Thought ISSN 2161-2234
Proving that the Mind Is Not a Machine?
University of Bristol
is piece continues the tradition of arguments by John Lucas, Roger Penrose and others to the
eect that the human mind is not a machine. Kurt Gödel thought that the intensional paradoxes
stand in the way of proving that the mind is not a machine. According to Gödel, a successful proof
that the mind is not a machine would require a solution to the intensional paradoxes. We provide
what might seem to be a partial vindication of Gödel and show that if a particular solution to the
intensional paradoxes is adopted, one can indeed give an argument to the eect that the mind is
not a machine.
Keywords Gödel’s disjunction; Gödelian arguments against mechanism; intensional paradox;
theories of truth; mechanism; incompleteness theorems
It has seemed to a number of prominent philosophers and scientists that Gödel’s incom-
pleteness theorems “prove that Mechanism is false, that is, that minds cannot be explained
as machines” (Lucas 1961, p. 112). Unfortunately, so far little evidence has been produced
a machine have not been generally accepted. Rather, these so-called proofs have been
widely found to be unsound and falling short of establishing that mechanism is false. In
this piece, we propose a new such “proof”: if one adopts a particular formalization of
mechanism and a specic solution to the semantic and intensional paradoxes, one can
show that the mind is not a machine.
e basic idea of these Gödelian arguments against mechanism is that Gödel’s incom-
pleteness theorems imply that no formal system, that is no machine, can prove all mathe-
matically true sentences.
e incompleteness theorems tell us that for each formal system
there will always be true sentences, for example the Gödel sentence of the system, which
the formal system cannot prove. However, by following the reasoning of the proof of
Gödel’s rst incompleteness theorem the human mind, so the argument usually goes,
can establish for any given formal system that the Gödel sentence of the system is true.
If this reasoning were correct, we could conclude that the theorems the human mind can
prove cannot be produced by a machine. Yet, as has been pointed out by a number of
authors, the Gödel sentence of a formal system is true, only if the system is consistent. So,
to establish that the Gödel sentence of a system is true, the human mind needs to be able
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Thought 7 (2018) 81–90 © 2018 The Thought Trust and Wiley Periodicals, Inc. 81