This paper discusses the problem of linguistic reconstruction in the Indo-European languages with particular attention to syntax. While many scholars consider syntactic reconstruction as being in principle impossible, other scholars simply apply to syntax the same tenets of the Comparative Method and of Internal Reconstruction, which were originally used in Indo-European studies for reconstructing phonology and morphology. Accordingly, it is assumed that synchronically anomalous syntactic structures are more ancient than productive syntactic constructions; the former are considered as being residues of an early stage of Proto-Indo-European, where they were also more regular and took part in a consistent syntactic system. Various hypotheses of Proto-Indo-European as a syntactically consistent language, which in the last years have witnessed resurgence, are here discussed and criticized. We argue that syntactic consistency is nowhere attested in the Indo-European languages, which in their earliest records rather document an amazing structural variation. Accordingly, we reconstruct Proto-Indo-European as an inconsistent syntactic system in the domains of word order, agreement, configurationality, and alignment, and we consider inconsistency and structural variation to be an original condition of languages. Moreover, we make some proposals for the appropriate use of typology in linguistic reconstruction, with some examples of what can or cannot be reconstructed in syntax.