The basic premise of ID is that something with complex components that function with a discernible purpose in the overall function of that something, has been designed by something else with intelligence. So a watch, with many moving parts all of which work other to the overall functioning of the watch, does not exist because of a random series of events but is the result of a purposeful design by an intelligent designer. In the same way the human body and millions of other complex living things and components of living things that function with discernible purpose, are evidence of being created by an Intelligent Designer.
Consider reading up on any of the many rebuttals to the watchmaker analogy and keep in mind please the conditions required in order for something to be considered scientifically accurate.
Logical conundrums, even well formulated ones (hint, the watchmaker analogy is not one of them), are proof of nothing other than our ability to conceive of abstract concepts, a function of what we perceive as consciousness.