In Memory: A Philosophical Study, Bernecker argues for an account of contiguity. This Contiguity View is meant to solve relearning and prompting, wayward causation problems plaguing the causal theory of memory. I argue that Bernecker’s Contiguity View fails in this task. Contiguity is too weak to prevent relearning and too strong to allow prompting. These failures illustrate a problem inherent in accounts of memory causation. Relearning and prompting are both causal relations, wayward only with respect to (...) our interest in specifying remembering’s requirements. Solving them requires saying more about remembering, not causation. I conclude by sketching such an account. (shrink)

Deleuze’s philosophy is permeated with the problem of the continuum. The idea that the coexistence of durations is implied in the concept of duration itself allows Deleuze to offer a fresh perspective on multiplicity, which is distinct from Bergson’s approach, and which proposes new perspectives on the continuum. While Deleuze critiques Leibniz’s view on this concept by highlighting the non-uniform nature of the continuum, the infinitesimal still plays a significant role in his analysis. However, in his late reading of Leibniz, (...) Deleuze emphasises that folds, rather than infinitesimals, should be considered as the smallest components of the continuum’s labyrinth. This implies that there is a union of indiscernible cuts in the continuity, cuts that do not create gaps or breaks in the overall coherence, but rather a labyrinth. I will show how, in exploring this problem, Deleuze and Guattari draw inspiration from Kafka, in order to relate continuity to contiguity. This relation reveals an internal difference that defines the distinction between what is continuous and what is contiguous. This, in our view, marks a considerable shift between Deleuze’s early reading of Bergson and his late reading of Leibniz, and it allows Deleuze to further develop his idea of the continuum. (shrink)

A computably enumerable (c.e.) degree is a maximal contiguous degree if it is contiguous and no c.e. degree strictly above it is contiguous. We show that there are infinitely many maximal contiguous degrees. Since the contiguous degrees are definable, the class of maximal contiguous degrees provides the first example of a definable infinite anti-chain in the c.e. degrees. In addition, we show that the class of maximal contiguous degrees forms an automorphism base for the c.e. degrees and therefore for the (...) Turing degrees in general. Finally we note that the construction of a maximal contiguous degree can be modified to answer a question of Walk about the array computable degrees and a question of Li about isolated formulas. (shrink)

We argue that Hume was wrong to identify constant conjunction in time as the sole associative principle responsible for belief. On principles that can be grounded on his own account, constant contiguity in space ought to produce the same effect. We close by examining some of the ways in which a recognition of the influence of contiguity relations might have assisted Hume in resolving problems that otherwise arise with his accounts of causality and objectivity.

The paper discusses the regularity account of causation but finds it insufficient as a complete account of our notion of causality. The attractiveness of the regularity account is its attempt to understand causation in terms of empirically accessible features of the world. However, this account does not match our intuition that singular causality is prior in normal epistemic situations and that there is more to causation than mere succession. Apart from succession and regularity, the concept of causality also contains a (...) modal feature which allows us to engage in counterfactual discourses about singular causal events and to claim that a particular cause is both sufficient and necessary for its effect in the circumstances. However, we may directly observe singular causes, but the modal element is not something we can possibly observe. Rather, this element is something we add to our perception of succession. Thus, the paper suggests that the modal feature of causality is a mental construction which was originally formed by our knowledge of certain structural features of similar events in other situations. It stems not from what we actually observe but from what we have observed or may observe under different but relevant circumstances. So the concept of causation has partly an empirical content and partly a constructed one. (shrink)

Hume notoriously maintains that contiguity, succession, and constant conjunction are individually necessary and jointly sufficient conditions of causation. While his arguments for the necessity of constant conjunction have been thoroughly dissected, his arguments for contiguity and succession have generally been either ignored or misstated. I hope both to correct this unfortunate state of affairs and to show some fatal defects in Hume's account.The pertinent passages in Hume's writings acknowledge three conceivable ways in which the temporal relation between causes (...) and effects might be construed: as separated by some interval; as perfectly contiguous, so that the effect succeeds the cause in the very next moment; as perfectly contemporaneous, existing at the same moment. Hume defends the correctness of and denies the tenability of both and. (shrink)

Hume is generally thought to hold that spatial contiguity is essential to the causal relation. Indeed, Pears, in his recent "Hume's System", adds to Hume's system the claim that perceptions must exist somewhere--have, that is, spatial coordinates--so that, he claims, we can identify them as well as solve the problem of sorting out one person's perceptions from another. Pears fails to accomplish his aims in this attempt, but, more seriously, he fails to understand Hume's commitment to some perceptions being (...) the sorts of things that do not have spatial coordinates. He thus fails to understand that Hume is attempting to displace a conception of causal relations which makes it impossible to have a unified theory of causation for everything that exists in the world. But Hume does not hold that all perceptions have spatial coordinates, and since he does hold that anything can be the cause of anything else, he holds that some causal relata are not spatially located. My willing to raise my arm is an instance of such a causal relation for Hume. (shrink)

There are some necessary conditions on causal relations that seem to be so trivial that they do not merit further inquiry. Many philosophers assume that the requirement that there could be no temporal gaps between causes and their effects is such a condition. Bertrand Russell disagrees. In this paper, an in-depth discussion of Russell’s argument against this necessary condition is the centerpiece of an analysis of what is at stake when one accepts or denies that there can be temporal gaps (...) between causes and effects. It is argued that whether one accepts or denies this condition, one is implicated in taking on substantial and wide-ranging philosophical positions. Therefore, it is not a trivial necessary condition of causal relations and it merits further inquiry. (shrink)

Downey and Lempp 1215–1240) have shown that the contiguous computably enumerable degrees, i.e. the c.e. Turing degrees containing only one c.e. weak truth-table degree, can be characterized by a local distributivity property. Here we extend their result by showing that a c.e. degree a is noncontiguous if and only if there is an embedding of the nonmodular 5-element lattice N5 into the c.e. degrees which maps the top to the degree a. In particular, this shows that local nondistributivity coincides with (...) local nonmodularity in the computably enumerable degrees. (shrink)