Eamon Duede

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for a particular derivation to ''correspond'' to a particular proof. Mere existence of a formalization is not enough, and a substantive account of the required correspondence resolves into two criteria---adequate representation (of the original theorem) and tracking (of the steps in the original proof). An examination of the actually-existing formalization systems we have today shows the variety of quasi-empirical ways we establish these criteria, and points towards new burdens that may be placed on the future evolution of mathematics itself.

Prevailing approaches to interpreting large language models (LLMs) risk addressing the field’s central questions at the wrong level of analysis. As LLMs develop, researchers have turned to “under-thehood” methods to investigate whether LLMs possess states analogous to beliefs, desires, or intentions. These methods typically map internal representations, feature directions, or neural circuits onto folk-psychological categories. We argue that these methods are too fragile to reap the results we need. Instead, interpretability ought to be reoriented toward and grounded in what we call “ecologically sensitive behavioral analyses” which integrates mechanistic tools with severe testing of behavioral signatures across ecological contexts, aligning interpretability efforts with emerging evaluation sciences for AI. We outline a multi-disciplinary trajectory for developing interpretability methods that are both philosophically coherent and practically relevant for the deployment of increasingly capable LLMs.

What does it take to properly recognize someone as having made a scientific discovery? According to the 'Cognitivist', discovery attribution properly depends on the exercise of distinctive cognitive capacities such as competence, meta-reflective awareness, or domain-general understanding. Since AI systems lack such capacities, they cannot, on this view, be discoverers. If the Cognitivist is right, AI-driven science will be a markedly impoverished enterprise. Here, we argue otherwise. We develop an alternative, non-cognitivist conception of scientific discovery according to which discovery turns on successfully negotiating epistemic gaps. This reconception, we argue, better captures both familiar human cases and novel AI contributions, thereby re-framing the grounds for attributions of discovery in contemporary science. AI systems, we argue, can be appropriately attributed scientific discoveries. Along the way we develop a general moral for philosophical reflection in the age of AI-infused science.

Can we acquire apriori knowledge of mathematical facts from the outputs of computer programs? People like Burge have argued (correctly in our opinion) that, for example, Appel and Haken acquired apriori knowledge of the Four Color Theorem from their computer program insofar as their program simply automated human forms of mathematical reasoning. However, unlike such programs, we argue that the opacity of modern LLMs and DNNs creates obstacles in obtaining apriori mathematical knowledge from them in similar ways. We claim though that if a proof-checker automating human forms of proof-checking is attached to such machines, then we can obtain apriori mathematical knowledge from them after all, even though the original machines are entirely opaque to us and the proofs they output may not, themselves, be human-surveyable.

Philosophers have recently focused on critical, epistemological challenges that arise from the opacity of deep neural networks. One might conclude from this literature that doing good science with opaque models is exceptionally challenging, if not impossible. Yet, this is hard to square with the recent boom in optimism for AI in science alongside a flood of recent scientific breakthroughs driven by AI methods. In this paper, I argue that the disconnect between philosophical pessimism and scientific optimism is driven by a failure to examine how AI is actually used in science. I show that, in order to understand the epistemic justification for AI-powered breakthroughs, philosophers must examine the role played by deep learning as part of a wider process of discovery. The philosophical distinction between the 'context of discovery' and the 'context of justification' is helpful in this regard. I demonstrate the importance of attending to this distinction with two cases drawn from the scientific literature, and show that epistemic opacity need not diminish AI's capacity to lead scientists to significant and justifiable breakthroughs.

Deep learning (DL) has become increasingly central to science, primarily due to its capacity to quickly, efficiently, and accurately predict and classify phenomena of scientific interest. This paper seeks to understand the principles that underwrite scientists’ epistemic entitlement to rely on DL in the first place and argues that these principles are philosophically novel. The question of this paper is not whether scientists can be justified in trusting in the reliability of DL. While today’s artificial intelligence exhibits characteristics common to both scientific instruments and scientific experts, this paper argues that the familiar epistemic categories that justify belief in the reliability of instruments and experts are distinct, and that belief in the reliability of DL cannot be reduced to either. Understanding what can justify belief in AI reliability represents an occasion and opportunity for exciting, new philosophy of science.