Three Kinds of Inference

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.

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?

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’s Ravens

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’s Ravens (Fast & Formal Version)

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.

Grue: Goodman’s Riddle

Goodman showed that you can turn a better inductive argument into a much worse one by changing a predicate from, say, green to grue. This raises the question: why is the new argument worse than the original?

Reading (optional):

• Goodman, Nelson. Fact, Fiction, and Forecast. Harvard University Press, 1983. (https://scholar.google.co.uk/scholar?q=goodman+riddle)
• Israel, Rami. ‘Two Interpretations of “Grue” - or How to Misunderstand the New Riddle of Induction’. Analysis 64, no. 4 (2004): 335–39.

--- do one micro task for this unit

Why Grue Is Relevant

Goodman’s puzzle (‘new riddle’) about grue shows that how good an inductive argument something is does not depend only on the argument’s form. Relatedly, in ‘Hempel’s Ravens’ we saw an obstacle to characterising the relation between an observation and a conclusion when the observation is evidence for the conclusion in purely formal terms. These considerations indicate that there cannot be a purely formal theory of inductive reasoning.

Reading (optional):

• Chapter 3 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.
• Godfrey-Smith, Peter. ‘Goodman’s Problem and Scientific Methodology’. The Journal of Philosophy 100, no. 11 (2003): 573–90.
• Goodman, Nelson. Fact, Fiction, and Forecast. Harvard University Press, 1983. (https://scholar.google.co.uk/scholar?q=goodman+riddle)

Is inductive validity irreducible to deductive validity?

Does the demonstration that there is no formal theory of inductive validity allow us to conclude that inductive validity is irreductible is deductive validity? No. There is no formal theory of deductive reasoning; and there are as yet unrefuted attempts to provide such reductions.

Confounding Grue

Goodman’s ‘New Riddle’ about grue and induction has a straightforward solution. What’s interesting about it isn’t that we don’t know how to solve it; it’s what the solution tells us about the relation between an observation and a theory when the observation is evidence for the theory.

Reading (optional):

• Chapters 3 and 14 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.
• Godfrey-Smith, Peter. ‘Goodman’s Problem and Scientific Methodology’. The Journal of Philosophy 100, no. 11 (2003): 573–90.
• Israel, Rami. ‘Two Interpretations of “Grue” - or How to Misunderstand the New Riddle of Induction’. Analysis 64, no. 4 (2004): 335–39.
• Goodman, Nelson. Fact, Fiction, and Forecast. Harvard University Press, 1983. (https://scholar.google.co.uk/scholar?q=goodman+riddle)

Proceedures and Observations

Whether an observation is evidence for a conclusion can depend on the procedure followed in making the observation.

Reading (optional):

• Chapters 3 and 14 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.

Conclusion on Induction

The relation between an observation and theory when the observation is evidence for the theory can not be characterisated in purely formal terms [from grue]; nor is it just a matter of the observation being an instance of the theory [from Hempel’s ravens/Ayesha’s traffic lights]. Instead, whether this relation obtains depends on how the observation is made: there must be no bias, and a good procedure must have been followed in making the observation.

Reading (optional): Chapters 3 and 14 of Godfrey-Smith, Peter. Theory and Reality: An Introduction to the Philosophy of Science. Chicago: University of Chicago Press, 2003.

Recording of Whole-Class Live Question Session

The whole-class live online question session in is based on questions on the topic of this weeks’ lectures posed in advance in the teams channel.