According to Australian biblical scholar Babara Thiering in her book, "The Book that Jesus Wrote John's Gospel," 'The Word' was a code name for Jesus. "The Word remained a code name for Jesus right up to the year AD 63 when Paul sent a coded message: 'The Word of God is not fettered', meaning Jesus was not in prison." 1 Tim 2:9
However, there would have been an additional meaning for these statements. "In the beginning" connects the statement to Genesis, "In the beginning God created the heavens and the Earth." In genesis 1:3, "And God said, 'Let there be light.'" Note that creation comes to being from God 'saying.' This saying is speech which is logos.
To Thiering, the above is an example of a pesher, coded meanings, in the gospels.
Finally, you mentioned that the terms logos can be used differently by philosphers and religionists. You are right on that!
To a philosoher, logos expresses the 'logical' character of speech that allows it to convey knowledge, truth. Logos is also the ability to take what people say and anylyze the statement to determine whether it is true or false. We get the word logic from logos.
To a religious thinker, the same meanings would apply but they would also add the word of god to the mix. Thus "logos" can also be found in revealed scriptures, eg., the Torah. This is pretty much the view of Philo of Alexandria.
I hope this helps.
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