## Constructing Arguments: Hypothetical Reasoning, Conditionalizing, and Universal Generalization

### Last revised date: September 15, 2003

Sometimes we engage in hypothetical reasoning to reach a prediction we hope to confirm by observation. (See Explanations, Predictions, and Arguments.) But sometimes we can use hypothetical reasoning to (try to) establish the truth of a conditional (if-then) statement that can in turn be generalized to a universal statement. (A universal statement is a statement logically equivalent to statements of the form "All S are P" or the form "No S are P").

Consider this argument:

Suppose John thinks that Mary likes him. Suppose further that John finds Mary pleasant to be around. Suppose further that John has no prior commitment preventing him from associating with Mary. [Conclusion] We can predict that John will probably try to spend more time with Mary.
This hypothetical reasoning, if it is valid, can support the following conditional (if-then) statement. This move is known as conditionalizing a hypothesis.
If John thinks that Mary likes him
and John finds Mary pleasant to be around and
John has no prior commitment preventing him from associating with Mary,
then John will probably try to spend more time with Mary.
The conditional form does not require that we know the supposition(s) restated in the antecedent (the part of the conditional after "if") to be true.

Now the reasoning was a thought experiment in which "John" and "Mary" here stood for any two persons. This fact, if the reasoning supporting the conditional was otherwise good, permits us to generalize from the conditional statement and draw the following conclusion, which is a universal statement:

Any person [who thinks that a second person likes him (or her) and finds this second person pleasant to be around and has no prior commitment preventing them from associating with this second person] is [a person who will probably try to spend more time with the second person].
I use the brackets only to make the logical structure of the universal conclusion more obvious.