Truth Analysis of the Gettier Argument

Gettier (1963) presented the now famous Gettier problem as a challenge to epistemology. The methods Gettier used to construct his challenge, however, utilized certain principles of formal logic that are actually inappropriate for the natural language discourse of the Gettier cases. In that challenge to epistemology, Gettier also makes truth claims that would be considered controversial in analytic philosophy of language. The Gettier challenge has escaped scrutiny in these other relevant academic disciplines, however, because of its façade as an epistemological analysis. This article examines Gettier's methods with the analytical tools of logic and analytic philosophy of language.     

Perceived optimality of competing solutions to the Euclidean travelling salesperson problem

The Travelling Salesperson Problem (TSP) is a nondeterministic-polynomial hard (NP-hard) combinatorial problem that occurs in a wide range of industrial domains, including logistics, route finding, and computer wiring. Interestingly, despite the problem’s inherent computational difficulty, when presented in Euclidean space (ETSP), human participants can produce close-to-optimal solutions in near-linear time. However, when asked to compare and select the most optimum solution from a set of pre-defined competing solution options, participants can struggle. In this study we investigate this paradox by asking participants to compare four closed-loop Euclidean TSP solutions, in order to determine which solution they perceived to have the most optimal tour cost. We hypothesise that the extracted geometric properties have an effect on stimulus selection in a discrimination task (selection or no selection). Accordingly, we extracted four geometric properties from competing stimuli in order to create a perceptual activation function. Predictive analytics demonstrated that a classification model could identify the most optimal solution 97% of the time using the perceptual activation scores alone, yet human participants only correctly determined the most optimal solution 47% of the time. Mixed-effects models suggest that ‘likelihood of stimulus selection’ can be modelled as a function of the weighted coefficients of competing perceptual activation scores within each trial; however only a small amount of the variance is explained by these perceptual activation scores. Finally, a drift–diffusion model was used to create a theoretical framework of how likelihood of stimulus selection is influenced by competing perceptual activators. Our study highlights a novel way of extracting and analysing the importance of geometric properties that influence ETSP discrimination tasks, and links this analysis to human behaviour when discriminating between competing ETSP solutions.     

Pigeons perceive a reversed Zöllner illusion

Pigeons are susceptible to several size and length illusions, but in some cases the bias has been shown to be opposite to that seen in humans. To further investigate how their perceptual system works, we asked how pigeons perceive orientation illusions. We used the Zöllner illusion, in which parallel lines look non-parallel due to series of short crosshatches superimposed on the lines. First, we trained six birds to peck at the narrower (or wider) of the two gaps at the end of a pair of non-parallel target lines. After adapting the subjects to target lines with randomly oriented crosshatches (which result in no illusion at least to humans), we tested the pigeons’ responses on randomly inserted probe trials, in which crosshatches that should induce the standard Zöllner-like illusion for humans replaced the random-oriented ones. The results suggested that pigeons do perceive an illusion from Zöllner figures, but in the direction opposite to that of humans. We propose that pigeons, contrary to humans, may assimilate the two lines of different orientations (each main line and crosshatch), which results in underestimation of acute angles, and this in turn may lead to a reversed Zöllner illusion. Such assimilation dominance appears consistent with previous reports obtained for line length and size illusions in this species.     

新时代“健康优先”的三重理论逻辑

新时代我国施行“健康优先”在理论上合乎天然的逻辑。基于法理逻辑、价值逻辑和生产逻辑构建一个三重维度的分析框架。公民的生命权、健康权和发展权的保障和维护,是从微观个体层面催生“健康优先”的法理逻辑。汇聚到人民群众层面,“健康优先”与“以人民为中心”的发展思想共轭产生“以人民健康为中心”的理念,其价值逻辑不言自明。“健康优先”的生产逻辑体现在着眼于“现实的人”这一具有能动性的生产要素,既有利于人力资本的“再生产”,也有利于改善和提升健康人力资本。

     

Interpolation and Amalgamation; Pushing the Limits. Part II

This is the second part of the paper [Part I] which appeared in the previous issue of this journal.     

A multiple-valued logic approach to the design and verification of hardware circuits

We present a novel approach, which is based on multiple-valued logic (MVL), to the verification and analysis of digital hardware designs, which extends the common ternary or quaternary approaches for simulations. The simulations which are performed in the more informative MVL setting reveal details which are either invisible or harder to detect through binary or ternary simulations. In equivalence verification, detecting different behavior under MVL simulations may lead to the discovery of a genuine binary non-equivalence or to a qualitative gap between two designs. The value of a variable in a simulation may hold information about its degree of truth and its “place of birth” and “date of birth”. Applications include equivalence verification, initialization, assertions generation and verification, partial control on the flow of data by prioritizing and block-oriented simulations. Much of the paper is devoted to theoretical aspects behind the MVL approach, including the reason for choosing a specific algebra for computations and the introduction of the notions of De Morgan Canonical Form and of verification complexity of Boolean expressions. Two basic simulation-based algorithms are presented, one for satisfying and verifying combinational designs and the other for equivalence verification of sequential designs.     

Bunched sequential information

It is known that the logic BI of bunched implications is a logic of resources. Many studies have reported on the applications of BI to computer science. In this paper, an extension BIS of BI by adding a sequence modal operator is introduced and studied in order to formalize more fine-grained resource-sensitive reasoning. By the sequence modal operator of BIS, we can appropriately express “sequential information” in resource-sensitive reasoning. A Gentzen-type sequent calculus SBIS for BIS is introduced, and the cut-elimination and decidability theorems for SBIS are proved. An extension of the Grothendieck topological semantics for BI is introduced for BIS, and the completeness theorem with respect to this semantics is proved. The cut-elimination, decidability and completeness theorems for SBIS and BIS are proved using some theorems for embedding BIS into BI.     

Can Hardcore Actualism Validate S5?

Hardcore actualism (HA) grounds all modal truths in the concrete constituents of the actual world (see, e.g., Borghini and Williams (2008), Jacobs (2010), Vetter (2015)). I bolster HA, and elucidate the very nature of possibility (and necessity) according to HA, by considering if it can validate S5 modal logic. Interestingly, different considerations pull in different directions on this issue. To resolve the tension, we are forced to think hard about the nature of the hardcore actualist’s modal reality and how radically this departs from possible worlds orthodoxy. Once we achieve this departure, the prospects of a hardcore actualist validation of S5 look considerably brighter. This paper thus strengthens hardcore actualism by arguing that it can indeed validate S5–arguably the most popular logic of metaphysical modality–and, in the process, it elucidates the very nature of modality according to this revisionary, but very attractive, modal metaphysics.