In Logic, what are Sound and Valid Arguments?

L. S. Wynn

There are several types of arguments, and one of the most common are deductive arguments. Deductive arguments are those who contain a string of related statements that taken in totality prove or establish a conclusion.

Such deductive arguments can be attacked on two different fronts: 1) call into question the premises of the argument itself, 2) call into question the structure of the argument, specifically that the conclusion does not follow from the premises.

This leaves us with four different possibilities for any deductive argument:

• Invalid and unsound: at least one premise is false, and conclusion does not follow from the premises. Example:

• All GPS satellites are positioned underwater.
• Everything positioned underwater becomes wet.
• therefore, GPS satellites are dry.

• Invalid: premises may be true but conclusion does not follow from them. Example:

• Mangosteen is a fruit.
• Mangosteen is purple.
• Therefore, all fruit is purple.

• Valid but unsound: conclusion follows from the premises but at least one of the premises is false. Example:

• All art movements started in India.
• Bauhaus was an art movement.
• Therefore, Bauhaus started in India.

• Sound: all premises are true and conclusion follows from the premises. Example:

• Investment strategies may be profitable.
• "Dogs of the Dow" is an investment strategy.
• therefore, the "Dogs of the Dow" strategy may be profitable.

Note that in all four of the examples above, the conclusion can be true. Even an invalid and unsound argument can have a true statement as its conclusion — its just that the conclusion may not follow from the premises, or that the premises that the conclusion is based on are not true. Let us imagine a non-sequitor, for example that is unsound and invalid, but the conclusion is true:

• non-sequitor:

• The Curse of the Bambino will never end.
• Sputnik was launched by China.
• Therefore, en-passant is a move in chess.

Also, arguments themselves are neither true or false, they are to be judged on their validity and soundness. It is the statements within an argument, namely the premises and conclusion that can have truth and falsity.

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anon322322

@JaneAir: How is that a non-sequitur? The premises conjointly imply the conclusion, do they not?

anon316721

@anon37203: They have the purple fruit one under invalid. They never said it was valid.

sweetPeas

@next correa - I took a logic class in college and really enjoyed learning the methods of deductive and inductive reasoning. Learning and practicing reasoning exercises helped me to think more clearly and evaluate what I read and heard. I think that every college student should be required to take such a class.

I know what you mean about watching cable news channels. I get pretty disgusted with some of the senseless banter. I'm also afraid that a good many of our politicians don't know a thing about presenting a logical argument.

I admire lawyers because most have the ability to think logically and present good arguments.

nextcorrea

I remember when I was first introduced to analytical logic an an into philosophy class in college I was alternately confused and thrilled. On the one hand it was really exciting to think that there was this near scientific level of meaning and relation buried in every statement we make. On the the hand it was kind of disappointing to think that nothing is exactly the way it seems, every argument is the sum of many smaller argument and together they can form twisted up castles.

But I stuck with it and I got to be pretty good and recognizing certain fallacies and logical incongruities. I am not a philosopher but this training still pops into my head all the time because the talking head culture we live in is filled with weak, false and even outrageously false arguments. Watch cable news for 30 minutes and you will begin to understand what sound and valid means.

starrynight

@JaneAir - Well at least you guys were paying attention in geometry! I don't even remember learning "if, then" statements, though I'm sure I did.

I feel like I hear a lot of valid but unsound arguments in daily life. I guess everyone is entitled to an opinion, but, as Mr. Spock might say, sometimes those opinions are quite illogical!

JaneAir

This reminds me of conditional "if, then" statements in geometry, which are a form of logical arguments regarding causation.

My girlfriends and I had a ton of fun using "if, then" statements as non-sequitors. For example, "if we go shopping tonight, then we won't have time to do our homework. If we don't do our homework, we will fail geometry. So, if we go shopping tonight we will fail geometry." Those "if, then" statements kept us entertained all year long!

anon114845

This page has expanded my knowledge more on logic and arguments. I say thank you to the writer.

anon92721

What does it mean by premises?

origami

to #2: it is correctly marked as Invalid in the article above, so I am not sure what your point is.

anon37203

Mangosteen is a fruit.

Mangosteen is purple.

Therefore, all fruit is purple.

This is not valid.

anon9707

Extremely helpful. Thank you!