Zwierzęta i ludzie, czyli granice moralności

A much neglected question in the foundations of ethics concerns the moral status of non-human beings. Our intuitions are equivocal, and various theories have been advanced to distinguish between men and animals with regard to inclusion in the scope of moral concern. Various ground for drawing the distinction such as evolutionary supremacy, can be rejected as morally irrelevant. The key distinction historically employed for effecting a demarcation is rationality, which has been linked with the possession of language. The most systematic attempt to link language, rationality, and moral status is that of Kant, who can be seen as attempting to prove that only rational, linguistic, beings – and thus only human beings – fall within the scope of moral concern. This intricate argument can be criticized in a variety of ways. lf correct, it would exclude children, the retarded, the insane, the comatose, etc. from moral concern. More important, is follows from Kant’s argument that rationality is the only morally relevant feature of a rational being, in which case it is difficult to see why features of a human being which are or may be irrelevant to rationality – fur example pleasure or pain – are worthy of moral attention. Clearly morality encompasses more than rationality; in fact, rationa1ity is morally relevant only because it is an interest for a rational being. It is the presence of interest, and needs, wants, desires, etc., which are subject to fulfilment, nurture, and impediment which makes a being an object of moral attention. Language is relevant as a vehicle for conveying needs and interests, but natural signs serve just as well. Thus if men are objects of moral concern, animals are also, since no morally relevant distinction can be drawn between men and animals, and because animals display the same morally relevant features that humans do.

Linear sampling and the ∀∃∀ case of the decision problem

Let Q be the class of closed quantificational formulas ∀x∃u∀yM without identity such that M is a quantifier-free matrix containing only monadic and dyadic predicate letters and containing no atomic subformula of the form Pyx or Puy for any predicate letter P. In [DKW] Dreben, Kahr, and Wang conjectured that Q is a solvable class for satisfiability and indeed contains no formula having only infinite models. As evidence for this conjecture they noted the solvability of the subclass of Q consisting of those formulas whose atomic subformulas are of only the two forms Pxy, Pyu and the fact that each such formula that has a model has a finite model. Furthermore, it seemed likely that the techniques used to show this subclass solvable could be extended to show the solvability of the full class Q, while the syntax of Q is so restricted that it seemed impossible to express in formulas of Q any unsolvable problem known at that time.In 1966 Aanderaa refuted this conjecture. He first constructed a very complex formula in Q having an infinite model but no finite model, and then, by an extremely intricate argument, showed that Q (in fact, the subclass Q2 defined below) is unsolvable ([Aa1], [Aa2]). In this paper we develop stronger tools in order to simplify and extend the results of [Aa2]. Specifically, we show the unsolvability of an apparently new combinatorial problem, which we shall call the linear sampling problem (defined in §1.2 and §2.3). From the unsolvability of this problem there follows the unsolvability of two proper subclasses of Q, which we now define. For each i ≥ 0, let Pi be a dyadic predicate letter and let Ri be a monadic predicate letter.