in the proof of a cut elimination theorem forG 2 (...) S +.W 1 S + has a weak rule of weakeningW 1 and it is not closed under a general transitivity rule. This allows the proof that A inS + iff A inW 1 S +. From the cut elimination theorem forG 2 S + it follows that if A inS +, then A inG 2 S +. In order to prove the converse,W 2 S + is needed. It contains modus ponens, transitivity, and a restricted weakening rule.G 2 S + is contained inW 2 S + and there is a proof that A inW 2 S + iff A inW 1 S +. (shrink)

Economists are often called upon as expert witnesses by the parties involved in antitrust litigation. One challenge they may face in US federal courts is compliance with the Daubert standard of admissibility of expert testimony. The interplay between model applicability and the Daubert standard is analyzed, suggesting the importance of distinguishing between weak applicability claims, those that state that a model’s critical assumptions are shared by the target, and strong applicability claims, those that connect empirical models and quantitative (...) market features. Recent antitrust cases in which expert testimonies based on economic models have been assessed following the Daubert standard are examined using this framework. Some normative implications are drawn concerning how to improve judges’ assessment of model-based arguments. (shrink)

The author gentzenizes the positive fragments T₊ and R₊ of relevant T and R using formulas with prefixes (subscripts). There are three main Gentzen formulations of $S_{+}\in \{T_{+},R_{+}\}$ called W₁ S₊, W₂ S₊ and G₂ S₊. The first two have the rule of modus ponens. All of them have a weak rule DL for disjunction introduction on the left. DL is not admissible in S₊ but it is needed in the proof of a cut elimination theorem for G₂ S₊. (...) W₁ S₊ has a weak rule of weakening W₁ and it is not closed under a general transitivity rule. This allows the proof that $\vdash A$ in S₊ iff $\vdash A$ in W₁ S₊. From the cut elimination theorem for G₂ S₊ it follows that if $\vdash A$ in S₊, then $\vdash A$ in G₂ S₊. In order to prove the converse, W₂ S₊ is needed. It contains modus ponens, transitivity, and a restricted weakening rule. G₂ S₊ is contained in W₂ S₊ and there is a proof that $\vdash A$ in W₂ S₊ iff $\vdash A$ in W₁ S₊. (shrink)

Published in 1933, at a time of widespread unemployment and bank failures, this book by the young Sidney Hook received great critical acclaim and established his reputation as a brilliant expositor of ideas. By "revolutionary interpretation" Hook meant quite literally that Marx's main objective was to stimulate revolutionary opposition to class society. Hook later abandoned the revolutionary views expressed in this volume, but he never abandoned his warm positive views of Marx as a thinker and a fighter for freedom. He (...) eventually concluded that 20th century history had proved both him and Marx wrong about the necessity of revolutionary means to achieve their mutual social goals. But, says his son Ernest B. Hook in an introduction, this concession of error "he did not see... as an admission of intellectual weakness, but the natural position of a reasonable person when, in the light of observation and experience, he concludes he has erred." This expanded edition makes readily available for scholars an influential work long out of print and provides critical insight into the intellectual development of one of the 20th-century's great thinkers. (shrink)

R. M. Friedberg demonstrated the existence of a recursive functional that agrees with no Banach-Mazur functional on the class of recursive functions. In this paper Friedberg's result is generalized to both α-recursive functionals and weak α-recursive functionals for all admissible ordinals α such that $\lambda , where α * is the Σ 1 -projectum of α and λ is the Σ 2 -cofinality of α. The theorem is also established for the metarecursive case, α = ω 1 , where (...) α * = λ = ω. (shrink)

When an anxiety‐reducing drug with virtually no side effects is used to enhance performance, is that cheating? Is it drug abuse? Is it an admission of professional weakness?

As far as logic is concerned, the conclusion of Michael Dummett's manifestability argument is that intuitionistic logic, as first developed by Heyting, satisfies the semantic requirements of antirealism. The argument may be roughly sketched as follows: since we cannot manifest a grasp of possibly justification-transcendent truth conditions, we must countenance conditions which are such that, at least in principle and by the very nature of the case, we are able to recognize that they are satisfied whenever they are. Intuitionistic logic (...) satisfies the semantic requirement that we should either eschew the notion of truth altogether and replace it by provability in principle, or constrain it by provability in principle (Dummett [1973] 1978). (Handout: 1-5). Some philosophers have argued that the traditional antirealist desideratum of decidability in principle is too weak, so that semantic antirealism properly construed must be committed to effective decidability. As such, it either leads to strict finitism (Wright [1982] 1993) [Handout: 6] or to a much stronger kind of logical revisionism than the one considered by intuitionists (whether or not they accept the manifestability argument): substructural logics, and in particular linear logics, rather than intuitionistic logic, satisfy the semantic requirements of strict antirealism (Dubucs and Marion 2004) [Handout: 8-9]. I shall develop two different kinds of replies. The first is concerned with the notion of meaning per se and looks to strict finitism directly, although not on the ground that it would provide a correct way of dealing with Soritic-type paradoxes (the original and primary focus of discussion in Wright [1982] 1993). The second is concerned with the justification of structural and logical rules in a natural deduction system à la Gentzen. It will deal in particular with the criticism of the structural rules of Weakening and Contraction [Handout: 10 and 11]. The first kind of reply, which Dummett has partially taken into consideration, is that if we jettison the effectively vs. in principle distinction, as applied to manifestability-type arguments, we end up with an unsatisfactory explanation of how the meaning of statements covering the practically unsurveyable or pro tempora undecided cases is fixed. The idea is that if we have a method which may be used over some small range, we have determined a way of applying the method everywhere in principle and that this is enough as far as fixing meaning is concerned. Decidability in principle is just what we need with respect to manifestation of grasp of meaning. In this perspective, antirealism shouldn't be strict and manifestability-type arguments need not be applied as far as the strict finitist would want to [Handout: 7]. It follows that there is no reason to think that practical feasibility should be built in assertibility conditions and proofs be construed dynamically as acts in the strict antirealist's acception of that term [Handout: 8]. I shall then look at one radical antirealist principle disqualifying structural rules, namely Token Preservation, arguing against Bonnay and Cozic's criticisms of Dubucs and Marion (Bonnay and Cozic 3 2007) that some conceptual support may be provided for Token Preservation, which doesn't rely on a causal misreading of the turnstile [Handout: 13, 14]. I shall then assess the merits and limits of radical antirealism and the logic of feasible proofs with respect to the original Dummettian argument in favour of semantic antirealism (provided it has indeed revisionist implications for logic), whether the radical antirealist merely stipulates what human feasibility amounts to, or dispenses with structural rules in order to argue in favour of a curb on the epistemic idealizations they unwarrantedly embed. It will be noted here that there is a great difference, conceptually speaking, between the rejection of classical logic via the curbing of the epistemic idealizations embedded in structural rules, and the rejection of classical logic via the criticism of the introduction and elimination rules which fix the meaning of the classical constants. The kind of logical revisionism envisaged by intuitionists from Heyting on is in many respects stronger than the one envisaged by advocates of linear logic, should they ground their arguments on an endorsement of strict antirealism. The crucial case of excluded middle is telling. Because of the splitting of the constants in linear logic (Handout: 12], two distinct laws of excluded middle may be formulated (Handout: 15), but the traditional arguments of Brouwer and Heyting against the classical law yield a stronger revision than the substructural revision with its admission of these two (very) weak versions of the law. (Project: a clearer conception is needed of how the introduction and elimination rules for the logical connectives in the intuitionistic calculus depend on the structural rules which the radical antirealist wishes to reject.). (shrink)

With small to modest sample sizes and complex models, maximum likelihood estimation of confirmatory factor analysis models can show serious estimation problems such as non-convergence or parameter estimates outside the admissible parameter space. In this article, we distinguish different Bayesian estimators that can be used to stabilize the parameter estimates of a CFA: the mode of the joint posterior distribution that is obtained from penalized maximum likelihood estimation, and the mean, median, or mode of the marginal posterior distribution that are (...) calculated by using Markov Chain Monte Carlo methods. In two simulation studies, we evaluated the performance of the Bayesian estimators from a frequentist point of view. The results show that the EAP produced more accurate estimates of the latent correlation in many conditions and outperformed the other Bayesian estimators in terms of root mean squared error. We also argue that it is often advantageous to choose a parameterization in which the main parameters of interest are bounded, and we suggest the four-parameter beta distribution as a prior distribution for loadings and correlations. Using simulated data, we show that selecting weakly informative four-parameter beta priors can further stabilize parameter estimates, even in cases when the priors were mildly misspecified. Finally, we derive recommendations and propose directions for further research. (shrink)

This paper examines public meetings in the Netherlands where experts and officials interact with local residents on the human health effects of livestock farming. Using Conversation Analysis, we reveal a ‘weapon of the weak’: a practice by which the residents resist experts’ head start in information meetings. It is shown how residents draw on the given question-answer format to challenge experts and pursue an admission of, for example, methodological shortcomings. We show how the residents’ first question functions as a (...) ‘foot-in-the-door’, providing them with a strong basis for skepticism. By systematically challenging the expert responses, the residents exploit the interaction’s sequential organization, with the effect that the goal becomes them being convinced rather than being informed. Consequently, the withholding of consent becomes the residents’ ‘weapon’. Finally, we argue that in an age where expertise is increasingly contested, it is crucial to understand how, and to what end, this contestation may occur. (shrink)

This paper focuses on the relevance of borders and national membership as barriers to first admission. Strengths and weaknesses of the different liberal arguments for open and restricted borders will be analysed, focusing on the ‘liberal paradox’ which holds that an asymmetrical view on entry and exit is compatible with the liberal commitment to equality and individual liberties. Finally, a proposal will be formulated in order to find a middle way between the idealism of open borders and more realist versions (...) of liberal egalitarianism by incorporating a hermeneutical account of human morality as a relational, contextual matter which does not think in terms of borders but instead of trans-boundary dialogical spaces. (shrink)

Plea bargains are the stock-in-trade of the modern American prosecutor’s office. The basic scenario, wherein a defendant agrees to plea guilty in exchange for a reduced sentence, is familiar to viewers of police procedurals. In an equally famous variation on the theme, the prosecutor requests something more than an admission of guilt: leniency will only be forthcoming if the defendant is willing to cooperate with the prosecutor in securing the conviction of another suspect. In some of these cases, the defendant (...) is a low-level criminal who has information on a high-level malefactor who is of more interest to the police. In others, the defendant and the person she is asked to testify against are of the same criminal rank, but evidentiary weaknesses induce the prosecutor to seek the aid of one suspect in order to convict the other. In this latter version, the classic tactic of film detectives is to offer the bargain to both defendants in the hopes that one will crack and agree to reveal what he knows about the other. The defendants could either be in custody for different crimes or be accomplices in the same offense. -/- The last variation (involving accomplices) is the subject of this Article. I take issue with the prosecutorial tactics in these cases because of the risk they create of punishing the comparatively virtuous person more than the comparatively vicious one for the same acts. As I will argue, it is the less honest person who is more likely to accept the prosecutor’s deal, leading the more honest person, who resisted temptation, to suffer greater penalties. -/- I contend that this scenario offends distributive justice, runs counter to the idea (accepted by some) that a proper goal of the state is the cultivation of good character in the citizenry, and is perverse insofar as a person will suffer more from the prosecutor's dilemma insofar as she is more or less a person of conscience. These negative considerations notwithstanding, I do not call for the abolition of accomplice plea bargaining but argue that the problems I raise should be considered when weighing its pros and cons. -/- This article was published in the company of a strong critical response by Guha Krishnamurthi, whose contribution I greatly appreciate. (shrink)

In a letter to Franz Overbeck from 1883 Nietzsche confessed that the more he read the German philosopher Gustav Teichmüller the more he realized »how poorly« he understood Plato and »how much Zarathustra Platonizes«. This is a striking admission from a thinker who defined his own philosophy as »inverted Platonism« and it has yet to be adequately explained. This article examines what Nietzsche may have meant by the verb »to Platonize« by drawing an explicit connection to Teichmüller's controversial views on (...) Platonic psychology. Two possible meanings of the verb are put forth, a weak and a strong meaning and a case in defense of the latter is made. In the strong sense of the word »to Platonize« meant that the Overman was a mythos in the Platonic sense, in that it made Nietzsche's much more recondite »Bundle Theory« of the self accessible to the average reader, but it did not correspond to a view of the self which Nietzsche espoused in his own voice. (shrink)

Let I be a countable jump ideal in $\mathscr{D} = \langle \text{The Turing degrees}, \leq\rangle$ . The central theorem of this paper is: a is a uniform upper bound on I iff a computes the join of an I-exact pair whose double jump a (1) computes. We may replace "the join of an I-exact pair" in the above theorem by "a weak uniform upper bound on I". We also answer two minimality questions: the class of uniform upper bounds on (...) I never has a minimal member; if ∪ I = L α [ A] ∩ ω ω for α admissible or a limit of admissibles, the same holds for nice uniform upper bounds. The central technique used in proving these theorems consists in this: by trial and error construct a generic sequence approximating the desired object; simultaneously settle definitely on finite pieces of that object; make sure that the guessing settles down to the object determined by the limit of these finite pieces. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:98 COMMENTS ON TWEYMAN AND DAVIS Tweyman contends that in Parts X and XI of the Dialogues Philo sets aside his Pyrrhonian or skeptical approach to theology, which consists in falsifying or casting doubt on the hypotheses of Cleanthes, and instead argues for a thesis of his own, viz. what we might call the "indifference thesis" that the original source of all things is morally indifferent. Davis counters with (...) an alternative interpretation of these two Parts of the Dialogues, arguing that Philo's approach to Cleanthes' arguments is consistent throughout the Dialogues and that Philo's aim is always the same, viz., to show that if cleanthes remains true to his principles and accepts their logical consequences, it is Cleanthes who is the Pyrrhonian and Philo who is the moderate skeptic. My position is that neither Tweyman nor Davis have given a proper analysis of Parts X and XI. I would agree with Davis that Tweyman' s position does seem to have an initial implausibility to it for at least two reasons. First of all, in Part II Philo commits himself to the "mystical incomprehensibility thesis" that the attributes of God are perfect but incomprehensible; and the mystical incomprehensibility thesis is incompatible with the indifference thesis. It cannot be the case both that God has perfect but incomprehensible attributes and that we also know he is morally indifferent. Moreover, the mystical incomprehensi2 bility thesis is reiterated in Part VI and more importantly, in Part X: "None but we mystics, as you were pleased to call us, can account for this strange mixture of phenomena, by deriving it from attributes, infinitely perfect, but incomprehensible" 99 (D 199). Since Philo appears to stick to the mystical incomprehensibility thesis, Tweyman has a problem explaining how Philo can hold one position on the attributes of God in Part X (the mystical incomprehensibility thesis) and then supposedly reverse himself in Part XI to argue for another (the indifference thesis). Second, Tweyman' s position seems to contradict the strategic position outlined by Philo in Part II: "You seem not to apprehend, replied Philo, that I argue with Cleanthes in his own way; and by showing him the dangerous consequences of his tenets, hope at last to reduce him to our opinion." (D 145) The strategy is to show Cleanthes that any position but that of the mystics has dangerous, i.e., skeptical or theologically unwelcome consequences, and so should be abandoned. Philo's strategy is not to defend his own position, but rather to reveal the weaknesses in Cleanthes' position. Thus far I would agree that Davis' interpretation is more consistent with both Philo's strategic position and with his mystical incomprehensibility thesis. Yet Davis does not directly take up the important point about Parts X and XI which Tweyman raises: that Philo changes his way of arguing in Parts X and XI from that which he had been employing previously in the first eight sections, i.e., that he changes from a Pyrrhonian to a non-Pyrrhonian way of arguing. This is how Tweyman puts it: In the first eight sections, Philo argues against Cleanthes' hypothesis by advancing his own hypotheses. His effort to advance hypotheses must be assessed in light of the fact that (by his own admission) all such hypotheses are based on insufficient 100 data, and, therefore, none is, strictly speaking, acceptable. Their use is not to establish truths about the nature of God, but to establish the conclusion which we find at the end of Part VIII that 'a total suspense of judgment is here our only reasonable resource.' The design of the world is compatible with, and could have arisen from, an indefinite number of designing principles. On the other hand, we have seen that in dealing with Cleanthes' hypotheses in Parts X and XI we are able to proceed more scientifically, and, in this manner, eliminate all but one of the hypotheses which can be introduced to explain the design of the world. (Tweyman 84-85) Now Tweyman does seem to have a point here. It is true that Philo takes his arguments in Parts X and XI to have a conclusiveness which he did not attribute to his... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Phenomenology of Superstition or a Phenomenological Superstition?Elena Ibáñez-Guerra (bio)KeywordsBehaviorism, constructionism, intentionality, operant behaviorWhen the editors of Philosophy, Psychiatry, & Psychology asked me to make some brief comments on two articles for the special issue edited by Pérez-Álvarez and Sass, I was delighted to accept, thinking that the task would be a straightforward one, and that I could easily meet the agreed deadline. But nothing could be further from (...) the truth. The articles were of such density and their content of such profundity that it took months of interpretation and study, and of bringing my own knowledge up to date, before I was in a position to understand the concepts, adjust my beliefs, and make some comments. I could certainly have delivered some kind of eulogy about the brilliance of their content; I might have countered with my own article. However, what seemed most coherent to me was to meet their arguments head on and deal with what I consider to be their principal weaknesses, leaving the bouquets for the end.The articles set out, as I understand them and within the clinical context, to relate phenomenology, in its most traditional form, with the most current form of Skinnerian behaviorism, situating themselves in a contextualism that is, at the same time, close to and removed from the most radical type of social constructionism.But let us begin by looking more closely at “Phenomenology and Behaviorism.” It is novel for me, though Professor Pérez-Álvarez had already proposed it several years ago (Pérez-Álvarez 1992), to view operant behavior as intentionality, or at least as involving final causality according to the Aristotelian classification. It is a surprising contention, not least because, as I recall, Skinner lived in a time and a context (historical reason) in which the basic goal of psychology was to convert itself into a natural science, comparable in all respects to physics, which it took as a model, focusing therefore on efficient causality (also according to Aristotle’s terminology), so that behavior was considered as the immediate consequence of a stimulus, and the stimulus–response association became the cornerstone of the discipline. It is true that the operant behavior concept refers to the functional relationship between behavior and reinforcement, but it is no less true that Skinner’s definition of reinforcement is totally empirical—“all that which increases or decreases the probability”—meaning that reinforcement can be considered neither as a motive nor as a reason for behavior, unless it be in the eyes of the observer. [End Page 251]Furthermore, even though Yela (1987) refers to Ortega y Gasset’s formula “I am myself and my circumstances” as a Skinnerian approach, the truth is that Yela himself argues that it is precisely the self that constitutes personality, such that I have a personality because I am me, and not vice versa, as Skinner would appear to argue. In this regard, Ortega’s celebrated formula has generally been interpreted, from the most personalist perspectives, as “the circumstances are myself”—to highlight the denial of the psychological subject by radical behaviorism (Mischel’s [1968] criticism of the concept of personality is relevant here). On top of this, Skinner’s rejection of all that was not directly observable, or at least, that could not be operationalized, calls into question the admissibility of anything called final cause or intentionality of behavior. In his philosophy, all the indications are that contingencies are what determine behavior; and that there would be no room for a structural causality, as Althusser would argue, or of a reciprocal determinism, in Bandura’s terms, or even of an interaction between subject and environment, as modern interactionists would maintain. “I am myself and my circumstances” seems in Skinner to become “the circumstances are me”, and indeed, the reinforcement history – which in the article in question is considered as something akin to the Sartrian idea of “life project” – is for Skinner nothing more than a continuous association of events. In my view, Ortega’s perspectivism would perhaps be closer to the sociology of the American action theorists, Merton, Parsons, etc., than to Skinnerian behaviorism, since “action”—as the action theorists... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:What Power Do I Have? A Nursing Student’s Concerns Lead to a Passion for EthicsAnonymous OneThe day began like many in our ten–week rotation, around the large table in the brightly lit ICCU nurses’ station. Report, which was given by the night charge nurse, included information on all the patients on the unit. Since I had cared for A. G. the previous day, I was eager to know how (...) she had spent the night. She had a debilitating neuro–muscular disease known as myasthenia gravis. Placed on the ventilator days before, it was reported that she was likely to be dependent on the machine for life. In the late 1970’s there were very few facilities that accepted ventilator dependent patients. She might be with us for a long time.When I entered her room for the first time, I saw a frail older woman with kind eyes and a warm smile. She was breathing with the help of the ventilator through her tracheostomy tube. I learned through her chart that she had no known family. On the day I took care of her, no one came to see her and she had no visitors the previous evening. She lived in a local long–term care facility and was brought to the hospital after she developed respiratory distress. A. G. was unable to move in the bed due to her condition and required frequent suctioning along with turning and repositioning for comfort.Despite her weakness, A. G. was able to communicate silently by mouthing the words for what she wanted and by nodding and shaking her head. I found her to be quite skilled in non–verbal [End Page 93] communication since it took minimal effort to understand what she wanted, but the activity tired her easily. I had just completed A. G.’s morning care when her physician came in to examine her. After completing his assessment, he stopped and leaned in closely to speak with her. He began asking a number of questions about whether she wanted to spend the rest of her life in this way, on a ventilator. She shook her head. Continuing the line of questioning in different ways, she responded to him. I wondered why he was asking these questions. After seeing her response, the physician asked me to get 30 mg of morphine from the narcotics cabinet. Although I didn’t understand the implication of the request, I complied.While I was retrieving the medication from the narcotics cabinet, the charge nurse came to tell me I was being reassigned to a new admission. When I asked why, she told me she couldn’t discuss it, but asked me to please do what she said. I left her standing there, wondering what was going on. After assisting with the new admission, I went back to see A.G.; her door was closed. When I opened the door, the ventilator tubing hung over the side of the machine. Looking down at the bed, I was shocked to find A.G. had been disconnected. She was dead. In a state of disbelief and panic, I sought out the charge nurse to find out what happened. It was clear that I was not to know. I asked her a number of questions but she adeptly changed the subject and redirected me to other activities. By then it was lunchtime and my instructor had left the unit. I asked to be excused and went to seek her out.When I told my instructor what happened, a look of doubt came over her face. “You think Doctor M. killed your patient? That would never happen.” Although I tried to tell her the story, she too, dismissed me, telling me my story didn’t make sense. I was distraught. An overwhelming sense of dread came over me and I began to cry. She encouraged me to go home, which I did.Happily, I had the weekend to recover before returning to clinical. I never found out what happened to A. G. and neither my instructor nor the charge nurse ever spoke to me about my experience. In fact, it seemed no one believed my story... (shrink)

There are two approaches to the study of Marx and Marxism. On the one hand, there is Marxism as a system. Here feudalism, capitalism, and communism succeed each other with neat precision. Then there is the study of the nuances of Marx’s work. Marx, a sensitive and insightful man, said things about political life that were both subtle and quite at odds with the main thrust of his thought. As Nietzsche pointed out, there is a sort of stupidity and weakness (...) about systems of thought. The weakness of systematic political thought is that it must exclude things which are quite real but which are not admissible to the system. Thus, Marx created a system of political thought and also said some quite intelligent things about politics. All too frequently, the two clashed. (shrink)

One difficulty in understanding recent debates is that not only have many terms been used to refer to weakness of will – “akrasia” and “incontinence” have often been used as synonyms of “weakness of will” – but quite different phenomena have been discussed in the literature. This is why the present entry starts with taxonomic considerations. The second section turns to the question of whether it is possible to freely and intentionally act against one’s better judgment.

This paper examines the exercise of individual or group rights within the game form approach. It focuses in particular on what it means for a strategy or action to be feasible and admissible. Admissibility is best discussed in relation to two basic distinctions among rights, passive and active rights on the one hand and negative and positive rights on the other. It is argued that while there are quite a few cases in which the outcomes of mutual rights exercising (...) are to the fore, there are many situations where the uninhibited exercise of individual or group rights and not particular outcomes are what society is primarily interested in. (shrink)

The?-admissibility is one of the most important problems in the realm of relevant logics. To prove the 7-admissibility, either the method of normal models or the method using metavaluations may be employed. The?-admissibility of a wide class of relevant modal logics has been discussed in Part I based on a former method, but the?-admissibility based on metavaluations has not hitherto been fully considered. Sahlqvist axioms are well known as a means of expressing generalized forms of formulas (...) with modal operators. This paper shows that? is admissible for relevant modal logics with restricted Sahlqvist axioms in terms of the method using metavaluations. (shrink)