Michele Pasin / Quotes

Penrose's Gödelian argument against computable thought

To support his argument, Penrose appeals to a fundamental theorem in mathematical logic – Gödel’s Theorem – which states that certain mathematical truths cannot be proved by using a computational procedure. Because human mathematicians evidently can arrive at these truths, Penrose claims that humans must be performing non-computable operations.

Saved 15 June 2022 / www.amazon.com ↗

#mathematics #logic #computation #mind

Logic might be the greatest hallucination

believe this logical bias might be the source of the “computational stance.” We are biased toward explaining the world with logic and computations because…

Beyond Zero and One (Andrew Smart) #logic #hallucinations #computation #mind

Gödel and the limits of AI

Roger Penrose argues that because humans can grasp Gödel’s theory, the mind is not a formal logical system. He argues that the source of our intuitions and…

Beyond Zero and One (Andrew Smart) #artificial-intelligence #logic #mathematics #quantum-theory

Leibniz: propagating faith through science

But Leibniz’s real reasons for wanting a binary numbering system were much deeper than the philistine goal of counting money. Leibniz, like almost all…

Beyond Zero and One (Andrew Smart) #mathematics #religion #logic #God

Penrose the mathematical Platonist

For all intents and purposes, Penrose is a Platonist when it comes to mathematical truth. This might seem at odds with his view that Gödel’s theorem shows…

Beyond Zero and One (Andrew Smart) #mathematics #metaphysics #truth #mind

There is no computation inside a computer

In an email discussion I had with Riccardo Manzotti, he writes: We use logic and computation to build artifacts—from chairs to spaceships. We need logic and…

Beyond Zero and One (Andrew Smart) #computation #logic #metaphor #artifacts

Computationalism as a form of dualism

Hardly any cognitive scientists are dualists in the Cartesian sense. While the Cartesians believed that the mind represented the world, they also believed it…

Beyond Zero and One (Andrew Smart) #dualism #computation #cognitive-science #mind