 Łukasiewicz was aware of many of these odd consequences, but continued to uphold his system. Despite a number of attempts to make sense of the system, it has generally been concluded that because of these oddities it is not really a system of modal logic. If there is one dominant reason for this it is Łukasiewicz’s adherence to the principle of extensionality (truth-functionality) even for modal operators, which forced his account of modality to go multivalent in the first place.