[5] In late modern philosophy, the concept of the "square circle" (German: viereckiger Kreis) had also been discussed before in Gottlob Frege's The Foundations of Arithmetic (1884).
Secondly, it avoids the conflict of existence/non-existence by claiming non-physical existence: by the MOTdc, it can only be said that the round square simply does not exemplify the property of occupying a region in space.
Making use of the notion of "non-physically existent" objects is controversial in philosophy, and created the buzz for many articles and books on the subject during the first half of the 20th century.
Meinong himself, however, found this solution to be inadequate in several ways and its inclusion only served to muddle the definition of an object.
[2] Similar to the ideas explained with possible worlds theory, this strategy employs the view that logical principles and the law of contradiction have limits, but without assuming that everything is true.
Enumerated and championed by Graham Priest, who was heavily influenced by Routley, this strategy forms the notion of "noneism".
Meinong, an Austrian philosopher active at the turn of the 20th century, believed that since non-existent things could apparently be referred to, they must have some sort of being, which he termed sosein ("being so").
Thus non-existent things like unicorns, square circles, and golden mountains can have different properties, and must have a 'being such-and-such' even though they lack 'being' proper.
[14] The name is credited to William C. Kneale, whose Probability and Induction (1949) includes the passage "after wandering in Meinong's jungle of subsistence ... philosophers are now agreed that propositions cannot be regarded as ultimate entities".
Russell's theory of descriptions, in the words of P. M. S. Hacker, enables him to "thin out the luxuriant Meinongian jungle of entities (such as the round square), which, it had appeared, must in some sense subsist in order to be talked about".
[16] As Colin McGinn puts it, "[g]oing naively by the linguistic appearances leads not only to logical impasse but also to metaphysical extravagance—as with Meinong's jungle, infested with shadowy Being.
The only trouble with that notorious thicket, Meinong's jungle, is that it has not been zoned, plotted and divided into manageable lots, better known as possible worlds.However, modal realists retain the problem of explaining reference to impossible objects such as square circles.