All of Vej_Kse's Comments + Replies

If all you want is be able to read, I don’t think translation flash cards are the way to go (these are useful if you want to to be able to quickly find a corresponding word in your native language). When learning to read in foreign languages, I create flash cards where the “question” is a sentence in the target language (German in your case) with one unfamiliar word, which I put in bold. I succeed if I correctly understand the word in the context of this sentence. In the answer, I put the definition in the target language (German here) for the appropria... (read more)

Not necessarily: see mathnerd314's comment below (or above). In fact, in “there is no other”, there is a double negation (the second being in “other”, which hides “not equal to”), which can be eliminated.

Coincidentally, a paper based on Yudkowsky and Herreshoff's paper has appeared a few days ago on the arXiv. It's Paradoxes of rational agency and formal systems that verify their own soundness by Nik Weaver. Here's the abstract:

We consider extensions of Peano arithmetic which include an assertibility predicate. Any such system which is arithmetically sound effectively verifies its own soundness. This leads to the resolution of a range of paradoxes involving rational agents who are licensed to act under precisely defined conditions.

2CronoDAS
I read the paper. It seems interesting. Apparently one key to the "assertibility" predicate is that it works on intuitionistic logic: the axioms that describe it don't include the law of the excluded middle: "(X is assertible) OR (It is not the case that X is assertable)" isn't assumed to be true for all X. In their assertibility logic, you can indeed construct the statement "This sentence is not assertible", and you can even prove that it's false... but you also can't prove that you can't assert it - you can only prove that if you could assert it, you could also assert a contradiction. Someone who's actually working on the real math should go look at it.

It seems that simply bombarding the brain isn't sufficient, even for language, and that social interaction is required (see this study), so that playing math games with the child would be a better idea.

3NoSignalNoNoise
How does the brain decide whether it thinks of something as a social interaction? I would assume that computer/video games with significant social components hack into that, so hacking into it to teach math should be doable.