Martin Peterson

You must either save a group of m people or a group of n people. If there are no morally relevant diff erences among the people, which group should you save? is problem is known as the number problem. e recent discussion has focussed on three proposals: (i) Save the greatest number of people, (ii) Toss a fair coin, or (iii) Set up a weighted lottery, in which the probability of saving m people is m / m + n , and the probability of saving n people is n / m + n . is contribution examines a fourth alternative, the mixed solution, according to which both fairness and the total number of people saved count. It is shown that the mixed solution can be defended without assuming the possibility of interpersonal comparisons of value.

In this paper we shed new light on the Argument from Disagreement by putting it to test in a computer simulation. According to this argument widespread and persistent disagreement on ethical issues indicates that our moral opinions are not influenced by any moral facts, either because no such facts exist or because they are epistemically inaccessible or inefficacious for some other reason. Our simulation shows that if our moral opinions were influenced at least a little bit by moral facts, we would quickly have reached consensus, even if our moral opinions were affected by factors such as false authorities, external political shifts, and random processes. Therefore, since no such consensus has been reached, the simulation gives us increased reason to take seriously the Argument from Disagreement. Our conclusion is however not conclusive; the simulation also indicates what assumptions one has to make in order to reject the Argument from Disagreement. The simulation algorithm we use builds on the work of Hegselmann and Krause (J Artif Soc Social Simul 5(3); 2002, J Artif Soc Social Simul 9(3), 2006).

It is a natural assumption in mainstream epistemological theory that ascriptions of knowledge of a proposition p track strength of epistemic position vis-à-vis p. It is equally natural to assume that the strength of one’s epistemic position is maximally high in cases where p concerns a simple analytic truth (as opposed to an empirical truth). For instance, it seems reasonable to suppose that one's epistemic position vis-à-vis “a cat is a cat” is harder to improve than one's position vis-à-vis “a cat is on the mat”, and consequently, that the former is at least as unambiguous a case of knowledge as the latter. The current paper, however, presents empirical evidence which challenges this intuitive line of reasoning. Our study on the epistemic intuitions of hundreds of academic philosophers supports the idea that simple and uncontroversial analytic propositions are less likely to qualify as knowledge than empirical ones. We show that our results, though at odds with orthodox theories of knowledge in mainstream epistemology, can be explained in a way consistent with Wittgenstein's remarks on 'hinge propositions' or with Stalnaker's pragmatics of assertion. We then present and evaluate a number of lines of response mainstream theories of knowledge could appeal to in accommodating our results. Finally, we show how each line of response runs into some prima facie difficulties. Thus, our observed asymmetry between knowing “a cat is a cat” and knowing “a cat is on the mat” presents a puzzle which mainstream epistemology needs to resolve.