The debate over wolf recovery and management in the United States is best understood as a value-based political conflict that transcends issues strictly pertaining to science, biology and techno-rational approaches to problem solving. Political and cultural context will shape the future of the wolf as it has its past. A policy-oriented approach has much to offer the debate, especially if it is contextual and places human values and ethics at the center of its analysis. It is also important for those (...) engaged in the debate to acknowledge its value-based character. The policy implications of not doing so are serious and will become only more so in the future. (shrink)

The Jordan decomposition theorem states that every function $f \colon \, [0,1] \to \mathbb {R}$ of bounded variation can be written as the difference of two non-decreasing functions. Combining this fact with a result of Lebesgue, every function of bounded variation is differentiable almost everywhere in the sense of Lebesgue measure. We analyze the strength of these theorems in the setting of reverse mathematics. Over $\mathsf {RCA}_{0}$, a stronger version of Jordan’s result where all functions are continuous is equivalent to (...) $\mathsf {ACA}_0$, while the version stated is equivalent to ${\textsf {WKL}}_{0}$. The result that every function on $[0,1]$ of bounded variation is almost everywhere differentiable is equivalent to ${\textsf {WWKL}}_{0}$. To state this equivalence in a meaningful way, we develop a theory of Martin–Löf randomness over $\mathsf {RCA}_0$. (shrink)

The ideas of continental philosopher Martin Heidegger have been influential in cognitive science and artificial intelligence, despite the fact that there has been no effort to analyze these ideas empirically. The experiments reported here are designed to lend empirical support to Heidegger’s phenomenology and more specifically his description of the transition between ready-to-hand and unready-to-hand modes in interactions with tools. In experiment 1, we found that a smoothly coping cognitive system exhibits 1/fβ type positively correlated noise and that its (...) correlated character is reduced when the system is perturbed. This indicates that the participant and tool constitute a self-assembled, extended device during smooth coping and this device is disrupted by the perturbation. In experiment 2, we examine the re-organization of awareness that occurs when a smoothly coping, self-assembled, extended cognitive system is perturbed. We found that the disruption is accompanied by a change in attention which interferes with participants’ performance on a simultaneous cognitive task. Together these experiments show that a smoothly coping participant-tool system can be temporarily disrupted and that this disruption causes a change in the participant’s awareness. Since these two events follow as predictions from Heidegger’s work, our study offers evidence for the hypothesized transition from readiness-to-hand to unreadiness-to-hand. (shrink)

It is time for a new paper about open questions in the currently very active area of randomness and computability. Ambos-Spies and Kučera presented such a paper in 1999 [1]. All the question in it have been solved, except for one: is KL-randomness different from Martin-Löf randomness? This question is discussed in Section 6.Not all the questions are necessarily hard—some simply have not been tried seriously. When we think a question is a major one, and therefore likely to be (...) hard, we indicate this by the symbol ▶, the criterion being that it is of considerable interest and has been tried by a number of researchers. Some questions are close contenders here; these are marked by ▷. With few exceptions, the questions are precise. They mostly have a yes/no answer. However, there are often more general questions of an intuitive or even philosophical nature behind. We give an outline, indicating the more general questions.All sets will be sets of natural numbers, unless otherwise stated. These sets are identified with infinite strings over {0, 1}. Other terms used in the literature are sequence and real. (shrink)

We use Demuth randomness to study strong lowness properties of computably enumerable sets, and sometimes of Δ20 sets. A set A⊆N is called a base for Demuth randomness if some set Y Turing above A is Demuth random relative to A. We show that there is an incomputable, computably enumerable base for Demuth randomness, and that each base for Demuth randomness is strongly jump-traceable. We obtain new proofs that each computably enumerable set below all superlow Martin-Löf random sets is (...) strongly jump traceable, using Demuth tests. The sets Turing below each ω2-computably approximable Martin-Löf random set form a proper subclass of the bases for Demuth randomness, and hence of the strongly jump traceable sets. The c.e. sets Turing below each ω2-computably approximable Martin-Löf random set satisfy a new, very strong combinatorial lowness property called ω-traceability. (shrink)

We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.

We investigate the strength of a randomness notion ${\cal R}$ as a set-existence principle in second-order arithmetic: for each Z there is an X that is ${\cal R}$-random relative to Z. We show that the equivalence between 2-randomness and being infinitely often C-incompressible is provable in $RC{A_0}$. We verify that $RC{A_0}$ proves the basic implications among randomness notions: 2-random $\Rightarrow$ weakly 2-random $\Rightarrow$ Martin-Löf random $\Rightarrow$ computably random $\Rightarrow$ Schnorr random. Also, over $RC{A_0}$ the existence of computable randoms is (...) equivalent to the existence of Schnorr randoms. We show that the existence of balanced randoms is equivalent to the existence of Martin-Löf randoms, and we describe a sense in which this result is nearly optimal. (shrink)

Demuth tests generalize Martin-Löf tests in that one can exchange the m-th component a computably bounded number of times. A set fails a Demuth test if Z is in infinitely many final versions of the Gm. If we only allow Demuth tests such that GmGm+1 for each m, we have weak Demuth randomness.We show that a weakly Demuth random set can be high and , yet not superhigh. Next, any c.e. set Turing below a Demuth random set is strongly (...) jump-traceable.We also prove a basis theorem for non-empty classes P. It extends the Jockusch–Soare basis theorem that some member of P is computably dominated. We use the result to show that some weakly 2-random set does not compute a 2-fixed point free function. (shrink)

We define a program size complexity function $H^\infty$ as a variant of the prefix-free Kolmogorov complexity, based on Turing monotone machines performing possibly unending computations. We consider definitions of randomness and triviality for sequences in ${\{0,1\}}^\omega$ relative to the $H^\infty$ complexity. We prove that the classes of Martin-Löf random sequences and $H^\infty$-random sequences coincide and that the $H^\infty$-trivial sequences are exactly the recursive ones. We also study some properties of $H^\infty$ and compare it with other complexity functions. In particular, (...) $H^\infty$ is different from $H^A$, the prefix-free complexity of monotone machines with oracle A. (shrink)

We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy–Young–Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class.

This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an n such (...) that n,2n,…,kn shifts of the point all end up in P. We consider multiple recurrence into closed sets that possess various degrees of effectiveness: clopen, Π10 with computable measure, and Π10. The notions of Kurtz, Schnorr, and Martin-Löf randomness, respectively, turn out to be sufficient. We obtain similar results for multiple recurrence with respect to the k commuting shift operators on {0,1}Nk. (shrink)

EveryK-trivial set is computable from an incomplete Martin-Löf random set, i.e., a Martin-Löf random set that does not compute the halting problem.

An infinite binary sequence X is Kolmogorov–Loveland random if there is no computable non-monotonic betting strategy that succeeds on X in the sense of having an unbounded gain in the limit while betting successively on bits of X. A sequence X is KL-stochastic if there is no computable non-monotonic selection rule that selects from X an infinite, biased sequence.One of the major open problems in the field of effective randomness is whether Martin-Löf randomness is the same as KL-randomness. Our (...) first main result states that KL-random sequences are close to Martin-Löf random sequences in so far as every KL-random sequence has arbitrarily dense subsequences that are Martin-Löf random. A key lemma in the proof of this result is that for every effective split of a KL-random sequence at least one of the halves is Martin-Löf random. However, this splitting property does not characterize KL-randomness; we construct a sequence that is not even computably random such that every effective split yields two subsequences that are 2-random. Furthermore, we show for any KL-random sequence A that is computable in the halting problem that, first, for any effective split of A both halves are Martin-Löf random and, second, for any computable, nondecreasing, and unbounded function g and almost all n, the prefix of A of length n has prefix-free Kolmogorov complexity at least n−g. Again, the latter property does not characterize KL-randomness, even when restricted to left-r.e. sequences; we construct a left-r.e. sequence that has this property but is not KL-stochastic and, in fact, is not even Mises–Wald–Church stochastic.Turning our attention to KL-stochasticity, we construct a non-empty class of KL-stochastic sequences that are not weakly 1-random; by the usual basis theorems we obtain such sequences that in addition are left-r.e., are low, or are of hyperimmune-free degree.Our second main result asserts that every KL-stochastic sequence has effective dimension 1, or equivalently, a sequence cannot be KL-stochastic if it has infinitely many prefixes that can be compressed by a factor of α<1. This improves on a result by Muchnik, who has shown that were they to exist, such compressible prefixes could not be found effectively. (shrink)

We study the sets that are computable from both halves of some (Martin–Löf) random sequence, which we call 1/2-bases. We show that the collection of such sets forms an ideal in the Turing degrees that is generated by its c.e. elements. It is a proper subideal of the K-trivial sets. We characterize 1/2-bases as the sets computable from both halves of Chaitin’s Ω, and as the sets that obey the cost function c(x,s)=Ωs−Ωx−−−−−−−√. Generalizing these results yields a dense hierarchy (...) of subideals in the K-trivial degrees: For k<n, let Bk/n be the collection of sets that are below any k out of n columns of some random sequence. As before, this is an ideal generated by its c.e. elements and the random sequence in the definition can always be taken to be Ω. Furthermore, the corresponding cost function characterization reveals that Bk/n is independent of the particular representation of the rational k/n, and that Bp is properly contained in Bq for rational numbers p<q. These results are proved using a generalization of the Loomis–Whitney inequality, which bounds the measure of an open set in terms of the measures of its projections. The generality allows us to analyze arbitrary families of orthogonal projections. As it turns out, these do not give us new subideals of the K-trivial sets; we can calculate from the family which Bp it characterizes. We finish by studying the union of Bp for p<1; we prove that this ideal consists of the sets that are robustly computable from some random sequence. This class was previously studied by Hirschfeldt [D. R. Hirschfeldt, C. G. Jockusch, R. Kuyper and P. E. Schupp, Coarse reducibility and algorithmic randomness, J. Symbolic Logic81(3) (2016) 1028–1046], who showed that it is a proper subclass of the K-trivial sets. We prove that all such sets are robustly computable from Ω, and that they form a proper subideal of the sets computable from every (weakly) LR-hard random sequence. We also show that the ideal cannot be characterized by a cost function, giving the first such example of a Σ03 subideal of the K-trivial sets. (shrink)

The tower number ${\mathfrak t}$ and the ultrafilter number $\mathfrak {u}$ are cardinal characteristics from set theory. They are based on combinatorial properties of classes of subsets of $\omega $ and the almost inclusion relation $\subseteq ^*$ between such subsets. We consider analogs of these cardinal characteristics in computability theory.We say that a sequence $(G_n)_{n \in {\mathbb N}}$ of computable sets is a tower if $G_0 = {\mathbb N}$, $G_{n+1} \subseteq ^* G_n$, and $G_n\smallsetminus G_{n+1}$ is infinite for each n. (...) A tower is maximal if there is no infinite computable set contained in all $G_n$. A tower ${\left \langle {G_n}\right \rangle }_{n\in \omega }$ is an ultrafilter base if for each computable R, there is n such that $G_n \subseteq ^* R$ or $G_n \subseteq ^* \overline R$ ; this property implies maximality of the tower. A sequence $(G_n)_{n \in {\mathbb N}}$ of sets can be encoded as the “columns” of a set $G\subseteq \mathbb N$. Our analogs of ${\mathfrak t}$ and ${\mathfrak u}$ are the mass problems of sets encoding maximal towers, and of sets encoding towers that are ultrafilter bases, respectively. The relative position of a cardinal characteristic broadly corresponds to the relative computational complexity of the mass problem. We use Medvedev reducibility to formalize relative computational complexity, and thus to compare such mass problems to known ones.We show that the mass problem of ultrafilter bases is equivalent to the mass problem of computing a function that dominates all computable functions, and hence, by Martin’s characterization, it captures highness. On the other hand, the mass problem for maximal towers is below the mass problem of computing a non-low set. We also show that some, but not all, noncomputable low sets compute maximal towers: Every noncomputable (low) c.e. set computes a maximal tower but no 1-generic $\Delta ^0_2$ -set does so.We finally consider the mass problems of maximal almost disjoint, and of maximal independent families. We show that they are Medvedev equivalent to maximal towers, and to ultrafilter bases, respectively. (shrink)

Przekład na podstawie: “The Frankfurt Cases: The Moral of the Stories”, Philosophical Review 119 : 315–336. Przekład za zgodą Autora Autor argumentuje, że morał przykładów frankfurtowskich jest następujący: jeśli determinizm przyczynowy wyklucza odpowiedzialność moralną, to nie na mocy eliminacji alternatywnych możliwości, a następnie odpowiada na najważniejsze wyzwanie dla tej tezy, mianowicie argument nazywany „obroną przez dylemat”.

This paper proposes a view of time that takes passage to be the most basic temporal notion, instead of the usual A-theoretic and B-theoretic notions, and explores how we should think of a world that exhibits such a genuine temporal passage. It will be argued that an objective passage of time can only be made sense of from an atemporal point of view and only when it is able to constitute a genuine change of objects across time. This requires that (...) passage can flip one fact into a contrary fact, even though neither side of the temporal passage is privileged over the other. We can make sense of this if the world is inherently perspectival. Such an inherently perspectival world is characterized by fragmentalism, a view that has been introduced by Fine in his ‘Tense and Reality’ (2005). Unlike Fine's tense-theoretic fragmentalism though, the proposed view will be a fragmentalist view based in a primitive notion of passage. (shrink)

There is a type of metaphysical picture that surfaces in a range of philosophical discussions, is of intrinsic interest, and yet remains ill-understood. According to this picture, the world contains a range of standpoints relative to which different facts obtain. Any true representation of the world cannot but adopt a particular standpoint. The aim of this paper is to propose a regimentation of a metaphysics that underwrites this picture. Key components are a factive notion of metaphysical relativity, a deflationary notion (...) of adopting standpoints, and two kinds of valid inference, one that allows one to abandon standpoints and one that does not. To better understand how theories formulated in terms of this framework are situated in dialectical space, I sketch a theory in the philosophy of time that admits both temporal and atemporal standpoints. (shrink)

This essay is dedicated to the memory of Katherine Hawley.1Bitcoin was invented to serve as a digital currency that demands no trust in financial institutions, such as commercial and central banks. This paper discusses metaphysical aspects of bitcoin, in particular the view that bitcoin is socially constructed, non-concrete, and genuinely exists. If bitcoin is socially constructed, then one may worry that this reintroduces trust in the communities responsible for the social construction. Although we may have to rely on certain communities, (...) I argue that social construction doesn’t imply a demand for trust because the relevant communities don’t take on any relevant commitments. Bitcoin is indeed trust-free. (shrink)

Fragmentalism is the view that reality is not a metaphysically unified place, but fragmented in a certain sense, and constituted by incompatible facts across such fragments. It was introduced by Kit Fine in a discussion of tense realist theories of time. Here I discuss the conceptual foundations of fragmentalism, identify several open questions in Fine’s characterization of the view, and propose an understanding of fragmentalism that addresses these open questions.

The views of John Dewey and Kurt Vonnegut are often criticized for opposite reasons: Dewey’s philosophy is said to be naively optimistic while Vonnegut’s work is read as cynical. The standard debates over the views of the two thinkers cause readers to overlook the similarities in the way each approaches tragic experience. This paper examines Dewey’s philosophic account of time and meaning and Vonnegut’s use of time travel in his autobiographical novel Slaughterhouse-Five to illustrate these similarities. This essay demonstrates how (...) both Dewey and Vonnegut embrace the ameliorative possibilities of art for preserving individuality and meaning in the face of tragic experience. (shrink)

There is a traditional interpretation of the work of Ralph Waldo Emerson that portrays him as a champion of nature, wilderness, or country life and an opponent of the city, technology, or urban life. Such a view, though, neglects the role of human activity in the universe as Emerson saw it. Furthermore, this view neglects the proper relation between soul and nature in the universe and risks entailing a philosophy of materialism--an unacceptable position for Emerson. An examination of Emerson's philosophy (...) will show that it is not fundamentally hostile to urban life or technology, and that, in fact, an anti-urban position is opposed to the most central themes of Emerson's philosophical vision. (shrink)

Fragmentalism was first introduced by Kit Fine in his ‘Tense and Reality’. According to fragmentalism, reality is an inherently perspectival place that exhibits a fragmented structure. The current paper defends the fragmentalist interpretation of the special theory of relativity, which Fine briefly considers in his paper. The fragmentalist interpretation makes room for genuine facts regarding absolute simultaneity, duration and length. One might worry that positing such variant properties is a turn for the worse in terms of theoretical virtues because such (...) properties are not involved in physical explanations and hence theoretically redundant. It will be argued that this is not right: if variant properties are indeed instantiated, they will also be involved in straightforward physical explanations and hence not explanatorily redundant. Hofweber and Lange, in their ‘Fine’s Fragmentalist Interpretation of Special Relativity’, object that the fragmentalist interpretation is in tension with the right explanation of the Lorentz transformations. It will be argued that their objection targets an inessential aspect of the fragmentalist framework and fails to raise any serious problem for the fragmentalist interpretation of special relativity. (shrink)

Although he was born in Spain, George Santayana became a uniquely American philosopher, critic, poet, and best-selling novelist. Along with his Harvard colleagues William James and Josiah Royce, he is best known as one of the founders of American pragmatism and recognized for his insights into the theory of knowledge, metaphysics, and moral philosophy. The Essential Santayana presents a selection of Santayana's most important and influential literary and philosophical work. Martin A. Coleman's critical introduction sets Santayana into the American (...) philosophical tradition and provides context for contemporary readers, many of whom may be approaching Santayana's writings for the first time. This landmark collection reveals the intellectual and literary diversity of one of American philosophy's most lively minds. (shrink)

Objects often manifest themselves in incompatible ways across perspectives that are epistemically on a par. The standard response to such cases is to deny that the properties that things appear to have from different perspectives are properties that things really have out there. This type of response seems worrying: too many properties admit of perspectival variance and there are good theoretical reasons to think that such properties are genuinely instantiated. So, we have reason to explore views on which things can (...) have the incompatible properties they appear to have across perspectives. This paper explores the view that things can have incompatible properties if the world is not a metaphysically unified place but is instead fragmented. There is a sensible notion of co-obtainment, on which two facts can each obtain without co-obtaining. Using this notion, we can step back from our embedded perspectives on the world without deeming the contents of those perspectives to be mere appearances. This renders th.. (shrink)

John Dewey gives an account of meaning that stands in significant contrast to contemporary theories of meaning. A readily apparent difference is Dewey's subordination of truth to meaning while much recent philosophizing about meaning, particularly in what is often referred to as the Analytic tradition, subordinates meaning to truth. Another difference, and one that helps account for the first, is philosophic method: Dewey is explicitly empirical in his attempt to understand meaning while prominent thinkers in the Analytic tradition have come (...) to reject empiricism as if it could mean only the empiricism of Locke and Hume . ;To understand these general differences in more detail, the present work contrasts Dewey's account with a particularly well-known theory of meaning in the Analytic tradition, that of Donald Davidson. Davidson proposes a theory of meaning that is strongly influenced by a rejection of an empirical approach. This non-empirical theory of meaning strives to account for the possibility of certainty in understanding, but it does so by placing serious limitations on meaning. Dewey's empirical approach removes these limitations by replacing the desire for absolute certainty with faithfulness to experience in inquiry. ;The main aim of the present work is to give a clear explication of Dewey's empirical approach to meaning and indicate its advantages for philosophy and human life. The present work follows Dewey in tracing the development of meaning from its experiential roots to its continued growth in interaction. Dewey's approach results in an evolutionary or developmental account of meaning. His account makes sense of extra-linguistic meaning, kinds of meanings, and new meanings that grow out of novel experiences. ;On Dewey's account philosophical activity shifts emphasis from truth to meaning. Truth is not denigrated or denied, rather it is now understood in the broader context of experience. Truth as a metaphysical concept is disambiguated from truths or warranted assertions as the product of specific inquiries; and the latter serve meanings as means to experiences, which includes more than cognitive experiences. (shrink)