Deductive Argument

A Deductive Argument is a logic argument based on a Sequence of Deductive Logic Operations which shows that a Logic Statement is true in all cases.

• AKA: Deductive Inference.
• Context:
  • It can (typically) be presented with Argument Premises, Deductive Operations, an Argument Conclusion.
  • It can range from being a Valid Deductive Argument to being an Invalid Deductive Argument.
  • It can range from being a Sound Deductive Argument to being an Unsound Deductive Argument.
  • It can be the outcome of a Deductive Reasoning Process.
  • It can substantiate a Proof of a Theorem.
  • …
• Example(s):
  • premises: All men are mortal; Socrates is a man.
    operation: Modus Ponens;
    conclusion: Socrates is mortal.
  • Given that if Human(X) then Mortal(X) and Human(Socrates) then it follows that Mortal(Socrates).
  • premise: If an intruder is detected, the alarm goes off.; Premise: The alarm does not go off. Deductive Logic Operation: Modus Tollens; Conclusion: No intruder is detected.
  • premise: If an intruder is detected, the alarm goes off.; Premise: The alarm does not go off. Deductive Logic Operation: Modus Tollens; Conclusion: No intruder is detected.
• Counter-Example(s):
  • an Invalid Deductive Argument (but a Valid Abductive Argument).
    • (Premise: All beings are mortal.]; (Premise: Socrates is mortal.]; (Logic Operation: Affirming the Consequent;] (Conclusion: Socrates is a being.].
  • an Inductive Logic Argument.
  • an Abductive Argument.
• See: Inductive Argument, Deductive Logic Formalism.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/deductive_reasoning#Simple_example Retrieved:2014-4-2.
  • An example of a deductive argument:
    1. All men are mortal.
    2. Sherlock Holmes is a man.
    3. Therefore, Sherlock Holmes is mortal.
  • The first premise states that all objects classified as "men" have the attribute "mortal". The second premise states that "Sherlock Holmes" is classified as a "man" – a member of the set "men". The conclusion then states that "Sherlock Holmes" must be "mortal" because he inherits this attribute from his classification as a "man".

2009

• http://www.uky.edu/~rosdatte/phi120/glossary.htm
  • deductive argument: An argument in which the premises are intended to provide necessary support for the conclusion. Deductive arguments are either valid or invalid.
• http://www.philosophy.uncc.edu/mleldrid/logic/logiglos.html
  • Deductive Argument: A deductive argument is one that derives the truth of the conclusion from the truth of the premises. If the argument form, or structure of the argument, is valid, then the conclusion will always follow from the premises. The hard determinism argument below is an example of a deductive argument that makes use of two modus ponens arguments in which the conclusion of the first serves as the premise of the second, or so it appears.
• http://mcckc.edu/longview/ctac/glossary.htm
  • Deductive Argument: Definition: An argument in which the truth of the premises guarantees the truth of the conclusion, in the sense that there is no possible way for the premises all to be true when the conclusion is false.

    Comment: We use the term deductive, in other words, as a synonym for valid. Not every argument presented as a deductive one (for example, by saying that in view of its premises its conclusion must be true) is really a deductive one (cf. the pseudo-inductive fallacy).

• (Wordnet, 2009) ⇒ http://wordnet.princeton.edu/perl/webwn
  • S: (n) tax write-off, tax deduction, deduction (a reduction in the gross amount on which a tax is calculated; reduces taxes by the percentage fixed for the taxpayer's income bracket)
  • S: (n) deduction, discount (an amount or percentage deducted)
  • S: (n) deduction, entailment, implication (something that is inferred (deduced or entailed or implied)) "his resignation had political implications"
  • S: (n) deduction, deductive reasoning, synthesis (reasoning from the general to the particular (or from cause to effect))
  • S: (n) subtraction, deduction (the act of subtracting (removing a part from the whole)) "he complained about the subtraction of money from their paychecks"
  • S: (n) discount, price reduction, deduction (the act of reducing the selling price of merchandise)
• http://en.wiktionary.org/wiki/deduction
  • 1. that which is deducted; that which is subtracted or removed
  • 2. a sum that can be removed from tax calculations; something that is written off. You might want to donate the old junk and just take the deduction.
  • 3. a conclusion; that which is deduced, concluded or figured out. He arrived at the deduction that the butler didn't do it.
  • 4. the ability or skill to deduce or figure out; the power of reason. Through his powers of deduction, he realized that the plan would never work.
  • 5. (logic)
    • a. a process of reasoning that moves from the general to the specific, in which a conclusion follows necessarily from the premises presented, so that the conclusion cannot be false if the premises are true.
    • b. a conclusion reached by this process
• CYC Glossary http://www.cyc.com/cycdoc/ref/glossary.html
  • deduction: A deduction is an argument supporting a remote or inferred assertion. It is composed of a set of assertions which together entail the inferred assertion.
• Wendy MacCaull. (2009). “Specification and Verification." Lecture Notes: Computer Science 471/543

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