• 22) DISJUNCTIONS

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    Disjunctions are helpful for creating analytical arguments.


    DEFINITION: (exclusive) disjunctions identify elements that CANNOT be true at the same time.

    (N.B. In logic, the specific term for exclusive disjunctions is "exclusive or," or "xor." Philosophers and computer scientists typically use the word "or" to refer to "inclusive or," meaning "either... or (or both)" can be true (Layman, 2005). "Disjunctions" in a broad sense includes both inclusive and exclusive "or." However for simplicity I will use the common, vernacular sense of the word "or": referring to exclusive disjunctions instead of the definition of "or" as inclusive disjunctions used in computer science).


    For example, we might state "Either the coin will land on heads or the coin will land on tails." When there are two mutually-exclusive outcomes (like a coin flip), we can term the exclusive disjunction a "dichotomy."


    Dichotomies are extremely useful for science. Dichotomies can help us analyze problems (i.e. break problems down into their constituent parts). 


    For example, if we can define a problem such that an experiment has only two possible outcomes, one of which rejects Hypothesis A and one of which rejects Hypothesis B, then we can be sure of an important conclusion regardless of the results of our experiment.


    A disjunctive argument could be:Disjunction Figure


    PREMISE: Either DNA or protein is the heritable genetic material that determines phenotype.
    PREMISE: Proteins do NOT heritably determine phenotype (Hershey and Chase, 1952).
    CONCLUSION: Therefore, DNA is the heritable genetic material that determines phenotype.


    TRUE dichotomies are EXTREMELY USEFUL (Platt, 1964). However, true dichotomies can also be challenging to identify. Moreover, it is important to be cautious of FALSE dichotomies, a common logical fallacy.


    For example, the dichotomy "Either exercise prolongs life or it doesn't" is a false dichotomy because it does not address several legitimate alternatives. Specifically, the statement doesn't specify how much exercise it refers to. Whereas moderate exercise has health benefits, excessive exercise can be fatal (Knechtle and Nikolaidis, 2018). 


    Therefore, when using exclusive disjunctions, it is important to have strong evidence that all the alternatives are mutually exclusive, and that intermediate possibilities do not exist. 


    Disjunctions involve the logical transition "or." In many cases, the clearest way to indicate disjunction is simply to use the word "or" or the couple "Either...or." However, other words such as "conversely," or "alternatively" can also indicate disjunction.


    Disjunctions are not only useful for reasoning. Disjunctions involve contrasts that are even stronger than "but" conjunctions. Therefore, disjunctions have from the same potential benefits (of keeping the audience interested and facilitating memory) that "but" conjunctions do.


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    Disjunctions, including dichotomies, are EXTREMELY USEFUL, both for analytical reasoning and writing. Discovering TRUE disjunctions is worth considerable effort. Disjunctions involve the "or" logical transition.


    21) BUT23) INDICATING CONCLUSIONS