There are four types of paradox: veridical, falsidic, antinomy, and dialetheia. Veridical paradoxes are logically true but nonsensical, while falsidic paradoxes use incorrect assumptions to justify false results. Antinomies pose questions with no valid answer, and dialetheia suggests that both a statement and its opposite can be true. Examples include the leap year birthday paradox and the Barber Paradox. Dialetheia has no actual examples.
There are four generally accepted types of paradox. The first is called a veridical paradox and describes a situation that is ultimately logically true, but is nonsensical or ridiculous. A forgery presents a problem that usually uses some kind of incorrect assumption to justify a result that is, in fact, false. A self-referential semantic antinomy or paradox poses a set of conditions and then poses a question, the resolution of which becomes self-contradictory, resulting in a lack of a valid answer. A dialetheia states that both a statement and the opposite of that statement can both be true at the same time.
True paradoxes are defined by the fact that the logic applied to a situation is ultimately true within the given context. The most famous example of a veridical problem involves a theoretical man who is 20 but has only had five birthdays. The solution to the problem is that his birthday falls on a leap day and occurs only once every four years. While the situation is logically true, the statement is quite nonsensical.
An example of a falsidic paradox is the idea of an arrow being shot at a target. The exercise assumes that in order for the arrow to reach the target, it will have to travel half the distance to get there. Once it is halfway to the target, it now has to travel half the remaining distance to reach the target. Each time the arrow travels half the remaining distance to reach the target, it must travel half the shortest remaining distance, down to infinitesimal measurements. This would lead to the conclusion that since the arrow always has to travel half the distance, it would never reach the target, which is an incorrect conclusion.
An antinomy presents a statement, question, or problem that appears to have no answer according to common sense or a predefined set of rules. The Barber Paradox, a variation of Bertrand Russell’s paradox, is one example. This antinomy assumes that there is a city in which “the barber shaves all and only those men in the city who do not shave themselves”. The question that arises is who shaves the barber? If he shaves, then he is shaving a man who shaves and violates the premise.
Finally, there is dialetheia. There are no actual examples of this, although there are many philosophical arguments as to why they should or shouldn’t exist. The general concept is that both a condition and the opposite of the condition can both be true at the same time and coexist together.
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