Emma Bird Philosophical Logic NOTES ON PROBABILITY Contents Philosophy of Probability .. 1 Kolmogorov Axioms. 2 Salmon's Criteria 3 # 1 Subjectivism 3 # 2 Objectivism 8 2 A Finite Frequentism 8 2 B Hypothetical Frequentism. 8 2 C Propensities. # 3 Epistemic. 8 3 A Classical 8 8 3 B Logical 8 3 C Evidential 9 Reasoning Fallacies 9 Philosophy of Probability · Probabilistic claims are a common feature of everyday language, as well as being pervasive throughout philosophy and the sciences. o Probability is fundamental to many aspects of the sciences, including statistics, explanation, causation and hypothesis confirmation o In a very basic form, it can be understood as a scale, from fi-1, with which we can measure things and make claims about things . Because of this, it is vital that we have a clear account of what is meant by such probabilistic claims o Eg what does it mean to say 'the probability of event E occurring is X'? o there is much disagreement on the nature of probability and how probabilistic statements, such as "the probability of this coin landing heads is fi.5" should be interpreted. . There are multiple subtly different issues which must be separated out o Be very clear on this o Think of different ways the question could be interpreted o Mention other ways and then narrow - but clarify Subjective vs objective · = need not necessarily exclude each other - probabilities can be two things o Subjective: . Probabilities express our relative ignorance about the world o Objective: . Probabilities are a feature of the world, mind-independent Page 1 of 16
Emma Bird Philosophical Logic o Can alter one without affecting the other Matching the world vs Matching KA . Can do one without the other o Which is more important? o Matching the world seems more useful etc and will help us make better decisions o But matching KA is needed to avoid being open to Dutch books " This only makes sense when interpreting probabilities as subjective " If they are objective features of the world, then they match the world by default o Arguably matching the world is more useful; " Presents a problem with the betting analysis - Dutch books aren't a feature of life so why does it matter that we cant avoid them? Descriptive vs Normative · Do our beliefs match KA/the world? o No - betting analysis, base rate fallacy o Yes - controversial studies " At the very least, not the role of philosophy to decide " In general, we seem okay at guessing mid range probabilities but much as they approach fi or 1 · Should our beliefs match KA/the world? o If so, which one is more important! Determinism · When we assign non-zero/one probabilities to future events, does this reflect: o Human ignorance - so La Place's omniscient demon would answer 1 or fi o Genuine metaphysical indeterminacy in the world " A good way of highlighting the