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Logical Reasoning (Deductive／Deduction - Inductive／Induction - Abductive／Abduction - Analogical)

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logical reasoning is a type of reasoning technique
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|precondition(s)/minor-premise(s)| — major-premise(s)/rule(s) —> |postcondition(s)/major/minor-premise(s)/rule(s)|
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Syllogism

major premise: All books from that store are new
minor premise: These books are from that store
conclusion: Therefore, these books are new

  • major premise (assumption?) of a syllogism makes a general statement that the writer believes to be true
  • minor premise (subsumption) presents a specific example of the belief that is stated in the major premise
  • conclusion presents a conclusion of the specific example based on the premises

Logical Reasoning Type

Logical Reasoning Type

Description

Example

Deductive Reasoning

Deductive reasoning determines whether the truth of a conclusion can be determined for that rule, based solely on the truth of the premises.

Mathematical logic and philosophical logic are commonly associated with this type of reasoning.
  • when it rains, things outside get wet
  • the grass is outside
  • therefore: when it rains, the grass gets wet

this is an example of syllogism

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|precondition(s)/minor-premise(s)| — major-premise(s)/rule(s) —> |?|
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Abductive Reasoning

a.k.a. inference to the best explanation, selects a cogent set of preconditions. Given a true conclusion and a rule, it attempts to select some possible premises that, if true also, can support the conclusion, though not uniquely.

This kind of reasoning can be used to develop a hypothesis, which in turn can be tested by additional reasoning or data. Diagnosticians, detectives, and scientists often use this type of reasoning

these arguments are not deductively valid, see or Sufficient conditions
  • when it rains, the grass gets wet.
  • the grass is wet
  • therefore, it might have rained

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|?| — major-premise(s)/rule(s) —> |postcondition(s)/major/minor-premise(s)/rule(s)|
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Inductive Reasoning

Inductive reasoning attempts to support a determination of the rule. It hypothesizes a rule after numerous examples are taken to be a conclusion that follows from a precondition in terms of such a rule.

While they may be persuasive, these arguments are not deductively valid, see the problem of induction. Science is associated with this type of reasoning.
  • the grass got wet numerous times when it rained
  • therefore: the grass always gets wet when it rains

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|precondition(s)/minor-premise(s)| — ? —> |postcondition(s)/major/minor-premise(s)/rule(s)|
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾

Analogical Reasoning

Analogical reasoning is a weaker form of inductive reasoning from a particular to a particular instead of the inductive reasoning’s use of large number of examples to reason from the particular to the general.

can lead to right and/or wrong conclusions

Example 1 (True Conclusion)

  • Premise 1: Socrates is human and mortal
  • Premise 2: Plato is human
  • Conclusion: Plato is mortal

Example 2 (False Conclusion)

  • Premise 1: Socrates is human and male
  • Premise 2: Ada Lovelace is human
  • Conclusion: Therefore Ada Lovelace is male

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|precondition(s)/minor-premise(s)| — ? —> |postcondition(s)/major/minor-premise(s)/rule(s)|
‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾ ‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾