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-We have observed that the color of a raven is black.

-Every non-blue thing I have observed in my room is non-raven.

-By inductive reasoning, every non-blue thing I will observe in my room is non-raven.

-Thus, All non-blue things in my room are non-raven.

-Thus we conclude that All ravens are blue things in my room.

The conclusion follows from true premises and so is true but at the same time is contradictory to the observation.

How to resolve this? Please explain specifically to this example.

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It is not a paradox, it is only a mistake.

The second premise: "Every non-blue thing I have observed in my room is non-raven" is logically equivalent to: "Every raven that I have observed in my room is blue", by Contraposition.

But there are no ravens in my rooms; thus, the conditional:

"if x is a raven in my room, then x is blue"

is True because the antecedent is False.


Maybe a bit of "formalization" will help...

The statement: ∀x ∈ MyRoom (not-Blue(x) → not-Raven(x)) is equivalent to:

∀x ∈ MyRoom (Raven(x) → Blue(x)).

Thus, if we assume that the first one is a correct "observational report", we have to consider as correct also the equivalent one.

As said above, if there are no ravens in my room, the correctness of the assertion above does not contradict the well-known fact that every raven is black.



It seems that you are reading the premise in a different way: in that case, there is another mistake.

If we consider "blue thing I have observed in my room" as a single predicate, the contraposed statement will be: ∀x (Raven(x) → Blue-thing-I-have observed-in-my-room(x)), that is "Every raven is a blue thing that I've observed in my room".

This statement is clearly False, ans thus also the equivalent formulation will be:

∀x (not-Blue-thing-I-have observed-in-my-room(x) → not-Raven(x)).

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  • @Zam - not clear... When you assert "Every non-blue thing I have observed in my room is non-raven" this means that e.g you have observed a red pencil (a non-blue non-raven). This is consistent with the previous assertion, that is equivalent to: "Every raven that I have observed in my room is blue", because you have not observed ravens. Thus, if the first assertion is true, also the "contraposed" one must be, because it is equivalent to the first one. Feb 4, 2021 at 15:08
  • Of course, I've assumed that there are no ravens in your room... If not, i.e. if there is a raven in your room, it is black, and thus it is false that "Every non-blue thing I have observed in my room is non-raven" Feb 4, 2021 at 15:10
  • How can the statement 'Every raven that I have observed in my room is blue' be true if there are no ravens in my room?
    – Zam
    Feb 4, 2021 at 16:03
  • @Zam - because a conditional with a FALSE antecedent is always TRUE. Feb 4, 2021 at 18:25
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    @Zam - Yes, according to the formal usage of "vacuous" here, Raven(x) -> Blue(x) would be vacuously true if there are no x's that are ravens in the domain of discourse (in this case, objects in your room).
    – Hypnosifl
    Feb 5, 2021 at 17:11

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