Two forms of reasoning: Deductive and Inductive

2026-02-14

Deductive Reasoning

A classical example is:

  P1:  Socrates is a man;
  P2:  Every man is mortal.

Therefore:

  C:   Socrates is mortal.

NOTE: P1 and P2 stand for Premise 1 and Premise 2. C stands for Conclusion.

There are two key features of deductive reasoning:

Firstly, it doesn't add any new information, in a strict logical sense. All the information contained in the conclusion was already contained in the premises, it was merely uncovered and made explicit.

Secondly, assuming the premises are true and the conclusion follows from the premises, the conclusion is necessarily true.

The ways to object to a deductive argument are, thus, either arguing that one of the premises is false or arguing that the conclusion does not necessarily follow.

Inductive Reasoning

An example of enumerative induction is:

I observed a hundred swans:

  O1: Swan is white;
  ...
  O100: Swan is white.

Therefore:

  C: Every swan (in the world) is white.

NOTE: O1, ..., O100 stand for Observation 1, ..., Observation 100. C stands for Conclusion.

This form of reasoning is a bit more interesting. You are hoping to draw an inference regarding a truth about the world, a new piece of information, from the body of data you've collected.

In contrast to deductive reasoning, the conclusion this time is not necessarily true. It is only provisionally true: it only takes observing a single black swan to disprove C.

Still, this form of reasoning is necessary. An individual cannot, as a matter of practicality, exhaustively examine all the possible instances of a claim before acting on it. One has to act on incomplete, probably true, information.

Another more sophisticated example of inductive reasoning is exemplified by statistical and probabilistic modeling. Say, before a general election takes place, you interview thousands of people about which candidate they plan to vote for. The hope of this exercise is to draw a truth about the general population -- which candidate most people will likely vote for -- from a limited set of observations of a sample -- which candidate the set of interviewees state they will vote for.