Logic is the foundation of science but not the foundation of life. Logic is applicable to dead things, to objects, because the basic method of logic is dissection. The moment you dissect something you kill it, so if you want to find life through logic you will never find it; the very method prohibits it.
You can cut a rose flower, you can dissect it, you can put all the ingredients separately into different bottles methodically labelled, but one thing will be missing: there will be no beauty to be found and no life to be found, no joy to be found, no dance of the rose flower in the wind, in the rain, in the sun; they will all be gone. There will be a few chemicals, but those chemicals are not the rose flower, those chemicals were simply the situation in which the rose has appeared. They don't constitute the rose, they only constituted the situation for the appearance of the rose. If you take them away, the rose disappears into its invisible world.