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I have a homework problem where I have to state if an argument is valid, conclusive or neither. However I am struggling to wrap my head around this one.

The argument goes:

Generally, a flood occurs only if there is too much water. Yet a flood is occurring, although there isn't too much water. So a flood isn't occurring.

I am having difficulty as the premises states that there is a flood occurring, however then the conclusion states that there is not.

So far I have attempted this method:

F: There is a flood occurring 

W: There is too much water

W -> F

F && ~W

Therefore ~F

However I am not too sure what to make of that.

Can the premises just be wrong like that and the argument still be valid?

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    "generally" means that it is not always true that... So, no valid inference here. – Mauro ALLEGRANZA Jan 28 at 7:36
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    @MauroALLEGRANZA Oh okay, so "generally" is the same as using "sometimes". – Bongo Jan 28 at 7:47
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    "Generally" means "in most cases", "typically", the correct conclusion is that this case is atypical. – Conifold Jan 28 at 10:34
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    The 1st premise is "if F, then W". The second one: "F and not-W" is equivalent to "not(if F, then W)". Thus, if we onit "generally", we have two contradictory premises. – Mauro ALLEGRANZA Jan 28 at 11:06
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    From contradictory premises, everything follows; thus, if we omit "generally", the argument is valid. – Mauro ALLEGRANZA Jan 28 at 11:08
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I'd say neither.

Generally, a flood occurs only if there is too much water. Yet a flood is occurring, although there isn't too much water. So a flood isn't occurring.

I think that from the above you can raise the following problems:

  1. If a flood occurs only if there too much water, how can there be a flood when there's isn't enough water?
  2. How can the conclusion be opposite to the premise that a flood is occurring?

If we're being pedantic, you can also add that:

  1. Generally and only are contradictory in the 1st premise
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    The first premise clearly means that there exist cases where a flood occurs although there is not too much water. Generally is a quantifier which should be understood as "in most cases". And even if we don't take this into consideration (eg. because the course did not involve quantifiers as of yet), as Mauro correctly stated in comments, the principle of explosion applies and the argument is valid since you can literally conclude anything from contradictory premises, including statements which are contradictory to either of the premises. – Philip Klöcking Jan 28 at 12:18
  • @PhilipKlöcking - I completely agree with your point that's why my answer was neither from the get-go. Thank you for putting it way more eloquently than me. – Ted Jan 28 at 12:57

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