Logic and ambiguity
Logic puzzles are a great thing to get you thinking and exercise your mind. However, many (most) are typically devised by time-wasting time wasters. What is more they have a tendency to put people off philosophy. Countless logic paradigms, arguments, thought experiments etc are best left in the dustbin of duff philosophical conjecture.
Whilst logic riddles can waste your time and waste your mental energy, understanding what is going on withing them is useful if you want to avoid being taken down a dangerous path.
Why is logic so often a waste of time? For many reasons, one being the ambiguity found in the English language. Ambiguity is often to blame. I see it time and time again. Ambiguity. Two ways of interpreting something. I will give you a couple of examples of ambiguity set in logical prose.
This sentence is false.
If we were saying X is false, all would be fine. 'X is false' is a true statement. All good. However, we are saying ‘this sentence’ is false. ‘This sentence’ can include the whole sentence ‘this sentence is false’. So, it becomes recursive. (This sentence is false) is false if you replace ‘this sentence’ with ‘this sentence is false’.
This sentence is false
This sentence is false is false
‘This sentence is false’ could be a true statement. So, this paradigm has a contradiction of sorts embedded within.
(This sentence) = false.
(This sentence is false) = true.
Thus, we have recursion and a contradiction arising from the two ways of reading the logic. Ambiguity gives rise to both the potential contradiction and the never ending recursive interpretation. Is this interesting and noteworthy? Not really. It simply highlights how arguments can brew because someone has formulated something seemingly clever to throw you off the scent. Look out for ambiguity and its misuse.
In the book (chapter Arguments), I point out a similar ambiguity issue.
Someone can be holding three cigarettes. If you ask, “Have you got two cigarettes?”, one can justifiably answer yes or no and be correct in both cases. Both yes and no are correct. No, I have three. Yes, I have two. I have more than two, but I do have two that I could give you. I have two and I have three.
| || - I have two.
| | | - I do not have two.
18th September 2026 © IgnoranceParadox
