Deductively sound arguments are also deductively valid?

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1260798

2026-05-04 10:50

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Yes, deductively sound arguments are also deductively valid. An argument is sound if and only if all of the premises are true (with respect to all cases of semantics) and the premises certainly prove the conclusion, which then must also be true.

An example of a valid, but not sound argument:

Everyone who lives on Mars is a martian

I live on Mars

Therefore I am a martian

An example of a sound argument (which then must also be valid):

All rodents are mammals

A rat is a rodent

Therefore a rat is a rodent

Recall that semantics are important and must be considered for an argument to sound and valid. Consider the following example:

Everyone from London is from England

Person A is from London

Therefore person A is from England

For the sake of this example, assume person A is indeed from London. This still does not mean that this argument is sound, or even valid. There are many places named London that are not in England (eg. London, Ontario, Canada). Thus, the argument is not sound and is invalid.

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