Process of elimination is a
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
al method to identify an entity of interest among several ones by excluding all other entities. In
educational testing
An examination (exam or evaluation) or test is an educational assessment intended to measure a test-taker's knowledge, skill, aptitude, physical fitness, or classification in many other topics (e.g., beliefs). A test may be administered verb ...
, it is a process of deleting options whereby the possibility of an option being correct is close to zero or significantly lower compared to other options. This version of the process does not guarantee success, even if only one option remains, since it eliminates possibilities merely as improbable. The process of elimination can only narrow the possibilities down, and thus, if the correct option is not amongst the known options, it will not arrive at the truth.
Method
The method of elimination is
iterative
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
. One looks at the answers, determines that several answers are unfit, eliminates these, and repeats, until one cannot eliminate any more. This iteration is most effectively applied when there is
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
al structure between the answers – that is to say, when by eliminating an answer one can eliminate several others. In this case one can find the answers which one cannot eliminate by eliminating any other answers and test them alone – the others are eliminated as a
logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically ''follows from'' one or more statements. A valid logical argument is on ...
; this is the idea behind optimizations for computerized searches when the input is sorted – as, for instance, in
binary search
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the m ...
.
In order for the method to work it is necessary to list all possible, even improbable, possibilities. Any omissions render the method invalid as a
logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
al method.
Medicine
A process of elimination can be used to reach a
diagnosis of exclusion
A diagnosis of exclusion or by exclusion (''per exclusionem'') is a diagnosis of a medical condition reached by a process of elimination, which may be necessary if presence cannot be established with complete confidence from history, examination or ...
. It is an underlying method in performing a
differential diagnosis
In healthcare, a differential diagnosis (abbreviated DDx) is a method of analysis of a patient's history and physical examination to arrive at the correct diagnosis. It involves distinguishing a particular disease or condition from others that p ...
.
See also
*
Law of excluded middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for every proposition, either this proposition or its negation is true. It is one of the so-called three laws of thought, along with the law of noncontradi ...
*
Philosophical razor
In philosophy, a razor is a principle or rule of thumb that allows one to eliminate ("shave off") unlikely explanations for a phenomenon, or avoid unnecessary actions.
Razors include:
* Occam's razor: Simpler explanations are more likely to be ...
*
Troubleshooting
Troubleshooting is a form of problem solving, often applied to repair failed products or processes on a machine or a system. It is a logical, systematic search for the source of a problem in order to solve it, and make the product or process ope ...
References
* Richard L. Burden, J. Douglas Faires (2000). ''Numerical Analysis'', 7th ed. Brooks/Cole. .
Philosophical logic
Philosophical methodology
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