Argument
Penrose–Lucas argument
Overview
The Penrose–Lucas argument is a logical argument partially based on Kurt Gödel's first incompleteness theorem. In 1931, Gödel proved that every effectively generated theory capable of proving basic arithmetic either fails to be consistent or fails to be complete. John Lucas and Roger Penrose postulate that this incompleteness does not apply to humans, and conclude that humans can have mathematical insights that Turing machines can't. Penrose and Stuart Hameroff proposed a quantum explanation, and used it to provide the basis of their theory of consciousness: orchestrated objective reduction. The argument is rejected by most scholars.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
Possible passages
Found by search and not yet checked by a person; they may only mention the idea in passing.
Twenty-five of the propositions which are employed in the proof for the existence of God, or in the arguments demonstrating that God is neither corporeal nor a force connected with a material being, or that He is One, have been fully established, and their correctness is beyond doubt. Aristotle and the Peripatetics who followed him have proved each of these propositions. There is, however, one proposition which we…
Moses Maimonides, The guide for the perplexed
States what Penrose–Lucas argument is.
Thus there are two sorts of truths,--those of reason, and those of fact. The truths of reason are necessary, and their opposites impossible; while those of fact are contingent, and their opposites possible. When a truth is necessary, its reason can be discovered by analysis, resolving it into ideas and truths that are simpler, until the primitive truths are arrived at. It is thus that the mathematicians proceed in…
John Dewey, Leibniz's New Essays Concerning the Human Understanding
Close in meaning to Penrose–Lucas argument; the term itself is not named.
The object of the ideal of reason—an object existing only in reason itself—is also termed the primal being (ens originarium); as having no existence superior to him, the supreme being (ens summum); and as being the condition of all other beings, which rank under it, the being of all beings (ens entium). But none of these terms indicate the objective relation of an actually existing object to other things, but merely…
Immanuel Kant, The Critique of Pure Reason
Close in meaning to Penrose–Lucas argument; the term itself is not named.
Philosophers who discussed Penrose–Lucas argument
Related ideas
- General relativity
- Alan Turing
- Merton College, Oxford
- Argument
- Paul Benacerraf
- Kurt Gödel
- Mind
- Classical mechanics
- Mathematical logic
- Marvin Minsky
- Person
- Platonism
- Quantum mechanics
- Roger Penrose
- Spacetime
- Turing machine
- Theorem
- Completeness (logic)
- George Boolos
- Solomon Feferman
- David Lewis (philosopher)
- Formal system
- Logical truth
- Paraconsistent logic