Deductively Valid vs. Invalid

Attribute	Deductively Valid	Invalid
Definition	An argument is deductively valid if the conclusion necessarily follows from the premises.	An argument is invalid if the conclusion does not necessarily follow from the premises.
Truth Preservation	If the premises of a deductively valid argument are true, then the conclusion must also be true.	Even if the premises of an invalid argument are true, the conclusion can still be false.
Logical Form	Deductively valid arguments follow a specific logical form that guarantees the truth of the conclusion.	Invalid arguments may have logical fallacies or errors in reasoning that lead to an incorrect conclusion.

Definition of Deductively Valid Arguments

In logic, an argument is considered deductively valid if the conclusion necessarily follows from the premises. This means that if the premises are true, then the conclusion must also be true. Deductively valid arguments are characterized by their structure, rather than the actual content of the premises and conclusion. In other words, the validity of the argument is determined by the logical relationship between the premises and the conclusion.

Attributes of Deductively Valid Arguments

One key attribute of deductively valid arguments is that they are truth-preserving. This means that if the premises are true, then the conclusion must also be true. Another attribute is that deductively valid arguments are not based on probability or likelihood, but on strict logical necessity. Additionally, deductively valid arguments are considered to be airtight - there are no gaps in the reasoning that would allow for the possibility of the conclusion being false even if the premises are true.

• Deductively valid arguments are truth-preserving.
• They are based on logical necessity, not probability.
• They are airtight with no gaps in reasoning.

Definition of Deductively Invalid Arguments

In contrast, deductively invalid arguments are those in which the conclusion does not necessarily follow from the premises. This means that even if the premises are true, the conclusion could still be false. Deductively invalid arguments are flawed in their structure, leading to a failure in logical reasoning. Invalid arguments can be identified by examining the logical connections between the premises and the conclusion.

Attributes of Deductively Invalid Arguments

One key attribute of deductively invalid arguments is that they are not truth-preserving. This means that even if the premises are true, the conclusion may still be false. Another attribute is that deductively invalid arguments often contain logical fallacies, such as circular reasoning or non-sequiturs. Additionally, deductively invalid arguments are based on faulty reasoning, which can lead to false conclusions even if the premises are true.

• Deductively invalid arguments are not truth-preserving.
• They often contain logical fallacies.
• They are based on faulty reasoning.

Examples of Deductively Valid and Invalid Arguments

Consider the following deductively valid argument: Premise 1: All humans are mortal.Premise 2: Socrates is a human.Conclusion: Therefore, Socrates is mortal.In this argument, if the premises are true, then the conclusion must also be true. The logical connection between the premises and the conclusion is sound, making it a deductively valid argument.

On the other hand, consider the following deductively invalid argument:Premise 1: All cats are animals.Premise 2: Dogs are animals.Conclusion: Therefore, all dogs are cats.In this argument, the conclusion does not necessarily follow from the premises. Even though the premises are true, the conclusion is false, making it a deductively invalid argument.

Conclusion

In conclusion, deductively valid arguments are characterized by their truth-preserving nature, logical necessity, and airtight reasoning. On the other hand, deductively invalid arguments fail to preserve truth, often contain logical fallacies, and are based on faulty reasoning. By understanding the attributes of deductively valid and invalid arguments, we can better evaluate the strength of reasoning and logic in various arguments and make more informed decisions based on sound reasoning.