Deductive Reasoning
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Deductive Reasoning
In order to fully understand deductive reasoning, there are certain points to be noted. First, what is the nature of deductive reasoning? Logical strength is defined as the property of an argument whose premises, if true provide support for its conclusion. Deductive and inductive arguments are also distinguished based on the point that logical strength is a matter of degree. This distinction makes it necessary to understand the nature of deductive reasoning. Therefore, deductive arguments are those whose premises guarantee the truth of the conclusion, and inductive arguments are those whose premises make it reasonable to accept the conclusion though do not absolutely guarantee its truth.
Deductive reasoning is somewhat different from an inductive argument (truth of premises doesnt guarantee the truth of conclusion) for the conclusion cant possibly be false if the premises are true. Consider the following example.
If you like listening to Metallica then you prefer rock music.
If you prefer rock music then you are a rocker.
Therefore, if you like listening to Metallica then you are a rocker.
In this argument, it can be said that the truth of the conclusion is guaranteed if its premises are true, unless at least one of the premises is false. Deductive arguments are able to guarantee their conclusions because the logical strength doesnt depend upon the specific content but on their form or structure.
* It is defined that the truth of the premises of a deductive argument guarantees the conclusion due to its form or structure. Then, as shown by the examples the, form of implication is followed (if-then statement)
Every deductive argument has at least one truth-functional statement. It is necessary to understand what a truth-functional statement is order to understand deductive reasoning.
Truth functional statements are a sub-class of complex statements (a kind of statement that contains another statement as a component part as opposed to the characteristic of a simple statement). They are distinguished by the way their truth is determined. In able to determine the truth of truth-functional statements, indirect procedure must be done, (different from the common procedure of looking directly for facts or reasons) that is seeing whether its components are true. In other words, the truth of truth-functional statements is thus a function of the truth values of its component statements. Consider the following example of truth functions:
I didnt study for the exam but I still got a perfect score. Ð- if both statements are true then the complex statement is also true but if either one of these is false, the complex statement will be false as a whole.
Neither I drank a beer nor somebody left the bottles. Ð- only one statement needs to be false for the whole statement to be true
It is false that he broke his promise. Ð- it is true when its component statement is false
Other statements, though complex may not be a truth. For example, the statement: Jon believes that Angel is afraid of the dark. Jon might believe that Angel is afraid of the dark though he is not in which case this statement will be true even the statement Angel is afraid of the dark is false.
Therefore, it can be said that those statements which are merely subjective or of personal feelings may not be considered as truth-functions for its truth is not a function of the truth value of its component statement. These statements are those that use Ðsubjective verbs in referring to the component statement. These verbs basically used in expressing personal thoughts, views, etc. thus, not absolutely guaranteeing the truth of component statement.
The logical operators also play crucial part in telling precisely how the truth of the statement as a whole is determined by the truth values of its component statements. They also define the different kinds of truth-functional statement as explained above.
Four kinds of truth-functions:
It is false that Keanu Reeves is gay. Negation – the statement p is false is true when the component statement is false and false when the component statement is true
Manny Pacquiao is the worlds featherweight champion and he has not been defeated so far. Conjunction Ð- true if and only if both statements are true and false it both is false or either one is false
Either he stole it or somebody else stole it. Disjunction Ð- true when either one of the components is true or if both are true, it is false when both are false