Malcolm was born in Selden, Kansas. He studied philosophy with O. K. Bouwsma at the University of Nebraska, then enrolled as a graduate student at Harvard University in 1933.

After serving in the United States Navy from 1942 to 1945, Malcolm, with his wife, Leonida, and their son, Raymond Charles Malcolm, resided in Cambridge again in 1946–47. He saw a good deal of Wittgenstein during that time, and they continued to correspond frequently thereafter. In 1947, Malcolm joined the faculty at Cornell University, where he taught until his retirement. In 1949, Wittgenstein was a guest of the Malcolms in Ithaca, New York. In that year Malcolm introduced O. K. Bouwsma to Wittgenstein. Bouwsma remained close to Wittgenstein until Wittgenstein’s death in 1951.

At Cambridge University in 1938–9, he met G. E. Moore and Ludwig Wittgenstein. Malcolm attended Wittgenstein’s lectures on the philosophical foundations of mathematics throughout 1939 and remained one of Wittgenstein’s closest friends. Malcolm’s memoir of his time with Wittgenstein, published in 1958, is widely acclaimed as one of the most captivating and most accurate portraits of Wittgenstein’s remarkable personality.

In 1959, his book Dreaming was published, in which he elaborated on Wittgenstein’s question as to whether it really mattered if people who tell dreams “really had these images while they slept, or whether it merely seems so to them on waking”. This work was also a response to Descartes’ Meditations.[1]

Malcolm was also a defender of a modal version of the ontological argument. In 1960 he argued that the argument originally presented by Anselm of Canterbury in the second chapter of his Proslogion was just an inferior version of the argument propounded in chapter three. His argument is similar to those produced by Charles Hartshorne and Alvin Plantinga. Malcolm argued that a God cannot simply exist as a matter of contingency but rather must exist in necessity if at all. He argued that if God exists in contingency then his existence is subject to a series of conditions that would then be greater than God and this would be a contradiction (referring to Anselm’s definition of God as That than which Nothing Greater can be Conceived).