Aggregative consequentialism and several other popular moral theories are threatened with paralysis: when coupled with some plausible assumptions, they seem to imply that it is always ethically indifferent what you do. Modern cosmology teaches that the world might well contain an infinite number of happy and sad people and other candidate value-bearing locations. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only a finite amount (...) of good or bad. In standard cardinal arithmetic, an infinite quantity is unchanged by the addition or subtraction of any finite quantity. So it appears you cannot change the value of the world. Modifications of aggregationism aimed at resolving the paralysis are only partially effective and cause severe side effects, including problems of “fanaticism”, “distortion”, and erosion of the intuitions that originally motivated the theory. Is the infinitarian challenge fatal? (shrink)

Renowned scholar Robert Adams explores the relation between religion and ethics through a comprehensive philosophical account of a theistically-based framework for ethics. Adams' framework begins with the good rather than the right, and with excellence rather than usefulness. He argues that loving the excellent, of which adoring God is a clear example, is the most fundamental aspect of a life well lived. Developing his original and detailed theory, Adams contends that devotion, the sacred, grace, martyrdom, worship, vocation, faith, and other (...) concepts drawn from religious ethics have been sorely overlooked in moral philosophy and can enrich the texture of ethical thought. (shrink)

Isn't probability 1 certainty? If the probability is objective, so is the certainty: whatever has chance 1 of occurring is certain to occur. Equivalently, whatever has chance 0 of occurring is certain not to occur. If the probability is subjective, so is the certainty: if you give credence 1 to an event, you are certain that it will occur. Equivalently, if you give credence 0 to an event, you are certain that it will not occur. And so on for other (...) kinds of probability, such as evidential probability. The formal analogue of this picture is the regularity constraint: a probability distribution over sets of possibilities is regular just in case it assigns probability 0 only to the null set, and therefore probability 1 only to the set of all possibilities. (shrink)

Williams and J. Fraser have recently argued that effective field theory methods enable scientific realists to make more reliable ontological commitments in quantum field theory than those commonly made. In this paper, I show that the interpretative relevance of these methods extends beyond the specific context of QFT by identifying common structural features shared by effective theories across physics. In particular, I argue that effective theories are best characterized by the fact that they contain intrinsic empirical limitations, and I extract (...) from their structure one central interpretative constraint for making more reliable ontological commitments in different subfields of physics. While this is in principle good news, this constraint still raises a challenge for scientific realists in some contexts, and I bring the point home by focusing on Williams’s and J. Fraser’s defense of selective realism in QFT. (shrink)

According to Friedrich Schleiermacher, religiosity is rooted in feeling (Gefühl). As a result of our engagement with the world, on which we depend and which we can influence, we have both a sense of dependence and of freedom. Schleiermacher speculated that a sense of absolute dependence in reflective beings with self-consciousness (human beings) gave rise to religion. Using insights from contemporary philosophy of biology and cognitive science, I seek to naturalize Schleiermacher's ideas. I moreover show that this naturalization is in (...) line with Schleiermacher's outlook on biology, as he already had evolutionary considerations in mind when he wrote the Christian Faith (1830). While Schleiermacher rejects natural theology in a narrow sense (proofs for the existence of God), his project is natural theological in a broader sense, as it roots religion in experiences that we can examine using naturalistic theories. (shrink)

‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to spell (...) out the infinity of real numbers mathematicians come to see the active role of emptiness. Pondering over the essence of self-awareness, the Japanese philosopher Nishida Kitarō comes to see the ‘place’ where it abides as absolute nothingness. Thus, the two ways of seeing coalesce into a perspective in which infinity and nothingness mirror each other. (shrink)

This paper presents an in-depth analysis of the anatomy of both thermodynamics and statistical mechanics, together with the relationships between their constituent parts. Based on this analysis, using the renormalization group and finite-size scaling, we give a definition of a large but finite system and argue that phase transitions are represented correctly, as incipient singularities in such systems. We describe the role of the thermodynamic limit. And we explore the implications of this picture of critical phenomena for the questions of (...) reduction and emergence. (shrink)

Using artificially synthesized stimuli, previous research has shown that cotton-top tamarin monkeys easily learn simple AB grammar sequences, but not the more complex AnBn sequences that require hierarchical structure. Humans have no trouble learning AnBn combinations. A more recent study, using similar artificially created stimuli, showed that there is a neuroanatomical difference in the brain between these two kinds of arrays. While the simpler AB sequences recruit the frontal operculum, the AnBn array recruits the phylogenetically newer Broca’s area. We propose (...) that on close inspection, reported vocal repertoires of Old World Monkeys show that these nonhuman primates are capable of calls that have two items in them, but never more than two. These are simple AB sequences, as predicted by previous research. In addition, we suggest the two-item call cannot be the result of a combinatorial operation that we see in human language, where the recursive operation of Merge allows for a potentially infinite array of structures. In our view, the two-item calls of nonhuman primates result from a dual-compartment frame into which each of the calls can fit without having to be combined by an operation such as Merge. (shrink)

Some compatibilists have responded to the manipulation argument for incompatibilism by proposing an historical theory of moral responsibility which, according to one version, requires that agents be morally responsible for having their pro-attitudes if they are to be morally responsible for acting on them. This proposal, however, leads obviously to an infinite regress problem. I consider a proposal by Haji and Cuypers that addresses this problem and argue that it is unsatisfactory. I then go on to propose a new solution (...) inspired by the libertarian theory of Robert Kane. (shrink)

It seems improbable that life would exist in a naturalistic universe. But if the universe were spatially infinite, then seemingly improbable events would be expected to happen; life would be expected to exist. It follows that the existence of life provides evidence that the universe is spatially infinite.

SC, CA, QA and QEA denote the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasi-polyadic algebras and quasi-polyadic equality algebras, respectively. Let ω ≤ α < β and let K ∈ {SC,CA,QA,QEA}. We show that the class of α -dimensional neat reducts of algebras in Kβ is not elementary. This solves a problem in [3]. Also our result generalizes results proved in [2] and [3].

In classical propositional logic, a theory T is prime iff it is complete. In Łukasiewicz infinite-valued logic the two notions split, completeness being stronger than primeness. Using toric desingularization algorithms and the fine structure of prime ideal spaces of free ℓ -groups, in this paper we shall characterize prime theories in infinite-valued logic. We will show that recursively enumerable prime theories over a finite number of variables are decidable, and we will exhibit an example of an undecidable r.e. prime theory (...) over countably many variables. (shrink)

Can a certain sort of property supervene on another sort of property without reducing to it? Many philosophers find the superveniencel irreducibility combination attractive in the philosophy of mind and in moral philosophy. They think that mental properties supervene upon physical properties but do not reduce to them, or that moral properties supervene upon natural properties without reducing to them. Other philosophers have tried to show that the combination is ultimately untenable, however attractive it might initially appear. Thus Ted Honderich (...) and Jaegwon Kim argue that the combination cannot explain the causal efhcacy of the supervening properties. And Simon. (shrink)

Can a certain sort of property supervene on another sort of property without reducing to it? Many philosophers find the superveniencel irreducibility combination attractive in the philosophy of mind and in moral philosophy (Davidson 1980 and Moore 1903). They think that mental properties supervene upon physical properties but do not reduce to them, or that moral properties supervene upon natural properties without reducing to them. Other philosophers have tried to show that the combination is ultimately untenable, however attractive it might (...) initially appear. Thus Ted Honderich and Jaegwon Kim argue that the combination cannot explain the causal efhcacy of the supervening properties (Honderich 1982, Kim 1984b). And Simon.. (shrink)

This article addresses “Creativity after Computation” by looking into the concept of artificial imagination, namely the machine’s ability to produce images that challenge artmaking and surprise human beings with the aid of machine learning algorithms. What is at stake is not only art and creativity but also the tension between the determination of machines and the freedom of human beings. This opposition restages Kant’s third antinomy in the contemporary technological condition. By referring to the debate on the question of imagination (...) in Kant, Heidegger, and Stiegler, the article suggests that imagination is always already artificial and that it is more productive to develop an organology of artificial imagination. It clarifies the notion of artificial imagination and offers an organological reading through a reinterpretation of Leibniz’s monadology, Kant’s sublime, and Schiller’s aesthetic education against the backdrop of recursive algorithms. (shrink)

The long-periodic/infinite discrete Gabor transform is more effective than the periodic/finite one in many applications. In this paper, a fast and effective approach is presented to efficiently compute the Gabor analysis window for arbitrary given synthesis window in DGT of long-periodic/infinite sequences, in which the new orthogonality constraint between analysis window and synthesis window in DGT for long-periodic/infinite sequences is derived and proved to be equivalent to the completeness condition of the long-periodic/infinite DGT. By using the property of delta function, (...) the original orthogonality can be expressed as a certain number of linear equation sets in both the critical sampling case and the oversampling case, which can be fast and efficiently calculated by fast discrete Fourier transform. The computational complexity of the proposed approach is analyzed and compared with that of the existing canonical algorithms. The numerical results indicate that the proposed approach is efficient and fast for computing Gabor analysis window in both the critical sampling case and the oversampling case in comparison to existing algorithms. (shrink)

Mate Meršić (Merchich, 1850-1928) sees the origin of Zeno’s paradox ‘Achilles’ in the ambiguities of the concept of the infinity. According to him (and to the tradition started by Gregory St. Vincent), those ambiguities are resolved by the concept of convergent geometric series. In this connection, Meršić proposes a general ontological theory with the priority of the finite over the infinite, and, proceeding from Newton’s concept of fluxion, he develops a modal interpretation of differential calculus.