Wittgenstein and the logical positivists attempted to explain logical necessity in terms of linguistic conventions. It is often thought that their respective accounts have been conclusively refuted by objections from Quine, Dummett and others. We argue that this verdict is premature. Several of the most popular anti‐conventionalist arguments fail, partly because they misconstrue the idea of truth by convention in Wittgenstein and/or logical positivism. Correctly understood, conventionalism claims that, given certain linguistic conventions, some sentences are unconditionally true, that is true (...) irrespective of how the world happens to be. This claim is difficult to deny, and the corresponding conventionalism about logical necessity remains a viable position. (shrink)

We argue that the later Wittgenstein’s philosophy of language and mathematics, substantially focused on rule-following, is relevant to understand and improve on the Artificial Intelligence (AI) alignment problem: his discussions on the categories that influence alignment between humans can inform about the categories that should be controlled to improve on the alignment problem when creating large data sets to be used by supervised and unsupervised learning algorithms, as well as when introducing hard coded guardrails for AI models. We cast these (...) considerations in a model of human–human and human–machine alignment and sketch basic alignment strategies based on these categories and further reflections on rule-following like the notion of meaning as use. To sustain the validity of these considerations, we also show that successful techniques employed by AI safety researchers to better align new AI systems with our human goals are congruent with the stipulations that we derive from the later Wittgenstein’s philosophy. However, their application may benefit from the added specificities and stipulations of our framework: it extends on the current efforts and provides further, specific AI alignment techniques. Thus, we argue that the categories of the model and the core alignment strategies presented in this work can inform further AI alignment techniques. (shrink)

The status of mathematical facts has long been taken to be unclear in Wittgenstein's philosophy of mathematics, and often, it seems that he wants to eliminate mathematical facts in favour of facts about our beliefs or behaviour. In this paper, I argue that by reading Wittgenstein as a radical conventionalist, we can give a reading of the relevant passages according to which Wittgenstein doesn't deny that there are mathematical facts, but rather denies that one needs a metaphysical account of what (...) mathematical facts are and how they relate to the world that goes beyond the minimal claims of radical conventionalism—that empirical facts about how we would find natural to project our training into new cases and the constitution of concepts by our agreement are enough. At the end of the paper, I discuss the implications of this reading on how to understand a rule's determination of its own application. (shrink)