In Honour of John Crossley’s 85th Birthday.

The proof of the Second Incompleteness Theorem consists essentially of proving the uniqueness and explicit definability of the sentence asserting its own unprovability. This turns out to be a rather general phenomenon: Every instance of self-reference describable in the modal logic of the standard proof predicate obeys a similar uniqueness and explicit definability law. The efficient determination of the explicit definitions of formulae satisfying a given instance of self-reference reduces to a simple algebraic problem-that of solving the corresponding fixed-point equation (...) in the modal logic. We survey techniques for the efficient calculation of such fixed-points. (shrink)

An adequate theory of rights ought to forbid the harming of animals to promote trivial interests of humans, as is often done in the animal-user industries. But what should the rights view say about situations in which harming some animals is necessary to prevent intolerable injustices to other animals? I develop an account of respectful treatment on which, under certain conditions, it’s justified to intentionally harm some individuals to prevent serious harm to others. This can be compatible with recognizing the (...) inherent value of the ones who are harmed. My theory has important implications for contemporary moral issues in nonhuman animal ethics, such as the development of cultured meat and animal research. (shrink)

Value capture occurs when an agent’s values are rich and subtle; they enter a social environment that presents simplified — typically quantified — versions of those values; and those simplified articulations come to dominate their practical reasoning. Examples include becoming motivated by FitBit’s step counts, Twitter Likes and Re-tweets, citation rates, ranked lists of best schools, and Grade Point Averages. We are vulnerable to value capture because of the competitive advantage that such crisp and clear expressions of value have in (...) our private reasoning and our public justification. There is, however, a price. In value capture, we take a central component of our autonomy — our ongoing deliberation over the exact articulation of our values — and we outsource it. And the metrics to which we outsource usually engineered for the interests of some external force, like a large-scale institution’s interest in cross-contextual comprehensibility and quick aggregability. That outsourcing cuts off one of the key benefits to personal deliberation. In value capture, we no longer adjust our values and their articulations in light of own rich experience of the world. Our values should often be carefully tailored to our particular selves or our small-scale communities, but in value capture, we buy our values off the rack. In some cases – like decreasing CO2 emissions – the costs of non-tailored values are outweighed by the benefit of precise collective coordination. In other cases, like in our aesthetic lives, they are not. This suggests that we should want different values suited to different scales. We should want value federalism. Some values are perhaps best pursued at the largest-scale level, others at smaller scales. The problem occurs when we exhibit an excess preference for the largest-scale values – when we consistently let the universal metrics swamp our quieter interests. (shrink)

In a recent paper, Montagna proved the undecidability of the first-order theory of diagonalisable algebras. This result is here refined — the set of finitely refutable sentences is shown effectively inseparable from the set of theorems. The proof is quite simple.

In The Case for Animal Rights, Tom Regan argues that although all subjects-of-a-life have equal inherent value, there are often differences in the value of lives. According to Regan, lives that have the highest value are lives which have more possible sources of satisfaction. Regan claims that the highest source of satisfaction, which is available to only rational beings, is the satisfaction associated with thinking impartially about moral choices. Since rational beings can bring impartial reasons to bear on decision making, (...) Regan maintains that they have an additional possible source of satisfaction that nonrational beings do not have and, consequently, the lives of rational beings turn out to have greater value.. (shrink)

Анотація. У статті проаналізовані досягнення Соціального Вчительства Католицької Церкви, репрезентовані працями Лева ХІІІ, Пія ХІ, Пія ХІІ, Івана Павла ІІ, що розкривають змістовні характеристики поняття «принцип субсидіарності», його роль і значення в системі християнських цінностей. Принцип субсидіарності робить можливими такі взаємовідносини в соціальному житті, коли спільнота вищого порядку не втручається у внутрішнє життя спільноти нижчого порядку, перебираючи на себе належні тій функції; заради спільного добра, спільного блага вона надає їй у разі потреби підтримку й допомогу, узгоджуючи у такий спосіб її (...) взаємодію з іншими соціальними структурами. Принцип субсидіарності скеровує соціальну практику на утвердження спільного блага в людському співтоваристві. Поширення і застосування принципу субсидіарності протистоїть небезпеці «одержавлення» суспільства та найзагрозливіших проявів колективізму, обмежує абсолютизацію влади, бюрократизацію державних і соціокультурних структур, стає одним із гарантів дотримання прав і свобод громадян своєї країни. (shrink)