Two methods of logical reasoning are deductive and inductive reasoning: (a) Deductive: Facts, certainty, syllogisms, validity, truth of premises sound arguments & conclusions, and (b) Inductive: Diverse facts, probability, generalizations, hypotheses, analogies inductive strength. This question is asking about deductive reasoning (e.g., syllogisms).
A syllogism is a form of logic using deductive reasoning consisting of a major premise, a minor premise, and a conclusion; for example, All humans are mortal, the major premise, I am a human, the minor premise, therefore, I am mortal, the conclusion. It is reasoning from the general to the specific, e.g. deduction. Thus, every syllogism is a sequence of three propositions such that the first two imply the third, the conclusion. There are three basic types of syllogism: hypothetical, disjunctive, and categorical.
In other words, when an argument claims that the truth of its premises guarantees the truth of its conclusion, it is said to involve a deductive inference. Deductive reasoning holds to a very high standard of correctness. A deductive inference succeeds only if its premises provide such absolute and complete support for its conclusion that it would be utterly inconsistent to suppose that the premises are true but the conclusion false. Notice that each argument either meets this standard or else it does not; there is no middle ground. Some deductive arguments are perfect, and if their premises are in fact true, then it follows that their conclusions must also be true, no matter what else may happen to be the case. All other deductive arguments are no good at all—their conclusions may be false even if their premises are true, and no amount of additional information can help them in the least.
1). Truth and Validity
Thus, logical syllogisms (deductive reasoning) requires such a strong relationship between premises and conclusion. It is therefore worthwhile to consider the standard of correctness for deductive arguments in some detail. A deductive argument is said to be valid when the inference from premises to conclusion is perfect. Here are two equivalent ways of stating that standard:
· If the premises of a valid argument are true, then its conclusion must also be true.
· It is impossible for the conclusion of a valid argument to be false while its premises are true.
(Considering the premises as a set of propositions, we will say that the premises are true only on those occasions when each and every one of those propositions is true.) Any deductive argument (syllogisms) that is not valid is invalid: it is possible for its conclusion to be false while its premises are true, so even if the premises are true, the conclusion may turn out to be either true or false. Notice that the validity of the inference of a deductive argument is independent of the truth of its premises; both conditions must be met in order to be sure of the truth of the conclusion. Of the eight distinct possible combinations of truth and validity, only one is ruled out completely:
SEE ATTACHED RESPONSE FOR FORMATING
Premises Inference Conclusion
True Valid True
XXXX
Invalid True
False
False Valid True
False
Invalid True
False
The only thing that cannot happen is for a logical syllogism (deductive reasoning) to have true premises and a valid inference but a false conclusion
2). Soundness
Some logicians designate the combination of true premises and a valid inference as a sound argument; it is a piece of reasoning whose conclusion must be true. The trouble with every other case is that it gets us nowhere, since either at least one of the premises is false, or the inference is invalid, or both. The conclusions of such arguments may be either true or false, so they are entirely useless in any effort to gain new information.
What is the meaning of validity, truth, and soundness as they relate to the area of logical syllogisms
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