Logical thinking, once embraced is a thing of beauty, which deserves our attention and admiration.
It’s become common in today’s world for people to confuse facts with fiction or conjecture. Observing and participating in many conversations will demonstrate how fact and conjecture are readily and easily exchanged, as one. During these conversations, if conjecture is called out cognitive dissonance shows it’s face blocking any further discussion or clarity. Logical thought does not stand a chance in this arena,
Wikipedia has a formidable layout on how to learn logical thought and some of it’s best known structures. It’s a bit dry but it covers the basics. It is still better than going to the dentist.
Logical thinking: Two kinds of logical reasoning can be distinguished in addition to formal deduction: induction and abduction.
Given a precondition or premise, a conclusion or logical consequence and a rule or material conditional that implies the conclusion given the precondition, one can explain the following.
DEDUCTIVE REASONING:
Deductive reasoning determines whether the truth of a conclusion can be determined by that rule, based solely on the truth of the premises.
Example: ” When it rains, things outside get wet. The grass is outside, therefore: when it rains, the grass gets wet.” Mathematics Logic and Philosophical Logic are commonly associated with this kind of reasoning.
INDUCTIVE REASONING:
Inductive reasoning attempts to support a determination of the rule.
Example: The grass got wet numerous times when it rained, therefore the grass always gets wet when it rains. ” While they are persuasive, these arguments are not deductively valid, see the problems with induction. Science is associated with this kind of reasoning.
ABDUCTION REASONING:
Abduction reasoning AKA 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.
Example: ” When it rains, the grass gets wet. The grass is wet. Therefore, it might have rained. ” 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.
Within the context of a mathematical model, the three kinds of reasoning can be described as follows:
The construction / creation of the structure of the model of abduction.
Assigning values (or probability distributions) to the parameters of the models is induction.
Executing/ running the model is deduction.
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