Logic in problem-solving
The better solution to many problems across all industries is to keep peeling back the layers to find the root cause.
In problem-solving, various logical scenarios can be applied, depending on the nature of the problem. That can be divided into problem-solving logic and reasoning. Problem solving involves systematically searching through possible actions to reach a goal, using both divergent and convergent thinking. Reasoning involves deriving inferences or conclusions from premises using logical rules and laws.
Conditional Reasoning: Draw a conclusion based on a conditional ("if...then") proposition.
Deduction: Deductive reasoning involves analyzing valid argument forms and drawing out conclusions implicit in their premises.
Syllogisms: Deductive arguments with two premises and a conclusion.
-Categorical Syllogism: Premises and the conclusion state that some or all members of one category are or are not members of another category.
-Linear Syllogism: Involve a quantitative comparison where each term displays more or less of a particular attribute, and the reasoner draws conclusions based on the quantification.
Induction: Inductive reasoning involves reasoning from a part to a whole, from particulars to generals, from the past to the future, or from the observed to the unobserved.
-Causal Inference: Reasoning to the conclusion that something is, or is likely to be, the cause of something else.
-Categorical Inference: Making a judgment about whether something is, or is likely to be, a member of a certain category.
-Analogical Inference: Apply what one has learned to another domain, using the structure "As A is to B, so C is to D," or "As A is in B, so C is in D".
Fallacies: Violations of rules governing correctness or efficiency in reasoning.
-Scope Mistakes: Confusion about the scope of terms, leading to misinterpretations.
-Fallacy of Many Questions: Ask a question whose presupposition has not been established.
-Begging the Question: Answer the main question by assuming the answer in the premises.
-Ad Hominem Reasoning: Do the reasons by reference to a person rather than the argument itself.
-Illicit Rhetorical Ploys: Appeal to pity, authority, or popular opinion.
Problem Types
-Well-Structured Problems: Have clear solution paths where the steps to reach a solution can be easily specified.
-Ill-Structured Problems: Do not have clear solution paths, and the steps needed to reach a solution cannot be easily specified.
Problem-solving is about seeing a problem and actually discovering a real solution to that problem, not just the band-aid approach to fixing the symptom. The better solution to many problems across all industries is to keep peeling back the layers to find the root cause. Therefore, taking a logical approach to solve a problem can significantly improve the effectiveness of the solution and eliminate side effects, generate value, and drive progressive changes.
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