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.
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.
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 appropriate sense.
Usually, this is enough for me to understand the word when I meet it in new sentences, assuming it’s used in the same sense. In cases where I failed to learn it, I just add a second flashcard with a new sentence containing that word.
For “encyclopaedic” words like species of animals or plants, kinds of food, towns, etc. it’s in fact more useful to put a translation in your language rather than a definition in the target language, assuming it is a familiar concept in your own language. (And not try to learn several similar animals, plants, … at once, otherwise I mix them up.)
I usually take the sentence from a dictionary targeted at learners (sometimes I use the sentence where I found the word, if it’s the only unfamiliar word in it). For English, I use The Cambridge Learner’s Dictionary. For German, Langenscheidt Großwörterbuch Deutsch als Fremdsprache might be a good one (what’s important is that there are example sentences).