Andy Taylor

Vopěnka’s Principle is a natural large cardinal axiom that has recently found applications in category theory and algebraic topology. We show that Vopěnka’s Principle and Vopěnka cardinals are relatively consistent with a broad range of other principles known to be independent of standard (ZFC) set theory, such as the Generalised Continuum Hypothesis, and the existence of a definable well-order on the universe of all sets. We achieve this by showing that they are indestructible under a broad class of forcing constructions, specifically, reverse Easton iterations of increasingly directed closed partial orders.

We present a new partial order for directly forcing morasses to exist that enjoys a significant homogeneity property. We then use this forcing in a reverse Easton iteration to obtain an extension universe with morasses at every regular uncountable cardinal, while preserving all n-superstrong, hyperstrong and 1-extendible cardinals. In the latter case, a preliminary forcing to make the GCH hold is required. Our forcing yields morasses that satisfy an extra property related to the homogeneity of the partial order; we refer to them as mangroves and prove that their existence is equivalent to the existence of morasses. Finally, we exhibit a partial order that forces universal morasses to exist at every regular uncountable cardinal, and use this to show that universal morasses are consistent with n-superstrong, hyperstrong, and 1-extendible cardinals. This all contributes to the second author’s outer model programme, the aim of which is to show that L-like principles can hold in outer models which nevertheless contain large cardinals.

I argue against two of the most influential contemporary theories of moral responsibility: those of Harry Frankfurt and John Martin Fischer. Both propose conditions which are supposed to be sufficient for direct moral responsibility for actions. (By the term direct moral responsibility, I mean moral responsibility which is not traced from an earlier action.) Frankfurt proposes a condition of 'identification'; Fischer, writing with Mark Ravizza, proposes conditions for 'guidance control'. I argue, using counterexamples, that neither is sufficient for direct moral responsibility. My counterexample cases are based on recent research in psychology which reveals many surprising causes of our actions. Some of this research comes from the field of situationist social psychology; some from experiments which reveal the influence of automatic processes in our actions. Broadly, I call such causes 'subverting' when the agent would not identify with her action, if she knew all the causes of the action. When an action has subverting causes, the agent is not directly morally responsible for it, even though she may meet the conditions specified by Frankfurt and Fischer. I also criticise the theories of Eddy Nahmias and John Doris, who have both engaged specifically with the threats posed to moral responsibility by situationist research. Against Doris and Nahmias, I argue that their conditions are neither necessary nor sufficient for direct moral responsibility. My final objective is to argue that there are many everyday actions for which we mistakenly hold agents morally responsible. I review evidence that there are many everyday actions which have subverting causes. Many of those are actions for which we currently hold agents morally responsible. But I argue that, in many of those same actions, the agents are not in fact morally responsible – they bear neither direct nor traced moral responsibility.