Online research in philosophy

Two types of truth table tasks are used investigating mental representations of conditionals: a possibilities-based and a truth-based one. In possibilities tasks, participants indicate whether a situation is possible or impossible according to the conditional rule. In truth tasks participants evaluate whether a situation makes the rule true or false, or is irrelevant with respect to the truth of the rule. Comparing the two-option version of the possibilities task with the truth task in Experiment 1, the possibilities task yields logical answer patterns whereas the truth task yields defective patterns. Adding the irrelevant option to the possibilities task in Experiment 2 leads to a considerable amount of defective patterns in the possibilities task, but still to more logical patterns in the possibilities task than in the truth task. Experiment 3 shows that directionality matters since rule-to-situation tasks yield more logical answer patterns than do situation-to-rule tasks. We conclude that both task types are not comparable as such since wording, number of options and directionality influence the results.

A semantics of vagueness should reject the principle that every statement has a truth-value yet retain the classical tautologies. A many-value, non-truth-functional semantics and a semantics of super-valuations each have this result. According to the super-valuation approach, 'if a man with n hairs on his head is bald, then a man with n plus one hairs on his head is also bald' is false because it comes out false no matter how the vague predicate 'is bald' is appropriately made precise. But why should a sentence in which components actually remain imprecise be regarded as actually false just because it would be false if its components were precise? On one of the alternative treatments of quantification allowed by the many-value approach, the sentence in question is assigned an intermediate value closer to 'false' than to 'true'. Despite the elegance of the super-valuation approach, there are reasons to prefer the many-value approach.

In his recent "Thomas vs. Thomas: A New Approach to Nagel's Bat Argument", Yujin Nagasawa interprets Thomas Nagel as making a certain argument against physicalism and objects that this argument transgresses a principle, laid down by Thomas Aquinas, according to which inability to perform a pseudo-task does not count against an omnipotence claim. Taking Nagasawa's interpretation of Nagel for granted, I distinguish different kinds of omnipotence claims and different kinds of pseudo-tasks, and on that basis show that Nagasawa's criticism of Nagel is unsuccessful. I also show how his reflections do nonetheless point to a limitation of the approach he means to criticize.

We formalise the notion of those infinite binary sequences z that admit a single program P which expresses the entire algorithmical structure of z. Such a program P minimizes the information which must be used in a relative computation for z. We propose two concepts with different strength for this notion, the learnable and the super-learnable sequences. We establish three different equivalent characterizations of learnable (super-learnable, resp.) sequences. In particular, we prove that a sequences z is learnable (super-learnable, resp.) if and only if there is a computable probability measure p such that p is Schnorr (Martin-Lof, resp.) p-random. There is a recursively enumerable sequence which is not learnable. The learnable sequences are invariant with respect to all total and effective transformations of infinite binary sequences.

One recently proposed solution to the Liar paradox is the contextual theory of truth. Tyler Burge (1979) argues that truth is an indexical notion and that the extension of the truth predicate shifts during Liar reasoning. A Liar sentence might be true in one context and false in another. To many, contextualism seems to capture our pre-theoretic intuitions about the semantic paradoxes; this is especially due to its reliance on the so-called Revenge phenomenon. I, however, show that Super-Liar sentences (where a Super-Liar sentence is a sentence which says of itself that it is not true in any context) generate a significant problem for Burge’s contextual theory of truth.

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time.

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time.

In the paper below the authors describe three super-tasks. They show that although the abstract notion of a super-task may be, as Benacerraf suggested, a conceptual mismatch, the completion of the three super-tasks involved can be defined rather naturally, without leading to inconsistency, by means of a particular kinematical interpretation combined with a principle of continuity.

Two types of truth table tasks are used investigating mental representations of conditionals: a possibilities-based and a truth-based one. In possibilities tasks, participants indicate whether a situation is possible or impossible according to the conditional rule. In truth tasks participants evaluate whether a situation makes the rule true or false, or is irrelevant with respect to the truth of the rule. Comparing the two-option version of the possibilities task with the truth task in Experiment 1, the possibilities task yields logical answer patterns whereas the truth task yields defective patterns. Adding the irrelevant option to the possibilities task in Experiment 2 leads to a considerable amount of defective patterns in the possibilities task, but still to more logical patterns in the possibilities task than in the truth task. Experiment 3 shows that directionality matters since rule-to-situation tasks yield more logical answer patterns than do situation-to-rule tasks. We conclude that both task types are not comparable as such since wording, number of options and directionality influence the results.