Valid Deductive Argument

A valid deductive argument is a deductive argument where there is a valid sequence of deductive operations from the true premises to an argument conclusion.

• AKA: Valid Inference.
• Context:
  • It can support a Justified Belief.
  • It can range from being a Sound Deductive Argument to being an Unsound Deductive Argument.
  • It can range from being an Valid Informal Deductive Argument to being an Valid Formal Deductive Argument.
  • It can (often) follow a Valid Deductive Pattern Pattern.
• Example(s):
  • All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
• Counter-Example(s):
  • an Invalid Deductive Argument, such as “All men are mortal. Socrates is mortal. Therefore, Socrates is a man.”
  • an Valid Inductive Argument.
  • an Valid Abductive Argument.
• See: Inductive Argument.

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References

2009

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Argument#Validity
  • Arguments may be either valid or invalid. If an argument is valid, and its premises are true, the conclusion must be true: a valid argument cannot have true premises and a false conclusion.
  • The validity of an argument depends, however, not on the actual truth or falsity of its premises and conclusions, but solely on whether or not the argument has a valid logical form. The validity of an argument is not a guarantee of the truth of its conclusion. A valid argument may have false premises and a false conclusion.
• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Validity
  • The term validity (also called logical truth, analytic truth, or necessary truth) as it occurs in logic refers generally to a property of particular statements and deductive arguments. Although validity and logical truth are synonymous concepts, the terms are used variously in different contexts.
  • …
  • When an argument is set forth to prove that its conclusion is true (as opposed to probably true), then the argument is intended to be deductive. An argument set forth to show that its conclusion is probably true may be relatively valid if, whenever all premises are true, the conclusion is also necessarily true.
  • An argument that is not valid is said to be ‘’invalid’’.
  • An example of a valid argument is given by the following well-known syllogism:
    • All men are mortal.
    • Socrates is a man.
    • Therefore, Socrates is mortal.
  • What makes this a valid argument is not the mere fact that it has true premises and a true conclusion, but the fact of the logical necessity of the conclusion, given the two premises. No matter how the universe might be constructed, it could never be the case that this argument should turn out to have simultaneously true premises but a false conclusion. The above argument may be contrasted with the following invalid one:
    • All men are mortal.
    • Socrates is mortal.
    • Therefore, Socrates is a man.
• http://www.logic-classroom.info/glossary.htm
  • valid inference An inference is valid whenever the form of the conclusion is true every time the forms of the premises are.
• http://mcckc.edu/longview/ctac/glossary.htm
  • Validity : Definition: An argument is valid (deductive) if and only if there are no possible circumstances under which all the premises would be true, and the conclusion would be false.

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