Online research in philosophy

Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.

Consider "Sam is sad" and "Sam exemplifies the property of being sad". The second sentence mentions a property and predicates the relation of exemplification. It belongs to a large class of sentences which mention such formal objects as propositions, states of affairs, facts, concepts and sets and predicate formal properties such as the truth of propositions, the obtaining of states of affairs and relations such as falling under concepts and being members of sets. The first sentence belongs to a distinct class of sentences in which only non-formal objects are mentioned and only non-formal properties and relations are predicated. We can, it seems, infer validly from the first sentence to the second. They are also equivalent. And Sam exemplifies the property of sadness because Sam is sad. What is the relation between inference, equivalence and explanation in the case of our two sentences and in analogous cases? What right have we to assume that there are formal objects?

For any objects x and y, and any integers c and d , if there exists something that is both c times as massive as y and d times as massive as x, then there exists something that is both c times as accelerated as x and d times as accelerated as y For a more general intrinsic statement, use the fact that real numbers correspond one-to-one to the sets of fractions that are less-than-or-equal-to them.

From the medieval and post-medieval analyses dealing with propositions and time one gathers that their relation can be considered from various points of view. It could be said that there is not one "time" connected with a proposition, but several "times": following d'Ors, I will distinguish at least three: the time of the utterance, the time of the copula, and the time of truth. These three times of the proposition may or may not coincide. In these pages I propose to examine one of the problems raised by the possible separation of times. I will use as a guide the reflections of the Spanish logician Jerónimo Pardo (†1502) regarding the question of whether or not the mental true contingent proposition can be falsified.

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version of the Church–Turing Thesis is unaffected by SAD computation.

In this essay, I discuss a few ways in which songs are used, ways in which listeners engage with and find meaning in music. I am most interested in sad songs—those that typically feature narratives about lost love, separation, missed opportunity, regret, hardship, and all manner of heartache. Many of us are drawn to sad songs in moments of emotional distress. The problem is that sad songs do not always make us feel better; to the contrary, they often make us feel worse. So, why do we listen to sad songs? I argue that we seek out sad songs, partly, to intensify distress, which helps us reflect on situations of profound personal significance.

This paper systematically reconstructs Boethius’s reflections on God, attempting to find the common element to which all of the variations in these reflections can be retraced. This common element is constituted by the continuous tension between kataphatic and apophatic theology. Boethius apparently both kataphatically defines God in his logical works, and maintains that God can only be defined apophatically in his theological works. This tension can, at times, cause some incoherence as one moves from one level of discourse to another: that is, from the logico-linguistic to the metaphysical-ontological level of discourse. Boethius’s thought manifests this incoherence. This incoherence is in part common to Neoplatonic thought and its sources, but would also seem to be dictated by the nature of the very operation of reflecting upon God.