An assumption was an accepted truth or fact without proof.
In 2268, Spock suggested that a release of bacteria or a helpless mental depression and a state of suicidal anxiety could have been chemically induced into the Starnes Exploration Party which resulted in their mass suicide on the planet Triacus. Not knowing what would have made the party's orphaned children immune, Captain James T. Kirk suggested that the children had been exempted by conscious design, which was a valid assumption according to Spock. (TOS: "And the Children Shall Lead")
In 2375, Seven of Nine stated that she had assumed that romantic love was a Human weakness, but saw that it could also be a source of strength. (VOY: "The Disease")