V'tosh ka'tur was a Vulcan term which translates as "Vulcans without logic". In the 22nd century, the term was taken as a name by a diverging branch of the Vulcan people who were considered "outcasts" by their brethren.
This was because the group believed that emotions should not be repressed but actually work in balance with logic. To continue their line of beliefs without interference from the Elders, the group journeyed in a starship and left their homeworld of Vulcan.
In 2270, Spock was accused of being v'tosh ka'tur after he had performed a mind meld with V'Ger and had decided to try balancing logic with emotion. (TOS novel: Ex Machina) Following the death of James Tiberius Kirk in 2293, Spock attempted to seek the enlightenment of the kolinahr discipline once more. This led to him petitioning Vulcan master T'Vora for the rite and when he revealed that he had attempted to live with emotions; she inquired whether he was a v'tosh ka'tur. Spock, however, disputed this and stated that he had sought to control his emotions whilst the "Vulcans without logic" did not. (TOS novel: The Fire and the Rose)
This line of thought was similar to that proposed by followers of Tu-Jarok.