Week 4 Day 3 - Invalid / Valid / Sound Arguments

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Bill Kerney

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Published on February 12, 2021 7:19:34 PM ● Video Link: https://www.youtube.com/watch?v=Cr94iWSo70A

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An argument is when you reason from premises (assumptions) to a conclusion. There are three kinds of arguments:


1) Invalid - the logic connecting the premises to the conclusion doesn't work. For example, if they make a denying the antecedent fallacy, then the conclusion does not actually follow from the premises (even if the premises are true), and the argument is invalid.
2) Valid but not Sound - the logic successfully connects the premises to the conclusion but one or more of the premises are false.
3) Sound - the logic successfully connects the premises to the conclusion AND the premises are true.


For example, consider the following argument:
Premise 1) If you drink coffee you will be awake
Premise 2) You are awake
Conclusion) Therefore, you drank coffee.


This seems, at first glance, to be not only valid but sound. The premises are both true (if nothing else, you have to be awake to be reading this, or to drink coffee, right?), however the conclusion does not follow from the premises. It's entirely possible that you are awake right now but did not drink coffee. So you'd respond to the person making this argument that the argument is invalid, and that they made an "Affirming the Consequent" logical fallacy.


Consider this argument:
P1) All triangles have three sides
P2) This YouTube video has four sides (i.e. the video is a rectangle)
C) Therefore, this YouTube is not a triangle.


The logic works, and the premises are both true. Therefore, this is a sound argument (some will say valid and sound, but since all sound arguments are valid, it's a bit redundant).


Consider this argument:
P1) Quadrupeds are defined as having four legs
P2) All pets have four legs
C) All pets are quadrupeds.


The logic is correct here (if the premises were true, the conclusion would be true), however the second premise is not true (some pets don't have four legs, like fish), so the argument is valid but not sound.