  In the course of this paper Leśniewski argues against Twardowski’s theory of general objects and Meinong’s theory of impossible objects, as well as offering solutions to the paradoxes of Grelling and the Liar. The paper is the richest of his early “logico-grammatical” works. The argument against Twardowski goes as follows. Call a general object one which has all and only the properties shared by some group of objects. For example the general horse has all and only the properties shared by all horses: it is neither black nor brown nor white, neither male nor female, neither young nor old, but it is indisputably equine, mammalian, and born of two equine parents. Leśniewski now reduces the definition to absurdity. Of any group of at least two objects, there will be some property that some of them have that others do not have. For example, some horses are black and others are not black. So the general horse is not black, because some horses are not black; but nor is it not black, because some horses are not not black. Hence the general horse is neither black nor not black, which is a contradiction. Hence there are no general objects for groups of more than one thing. Leśniewski liked this argument well enough to retain his allegiance to it even while repudiating all other parts of his early work; he rejected universals consistently thereafter. But the argument does not affect those theories of universals which are happy to accept that universals may have properties their instances do not, for example being instantiated, or repeated.