Many would argue that modernity brought with it an increase in self awareness among individuals. Others would say that such awareness has been lessened in our time (maybe we’ll debate it in the advanced conversation group I’m starting to teach tonight in Jerusalem).
In any case, the Hebrew word for awareness is a Modern one –
מוּדָעוּת - though it comes from a verb root introduced in the very first portion of the Torah: י.ד.ע(y.d.a), meaning knowledge.
בִּישְׂרָאֵל יֵשׁ מוּדָעוּת מֻגְבֶּרֶת לְחֲפָצִים חֲשׁוּדִים.
In Israel there is increased awareness of suspicious objects.
And self awareness is מוּדָעוּת עַצְמִית.
If you wish to say, this person is self-aware or aware of himself, you’d say:
הָאָדָם הַזֶּה מוּדָע לְעַצְמוֹ.
Note that מודעis followed by …לְmeaning to.
Here’s an example in the feminine:
הָאִשָּׁה הַזֹּאת מוּדַעַת לְעַצְמָהּ.
This woman is self-aware.
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