# Truth-Preserving, Logical Validity, Soundness, and Inductive Strength

*Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.*

## Indicator Words

Words That Indicate A Premise | Words That Indicate A Conclusion |
---|---|

Since | Therefore |

For | Thus |

Because | It follows that |

On account of | So |

Inasmuch as | Hence |

For the reason that | Consequently |

## Premises and Conclusions

In symbolic logic, we make many important distinctions between various statements in an effort to reach a judgment that we can then utilize in making sound decisions. We need to weed through the thicket to find the clearing sometimes, and we gather tools to help us accomplish this. One very important distinction along this path is the difference between premises and conclusions. A premise* *is a statement that has a truth value of either true or false. A conclusion is a statement that is based off premises and also has a true or false value.

## Truth Preserving

When we reach a conclusion, we want to make sure that truth preserving, or never getting a false conclusion from true premises, occurs (Bergmann 2). This is because frequently in life we can find many scenarios when we started with false ideas and arrived at truth. This happens frequently in the hypothesis-conclusion dynamic of science. But nowhere should we find a situation where ideas we know to be true are used to take us to a false conclusion. We look for truth in logic, and while knowing what is false is also powerful, if we arrive at a false conclusion from true premises, then we did not use good reasoning and should perhaps reexamine both the premises and conclusion.

## Validity

When we have an argument (a conclusion based off two or more premises), if it is truth preserving then it is valid. If the argument is not truth preserving, then we call it invalid (3). We find that valid arguments are the most useful, for if we relied on invalid arguments for decisive actions, we would find ourselves unable to make progress in any regard. Invalid arguments have no practicality in the real world, for we cannot act upon a false conclusion if it stemmed from what should be true. When someone tells you the store ran out of milk, would you go to that store and anticipate to find that particular dairy product available? Hence, we seek out valid arguments in our quest for logical conquest.

It may come as a surprise, but this is not the only type of validity we can talk about. A deductively valid argument cannot have true premises and a false conclusion. A deductively invalid argument is not deductively valid, or can have true premises and a false conclusion. (13). Now, many situations that would have otherwise have to have been discarded out of inability to talk about them can now be dealt with. If false premises lead to a true conclusion, false premises lead to a false conclusion, or that true premises lead to a true conclusion, then the argument is deductively valid. Also note that just because an argument is deductively invalid, that does not mean that it cannot be one of the cases that was mentioned for deductively valid (15). We have to be careful and look at the reasonableness of the argument (16)

## Soundness

Another quality that will help us to reach a decision on how valid an argument can be considered is the concept of soundness, or the truth to the premises. An argument is deductively sound if and only if it is deductively valid and the premises are true. Many times we can have true premises but lead us to a conclusion that is not necessarily a good stem of reasoning, so we use soundness to aid us. Likewise, a deductively unsound argument is not deductively sound, or it is either invalid and/or the premises are false (14). Since we aim to have true premises, any sound argument means that we either have a true conclusion or a false conclusion. But how do we know that the conclusion should even be measured against the premises we claim support it?

## Inductive Strength

The answer lies in inductive strength, or the likelihood that the conclusion stems from the given premises (18). While not a guarantee, it is more of a probability that can give confidence in our conclusion. We want to use deductive reasoning when true premises absolutely lead to a true conclusion and inductive reasoning when true premises likely mean a true conclusion but it is not guaranteed (18). That way, we can proceed with a great amount of confidence in our conclusion if we know what type of reasoning was applied to it.

## Works Cited

Bergmann, Merrie, James Moor, and Jack Nelson. *The Logic Book*. New York: McGraw-Hill Higher Education, 2003. Print. 2, 3, 9 13-6, 18.

**© 2013 Leonard Kelley**