As a more substantial example, the Intergovernmental Panel on Climate Change (IPCC) issues periodic reports, widely regarded as the most authoritative analysis of scientific understanding of climate change caused by human activity. Future predictions involve uncertainty, and they want their many authors to be consistent in how they write about uncertainty, so provide technical documents such as Guidance Notes for Lead Authors of the IPCC Fourth Assessment Report on Addressing Uncertainties from which I have extracted the table below, there labelled "A simple typology of uncertainties".

Type | Indicative examples of sources | Typical approaches or considerations |
---|---|---|

Unpredictability | Projections of human behaviour not easily amenable to prediction (e.g. evolution of political systems). Chaotic components of complex systems. | Use of scenarios spanning a plausible range, clearly stating assumptions, limits considered, and subjective judgments. Ranges from ensembles of model runs. |

Structural uncertainty | Inadequate models, incomplete or competing conceptual frameworks, lack of agreement on model structure, ambiguous system boundaries or definitions, significant processes or relationships wrongly specified or not considered. | Specify assumptions and system definitions clearly, compare models with observations for a range of conditions, assess maturity of the underlying science and degree to which understanding is based on fundamental concepts tested in other areas. |

Value uncertainty | Missing, inaccurate or non-representative data, inappropriate spatial or temporal resolution, poorly known or changing model parameters. | Analysis of statistical properties of sets of values (observations, model ensemble results, etc); bootstrap and hierarchical statistical tests; comparison of models with observations. |

This table is addressing the issue of uncertainty and mathematical modeling. It makes the point that, within a complex setting (such as future climate change), any asserted numerical probability is (at best) an output from some complicated model in which all these different kinds of uncertainty are present. This point is obvious once you think about it; but it's just different from what's said in textbooks on the mathematics or philosophy of probability.