"When a people who have been brainwashed since birth, forcefully colonized, and illegitimately ruled by a colonial power, throw off the shackles of that colonial power, it is properly called a revolution." - Michael Bunker "Surviving Off Off-Grid: Decolonizing the Industrial Mind"
Traditionaly you would set your joists on top of a tie beam. Your tie beam acts as a ledger for your joists to rest on. This is the top part of your post and beam. It looks like you have something like that with the 2x material you have attached to your posts, unless that is just temporary bracing. If not I would at least double the thickness of your tie beam before you attempt setting your joists on top. Dont forget to use cross braces between your joists to prevent racking.
Dido what Aron said. Is this a temporary structure? I see the post are directly into the ground, even if cedar, you have only limited life span, unless over hangs are at least 3 meters out. Charring and back-filling with stone/gravel can greatly extend lifespan. Did you consider timber framing?
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