Deductive arguments contain related statements that prove a conclusion, but can be attacked by questioning the premises or structure. There are four possibilities: invalid and unfounded, invalid, valid but invalid, and sound. The conclusion can be true even in invalid arguments. Arguments are judged on validity and soundness, not truth.
There are different types of arguments and one of the most common is deductive arguments. Deductive arguments are those that contain a series of related statements which, taken in their entirety, prove or establish a conclusion.
Such deductive arguments can be attacked on two different fronts: 1) questioning the premises of the argument itself, 2) questioning the structure of the argument, especially that the conclusion does not follow from the premises.
This leaves us with four different possibilities for any deductive argument:
Invalid and unfounded: at least one premise is false and the conclusion does not follow from the premises. Example: All GPS satellites are located underwater.
Anything placed under water gets wet.
therefore, GPS satellites are dry. Invalid: The premises may be true but the conclusion does not follow from them. Example: Mangosteen is a fruit.
Mangosteen is purple.
Therefore, all fruits are purple. Valid but invalid: The conclusion follows from the premises but at least one of the premises is false. Example: All art movements originated in India.
The Bauhaus was an art movement.
Therefore, the Bauhaus started in India. Sound: All premises are true and the conclusion follows from the premises. Example: Investment strategies can be profitable.
“Dogs of the Dow” is an investment strategy.
therefore, the “Dogs of the Dow” strategy can be profitable.
Note that in all four of the above examples, the conclusion can be true. Even an invalid and unsubstantiated argument can have a true statement as its conclusion: it is just that the conclusion may not follow from the premises, or that the premises on which the conclusion is based are not true. Let’s imagine a non-sequitor, for example that is not sane and invalid, but the conclusion is true:
non-sequitor: The Curse of the Child will never end.
Sputnik was launched from China.
Therefore, en-passant is a move in chess.
Furthermore, the arguments themselves are neither true nor false, they must be judged on their validity and soundness. They are the statements within an argument, i.e. the premises and the conclusion that can have truth and falsehood.
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