1.2 Arguments – Types of Reasoning

The two main types of reasoning involved in the discipline of Logic are deductive reasoning and inductive reasoning.

  • Deductive reasoning is an inferential process that supports a conclusion with certainty.
  • Inductive reasoning is an inferential process providing support strong enough to offer high probability (but not absolute certainty) for the conclusion.

1.2.1 Attributes of Deductive Arguments

Validity

Validity is the attribute of deductive arguments that denotes logical strength. Validity is about the strength of the inference, or reasoning, between the premises and the conclusion. A deductive argument is valid when you have the following:

If all its premises were true, then its conclusion must be true, by necessity.

To determine if an argument is valid or invalid (not valid):

  1. First assume that the premises are true, even if they are not; pretend that they are true.
  2. Then ask yourself whether the conclusion would need to be true, assuming/pretending that the premises are true.

Here is an example:

Premise 1: All dogs are snakes.
Premise 2: All snakes are birds.
Conclusion: All dogs are birds.

This is a valid argument because if all of the premises were true then the conclusion would follow by necessity. The argument has logical strength, or validity. Validity is about the form of the argument, not the truth of its premises.

Valid arguments may have:

  • True premises, true conclusion
  • False premises, false conclusion
  • False premises, true conclusion

Valid arguments can never have:

  • True premises, false conclusion.

In a valid deductive argument, if the premises are true, it is impossible for the conclusion to be false.

It is important to keep in mind that just because an argument does have a possibly valid combination of premise-conclusion truth values (for example, true premises and true conclusion), it is not necessarily valid. It must also be logically strong. That example with dogs, snakes, and birds is valid, because the reasoning works. If those premises were true, the conclusion would necessarily follow. Even if the premises are true and the conclusion is true, it does not mean that the reasoning is valid.

Here is an example of an argument with true premise and a true conclusion, but the strength of the connection, the reasoning, from the premises to the conclusion is not valid. The conclusion happens to be true but not due to any reason provided by those premises. The argument’s form is invalid.

Premise 1: All dogs are mammals.
Premise 2: All collies are mammals.
Conclusion: All collies are dogs.

To summarize, a valid deductive argument is one where it would be impossible for the conclusion to be false given that the premises were true. The conclusion follows necessarily from the logical connections or reasoning established by the premises.

Soundness

Soundness is the attribute of a deductive argument that denotes both the truth of its premises and its logical strength. A deductive argument is sound when:

  1. It is valid, and
  2. It has all true premises.

For example:

Premise 1: All cats are mammals.
Premise 2: All mammals are animals.
Conclusion: All cats are animals.

This argument is sound because (1) it is valid (the premises support the conclusion by necessity) and (2) all of the premises are actually true!

On the other hand, the example above used to demonstrate validity (with dogs, snakes and birds) is not sound, because it does not have all (any!) true premises. (But it’s form is still valid.)


1.2.2 Attributes of Inductive Arguments

Inductive Strength

Inductive strength is the attribute of inductive arguments that denotes logical strength. An inductive argument is inductively strong when you have the following:

If all its premises were true, then it its highly likely or probable that its conclusion would also true.

“Strong” and “weak” are the terms used to describe the possibilities for the logical strength of inductive arguments. To determine if an argument is strong or weak:

  1. First assume the premises are true, even if they are not; pretend for now that they are true.
  2. Then ask yourself whether it is likely/probable that the conclusion would be true, assuming/pretending that those premises are true.

Here is an example:

Premise 1: Most peacocks eat oatmeal for breakfast.
Premise 2: This bird is a peacock.
Conclusion: Therefore, probably this bird eats oatmeal for breakfast.

This argument is inductively strong because if all its premises were true, then it would be highly likely or probable that its conclusion would also true.

Inductively strong arguments may have:

  • True premises, true conclusion
  • False premises, false conclusion
  • False premises, true conclusion

Inductively strong arguments cannot have:

  • True premises, false conclusion

To summarize, a strong inductive argument is one where it is improbable for the conclusion to be false, given that the premises are true. A weak inductive argument is one where the conclusion probably would not follow from the premises, if they were true.

Cogency

Cogency is the attribute of an inductive arguments that denotes the truth of its premises and its logical strength. An inductive argument is cogent when:

  1. It is inductively strong, and
  2. It has all true premises

Here’s an example:

Premise 1: Europa (a moon of Jupiter) has an atmosphere containing oxygen.
Premise 2: Oxygen is required for life.
Conclusion: Thus, there may be life on Europa.

This argument is cogent because (1) it is inductively strong (if the premises were true, then the conclusion would probably be true) and (2) the premises actually are true.

On the other hand, the example above concerning peacocks, used to demonstrate inductive strength, is not cogent, because it does not have all true premises.

In summary, an inductive argument is one in which it is improbable that the conclusion is false given that the premises are true.


1.2.3 Good Arguments

The important take-away from the information on the attributes of both deductive and inductive arguments is this:

good argument proves, or establishes, its conclusion and has two key features:

  1. It is logically strong.
  2. All of its premises are true.

Logical Strength

Logical strength is the degree of support that the premises, if true, confer on the conclusion. This attribute applies to both deductive arguments (by virtue of validity) and inductive arguments (by virtue of inductive strength.)

  • A good deductive argument is not only valid, but is also sound.
  • A good inductive argument is not only inductively strong, but is also cogent.