Albert Einstein and Kurt Godel |

The
mathematician and educator,

__Morris Kline__, once made a rather grand claim about__Kurt Gödel__’s__Incompleteness Theorems__when he (in his__)__*Mathematics: The Loss of Certainty***said that it**
"was
a response to Leibniz’s 250-year-old dream of finding a system of
logic powerful enough to calculate questions of law, politics, and
ethics".

Perhaps
Leibniz’s dream had nothing to do with applying logic to the

*content*of law, politics and ethics; but only to the*form*of the arguments in which these things were expressed. For example, in ethics, logic can't show us “what is good”. However, it can detect good and bad arguments as to what constitutes “the Good”.
Similarly
logic can show faulty reasoning in political and legal debate;
regardless of the actual content of these debates.

So,
in that sense, it's indeed true that logic can be applied to law,
politics and ethics – indeed to

*anything*! So just as the premises of a__deductive argument__needn't be true in order for the argument to be__valid__; so the content of political, legal and ethical statements doesn't matter to the logician - though what follows from them, logically, does matter him.
Logic
can "provide the tools to resolve ethical questions by mere
calculation" if it dealt only with form and not with
metaphysical, epistemological and semantic content.

In
any case, were Gödel’s theorems
really a response to Leibniz’s dream? Perhaps it was just Gödel’s
way of showing us that, well, an axiomatic system (or mathematics
generally) can't be both fully consistent and complete – that’s
it (without philosophical knobs on).

Much
has been made of Gödel’s theorem by non-mathematicians and by many
non-philosophers. Morris Kline expresses much of this here. He writes
that
we

"might
think that Gödel’s proof implies that the rational mind is limited
in its ability to understand the universe".

How
a result in metamathematics
could do that (even in principle), I’m not sure. In any case, the
mind, again in principle, must surely be limited in some way or ways.
Perhaps that means that it could never understand everything there is
to know about an infinite universe. Indeed this is bound to be the
case. Only an omniscient mind could know everything there is to know
about the universe.

Kline
makes this point. He says
that

"though
the mind may have its limitations, Gödel’s result doesn’t prove
that these limitations exist".

What
is limited isn't the mind as such; but that "axiomatic
systems

**a**re limited in how well they can be used to model other types of phenomena". This has nothing to do with the mind of man taken generically! It's to do with axiomatic systems and the modelling of other types of phenomena.
Not
only that: the "mind
may possess
far greater capacities than an axiomatic system or a

__Turing machine__". I would say that of course the mind does actually possess far greater capacities than an axiomatic system or a Turing machine. Evidently! For a start, the mind can create great poems or pieces of music. It has memory, experience, imagination, the ability to dream, create, invent, manipulate the environment and so on. Some of these things Turing machines can do; though many of them they can’t do. And no single axiomatic system or Turning machine can do all the things a human mind can do – not even a deranged or damaged human mind!
Another
common supposed result of Gödel’s theorems is to assume that his
proof implies a limit to

__artificial intelligence__. Perhaps this is a more feasible idea because it must be about the mathematical limitations of artificial intelligence – and that would be relevant to Gödel’s proof. That is, would an indefinite advance in AI be halted by the result of Gödel’s proof which showed that if a mathematical system (therefore all combined) can't be both complete and fully consistent, then a project that relies on mathematics (that is, AI) will never be both complete and fully consistent? Thus there will be a limit to what AI can do.
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