Alvin Plantinga’s 1960 paper “A Valid Ontological Argument?” found in Philosophical Review , is where we find his critique of Norman Malcolm’s highly noted version  of Anselm’s ontological argument. This argument, Malcolm believes, contains
two different pieces of reasoning which [Anselm] did not distinguish from one another, and that a good deal of light may be shed on the philosophical problem of ‘the ontological argument’ if we do distinguish them. (p. 41)
Plantinga in other works  has offered critiques of Anselm’s ontological argument and various other versions of it, and has even dedicated special attention to Norman Malcolm’s modal version of the argument. Plantinga (so far as his interpretation of Malcolm goes) outlines Malcolm’s argument as follows :
- (1) If God does not exist, His existence is logically impossible.
- (2) If God does exist, His existence is logically necessary.
- (3) Hence either God’s existence is logically impossible or it is logically necessary.
- (4) If God’s existence is logically impossible, the concept of God is contradictory.
- (5) The concept of God is not contradictory.
- (6) Therefore God’s existence is logically necessary.
Plantinga gathers this scheme from Malcolm’s “summary” of Anselm’s proof:
Let me summarize the proof. If God, a being a greater than which cannot be conceived, does not exist then He cannot come into existence. For if He did He would either have been caused to come into existence or have happened to come into existence, and in either case He would be a limited being, which by our conception of Him He is not. Since He cannot come into existence, if He does not exist His existence is impossible. If He does exist He cannot have come into existence (for the reasons given), nor can He cease to exist, for nothing could cause Him to cease to exist nor could it just happen that he ceased to exist. So if God exists His existence is necessary. Thus God’s existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists. 
Of course, in referring back to our argument, our main focus should be on premise (3) and how it might follow from (1) and (2). Particularly, what exactly does Malcolm mean by logically necessary? We may revert to the understanding that logically necessary merely means that the proposition “God exists” is logically necessary. However, logical necessity according to Malcolm simply means that “the notion of contingent existence or of contingent nonexistence cannot have any application to God” .
However, some understanding should be given to what Malcolm means here by God having necessary existence. God as understood to be omnipotent or omniscient is not understood as such by some application of criteria that might determine those attributes. Rather, it is the conception of God that carries with it internally these sorts of properties once the being as understood by Anselm is described (“greatest conceivable being” or GCB). Thus, it is not the case that God merely has the property of omniscience, but rather necessary omniscience. Like omnipotence and omniscience too, it is just as well the case that God has necessary existence too; essential to the properties of the GCB do we find omniscience, omnipotence, completeness, existence, and other properties.
Furthermore, according to Malcolm, “[t]he a priori proposition ‘God necessarily exists’ entails the proposition ‘God exists,’ if and only if the latter also is understood as an a priori proposition: in which case the two propositions are equivalent” . Thus, we can see here that it might be fair to say that logical necessity and a priori truth [according to Malcolm] are to some degree synonyms. Plantinga thence comments that in light of the following (above), “[i]f Malcolm’s reconstruction of Anselm’s argument is correct, therefore, the proposition ‘God does not exist’ is self-contradictory” .
Plantinga’s Critique of the Argument
Through this stage of the argument, Plantinga so far concedes to Malcolm’s point that if God’s existence were somehow contingent, then surely He would be a limited being (and thus, not be God). However, Plantinga suggests that from our conception of God, it seems to be the case that 
- (a) N (God never has and never will come into existence).
According to the above summary, it seems that Malcolm is deducing (1) from (a) – and that deduction is false (i.e., the latter doesn’t entail the former). For, “[t]aking (a) and the antecedent of (1) as premises and the consequent of (1) as the conclusion,”  you receive the following equivalent argument:
- (a) N (God never has and never will come into existence)
- (1a) God does not exist – antecedent of (1).
- (1c) N (God does not exist) – consequent of (1).
However, (1c) doesn’t follow from (1a) and (a), but rather a stronger proposition that would entail
- (1c’) God will never exist.
In other words, the proposition “it is logically necessary that God never comes into existence” entails the other given premise
- (1′) N (If there is a time at which God does not exist, then there is no subsequent time at which he does exist.
Plantinga further summarizes his position that “an adequate definition of the word ‘God’ must include or entail that He is dependent upon nothing whatever” . However, “the assertion that a being so defined exists, that the definition actually applies to something, may well be, for all that Malcolm and Anselm have said, a contingent assertion” . Plantinga’s criticism then is showing Malcolm’s argument to be inadequate in establishing such propositions as “God exists” and “There is a being who neither comes into nor goes out of existence and who depends upon nothing” to be necessary propositions.
-  Alvin Plantinga, “A Valid Ontological Argument?” in The Philosophical Review 70: 93-101
-  Norman Malcolm, “Anselm’s Ontological Arguments” in The Philosophical Review, LXIX (1960), pp. 41-62
-  See Alvin Plantinga, God and Other Minds, 2nd edn. (Cornell University Press: 1992)
-  Of course, as I always find, it is better to outline and scheme the argument in the beginning so as to create clearer thinking and form a frame of reference.
-  Quoted from Plantinga (1960), pp. 93-94
-  Malcolm (1960), p. 49
-  Ibid., p. 50
-  Plantinga (1960), p. 95
-  The letter “N” (the same in Plantinga’s scheme) simply means that the proposition associated with it is logically necessary.
-  Ibid., p. 95
-  Ibid., p. 101
-  Ibid.