The superhyperbolic doubt is the principle that 'anything may be possible'. Anything may be possible because that which is otherwise believed to be impossible at present could be possible as the intellectual capacities of the believer may be limited. That is, the proposition/s, for example, that are otherwise thought to be absolutely certainly true could be false. The superhyperbolic doubt is compared and attempted to shown to be superior to the hyperbolic Cartesian doubt and the idea/proposition that 'anything is possible'. Furthermore, its implications are stated and discussed, the implications like 'all axioms as 99.99% certainly true' and 'all mathematics as philosophy'. Since the superhyperbolic doubt is the first and the most basic principle of my superultramodern science and philosophy, it could also be referred to as the superultramodern doubt. Note: The statement ‘anything is possible’ is self-contradictory, for if ‘anything is possible’ ‘it is possible that something is not possible’. But, the statement ‘anything may be possible’ is not self-contradictory, for if ‘anything may be possible’ ‘it may be possible that something may not be possible’ or ‘it may be possible that something is not possible’, which do not contradict the statement ‘anything may be possible’, since it is equivalent to the statement ‘may be anything is possible’, as opposed to ‘anything is possible’ which is equivalent to ‘anything must be possible’. The real, universal doubt, therefore, is ‘anything may be possible’, not ‘anything is possible’.