We introduce multifunction algebras B i τ where τ is a set of 0 or 1-ary terms used to bound recursion lengths. We show that if for all ℓ ∈ τ we have ℓ ∈ O then B i τ = FP Σ i−1 p , those multifunctions computable in polynomial time with at most O )) queries to a Σ i−1 p witness oracle for ℓ ∈ τ and p a polynomial. We use our algebras to obtain independence results (...) in bounded arithmetic. In particular, we show if S 2 i proves Σ j b = PH for some j⩾i then S 2 i ≼ B S 2 . This implies if P NP ≠ P NP then S 2 1 does not prove the polynomial hierarchy collapses. We then consider a subtheory, Z , of the well-studied bounded arithmetic theory S 2 = ∪ i S 2 i . Using our algebras we establish the following properties of this theory: Z cannot prove the polynomial hierarchy collapses. In fact, even Z+ Π ̂ 0 b -consequences of S 2 cannot prove the hierarchy collapses. If Z ⊆ S 2 i for any i then the polynomial hierarchy collapses. If Z proves the polynomial hierarchy is infinite then for all i , S 2 i ⊢ Σ i p ≠ Π i p. (shrink)

Attention to care in modern society has fallen out of view as an ethos of personal responsibility, free markets, and individualism has been in the ascendant. The Liberalism of Care argues that contemporary liberalism is suffering from a crisis of care, manifest in a decaying sense of collective political responsibility for citizens' well- being and for the most vulnerable members of our communities. The book maintains that this practical crisis stems from a theoretical one. We have lost the political language (...) of care, which, prior the 19th century, was commonly used to express these dimensions of political life. To recover that language, Shawn C. Fraistat turns to three prominent philosophers-Plato, Jean-Jacques Rousseau, and William Godwin-who illuminate the varied ways caring language and caring values have structured core debates in the history of Western political thought about the proper role of government, as well as the rights and responsibilities of citizens. The Liberalism of Care presents a distinctive vision for our liberal politics where political communities and citizens can utilize the ethic and practices of care to face practical challenges. (shrink)

The bounded arithmetic theories R2i, S2i, and T2i are closely connected with complexity theory. This paper is motivated by the questions: what are the Σi+1b-definable multifunctions of R2i? and when is one theory conservative over another? To answer these questions we consider theories , and where induction is restricted to prenex formulas. We also define which has induction up to the 0 or 1-ary L2-terms in the set τ. We show and and for . We show that the -multifunctions of (...) are FPΣip and that those of are FPΣip. For -definability we get FPΣi+k+1p for all these theories. Write for the set of terms 2min,t) where ℓ is a finite product of terms in τ and tL2. We prove and we show - INDτ provided τO2. This gives a proof theoretic proof that S2iΔi+1b-LIND and -LLIND solving an open problem. For τO2, we define using weak replacement axioms and show . We show if or if or if where τ′ has an unbounded term then PH=B. We separate PΣip from PΣip for behaved ℓ and deduce theory separations. We lastly introduce a notion of a model separating two theories and derive some consequences. (shrink)

In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds (...) of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics. (shrink)

Presence suggests that adapting the experiences of leading innovators may address a nightmare scenario of environmental destruction, a growing divide between the rich and poor, and escalating violence around the world. Innovation occurs by transforming sensing to identify limitations in existing solution sets, transforming perception to envision an entire whole, and transforming action to realize the future seeking to emerge from the whole. This U sequence follows the rite-of-passage phases of separation, liminality, and reincorporation documented by Victor Turner. By ending (...) in spontaneous communitas and avoiding a normative model, the U does not discuss how to mobilize resources and develop systems of social control. This omission, as well as depending on the constructive power of human ritual without recognition of its destructive potential, significantly limits the U’s analytic validity. Despite these limitations, Presence is an encouraging set of stories of attempts within the industrial context to mitigate the nightmare scenario and work toward a sustainable future. (shrink)

Classical Liberalism is a view that the only justifiable restraints on the actions and choices of individuals in political orders are ones necessary to preserve individual liberty. Central to this view of liberty is the individual being left free from coercive interference from other individuals and society as a whole. This view presumes the idea that the individual is, firstly, able to choose his ends and actions, and secondly, that the individual is the best judge of these. Thus, the individualism (...) of classical liberalism presupposes a view of human consciousness that is volitional: capable of engaging in choice and individual self-direction. If this view of human consciousness is in conflict with the physical casual and evolutionary accounts of the world, then classical liberalism would seem to have serious problem. Therefore, I argue that the correct conception of volitional consciousness is consistent with the physical causal and evolutionary accounts of the world. Presenting a conception of volitional consciousness that makes the best sense of our introspective experience and knowledge of the world, I then show how such a volitional consciousness is consistent with causality and biological evolution. (shrink)

Advocates an existential, phenomenological reading of Heraclitus suggested by Hans-Georg Gadamer. Gadamer observes that within the Heraclitean fragments lay a subliminal wonder at the contradiction and groundlessness of the human experience, particularly the unmediated experience of thinking. I take Gadamer to suggest in part that Heraclitus writes the fragments motivated by a sort of phenomenological disclosure, not necessarily of Being (pace Heidegger), but of the human experience as one of contradictory transitions and unrestricted movements between poles of opposition.

The question of whether the bounded arithmetic theories and are equal is closely connected to the complexity question of whether is equal to. In this paper, we examine the still open question of whether the prenex version of,, is equal to. We give new dependent choice‐based axiomatizations of the ‐consequences of and. Our dependent choice axiomatizations give new normal forms for the ‐consequences of and. We use these axiomatizations to give an alternative proof of the finite axiomatizability of and to (...) show new results such as is finitely axiomatized and that there is a finitely axiomatized theory,, containing and contained in. On the other hand, we show that our theory for splits into a natural infinite hierarchy of theories. We give a diagonalization result that stems from our attempts to separate the hierarchy for. (shrink)

In this paper we provide a new arithmetic characterization of the levels of the og-time hierarchy . We define arithmetic classes equation image and equation image that correspond to equation image-LOGTIME and equation image-LOGTIME, respectively. We break equation image and equation image into natural hierarchies of subclasses equation image and equation image. We then define bounded arithmetic deduction systems equation image′ whose equation image-definable functions are precisely B. We show these theories are quite strong in that LIOpen proves for any (...) fixed m that equation image, TAC, a theory that is slightly stronger than equation image′ whose equation image-definable functions are LH, proves LH is not equal to equation image-TIME for any m> 0, where 2s ∈L, s ∈ ω, and TAC proves LH ≠ equation image for all k and m. We then show that the theory TAC cannot prove the collapse of the polynomial hierarchy. Thus any such proof, if it exists, must be argued in a stronger systems than ours. (shrink)

Gilroy and Wade wrote 20 years ago that every policy presupposes an underlying moral argument that justifies it. This claim is now rarely contested: policy making is an inescapably moral enterprise...

In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition.

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.

This paper will develop ideas from [44]. We will generalize their work in two directions. First, we provide axioms for justification logics over the base logic B and show that the logic permits a proof of the internalization theorem. Second, we provide alternative frames that more closely resemble the standard versions of the ternary relational frames, as well as a more general approach to the completeness proof. We prove that soundness and completeness hold for justification logics over a wide variety (...) of base logics. Finally, we will strengthen Belnap’s variable sharing for the justification logic context, demonstrating that the justifications are properly relevant justifications. (shrink)

The paper establishes lower bounds on the provability of.

Gilbert Meilaender argues that universities should eschew efforts to improve students’ moral character. I show that Meilaender’s arguments fail to offer any cogent reason for shunning university-based moral education. I then look to Thomas Aquinas in order to explain the connection between moral virtue and the practices common in university life. Using Aquinas as a guide, I argue that exemplary intellectual practice requires virtues that are subsidiary habits of the cardinal moral virtues themselves. The implication of this argument is as (...) follows: students require scrupulous moral training if they are to engage in exemplary intellectual practice. (shrink)

The use of $Nepomnja\check{s}\check{c}i\check{i}'s$ Theorem in the proofs of independence results for bounded arithmetic theories is investigated. Using this result and similar ideas, it is shown that at least one of S1 or TLS does not prove the Matiyasevich-Robinson-Davis-Putnam Theorem. It is also established that TLS does not prove a statement that roughly means nondeterministic linear time is equal to co-nondeterministic linear time. Here S1 is a conservative extension of the well-studied theory IΔ0 and TLS is a theory for LOGSPACE (...) reasoning. (shrink)

The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and (...) model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course. (shrink)

Growth in CSR-washing claims in recent decades has been dramatic in numerous academic and activist contexts. The discourse, however, has been fragmented, and still lacks an integrated framework of the conditions necessary for successful CSR-washing. Theorizing successful CSR-washing as the joint occurrence of five conditions, this paper undertakes a literature review of the empirical evidence for and against each condition. The literature review finds that many of the conditions are either highly contingent, rendering CSR-washing as a complex and fragile outcome. (...) This finding runs counter to the dominant perception in the general public, among activists, and among a vocal contingent of academics that successful CSR-washing is rampant. (shrink)

In this article, we present a definition of a hyperintensionality appropriate to relevant logics. We then show that relevant logics are hyperintensional in this sense, drawing consequences for other non-classical logics, including HYPE and some substructural logics. We further prove results concerning extensionality in relevant logics. We close by discussing related concepts for classifying formula contexts and potential applications of these results.

In classically based modal logic, there are three common conceptions of necessity, the universal conception, the equivalence relation conception, and the axiomatic conception. They provide distinct presentations of the modal logic S5, all of which coincide in the basic modal language. We explore these different conceptions in the context of the relevant logic R, demonstrating where they come apart. This reveals that there are many options for being an S5-ish extension of R. It further reveals a divide between the universal (...) conception of necessity on the one hand, and the axiomatic conception on the other: The latter is consistent with motivations for relevant logics while the former is not. For the committed relevant logician, necessity cannot be the truth in all possible worlds. (shrink)

In the aftermath of World War II, the government of the United States provided considerable funding for military projects that promised to provide a technological edge during the nascent Cold War. The most famous example is likely the V-2 rocket-testing program that began in the late 1940s. The 67 rockets launched from White Sands developed a knowledge base that was critically important to the launch of the first U.S. satellite in 1958 and to the subsequent manned space program. Less well (...) known are the large-scale information technology projects, undertaken in the 1950s and early 1960s, that provided a significant catalyst for research into digital computing, information processing, and the. (shrink)

In this paper, I develop some internal problems with Alvin Plantanga's proper functionalist epistemology. I focus on: (1) how we know that a belief is the result of proper function and the special difficulties this occasions for religious beliefs; (2) what a properly functioning person should believe in various circumstances, and (3) the problem of design -- whether the claim that God designed us can be reconciled with the claim that He was subject to trade-offs, compromises and unintended by-products. These (...) serious internal problems cast doubt upon proper functionalism's fruitfulness as a theory of knowledge. (shrink)

The results of Vatican II for the study of Scripture produced both expected and unexpected fruits. Those combined fruits provide the opportunity for some reflection on the current status of biblical scholarship in relation to the Church. This current status helps identify what we must appreciate and celebrate, but also helps identify remaining gaps to be filled. By assessing some of the gaps, the fruits of the second Vatican council are used to provide one way of approaching these remaining gaps, (...) and charting a hopeful way ahead. (shrink)

This article examines Martin Heidegger's concept of conscience in Being and Time as it is manifested by the characters Don Draper from the television series Mad Men (Matthew Weiner, 2007-2013) and Chauncey Gardiner in the film Being There (Hal Ashby, 1979). The article suggests that Draper hears and occasionally responds to what Heidegger terms the “call of conscience,” whereas Gardiner neither hears this call nor responds to it. Gardiner poses a problem case for Heidegger’s account of Dasein by virtue of (...) failing to exhibit conscience. A question latent in Gardiner’s makeup is what causes him to be this way. The contrast of the characters Draper and Gardiner is approached through the lens of the portrayal of secret identity in filmic media. Both characters live public lives that are at odds with their genuine selves, but they react to this disconnect differently. Core concepts addressed vis-a-vis Heidegger’s account of conscience include facticity, falling, discourse, authenticity, and death. The article concludes that Draper hears and responds to conscience’s call because he has a discursive comprehension of the disconnect between his true self and the public life he has lived; a crucial component of the phenomenon of conscience according to Heidegger is the existential capacity for discourse. Gardiner, in contrast, does not hear conscience at all because his Dasein lacks the discursive element that conscience requires in order to be activated. Gardiner’s being-in-the-world is such that he fails to understand the divide between his lived self and his public self. For Gardiner, these are the same. (shrink)

ABSTRACTGiven its intimate relationship with the human body and its environment, biotechnology innovation, and more particularly stem cell research innovations as a part thereof, implicate diverse social and moral/ethical issues. This paper explores some of the most important and controversial moral concerns raised by human embryonic stem cell research , focusing on concerns relating to the wellbeing of the embryo and the wellbeing of society . It then considers how and whether these concerns are dealt with in regulatory instruments in (...) Argentina, a southern developing country, examining in particular whether the values underlying these concerns have been translated into practical and effective rules reflective of the primary moral positions advanced. It concludes that Argentina's current state of stem cell research governance fails to consistently reflect the moral positions that have formed and is inadequate given Argentina's activity in this field. (shrink)