Inferences can be deductive, inductive or abductive. Deductive inference is distinguished from the other two kinds of inference by logical validity (there is no possible situation in which the premises of a deductive inference are true and the conclusion false). Inductive inferences ‘may be characterized as those inferences that are based purely on statistical data’ (Douven, 2017). Abductive inferences are inferences to the best explanation.

Thanks to George Morina (London) for jumping the traffic light.

Reading (optional):

• Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.
• Douven, Igor. ‘Abduction’. In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta, Summer 2017. Metaphysics Research Lab, Stanford University, 2017. https://plato.stanford.edu/archives/sum2017/entries/abduction/.
• Hume, D. (1739). A Treatise of Human Nature. Oxford University Press, Oxford.

What is a purely formal theory of a kind of reasoning (deductive, abductive or inductive)? It is a theory according to which the form of an argument is what determines whether it is valid.

Reading (optional): Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.

Hempel showed that two tempting principles lead to an apparently false theory of inductive reasoning. Here we cover the principles and why at least one of them should be rejected using informal examples. (Those who prefer a formal approach may use the next section instead.) Although often overlooked, the problem Hempel identified is in some ways deeper and more revealing than the more famous ‘New Riddle of Induction‘ about grue.

Reading (optional):

• Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.
• Hempel, Carl G. ‘Studies in the Logic of Confirmation (I.)’. Mind 54, no. 213 (1945): 1–26.
• Hempel, Carl G. ‘The White Shoe: No Red Herring’. The British Journal for the Philosophy of Science 18, no. 3 (1967): 239–40. https://doi.org/10.1093/bjps/18.3.239.

Hempel showed that two tempting principles lead to an apparently false theory of inductive reasoning. Here we cover the principles and why at least one of them should be rejected using formal examples. (Those who prefer a less formal approach may use the previous section instead.) Although often overlooked, the problem Hempel identified is in some ways deeper and more revealing than the more famous ‘New Riddle of Induction‘ about grue.

Reading (optional):

• Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.
• Hempel, Carl G. ‘Studies in the Logic of Confirmation (I.)’. Mind 54, no. 213 (1945): 1–26.
• Hempel, Carl G. ‘The White Shoe: No Red Herring’. The British Journal for the Philosophy of Science 18, no. 3 (1967): 239–40. https://doi.org/10.1093/bjps/18.3.239.