Seminar

The sensitivity condition on knowledge—the ‘spirit’ of which is that ‘one would notice if things were different’ (Greco, 2012)—is supposed to preserve the allure of scepticism without denying Moorean facts. The real threat for sensitivity, then, is that in clear cases of knowledge sceptical worlds might be closer neighbours than the worlds where our methods of knowing work as intended. Williamson (2002) suggests such a case:

My knowing by sight in the ordinary way that a mountain stands here seems compatible with the assumption that if no mountain had stood here, a bizarre chain of circumstances would have occurred as a result of which I would have hallucinated a mountain of just this appearance. That type of hallucination occurs only in worlds very unlike the actual world, we may suppose, and the mechanism that produces it is absent from the actual world.

Becker is able to dismiss this case with only a footnote, however, because ‘it seems that, even if this were a possibility, which I grant, it is not among the closest possibilities, and only the closest ones are relevant to assessing sensitivity’ (2009). Williamson’s worry will only become compelling if there is an argument that such sceptical worlds may be the closest counterfactuals. I present two such cases, both central examples of knowledge, one in a common-sense and one in a scientific context.

A Case of Insensitive Common Knowledge

(SUN) Zoya watched the film WALL-E, then had a primary school astronomy lesson where she learned that Earth’s sun is called Sol. She asserts ‘I know that Sol lights up Earth.’ When asked what she would be doing if Sol did not light up Earth, she first expresses confusion, then responds ‘I’d be in a spaceship with Virtual Reality movies of Earth, like in the movie WALL-E!’ Zoya certainly knows that Sol lights up Earth, and nothing less than a full sceptical scenario will cause us to doubt Zoya’s knowledge. Nonetheless the sensitivity of Zoya’s belief fares poorly under all four meanings of closeness for possible worlds elaborated by David Lewis (1979):

1. The possible world which matches actuality precisely up until the time of counterfactual divergence, when a small miracle causes the counterfactual divergence which then proceeds deterministically.

2. The possible world whose history differs from actuality by the minimum amount to cause the divergence, but otherwise obeys the same laws as the actual world.

3. The possible world which matches actuality precisely up until the time of counterfactual divergence, when a small miracle causes the counterfactual divergence, but then experiences a second miracle which restores gross similarity to the actual world.

4. The possible world which matches actuality precisely up until the time of counterfactual divergence, when a small miracle causes the counterfactual divergence, but then experiences a second (series of) miracle(s) which restore(s) exact similarity to the actual world.

On (4), Zoya will continue to believe that Sol illumines Earth, by all of the same methods as in the actual world, since methods are individuated by their ‘upshot in experience’ as qualitatively identical ‘from the inside’ (Nozick, 1981, p. 184), and Zoya’s experience will not have changed. Option(3) implies a miracle which restores an illumination source of roughly similar intensity, spectrum, period, etc. as Sol, so Zoya, seeing its light and feeling its warmth, would presumably believe that Sol still illumined Earth. Any unexplained changes would be much more naturally attributed to changes in Sol rather than the sudden miraculous switch of Sol for a near-duplicate star, so Zoya’s belief would be insensitive.

2

On (2), the history of the world is different in some way that causes Sol to no longer illuminate Earth shortly before Zoya’s assertion, but as Lewis (1979) notes, it is hard to see how this backward divergence could be kept in check. If the star is about to stop emitting light, then it is not a main-sequence star. Perhaps Earth is no longer illumined because it no longer exists, having been recently consumed by Sol’s growth into a red giant, or perhaps Earth was always in an orbit too far to be consumed, and ceases to be illumined because the white dwarf it has orbited for trillions of years finally winks out. For Zoya’s belief to be sensitive, she would have to exist and attempt the same method of knowing in this counterfactual. She is not on an uninhabitable Earth—so it is not fanciful to think that she is suspended in virtual reality in a spaceship somewhere, thinking that Sol still illumines Earth. Nozick does not consider the switch to virtual reality to constitute a different method of knowing (1981, p. 190), because if it were a different method then again sensitivity would let us know that we are not in sceptical situations.

On Lewis (1979)’s preferred option (1), a small miracle (unpredicted sudden divergence between the counterfactual and actual worlds) causes Sol to stop lighting up Earth just before Zoya’s assertion.

The counterfactual world is presumed to evolve deterministically, but without a certain regularity (main sequence stars not suddenly winking out, in this case) guaranteed by the natural laws of the actual world. But what laws could govern the evolution of such a counterfactual world? Surely nothing remotely like the relativistic quantum physics of the actual world, where main sequence stars do not stop illumining their planets without going through many dramatic steps taking billions of years. How are we to evaluate the implications of such wildly counterfactual physics? Perhaps in such physics main-sequence stars can near-instantly become supernovas, which would blind Zoya and burn her skin with their last emission of light. As in option (2), either Zoya and her methods would cease to exist, or the positive afterimage and her warm skin would still lead Zoya to believe that Sol still lit up Earth, making her belief insensitive. Lewis (1979) does admit another possibility: that the counterfactual world may lack natural laws at all. But if the counterfactual world lacks natural laws, how can we say anything intelligible about its evolution after it diverges from the actual world?

The trouble is that sensitivity demands that we check our beliefs in counterfactual worlds where the facts are different, and in those cases where our knowledge is safest the closest such worlds are tremendously far away. No matter which of Lewis’s options (1)-(4) we use to identify the closest such world, we are unable to assure ourselves that sensitivity obtains, so sensitivity cannot do its work in avoiding the sceptical conclusion.

A Case of Insensitive Scientific Knowledge

(BLACKHOLE) Amare, a physics undergraduate taking a course on general relativity, comes to believe that the solution to the Einstein field equations in the actual universe is not the Schwarzchild metric, which includes only a single black hole and empty space.

Amare’s belief is obviously safe, but insensitive on all of Lewis’s options. On (3) and (4), just before Amare formulates her belief a miracle causes the Einstein field equations of the universe containing her to be correctly solved by the Schwarzchild metric, but then another offsetting miracle restores the similarity to the actual world. This seems straightforwardly incoherent: there is no world where the Schwarzchild solution to the Einstein field equations is correct that is similar to the actual world, because the actual world is not remotely similar to any world in which only a black hole and empty space exist, so the sensitivity condition becomes a vacuously true counterpossible. Option (2), where the history of the world is different in some way that causes the Schwartzchild metric to correctly describe it shortly before Amare comes to formulate her belief, goes similarly. Here we have the very exemplar of Lewis’s divergence worry: a world which was never one iota like the actual one. Either this makes (2) incoherent like (3) and (4) or this is a world in which Amare and her methods never existed, so sensitivity is vacuous.

3

On (1), a small miracle causes the Schwartzchild metric to correctly describe the solution of the Einstein field equations just before Amare formulates her belief. Obviously the considerations discussed in SUN apply here: we could have very little understanding of such a universe. If we work with the more general (and intelligible) notion of the universe being swallowed by a black hole, however, the outcome for sensitivity is even worse. According to one plausible model, ‘a person falling into a black hole would actually be absorbed into a hologram—without even noticing’ (Taylor, 2015). The sensitivity counterfactual is then a sceptical scenario where any attempt to individuate methods in a way that makes Amare’s belief insensitive will similarly apply to other sceptical scenarios. Yet if her belief turns out to be insensitive, then results in some of the least contested facts in basic science being unknowable. In BLACKHOLE, as in SUN, none of Lewis’s options for finding the closest possible world where the belief is false seem to make the belief sensitive, so sensitivity cannot be a necessary condition for knowledge.

According to robust virtue epistemology, a belief amounts to knowledge if and only if the subject believes the truth because of the exercise of cognitive ability. It has been argued that the satisfaction of the virtue condition does not suffice for the elimination of knowledge-precluding luck. Therefore, robust virtue epistemology falls short of anti-luck epistemology. Drawing on the idea that cognitive success depends on ability and luck in a gradient way rather than a rigid way, it is argued in this paper that knowledge is achieved just in case cognitive success sufficiently depends more on ability than on luck in the sense that the exercise of cognitive ability significantly enhances the modal profile of the target belief relative to the modal profile of a belief in the target proposition formed by sheer luck. Robust virtue epistemology understood in this way is also a kind of anti-luck epistemology because the satisfaction of the virtue condition ensures a kind of safety condition which, in turn, helps to eliminate luckily true beliefs from the realm of knowledge. 

In this talk, I explore a non-canonical version of the abstractionist projects in philosophy of mathematics. It is featured by an arbitrary interpretation of the abstractionist vocabulary, that is able to preserve the mathematical role of the abstraction principles but implies decisive challenges to the philosophical theses usually involved in these programs and specifically in the Neo-logicist project (cf. Hale, Wright 2001). The investigation aims at showing that an arbitrary interpretation of the abstractionist vocabulary, while blocking the arguments supporting Platonist metaphysics of the abstract objects, is still compatible with a realist account of truth-values and, moreover, provides the tools to get closer to the Fregean goal of logicality of arithmetic. By spelling out such a notion in Tarskian terms of isomorphism invariance, different criteria can be formulated and tested on the abstraction operators. A taxonomy of such criteria will be suggested and adopted to show the advantages (and the risks) of such an arbitrary logicist project.

In the spirit of Tarski’s 1930 work, “The concept of Truth in Formalized languages”, we define probability in terms of satisfaction. The novelty here consists in giving quantified sentences an extension, rather than a truth-value, in the domain of a specific first-order model. Quantified sentences are interpreted as defining events in a probability space, constructed from a first-order model.

In a recent paper, Kilov and Hendy (2022) argued, based on the results of an experimental study, that philosophers are not modal experts. According to the results of their survey, philosophers suffer from illusions of logical (im)possibility more than mathematicians and slightly less than laymen. From this result, they concluded that philosophers are not likely candidates for expertise with respect to metaphysical modality.

We will argue that Kilov and Hendy’s results with respect to logical modality do not necessarily entail the conclusion that philosophers are not modal experts with respect to metaphysical modality. Kilov and Hendy’s results assess (deficiencies in) purported modal expertise only partially, as they are relevant merely for identifying modal truths and justifying modal beliefs by way of deductive reasoning. We aim to argue there is both more and less to modal expertise than Kilov and Hendy assume. There is more in the sense that there are other abilities and types of knowledge that are required for modal expertise, such as analogical and similarity reasoning, knowledge and justification of modal principles, justifying theories that explain modal knowledge, and clarifying various types of concepts involved in modal judgement. There is also less, in the sense that the inferences we employ in order to derive modal truths are usually less complex than the ones that are evaluated in Kilov and Hendy’s approach.

Our reply is inspired by the extant literature on expertise, especially moral expertise, in which more permissive constraints are associated to the skill that an epistemic expert must display, that is, experts are not required to be right concerning the truth of statements pertaining to their field of expertise. What experts must do is provide stronger justification for their claims, when compared to non-experts. Moreover, Kilov and Hendy’s experiments ignore the subjects’ capacity to resist informal fallacies, which may be a critical thinking skill just as crucial for modal thinking as our ability to handle (modal) deductions.

Contrastivism about knowledge is the claim that knowledge is relative to a question: to know that p is to know that p rather than q, where q stands for the alternative answers to the relevant question. Schaffer (2004; 2007) has argued that one of the benefits of contrastivism is that it offers an explanation of why sceptical arguments relying on a closure principle for knowledge fail that retains the knowledge obtained through ordinary cases of competent deduction. Following Kvanvig (2007), I'll argue that, by itself, contrastivism can offer no such explanation: if the proposed explanation rules out sceptical cases, it also rules out cases of competent deduction. I'll suggest that the intended result can be recovered if contrastivism about knowledge is paired with a topic-sensitive account of belief and concepts (Yalcin, 2018). I'll conclude by exploring the relation between this hybrid account and two principles of higher-order knowledge: positive introspection and reflexive luminosity.