No mathematical proposition can

Answer choices

1. A

   Bad Trigger Match10% picked this

   Only propositions that can be proven true can be known to

   "only" and "only if" indicate necessary (right side) ideas, so this rule looks like this: Can be known → can be proven to be true true This gives us a contrapositive of "IF can't be proven true, THEN impossible to know it's true". That's a good match for the conclusion language we're trying to prove (it's impossible to know if any math proposition is true). Can we trigger this rule? Were we told that "Math propositions can't be proven true?" No. We were told they can't be proven true by observation, but they can potentially be proven true by other means (deductive proofs, for example). This rule would allow us to prove the conclusion, but we have no way of saying that mathematical propositions qualify under the trigger of this rule.

   10%
2. B

   Unrelated to Goal11% picked this

   Observation alone cannot be used to prove the truth of

   This is saying, "observation can't proven any proposition true". We already knew from the premise that "observation can't prove any mathematical proposition true". This answer is saying, "Hey, that premise don't just apply to math propositions but to any proposition!" We don't care. The conclusion is only about math propositions. We already know they can't be proven by observation, so this answer choice tells us nothing new about them. We need a rule that says, "If it can't be proven by observation, then it's impossible to know it's true".

   11%
3. C

   Opposite Logic11% picked this

   If a proposition can be proven true by observation, then it can be known

   We need a rule that says, "If it can't be proven by observation, then it's impossible to know it's true". This is giving us the illegal negation of that -- "If it can be proven by observation, then it is possible to know it's true".

   11%
4. D

   Reversed Logic10% picked this

   Knowing a proposition to be true is impossible only if it cannot be proven

   "only if" and "only" are necessary (right side) indicators, so this answer choice looks like this "If it's impossible to know it's true, then it can't be proven true by observation". We need a rule that says, "If it can't be proven by observation, then it's impossible to know it's true". (D) and (C) are the same claim (just in contrapositive form of each other), so neither of them could be the correct answer, because otherwise they both would be the correct answer.

   10%
5. E

   Correct58% picked this

   Knowing a proposition to be true requires proving it true

   Why this is right

   "Requires" is the same thing as the conditional arrow itself. X → Y can be read as "X requires Y". So this rule is saying, know something → proven true by to be true observation The contrapositive matches what we wanted, "If it can't be proven by observation, then it's impossible to know it's true".

   Skill tested: Sufficient Assumption · how this choice captures the argument's function is the move to repeat next time.

   58%