In order to explore the quantifiability and formalizability of uncertainty a wide range of uncertainties are investigated. They are summarized under eight main categories: factual, possibilistic, metadoxastic, agential, interactive, value, structural, and linguistic uncertainty. This includes both classical uncertainty and the uncertainties commonly called great, deep, or radical. For five of the eight types of uncertainty, both quantitative and non-quantitative formalizations are meaningful and available. For one of them (interactive uncertainty), only non-quantitative formalizations seem to be meaningful, and for two (agential and structural uncertainty) neither quantitative nor non-quantitative formalization seems to be a useful approach.