Related papers: Intuition, iteration, induction
It is quite well-known from Kurt Godel's (1931) ground-breaking result on the Incompleteness Theorem that rudimentary relations (i.e., those definable by bounded formulae) are primitive recursive, and that primitive recursive functions are…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
I will argue, pace a great many of my contemporaries, that there's something right about Boltzmann's attempt to ground the second law of thermodynamics in a suitably amended deterministic time-reversal invariant classical dynamics, and that…
I am most honoured to have the privilege to present the Foreword to this fascinating and wonderfully varied collection of contributions, concerning the nature of computation and of its deep connection with the operation of those basic laws,…
William Tait and Peter Koellner have written on the topic of which reflection principles are intrinsically justified. Phillip Welch and Sam Roberts have recently sought to motivate much stronger reflection principles. This work also had…
Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…
The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…
A core tension in models of concept learning is that the model must carefully balance the tractability of inference against the expressivity of the hypothesis class. Humans, however, can efficiently learn a broad range of concepts. We…
The principle of `information causality' can be used to derive an upper bound---known as the `Tsirelson bound'---on the strength of quantum mechanical correlations, and has been conjectured to be a foundational principle of nature. To date,…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…
Machine learning with application to questions in the physical sciences has become a widely used tool, successfully applied to classification, regression and optimization tasks in many areas. Research focus mostly lies in improving the…
The problem of explaining the relationship between subjective experience and physical reality remains difficult and unresolved. In most explanations, consciousness is epiphenomenal, without causal power. The most notable exception is…
In inductive learning of a broad concept, an algorithm should be able to distinguish concept examples from exceptions and noisy data. An approach through recursively finding patterns in exceptions turns out to correspond to the problem of…
In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…
The statement of the Gauss-Bonnet theorem brings up an unexpected form of reflexivity (major concept of philosophy of mathematics), so that geometry contemplates itself in it. It is therefore the revolutionary and multifaceted concept of…
This paper grew out of the observation that the possibilities of proof by induction and definition by recursion are often confused. The paper reviews the distinctions. The von Neumann construction of the ordinal numbers includes a…
I review the works of G\"ardenfors (1990) and Scorzato (2013) and show that their combination provides an elegant solution of Goodman's new riddle of induction. The solution is based on two main ideas: (1) clarifying what is expected from a…
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
Humans have the capacity to draw common-sense inferences from natural language: various things that are likely but not certain to hold based on established discourse, and are rarely stated explicitly. We propose an evaluation of automated…
The science of consciousness has made great strides by focusing on the behavioral and neuronal correlates of experience. However, correlates are not enough if we are to understand even basic neurological fact; nor are they of much help in…