DeepAI AI Chat
Log In Sign Up

Embracing undecidability: Cognitive needs and theory evaluation

by   André C. R. Martins, et al.

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Goëdel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things get even harder. We want to compare the results of our mathematical theories to observations, and that means the use of inductive methods. While we can demonstrate how an ideal probabilistic induction should work, the requirements of such a method include a few infinities. Furthermore, it would not be even enough to be able to compute those methods and obtain predictions. There are cases where underdeterminacy might be unavoidable, such as the interpretation of quantum mechanics or the current status of string theory. Despite that, scientists still behave as if they were able to know the truth. As it becomes clear that such behavior can cause severe cognitive mistakes, the need to accept our limits, both our natural human limits and the limits of the tools we have created, become apparent. This essay will discuss how we must accept that knowledge is almost only limited to formal systems. Moreover, even in those, there will always be undecidable propositions. We will also see how those questions influence the evaluation of current theories in physics.


page 1

page 2

page 3

page 4


On Building a Knowledge Base for Stability Theory

A lot of mathematical knowledge has been formalized and stored in reposi...

Further results and examples for formal mathematical systems with structural induction

In the former article "Formal mathematical systems including a structura...

Building the Signature of Set Theory Using the MathSem Program

Knowledge representation is a popular research field in IT. As mathemati...

Behaviour-based Knowledge Systems: An Epigenetic Path from Behaviour to Knowledge

In this paper we expose the theoretical background underlying our curren...

Biform Theories: Project Description

A biform theory is a combination of an axiomatic theory and an algorithm...

The Limits to Machine Consciousness

It is generally accepted that machines can replicate cognitive tasks per...

Epistemology of Modeling and Simulation: How can we gain Knowledge from Simulations?

Epistemology is the branch of philosophy that deals with gaining knowled...