Logical Reasoning

PT101 · S2 · Q24 No mathematical proposition can

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No mathematical proposition can be proven true by observation.

Conclusion (it follows that)

It's impossible to know any mathematical proposition to be true.

Evidence

No mathematical proposition can be proven true by observation.

Evaluate

The overlapping idea is mathematical proposition. The dangling ideas that need to be connected are "whether it can be proven true by observation" and "whether it can be known to be true".

If we wrote out the conclusion, and elongated the line of its logic path, it would look like this. This is what we're trying to assemble.

Math -----------------------------> impossible to prop know if true

The evidence provides this piece:

Math --------> can't be prop proven true by observ.

Goal

So the correct answer needs to provide this missing piece:

can't be ----------> impossible to proven true know if true by observ.

.

However, since Sufficient Assumption loves to give us the missing link in contrapositive form, we should also pre-phrase what that would sound like:

.

24.

The conclusion follows logically if which one of the following is assumed?

  1. Only propositions that can be

    Bad Trigger Match

    "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% picked this

  2. Observation alone cannot be used

    Unrelated to Goal

    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% picked this

  3. If a proposition can be

    Opposite Logic

    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% picked this

  4. Knowing a proposition to be

    Reversed Logic

    "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.

    9% picked this

  5. Correct

    Knowing a proposition to be

    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.

    59% picked this

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