German secondary school teacher Kurt Grelling was part of the Vienna Circle, a group of philosophers devoted to logical positivism, or the logical analysis of scientific knowledge. Logical positivists believed that knowledge can only come from logical reasoning and empirical experience, and that scientific theories are useful only if they can be proved true or false through observed experience.

In 1908, Grelling proposed Grelling's paradox. This semantic paradox was based on the idea of autological and heterological words. Autological words are self-descriptive, meaning that they possess the property they represent, such as the words one, visible, and multi-syllabic. Heterological words are non-self-descriptive, meaning that they do not contain the property they represent, such as the words edible, long, and incomplete. Grelling's paradox was whether or not heterological is in fact a heterological world. If heterological was autological, or self-descriptive, it would have to have a heterological meaning by definition, but if it had a heterological meaning, it would have to be non-self-descriptive. Thus, heterological can only be a heterological word if it is not the word heterological.

Grelling also worked with mathematician and logician Kurt Gödel, a key figure in the development of mathematical logic. In 1936, Grelling published an article defending Gödel's incompleteness theorem, which states that arithmetic can never be completely axiomatized.

This work on paradoxes and logical mathematical theory was significant in that it established that there are certain contridictions, or exceptions to rules, that challenge the nature of observed experience and scientific theory itself. In simplest terms, it established that consistency in mathematical theory was something that could never be taken for granted.

The exact date and circumstances of Grelling's death is unknown. Many believe he was taken to the Auschwitz concentration camp and killed, along with his wife, in 1942. One of Grelling's philosophy colleagues, Carl Hempel, tells a similar story, recounting that Grelling was attempting to cross the border from France to Spain in 1941 to escape the Nazi regime, when he was caught and sent to a Polish concentration camp.