I saw this on a industrial company billboard on my commute...
What are they trying to encourage here? The suppression of logical thought to promote hope? The assertion that one cannot be simultaneously logically hopeful?
I would argue that logic is the basis of hope.
Hope is the basis that a thing can happen - often contextually in the case of overwhelming odds. Odds are what one comes to when analyzing a situation's logical outcome. Through this, we can have hope in all things wherein the odds are not reduced to zero. Even if the odds are "negligible" - that does not correspond to impossible. Moreover, logic enables hope.
Anything in the realm of possibility can be hoped for - one only arrives at and determines that "realm of possibility" through analytical, logical thought.
To say there is no hope in logic is to silence the thought process. This train of thought can even weaken the odds of that hoped for thing as reducing our thoughts on the matter reduces the chances of a new more encouraging avenue of approach.
Take that, billboard.
Maybe I'm overthinking it and overly offended by those 6 blunt words and they do really just mean simply that; there is no hope in the logical process. That makes more sense - but it is too black and white to put it in the original way. Saying there's no hope in the logical process is correct, but that's because they are entirely separate human engines. They enable each other.
To put it another way by just reversing the sentence; "There is no logic in hope" is even more insulting. Clearly this cannot be the case as a hope in the illogical or zero'd-odds outcome is irresponsible.