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Truthlikeness and the Number of Planets
Journal of Philosophical Logic Pub Date : 2024-01-25 , DOI: 10.1007/s10992-023-09739-y
Theo A. F. Kuipers

Examples of hypotheses about the number of planets are frequently used to introduce the topic of (actual) truthlikeness but never analyzed in detail. In this paper we first deal with the truthlikeness of singular quantity hypotheses, with reference to several ‘the number of planets’ examples, such as ‘The number of planets is 10 versus 10 billion (instead of 8).’ For the relevant ratio scale of quantities we will propose two, strongly related, normalized metrics, the proportional metric and the (simplest and hence favorite) fractional metric, to express e.g. the distance from a hypothetical number to the true number of planets, i.e. the distance between quantities. We argue that they are, in view of the examples and plausible conditions of adequacy, much more appropriate, than the standardly suggested, normalized absolute difference, metric.

Next we deal with disjunctive hypotheses, such as ‘The number of planets is between 7 and 10 inclusive is much more truthlike than between 1 and 10 billion inclusive.’ We compare three (clusters of) general ways of dealing with such hypotheses, one from Ilkka Niiniluoto, one from Pavel Tichý and Graham Oddie, and a trio of ways from Theo Kuipers. Using primarily the fractional metric, we conclude that all five measures can be used for expressing the distance of disjunctive hypotheses from the actual truth, that all of them have their strong and weak points, but that (the combined) one of the trio is, in view of principle and practical considerations, the most plausible measure.



中文翻译:

真实性和行星数量

关于行星数量的假设的例子经常被用来介绍(实际)真实性的主题,但从未进行过详细分析。在本文中,我们首先参考几个“行星数量”的例子来处理奇异数量假设的真实性,例如“行星数量是 10100 亿(而不是 8)”。对于数量的相关比例尺度,我们将提出两个强相关的归一化度量,即比例度量和(最简单且最受喜爱的)分数度量,以表达例如从假设数字到真实行星数量的距离,即数量之间的距离。我们认为,鉴于示例和合理的充分性条件,它们比标准建议的标准化绝对差度量更合适。

接下来我们处理析取假设,例如“行星数量在 7 到 10 之间(含)比 1 到 100 亿之间更真实”。我们比较了处理此类假设的三种(一组)一般方法,一种来自 Ilkka Niiniluoto,一种来自 Pavel Tichý 和 Graham Oddie,以及三种来自 Theo Kuipers 的方法。主要使用分数度量,我们得出结论,所有五个度量都可以用于表达析取假设与实际真相的距离,它们都有自己的优点和缺点,但是(组合的)三个度量之一是,从原则和实际考虑来看,这是最可行的措施。

更新日期:2024-01-25
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