Related papers: Falsification or Confirmation: From Logic to Psych…
The role of probability appears unchallenged as the key measure of uncertainty, used among other things for practical induction in the empirical sciences. Yet, Popper was emphatic in his rejection of inductive probability and of the logical…
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 proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…
The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
Humans engage in informal debates on a daily basis. By expressing their opinions and ideas in an argumentative fashion, they are able to gain a deeper understanding of a given problem and in some cases, find the best possible course of…
Large language models (LLMs) are increasingly used in group decision-making, but their influence risks fostering conformity and reducing epistemic vigilance. Drawing on the Argumentative Theory of Reasoning, we argue that confirmation bias,…
We revisit Popper's falsifiability criterion. A tester hires a potential expert to produce a theory, offering payments contingent on the observed performance of the theory. In our model, instead of knowing the true data-generating process,…
The search for a scientific theory of consciousness should result in theories that are falsifiable. However, here we show that falsification is especially problematic for theories of consciousness. We formally describe the standard…
The classical conception of falsification presents scientific theories as entities that are decisively refuted when their predictions fail. This picture has long been challenged by both philosophical analysis and scientific practice, yet…
This is a short, light spirited account of how some possibly important science actually happened. It very much conflicts with Popper's contention that the key to scientific progress is falsification.
Hypotheses are central to information acquisition, decision-making, and discovery. However, many real-world hypotheses are abstract, high-level statements that are difficult to validate directly. This challenge is further intensified by the…
Misinformation remains one of the most significant issues in the digital age. While automated fact-checking has emerged as a viable solution, most current systems are limited to evaluating factual accuracy. However, the detrimental effect…
The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
As LLMs are deployed in high-stakes settings, users must judge the correctness of individual responses, often relying on model-generated justifications such as reasoning chains or explanations. Yet, no standard measure exists for whether…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
The study of opinions, their formation and change, is one of the defining topics addressed by social psychology, but in recent years other disciplines, as computer science and complexity, have addressed this challenge. Despite the…
Large Language Models are increasingly used in applications requiring objective assessment, which could be compromised by political bias. Many studies found preferences for left-leaning positions in LLMs, but downstream effects on tasks…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…