Inductive Reasoning and Arguments

Inductive Reasoning and Arguments

In an inductive argument, the conclusion is supposed to follow likely or probably from the premise(s), not necessarily – in other words, the inference to the conclusion is one of degree and on a probability scale from 0.000…1, which is the least likely or probable case where the conclusion may be drawn from the premise(s), through 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 0.9 to 0.9999…, which is the most likely or probable case where the conclusion may be drawn from the premise(s).

If all of the premises are true, then it is still possible for the conclusion to be false.

The premise(s) does/do not entail the conclusion – the conclusion cannot already be found in the premise(s), at least not in the same way the conclusion is entailed by the premise(s) of a deductive argument.

These arguments are all inductive arguments utilizing inductive reasoning:

1. My old running shoes were Brand X, genuine leather, and lasted me a year.
2. These new shoes I’m thinking of buying are Brand X and genuine leather.
3. So, these new shoes will last me a year, too.

Note that it’s still possible that the new shoes won’t last you a year. Also, it’s more appropriate to conclude, “So, it’s likely that or probably the case that these new shoes will last me a year, too.” Finally, you’d feel more confident about the conclusion if you had more cases/examples of other running shoes lasting a year – one case offers some support for the conclusion, while 100 similar cases would offer more support for the conclusion, and 1,000 similar cases would offer even more support for the conclusion, etc.

(5)	(1) Team X won the championship game the last two years.
	(2) Team X has had the best statistics of all of the teams this season.
	(3) Thus, Team X will win the championship game against Team Y today.

Again, it’s still possible that Team X loses the game for any number of reasons. And again, it’s better to state, “Thus, Team X probably or likely will win the championship game against Team Y today.” Finally, you’d feel more confident about the conclusion if we knew this information, too: “Team Y’s star player has an injury and won’t be playing in the game” and “Team Y is playing in Team X’s arena.”

(6)	(1) I know there are 10 beans total in this bag, but I don’t know their color.
	(2) The last nine beans I pulled from this bag have been red.
	(3) The next bean I pull out will be red, too.

Could the last bean you pull out be a different color? Of course. So, you might want to conclude that the last one has a chance of being red and not that it will absolutely, positively, definitely, without a shadow of a doubt, be red. Notice that you’d feel less confident about the conclusion following from the premises if the second premise was “The last five beans I pulled out of this bag have been red” and even less confident if that premise was “The last two beans I pulled out of this bag have been red.”