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In modern usage, it has come to refer to an argument in which the premises assume the conclusion without supporting it. This makes it an example of circular reasoning. [1] [2] Some examples are: "People have known for thousands of years that the earth is round. Therefore, the earth is round." "Drugs are illegal so they must be bad for you.
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word ἀξίωμα ( axíōma ), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'.
For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work.
Example 1. One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example: If someone lives in San Diego, then they live in California. Joe lives in California. Therefore, Joe lives in San Diego. There are many places to live in California other than San Diego.
Since assuming P to be false leads to a contradiction, it is concluded that P is in fact true. An important special case is the existence proof by contradiction: in order to demonstrate that an object with a given property exists, we derive a contradiction from the assumption that all objects satisfy the negation of the property.
The definition of a formal proof is intended to capture the concept of proofs as written in the practice of mathematics. The soundness of this definition amounts to the belief that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done in practice.
The post 16 of the Most Famous Malapropism Examples appeared first on Reader's Digest. You've made a malapropism—and everyone from politicians to famous literature characters is guilty of errors ...
Arguendo is a Latin legal term meaning for the sake of argument. "Assuming, arguendo, that ..."and similar phrases are used in courtroom settings, academic legal settings, and occasionally in other domains, to designate provisional and unendorsed assumptions that will be made at the beginning of an argument in order to explore their implications.