To me it seems like "thinking something is true" is much more of a fuzzy
category that "asserting something is true" (even assertions can be
ambiguous when stated in natural language, but they can be made non-fuzzy
by requiring that each assertion be framed in terms of some formal language
and entered into a computer, as in my thought-experiment). Is there any
exact point where you cross between categories like "being completely
unsure whether it's true" and "having a strong hunch it's true" and "having
an argument in mind that it's true but not feeling completely sure there
isn't a flaw in the reasoning" and "being as confident as you can possibly
be that it's true"? I never really feel *absolute* certainty that anything
I think is true, even basic arithmetical statements like 1+1=2, because I'm
aware of how I've sometimes made sloppy mistakes in thinking in the past,
and because I know intelligent people can seem to come to incorrect
conclusions about basic ideas when hypnotized, or when dreaming (like the
logic of various characters in Alice in Wonderland). I think of certain
truth as being like an asymptote that an individual or community of
thinkers can continually get closer to but never quite reach.
If I consider the statement "Jesse Mazer will never think this statement is
true", I may imagine the perspective of someone else and see that from
their perspective it must be true if Jesse's thinking is trustworthy, but
then I'll catch myself and see that this imaginary perspective is really
just a thought in Jesse's head--at that point, have I had the thought that
it's true? And at some point in considering it I can't really help thinking
some words along the lines of "oh, so then it *is* true" (it's hard to
avoid thinking something you know you are "forbidden" to think, like when
someone tells you "don't think of an elephant"), but is merely thinking the
magic words enough to count as having thought it's true, and therefore
having made it false once and for all?
On Thu, Dec 19, 2013 at 3:46 PM, meekerdb <meeke...@verizon.net> wrote:
> A nice exposition, Jesse. But it bothers me that it seems to rely on the
> idea of "output" and a kind of isolation like invoking a meta-level. What
> if instead of "Craig Weinberg will never in his lifetime assert that this
> statement is true" we considered "Craig Weinberg will never in his lifetime
> think that this statement is true"? Then it seems that one invokes a kind
> of paraconsistent logic in which one just refuses to draw any inferences
> from this sentence that one cannot think either true or false.
> On 12/19/2013 8:08 AM, Jesse Mazer wrote:
>> The argument only works if you assume from the beginning that an A.I. is
>> unconscious or doesn't have the same sort of "mind" as a human (and given
>> your views you probably do presuppose these things--but if the conclusion
>> *requires* such presuppositions, then it's an exercise in circular
>> reasoning). If you are instead willing to consider that an A.I. mind works
>> basically like a human mind (including things like being able to make
>> mistakes, and being able to understand things it doesn't "say out loud"),
>> and are willing to "put yourself in the place" of an A.I. being faced with
>> its own Godel statement, then you can see it's like a more formal
>> equivalent of me asking you to evaluate the statement "Craig Weinberg will
>> never in his lifetime assert that this statement is true". You can
>> understand that if you *did* assert that it's true, that would of course
>> make it false, but you can likewise understand that as long as you try to
>> refrain from uttering any false statements including that one, it *will*
>> end up being true.
>> Similarly, an A.I. who is capable of making erroneous statements, and of
>> understanding things distinct from its "output" to the world outside the
>> program, might well understand that its own Godel statement is
>> true--provided it never outputs a formal judgment that the statement is
>> true, which would mean it's false! So if the A.I. in fact avoided ever
>> giving as output a judgment about that the statement is true, it need not
>> be because it lacks an understanding of what's going on, but rather just
>> because it's caught in a bind similar to the one you're caught in with
>> "Craig Weinberg will never in his lifetime assert that this statement is
>> To flesh this out a bit, imagine a community of human-like A.I.
>> mathematicians (mind uploads, say), living in a self-contained simulated
>> world with no input from the outside, who have the ability to reflect on
>> various arithmetical propositions. Once there is a consensus in this
>> community that a proposition has been proven true or false, they can go to
>> a special terminal (call it the "output terminal") and enter it on the list
>> of proven statements, which will constitute the simulation's "output" to
>> those of us watching it run in the real world. Suppose also that the
>> simulated world is constantly growing, and that they have an internal
>> simulated supercomputer within their world to help with their mathematical
>> investigations, and this supercomputer is constantly growing in memory too.
>> So if we imagine a string encoding the *initial* state of the simulation
>> along with the rules determining its evolution, although this string may be
>> very large, after some time has passed the memory of the simulated
>> supercomputer will be much larger than that, so it's feasible to have this
>> string appear within the supercomputer's memory (and it's part of the rules
>> of the simulation that the string automatically appears in the
>> supercomputer's memory after some finite time T within the simulation, and
>> all the A.I. mathematicians knew that this was scheduled to happen).
>> Once the A.I. mathematicians have the program's initial conditions and
>> the rules governing subsequent evolution, they can construct their own
>> Godel statement. Of course they can never really be sure that the string
>> they are given correctly describes the true initial conditions of their own
>> simulated universe, but let's say they have a high degree of trust that it
>> is--for example, they might be mind uploads of the humans who designed the
>> original simulation, and they remember having designed it to ensure that
>> the string that would appear in the supercomputer's memory is the correct
>> one. They could even use the growing supercomputer to run a
>> simulation-within-the-simulation of their own history, starting from
>> those initial conditions--the sub-simulation would always lag behind what
>> they were experiencing, but they could continually verify that the events
>> in the sub-simulation matched their historical records and memories up to
>> some point in the past.
>> So, they have a high degree of confidence that the Godel statement
>> they've constructed actually is the correct one for their own simulated
>> universe. They can therefore interpret the conceptual meaning of the
>> statement as something like "you guys living in the simulation will never
>> enter into your output terminal a judgment that this statement is true". So
>> they could understand perfectly well that if they ever *did* enter such a
>> judgment into their output terminal, that would mean the statement was a
>> false statement about arithmetic. But provided that they *don't* ever enter
>> any such judgment into their output terminal, they can see it's a true
>> statement about arithmetic (and can discuss this fact among themselves and
>> reach a consensus about this fact, as long as they don't enter it as output
>> to the terminal). If they are mathematical platonists, they realize that
>> this feeling of it being their choice whether to output the statement or
>> not, with the statement's truth or falsity depending on that choice, is a
>> sort of illusion--really the truth-value of the statement is a timeless
>> fact about arithmetic. But presumably, in such a situation they would adopt
>> a "compatibilist" view of free will as many real-world philosophers have
>> done (http://plato.stanford.edu/entries/compatibilism/), a view which
>> sees no conflict between the feeling of free will and the idea that our
>> actions are ultimately completely determined by natural laws and initial
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