Perception and intellectual apprehension are modes of sensory information input. It is simply an awareness of the mind receiving a stimulus. If these two are thought of as data input, inference would be thought of as data output. To infer, one must first perceive and apprehend information first. Then, from collected information via the human senses, judgments are formulated to conclude things that the human senses cannot grasp alone.
Arguments can be classified as deductive or non-deductive. There are arguments which if the premises are true, the conclusion must be true. These arguments which have an impenetrable bond between premises and conclusion are classified as “deductive.” For example, if I put forth the premise: “That thing is a water bottle” and “Water bottles can hold water,” the conclusion “That thing can hold water” must be true (if the two premises were indeed true.)
Like deductive arguments, non-deductive arguments have a set of premises with a following conclusion as well. The difference is the relationship between premises and conclusion. In a non-deductive argument, the conclusion can still be false even the premises are true. Non-deductive don’t bear as much weight as deductive arguments. ...
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... relative in their subjective strength.
A sound argument is a type of valid argument which has the added requirement of having the premises actually being true. Compare the previously used argument: [1.) All lamps are watches. 2.) All watches are green. 3.) Therefore, all lamps are green.] with [1.) All people who are reading this are literate. 2.) You are reading this. 3.) Therefore you are literate.] Both arguments have conclusions that must follow making them both valid. The truth of the premises is irrelevant to its validity. The truth of premises is mandatory for soundness. Only the second argument is valid.
A proof in the most basic sense is just a sound argument. The only difference is that calling it a proof implies that the particular sound argument concludes new/relevant/important information that people can generally learn from and use.
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