In questions under the discipline of philosophy, and more so under epistemology (the theory of knowledge) particularly, we often find ourselves having to wrestle with certain beliefs, claims, and scenarios that might affect how we truly know things or whether we know anything at all. For instance, French philosopher René Descartes (1596-1650) in his Meditations on First Philosophy (1641) once wrote:
But what about when I considered something very simple and easy in the areas of arithmetic or geometry, for example that 2 plus 3 make 5, and the like? Did I not intuit them at least clearly enough so as to affirm them as true? To be sure, I did decide later on that I must doubt these things, but that was only because it occurred to me that some God could perhaps have given me a nature such that I might be deceived even about matters that seemed most evident. 
How are we to know if we aren’t being deceived by some evil demon about our most basic beliefs? That 2 and 3 make 5, or that triangles have three sides? Although Descartes solved this dilemma along the lines of his cogito (“I think therefore I am”), he still maintained a level of methodological skepticism that functioned for purely intellectual purposes; it is what Gerald Erion calls “a matter of heuristics.”  However, a more contemporary discussion on this dilemma of beliefs can be found in Peter Unger’s Ignorance (1975), where instead of an evil demon deceiving us, it is an evil scientist . As Barry Smith explains,
In Unger’s scenario, [ … ] the common belief that there are chairs, books, and other similar objects in the world around is simply an elaborate deception stimulated in our brains by an evil scientist, a super-neurologist who uses a computer to generate electrical impulses that are then transmitted to electrodes fastened to the relevant parts of our central nervous systems. Using these impulses to stimulate our brains, the scientist deceives us into thinking that there are chairs and books, even though there are no such things in the world. 
It was Unger’s position that “if skepticism is right, then all is not well with common sense, however useful those beliefs have been as a basis on which science might grow.”  Hilary Putnam (1981)  moreover argues a stronger thesis that “an evil scientist deceives us not just about rocks, but about everything we think we perceive through the senses” . This scenario runs along the lines to say that we are not merely being deceived by a super-neurologist who uses a computer to generate certain electrical impulses, but rather that we are brains in a vat, surgically placed in brain-nourishing chemicals from which a highly powerful computer sends impulses to our brains and has us belief that our experiences are simply illusions .
Now you of course might agree with Daniel Dennett when he says that “[s]ometimes philosophers clutch an insupportable hypothesis to their bosoms and run headlong over the cliff edge. Then, like cartoon characters, they hang there in mid-air, until they notice what they have done and gravity takes over.”  Surely this seems to be the case. However, even given these hypotheses and their mere (absurd?) possibilities, what about the idea that we might trapped within a virtual world, and are actually apart of the Matrix, sitting in pink vats of goo being farmed and kept by spider-like robots? What is the possibility that we are in the Matrix now?
The Matrix Possibility
First, in respect to understanding what is meant by beliefs in epistemological philosophy, it is also important to understand the difference between “warranted” and “justified” beliefs. In his discussion on our faculties of knowledge, Mortimer Adler remarks that beliefs are sometimes understood “to signify that we have some measure of doubt about the opinion we claim to be true on the basis of evidence and reasons” . Furthermore that beliefs can also be otherwise understood “to signify total lack of evidence or reasons for asserting an opinion” .
However, beliefs are only properly designated under the correct epistemological context. For instance, we do not say that we believe 2 and 2 make 4, but rather that we know 2 and 2 makes 4. According to one line of philosophical thinking we do contain a framework of given beliefs that could be rejected if they are without proper justification, while some others do not require that same justification .
For now then, let us stick with David Nixon’s proposal known as The Matrix Possibility: “It’s possible that I am (or you are) in the Matrix right now” . However, this proposal is merely saying that it is possible that I am in the Matrix right now, not necessarily that I am in it currently. This is where I believe the distinction (but relationship) between belief and knowledge becomes interesting. One reaction to this proposal might be that
- (A) If a given belief has the possibility of being false, then it is not one that we can say we really know.
It seems to be the case that the mere possibility of an evil demon deceiving him of even the most simplest truths was enough for Descartes to cast doubt on his having knowledge. However, what about another given reaction to the proposal? Namely, that
- (B) If a belief is possible and yet we recognize its capability of being false, we may still recognize these kinds of circumstances as having knowledge.
This reaction is far more interesting than the former reaction (A), where (B) is concerned more so with the probability of beliefs rather than the mere possible false-hoods of them.
What Should We Be Left to Think?
If Descartes’ demon or Unger’s mad scientist were in fact true, then we have good reasons to be skeptics in respect to most if not all the beliefs that we hold. However, from the current existential standpoint, we should not be skeptics on the basis of the possibilities of these scenarios. It is not until we are concerned with the probability of those scenarios that we should entertain the truth-hood of their proposals.
Until sufficient probability has been established, the belief that we are in the Matrix is epistemically unreasonable.
-  Rene Descartes, Philosophical Essays and Correspondence, ed. Roger Ariew (Hackett: 2000) p. 113
-  Gerald J. Erion and Barry Smith, “Skepticism, Morality, and the Matrix” in The Matrix and Philosophy, ed. William Irwin (Open Court Publishing: 2002) p. 18
-  Peter Unger, Ignorance: A Case for Skepticism (Clarendon Press: 1979)
-  Ibid., p. 4
-  Hilary Putnam, Reason, Truth, and History (Cambridge University Press: 1981)
-  Gerald Erion and Barry Smith (2002), p. 21
-  See Putnam (1981), pp. 5-8
-  Daniel Dennett, “The Unimagined Preposterousness of Zombies” in Journal of Consciousness Studies (vol. 2, no. 4, 1995). See the passage at this link: http://ase.tufts.edu/cogstud/papers/unzombie.htm
-  Mortimer J. Adler, Ten Philosophical Mistakes (Simon and Schuster: 1985) p. 87
-  Ibid.
-  Alvin Plantinga in his book God and Other Minds (1967) argues for instance that belief in the existence of God is properly basic. According to James Beilby on Plantinga’s view: “For Plantinga, beliefs formed by the sensus divinitatis and the internal instigation of the Holy Spirit are both psychologically direct – they are not inferred or accepted on the evidential basis of other beliefs – and epistemically direct – they do not receive their warrant from another belief” (James Beilby, “Plantinga’s Model of Warranted Christian Belief” in Alvin Plantinga, ed. Deane-Peter Baker (Cambridge University Press: 2007) p. 47).
-  David Mitsuo Nixon, “The Matrix Possibility” in The Matrix and Philosophy (2002), p. 28