An inference is a way of reaching a conclusion from statements that are assumed to be true: called premises. The conclusion includes new knowledge that the premises did not make explicit. For example, we might have two statements that are assumed to be true. 1.) “Steve is in the choir.” 2.) “Everyone in the choir sings.” From these two statements, we can deduce a conclusion of 3.) “Steve sings.” We were able to reasonably produce new information from two previously established pieces of information. Perception and intellectual apprehension are ways of inputting sensory information. It is simply the awareness of the mind receiving a stimulus. If these two were thought of as data inputs, inference would be thought of as data outputs. To infer, you must first perceive and learn the information. Then, from the information gathered through the human senses, judgments are made to conclude things that the human senses cannot grasp on their own. Arguments can be classified as deductive or non-deductive. There are arguments that if the premises are true, the conclusion must be true. These arguments that have an impenetrable link between premises and conclusion are classified as “deductive”. For example, if I state the premise: "That thing is a water bottle" and "Water bottles can contain water", the conclusion "That thing can contain water" must be true (if the two premises were actually true ). deductive arguments, even non-deductive arguments have a set of premises with a subsequent conclusion. The difference lies in the relationship between premises and conclusion. In a non-deductive argument, the conclusion can still be false even if the premises are true. Non-deductive arguments do not carry the same weight as deductive arguments. ...... half of the paper ...... relative in their subjective strength. A valid argument is a type of valid argument that has the additional requirement that the premises are actually true. Compare the argument used above: [1.) All lamps are clocks. 2.) All watches are green. 3.) Therefore, all lights are green.] with [1.) All people reading this are literate. 2.) You're reading this. 3.) So 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 the premises is necessary for solidity. Only the second argument is valid. A proof in the most basic sense is just a valid argument. The only difference is that calling it a proof implies that the particular valid argument concludes new/relevant/important information that people can generally learn and use from.