Related papers: Intuitionism and the liar paradox
The handling of probabilities in the form of uncertainty or partial information is an essential task for LLMs in many settings and applications. A common approach to evaluate an LLM's probabilistic reasoning capabilities is to assess its…
Every philosophy has holes, and it is the responsibility of proponents of a philosophy to point out these problems. Here are a few holes in Bayesian data analysis: (1) the usual rules of conditional probability fail in the quantum realm,…
An indeterministic interpretation of classical physics has been proposed recently, in which the argument relies on attacking an alleged unwarranted metaphysical hidden assumption of the standard deterministic interpretation. This short…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our…
We investigate properties of monadic purely negational fragment of Intuitionistic Control Logic (ICL). This logic arises from Intuitionistic Propositional Logic (IPL) by extending language of IPL by additional new constant for falsum.…
We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a…
Classical interpretations of Goedel's formal reasoning imply that the truth of some arithmetical propositions of any formal mathematical language, under any interpretation, is essentially unverifiable. However, a language of general,…
We investigate the reasons of having confidence in mathematical theorems. The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to this confidence. Opposing…
Edgar Allan Poe noted, "Truth often lurks in the shadow of error," highlighting the deep complexity intrinsic to the interplay between truth and falsehood, notably under conditions of cognitive and informational asymmetry. This dynamic is…
Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…
This paper provides a critical overview of Georg Kreisel's method of informal rigour, most famously presented in his 1967 paper `Informal rigour and completeness proofs'. After first considering Kreisel's own characterization in historical…
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…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
If a quantum system is prepared and later post-selected in certain states, "paradoxical" predictions for intermediate measurements can be obtained. This is the case both when the intermediate measurement is strong, i.e. a projective…
The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they…
We posit that large language models (LLMs) should be capable of expressing their intrinsic uncertainty in natural language. For example, if the LLM is equally likely to output two contradicting answers to the same question, then its…
In this paper, we show how game-theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias. Interpretive bias is an essential feature of learning and understanding but…
Analogy has received attention as a form of inductive reasoning in the empirical sciences. However, its role in pure mathematics has received less consideration. This paper provides an account of how an analogy with a more familiar…
In this paper, we consider the complexity of propositional proofs of classical and intuitionistic tautologies. In fact, we describe a nondeterministic polynomial-time decision procedure for intuitionistic implicational tautologies. For this…