The Master Argument refers to George Berkeley's argument that mind-independent objects do not exist because it is impossible to conceive of them. The argument is against intuition and has been widely challenged. The term “Berkeley's master argument” was introduced by Andre Gallois in 1974. His term has firmly become currency of contemporary Berkeley scholarship.
In order to determine whether it is possible for a tree to exist outside of the mind, we need to be able to think of an unconceived tree. But as soon as we try to think about this tree, we have conceived it. So we have failed and there is no good reason to believe that trees exist outside of the mind.
The Master Argument has been seen by several prominent philosophers as having a crucial mistake; see criticisms of idealism. However, it is difficult to pinpoint the exact mistake Berkeley makes. Bertrand Russell among others believed the problem is Berkeley fails to differentiate between the act of perception and the content of it:
"If we say that the things known must be in the mind, we are either un-duly limiting the mind's power of knowing, or we are uttering a mere tautology. We are uttering a mere tautology if we mean by 'in the mind' the same as by 'before the mind', i.e. if we mean merely being apprehended by the mind. But if we mean this, we shall have to admit that what, in this sense, is in the mind, may nevertheless be not mental. Thus when we realize the nature of knowledge, Berkeley's argument is seen to be wrong in substance as well as in form, and his grounds for supposing that 'idea'-i.e. the objects apprehended-must be mental, are found to have no validity whatever. Hence his grounds in favour of the idealism may be dismissed." 
Some claim that Berkeley was not making a Master Argument at all and that what he was actually trying to show was that the substance 'matter' was actually an abstract concept that passed itself off in peoples' minds as an object of immediate experience. Rather than say that the matter cannot exist, the critics claim, Berkeley is saying that it can only exist as an abstract concept and that this abstract concept was conceptually useless.
“Master Argument” at International Berkeley Conferences
- Katia Saporiti (Zurich): "A Bet with High Stakes: Reflections on Berkeley's Master Argument" // 6–9 April 2010, International Berkeley Conference, University of Neuchâtel, Switzerland.
- Samuel Rickless, University of California, San Diego: “Berkeley’s Master Argument” // 26th-28th June 2008, International Berkeley Conference, Newport, Rhode Island.
- George Berkeley, A Treatise Concerning the Principles of Human Knowledge, §22 to §23.
- Gallois, Andre. "Berkeley's Master Argument." Philosophical Review 83 (1974): 55-69.
- Bertrand Russell, The Problems of Philosophy, pages 42 to 43.
- Philip Pilkington, Berkeley's 'Master Argument' Doesn't Exist, Fixing the Economists.