There are formal poetry standards but the first haiku was a creative solution to express someone's thoughts or feelings that got formalized so that others could write a similar poem.In real life, we may encounter situations that are not easy to deal with, and there’s no definite answer to them. The formal system is itself a creative solution for "how can I assure others can recreate my creation themselves?". Hundreds of examples exist on the different and often very creative or impractical solutions for "how do I get from here to there?". Inventions, including the Turning Machine, were also initially creative until they become integral aspects of a formal system. Including both verbal and written, we now have hundreds, if not thousands, of formal communication systems because groups creatively solved the problem of "how do I communicate with another?". The best example I can give is communication. Moreover, as neither the claim nor its converse are falsifiable, there is no obvious default position on this either.Įvery formal system was once the creative construction of an individual or a group of individuals to solve a problem that an existing formal system had not already solved. Any proof you could give me that you really can keep writing poetry (issues of mortality aside), I could turn into a TM that keeps writing poetry.Īs poetry is just a stand-in for an arbitrary candidate, the arguments above should show that there is no easy way to get people to agree that a certain problem matches your criteria. Maybe any human has only the capacity for a certain number of poems. On the other hand, it is no longer obvious that a human can do that.
#LOGIC WORLD PROBLEMS CODE#
Depending on what substantially different means, it might still be easy enough to code a TM for that. Will creativity show in the long run? So we could ask for a steady stream of "substantially different" poems.
So far we have discussed only a single poem. Short of a Chinese Room argument, it becomes difficult to reject this. If the objection is that someone else has written the poem before, and the TM merely replicates it: With access to a thesaurus, some basic verse rules and a few complex calculations I could create a TM that writes something that looks like a poem, without me or anyone else having had an explicit mental representation of the poem before reading the output. In particular, I could obfuscate the code so much that finding out that the TM writes that poem essentially requires running it. However, looking at Kolmogorov complexity and the results in that area, it becomes clear that "hard-coded into the machine" is not really a well-behaved notion. One might say no, because the poem is hard-coded into the machine. Now, I can of course take my favourite poem, and code it into a Turing machine that prints it. There clearly are problems not solvable by a Turing machine, so we can ask whether there are any problems not solvable by a Turing machine, but by a human.Ī typical candidate could be something like "writing poetry".
The question already mentions Turing machines, so let's go for that.
So, we need to fix the formal system we want to talk about. If you disagree that this defines a formal system, I am going to return the challenge and claim that your problem was not well-defined in the first place. If you state the problem you want to use, I can simply put solving that problem as a basic entity in a formal system, and thus find a formal system to solve it. There is no agreed upon example of this kind.įirst, we cannot even come up with a decent example of a problem not solvable by any formal system.
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