Etymology of 'but', from West Germanic to Old English

Question

but (adv., prep.) [<--] Old English butan, buton "unless, except; without, outside,"
from West Germanic * be-utan, a compound of * be- "by" (see by)
+ * utana "out, outside; from without,"  from ut "out" (see out (adv.)).
Not used as a conjunction in Old English. As a noun from late 14c.

How did the two bolded West Germanic etymons (* be- + ut), combine to mean unless?

My guess: If an object is out by you, then the object is outside (of) you. To wit, you are without the object.
But how does this evolve to mean unless?

Please expose, explain, and bridge all hidden, missing semantic drifts and links. What is a right way of interpreting the etymology, to understand how the semantic jumps abstracted and strayed from the original literal meaning?

I don't quote OED, whose etymology stops at Old English and so doesn't retrograde enough.

Answer 1

I don't know enough about West Germanic (or Dutch) to trace the etymology of composition of be ("by") and ut/utan. However, here are a few observations on that topic.

1. In OE, you have both utan ("outside") and innan ("inside"). Often found side by side (just as we do today): "inside and outside" => innan and utan (e.g. Genesis 1320).¹
2. Not only do you have butan as "outside => except/unless" but also binnan "within", formed on the same model (be+innan).
   So yes, the adjunction of be ("by", PDG bei) to indicate a positioning relative to self is confirmed. PDG still has innen and binnen.
   Dutch as well retains binnen and buiten.²
   If you think of it, it is also present in Present Day English: that's the with- in within and without.
   So far so good.
3. Now about the semantic shift from "outside" to "unless" which ultimately led to the displacement of ac/ak (the "but" as a conjunction in Old English).
   Here are a few examples I picked from the corpus of Old English Poetry gradually evolving from from "outside" to "unless". All 'translations' are mine and are deliberately literal in order to facilitate the word to word correspondence.
   
   
   1. Let's start with a real meaning of "outside". This is from the Genesis (as you can recognise). v 1355.

      Feowertig daga fæhe ic wille
      on weras stælan and mid wægþreate
      æhta and agend eall acwellan
      þa beutan beo earce bordum
      þonne sweart racu stigan onginne.
      

      For forty days [my] vengence I will
      on mankind set, and with a deluge
      all possessions and possessors destroy
      that outside are [of the] Ark's boards
      when the black storm begins
      

      In this excerpt, we even have a more archaic form beutan. Clearly, the intended meaning here is "outside".
      
      
   2. Here is an example taken from The Meters of Boethius: (20).

      Hwæt, þu, fæder engla, eall þing birest e[ð]elice buton geswince.

      What, Thou, Father of Angels, all things bearest easily, never tired.

      Here we don't have "outside" but more like "immune to" => "except" (fatigue).
      
      
   3. Finally, here is a sample meaning of "except/unless". Pater Noster (ii)

      Ac hwar cym heo nu, buton þu, engla god,

      But where comes she [the soul] now, except/unless from Thee, God of Angels.

      As a bonus, we can see here in the same sentence, that "but" is 'ac'/'ak'.

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1. As well as ufan and utan "above and outside" for the rhyme.

2. In Dutch, innen has survived as a verb: "to cash in"