Well one reason why logic could be be important to you is this sentence in Koine Greek:
Ἐν ἀρχῇ ἦν ὁ Λόγος, καὶ ὁ Λόγος ἦν πρὸς τὸν Θεόν, καὶ Θεὸς ἦν ὁ Λόγος.
In our alphabet we use today, it looks a bit like this:
"en arche en ho logos kai ho logos en pros ton theon kai theos en ho logos."
In the weird line above the word "logos" is used 3 times; "logos" is just Greek for "word". "Logika" might translate into something like "on all things word", or "study of word(s)"; today we use the Latinized version "logic(a)".
The reason why I feel a bold freethinker like yourself might be interested in taking a closer look at logika/logic, is best explained by an English translation of the Greek sentence above, which you can find
here.