We explore depth substitution invariance, or hyperformalism, and extend known results in this realm to justification logics extending weak relevant logics. We then examine the surprising invariance of justifications over formulas and restrict our attention to the substitution of proofs in the original relevant logic. The results of this paper indicate that depth invariance is a recalcitrant feature of the logic and that proof structures in hyperformal logics are quite inflexible.

Weak enough relevant logics are often closed under depth substitutions. To determine the breadth of logics with this feature, we show there is a largest sublogic of R closed under depth substitutions and that this logic can be recursively axiomatized.

Although expert consensus states that critical thinking (CT) is essential to enquiry, it doesn’t necessarily follow that by practicing enquiry children are developing CT skills. Philosophy with children programmes around the world aim to develop CT dispositions and skills through a community of enquiry, and this study compared the impact of the explicit teaching of CT skills during an enquiry, to The Philosophy Foundation's philosophical enquiry (PhiE) method alone (which had no explicit teaching of CT skills). Philosophy with children is (...) also said to improve metacognitive (MC) skills but there is little research into this claim. Following observable problems with ensuring genuine metacognition was happening in PhiE sessions - on a reasonably strong understanding of what metacognition is – a method has been developed and trialed in this study to bring together, in mutual support, the development of critical thinking and metacognitive skills. Based on the work of Peter Worley and Ellen Fridland (KCL)The Philosophy Foundation ran an experimental study with King's College London in Autumn 2017 and Autumn 2018 to compare the impact of teaching CT skills and MC skills against classes that just have philosophical enquiry. The approach developed and used for the study employs the explicit teaching of some CT and MC skills within the context of a philosophical enquiry (as opposed to stand-alone teaching of these skills) and yields some positive findings both qualitative and quantitative. Both studies took place over one term (12 weeks) and a control and intervention group were used in each study. This report focuses on the second year of the study, with 220 ten and eleven-year-old children involved in eight classes across three state schools in South East London. Although there were limitations to the study the results indicate that the explicit teaching of these skills during a philosophical enquiry can help children use CT and MC skills more successfully than philosophical enquiry alone. (shrink)

The AGI alignment problem has a bimodal distribution of outcomes with most outcomes clustering around the poles of total success and existential, catastrophic failure. Consequently, attempts to solve AGI alignment should, all else equal, prefer false negatives (ignoring research programs that would have been successful) to false positives (pursuing research programs that will unexpectedly fail). Thus, we propose adopting a policy of responding to points of philosophical and practical uncertainty associated with the alignment problem by limiting and choosing necessary assumptions (...) to reduce the risk of false positives. Herein we explore in detail two relevant points of uncertainty that AGI alignment research hinges on---meta-ethical uncertainty and uncertainty about mental phenomena---and show how to reduce false positives in response to them. (shrink)

The AGI alignment problem has a bimodal distribution of outcomes with most outcomes clustering around the poles of total success and existential, catastrophic failure. Consequently, attempts to solve AGI alignment should, all else equal, prefer false negatives (ignoring research programs that would have been successful) to false positives (pursuing research programs that will unexpectedly fail). Thus, we propose adopting a policy of responding to points of metaphysical and practical uncertainty associated with the alignment problem by limiting and choosing necessary assumptions (...) to reduce the risk false positives. Herein we explore in detail some of the relevant points of uncertainty that AGI alignment research hinges on and consider how to reduce false positives in response to them. (shrink)