A Note on the Problem of Induction

Induction is a thinking process where one makes conclusions by moving from the particular to the general. Arguments based on induction can range in probability from very low to very high, but always less than 100%. Here is an example of induction:

I have observed that punching a boxing bag properly with protective gloves never causes injury. Therefore no one will be injured using a boxing bag.

As can be seen from the example above, induction faces a key problem which is the inability to guarantee the conclusion, because a sweeping generalisation cannot be made from a limited number of observations. The best it can provide are probabilities, ranging from low to very high.[A] In the aforementioned example the person who made the statement could not logically prove that the next person to punch a boxing bag will not get injured.

Therefore, the problem with induction is that it can’t produce certainty.[B] This issue was raised by the 18th century Scottish philosopher David Hume in his book, An Enquiry Concerning Human Understanding. Hume argued that inductive reasoning can never produce certainty. He concluded that moving from a limited set of observed phenomena to making conclusions for an unlimited set of observed phenomena is beyond the present testimony of the senses, and the records of our memory.[1]

From a practical scientific perspective, generalisations made for an entire group or for the next observation within that group based on a limited set of data, will never be certain. For example, a scientist travelled to Wales and wanted to find out the colour of sheep (assuming he does not know the colour of sheep), and he started observing the sheep and recording what colour they are. Say after 150 sheep observations he found that all of them were white. The scientist would conclude based upon his data, using induction, that all sheep are white. This basic example highlights the problematic nature with the process of induction as we know sheep can also be black. Certainty using induction will never be achieved. Professor Alex Rosenberg in his book Philosophy of Science: A Contemporary Introduction explains the problem of induction and he concludes that this is a key problem facing science; he writes,

Here we have explored another problem facing empiricism as the official epistemology of science: the problem of induction, which goes back to Hume, and added to the agenda of problems for both empiricists and rationalists. [2]

Notes & References

[A] There are two main types of induction, strong induction and weak induction. Strong induction moves from the particular to the general in a way that makes a conclusion for the whole group. Weak induction moves from the particular to the general in a way that makes a conclusion for the next observation.

An example of strong induction is the conclusion that all ravens are black because each raven that has ever been observed has been black.

An example of weak induction is that because every raven that has ever been observed has been black, the next observed raven will be black.

[B] Induction can reach certainties but not in the form of generalisations. For example,

I observe an instance of A with the quality B.

Therefore, the nature of A allows B.

If you have observed Crows that are black you can conclude with certainty that some Crows are black. But you could not achieve certainty if you concluded that all Crows were black based on a limited set of observations. This type of induction that produces certainty doesn’t apply to evolution as inductive reasoning in the form of generalisations is not certain.

[1] David Hume. An Enquiry Concerning Human Understanding, p. 108.

[2] Professor Alex Rosenberg. Philosophy of Science: A Contemporary Introduction. 2012, p. 198.

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