Agreed!

Muslims do not eat pork.  Fish is pork.  So Muslims don’t eat fish.  "Invalid and unsound arguments."  Could you explain this?

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Answer:

Upon careful reading of your question, it seems two different ideas are coming into play here.  In logic, an invalid and unsound argument means at least one premise is false and the conclusion does not follow from the premise.  An example of this is explained as follows:

  • All solar satellites are positioned in the ocean. (False)
  • Everything positioned in the ocean becomes wet. (True)
  • Therefore, solar satellites are dry. (??)

The first bullet is the "unsound" premise.  Solar satellites are not positioned in the ocean at all.  The second bullet point is true, but the "dry" part of the conclusion is invalid.  It is completely illogical to conclude that if a solar satellite were in the ocean it would be dry.  Even though the first point is not true, a valid but unsound conclusion would be to say, "Therefore, GPS satellites are wet."  This conclusion logically follows the incorrect argument.  The valid and sound argument is:

  • No solar satellites are positioned in the ocean.
  • Everything positioned in the ocean becomes wet.
  • Therefore, all solar satellites are dry.

The example provided in your question is actually a valid but unsound logical fallacy.  The conclusion is valid, meaning it follows the argument, but one of the premises in the argument is unsound or false.  Notice:

  • Muslims do not eat pork.  (True)
  • Fish is pork. (False)
  • Therefore, Muslims do not eat fish. (Would be true if fish was pork.)

A corrected version of the above argument might be something more like this:

  • Muslims do not eat pork.
  • Bacon is pork.
  • Therefore, Muslims do not eat bacon.
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