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According to Armstrong & Fogelin (2005), an argument is a premise that may or may not be true. The writers noted that there is always a minimum of one premise in every statement. According to them, premises help qualify the conclusion by giving enough reasons.
Armstrong & Fogelin (2005) stated that an argument means to be deductive if it is believed that the premises provide a guarantee of the truth in the conclusion. They noted that in a deductive argument, the premises are intended to provide support for the conclusion that is so strong that, if the premises were true, it would be impossible for the conclusion to be false. Armstrong & Fogelin (2005) noted that contrary to this, inductive arguments are those whose premises have enough justification of the proposed truth in the conclusion. Such arguments require to be supported by strong premises, which can never lead to a false conclusion if they remain true.
Argument 1 is a deductive argument. The fact that apple is perched at the top of a high tower makes it experience the force of gravity directed toward the center of the earth. On the other hand, the gust of wind that blows the apple has a mass that will eventually displace the apple. Moreover, the force of gravity that will act on the apple is dependent on the mass of apple and wind based on the distance the apple is from the center of the earth. Therefore, the truths of the premises have definitely established that there is truth of conclusion that apple will mathematically fall on the ground.
On the other hand, Argument 2 is an inductive argument. According to the argument 2, the apple perched at the top of the tower under the influence of gust of wind flowing will not fall to the ground. The premises indicate that the falling of the apple to the ground (point C) is dependent on the infinite midway points rather than mass and distance. The premises also show that due to infinite midway point that the apple encounters, it will never fall on the ground (point C). The argument is based on the probability of the apple falling on the ground. There is no truth emanating from the premises that establishes the truth of the conclusion but rather there is a belief that the truth of premises provides a compelling reason to believe in the conclusion.
The write up is a proof that to some extent, even the scientists require an appropriate level of mathematical knowledge. It is so, because this knowledge is necessary in coming up with both the theories and the natural laws. Argument 1 is a clear proof that the apple fell because of the force of gravity. It is, therefore, true that with the premises remaining true, the truth of the conclusion cannot be doubted.
On the other hand, the analysis has demonstrated that the knowledge of science is not necessarily essential to all mathematicians. According to Argument 2, the logical expression of the falling of the apple is based on mathematical probability, rather than the nature of falling apple (science) and is indicated by the way the probability is expressed. The notion of infinite distance here rules out an effect of the gravity force.
In conclusion, the analysis of the arguments has proved that both science and mathematics are relevant while the premises have great influences over the kind of any premise and may have one various conclusions. The write up has also provided a proof that the way in which the arguments may be classified is almost entirely based on inferences from a number of proves or evidences.