Debates on meaning and cognition suggest that an embodied cognition account is exclusive of a symbolic cognition account. Decades of research in the cognitive sciences have, however, shown that these accounts are not at all mutually exclusive. Acknowledging cognition is both symbolic and embodied generates more relevant questions that propel, rather than divide, the cognitive sciences: questions such as how computational symbolic findings map onto experimental embodied findings, and under what conditions cognition is relatively more symbolic or embodied in nature. The current paper revisits the Symbol Interdependency Hypothesis, which argues that language encodes perceptual information and that language users rely on these language statistics in cognitive processes. It argues that the claim that words are abstract, amodal, and arbitrary symbols and therefore must always be grounded to become meaningful is an oversimplification of the language system. Instead, language has evolved such that it maps onto the perceptual system, whereby language users rely on language statistics, which allow for bootstrapping meaning also when grounding is limited.