Cosmology deals with a unique object which comprises everything and yet is self-contained and singular. To describe this object in the language of physics, certain conditions must be in place. The increased role of such conditions finds its manifestation in distinct argument patterns. One popular case in point has to do with the anthropic arguments, some of which can be looked upon as varieties of transcendental reasoning, broadly construed. After reviewing this aspect of anthropic arguments, I show that the scope of transcendental inference at work in twentieth-century cosmology has been more extensive. Indeed, one important thread of such inference – the claim that, in order to be mathematically tractable, the Universe as a whole has to be a certain way–can be traced back to the first relativistic cosmological model proposed by Einstein in 1917. A somewhat different strategy of the same broad sort played a major role in shaping the steady-state theory, the main rival of big-bang cosmology in 1948–1965. Finally, the famous "no-boundary" condition for quantum cosmology would (if it could bear the weight of far-reaching interpretations put on it) be another example of grounding the mere possibility of the physical description of the Universe in its global properties.