In deductive syllogism, the logic behind the conclusion is defined by the essence of validity or invalidity. In this case, I will provide a premise via illustrations to support validity and invalidity of the outcome. For instance, if all snakes and frogs are cold-blooded, then snakes are frogs. In the illustration, frogs and snakes might overlap in the category but also could be in the largest circle without overlapping thus deducing the invalidity of the syllogism (fig. 1). On the other hand, on deductive syllogism some premises confirms validity as opposed to true premises. For instance, if all humans are selfish and Confucius is human, then Confucius is selfish. In this case, we fail to agree that the individual premises are true but acceptance of the premises concludes the logical consistence (fig. 2).
In inductive argument, statistical syllogism attempts to conclude from generalization. In contrast to deductive syllogism where the premise logically confirms or supports the conclusion without strictly applying it. There is the possibility of the premise being true and a false conclusion which is unlikely. Unlike other forms of syllogism, statistical syllogism confirms to be inductive in almost all dimensions of conclusion. It considers evaluating every argument on how strong or weak it is in respect to other rules of induction as opposed to deduction. The probability of statement is traced via direct inference. Hence the use of confidence intervals in statistics guarantees justification through a statistical syllogism. For instance, if 99% of the population are taller than 20 inches, then the probability of concluding it being true is 99% accurate.
However, deductive and inductive syllogism face problems in attempts to provide a logic solution. In the case of statistical syllogism, it is affected by the problem of induction via majority of the large samples of a population approximately matches with the population (proportion anatomy). Statistical syllogism is used as a legal evidence even though legal decision should not solely depend on then. For instance, if 51 of the 100 attendees have not paid entrance fees, the balance of probabilities of attendees have not paid. Therefore, the judge might rule under statistical syllogism and charges the random attendees for non-payment.
Fig 1. (Invalidity)
Fig 2 (validity)
 Barnes, J. (2017). Statistical syllogism? Truth ,etc.,448528.doi:10.1093/acprof:oso/9780199568178.003.0006
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