Where Tracking Loses Traction

Tracking theories see knowledge as a relation between a subject's belief and the truth, where the former is responsive to the latter. This relationship involves causation in virtue of a sensitivity condition, which is constrained by an adherence condition. The result is what I call a stable causal relationship between a fact and a subject's belief in that fact. I argue that when we apprehend the precise role of causation in the theory, previously obscured problems pour out. This paper presents 13 distinct and original counterexamples to Nozick's tracking theory – many of which also constitute problems for more recent tracking theories. I begin by discussing how tracking relates to causation: Nozick invokes causation through conditions similar to those of Lewisian causal dependence. As a result, when causal dependence is not necessary for causation, Nozick fails to identify knowledge. I then address the inability of causation to capture epistemically important concepts, such as justification and truth. I conclude by discussing the underlying asymmetries between causation and knowledge that undermine any attempt to reduce knowledge to a purely metaphysical relation.

Sensitivity Principle in Epistemology

Sensitivity is a modal epistemic principle. Modal knowledge accounts are externalist in nature and claim that the knowledge yielding connection between a true belief and the truthmaker must be spelled out in modal terms. The sensitivity condition was introduced by Robert Nozick. He suggests that if S knows that p, then S’s belief that p tracks truth. Nozick argues that this truth-tracking relation can be captured by subjunctive conditionals. As a first approximation, he provides the following modal analysis of knowledge: S knows that p iff (1) p is true; (2) S believes that p; (3) if p were false, S wouldn’t believe that p and (4) if p were true, S would believe that p. The dominant terminology in the literature, also adopted here, is to call condition (3) the sensitivity condition and condition (4) the adherence condition. The sensitivity condition is intuitively appealing since it states that a subject does not know that p if she would believe that p even if p were false. Nozick used the sensitivity condition to accomplish two major tasks. First, he provided a solution to the Gettier problem by arguing that in Gettier cases subjects do not know since the sensitivity condition is violated. Second, he presented a controversial solution to the skeptical problem according to which we have external world knowledge but do not know that the skeptical hypothesis is false. This solution is available because sensitivity is not closed under known entailment. Quickly, criticism of the sensitivity condition emerged. First, most epistemologists regarded the price of abandoning knowledge closure as a price too high to pay. Second, it was noted that sensitivity leads to the counterintuitive consequence of precluding us from inductive knowledge since induction typically yields insensitive beliefs. The most dominant reaction to these problems was to replace sensitivity by the modal principle of safety, nowadays the most popular modal principle. However, sensitivity is not only important as a starting point of modal epistemology. Because of its intuitive attractiveness, many authors aimed at refining the original sensitivity account in order to avoid well-known problems. This has led to a second wave of sensitivity accounts. As of today, various sensitivity-based theories are on the market, including accounts that avoid closure failure, probabilistic interpretations of sensitivity and adherence, and contextualist approaches. There is thus a vivid and ongoing debate about the sensitivity principle in epistemology.

Truth Tracking and Knowledge from Virtual Reality

Is it possible to gain knowledge about the real world based solely on experiences in virtual reality? According to one influential theory of knowledge, you cannot. Robert Nozick's truth-tracking theory requires that, in addition to a belief being true, it must also be sensitive to the truth. Yet beliefs formed in virtual reality are not sensitive: in the nearest possible world where P is false, you would have continued to believe that P. This is problematic because there is increasing awareness from philosophers and technologists that virtual reality is an important way in which we can arrive at beliefs and knowledge about the world. Here I argue that a suitably modified version of Nozick's sensitivity condition is able to account for knowledge from virtual reality.

Insensitivity

In this chapter insensitivity accounts, on which various puzzling appearances of ignorance are explained by appeal to the fact that the beliefs in question would have been held even if they had been false, are defended from counterexamples. In some cases, the defense is accomplished by means of modifications to the notion of insensitivity, where the resulting more sophisticated understanding is able to handle the examples. In other cases, it is argued that the insensitivity account is a viable explanation of the phenomena it is designed to explain, despite the presence of counterexamples to it. Direct insensitivity accounts, on which a sensitivity condition for knowledge is posited, are distinguished from indirect insensitivity accounts, like the one employed in Chapters 1 and 5, on which our tendency to deny knowledge in cases of insensitive beliefs has a different basis.

Sensitivity, Reflective Knowledge, and Skepticism

Michael Huemer, Ernest Sosa, and Jonathan Vogel have offered a critique of the sensitivity condition on knowledge. According to them, the condition implies that you cannot know of any particular proposition that you do not falsely believe it. Their arguments rest on the claim that you cannot sensitively believe of any particular proposition that you do not falsely believe it. However, as we shall see, these philosophers are mistaken. You can do so. That said, these philosophers were close to the mark. There are some related propositions that you cannot believe sensitively. These propositions are interesting in another respect: they can be used to construct a new skeptical argument that is superior in some respects to a more traditional skeptical argument. This new skeptical argument also reveals insights about the relationship between internalism, externalism, and skepticism.

MIND THE GAP

We discuss an optimisation criterion for the exact renormalisation group based on the inverse effective propagator, which displays a gap. We show that a simple extremisation of the gap stabilises the flow, leading to better convergence of approximate solutions towards the physical theory. This improves the reliability of truncations, most relevant for any high precision computation. These ideas are closely linked to the removal of a spurious scheme dependence and a minimum sensitivity condition. The issue of predictive power and a link to the Polchinski RG are discussed as well. We illustrate our findings by computing critical exponents for the Ising universality class.