logic logic logic

Which of the following statements is true?

(1) If the Alamo is in Boston, then the Alamo is in Texas. (2) If the Alamo is in Houston, then the Alamo is not in Texas. (3) If the Alamo is not in Boston, then the Alamo is in Texas.

SPOILER

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(1) If the Alamo is in Boston, then the Alamo is in Texas.

True.

As in fact, the Alamo is in Texas, it would be in Texas even if it was in Boston, which city is not presently in Texas. Therefore the first statement is true, because it did not employ the condition, 'if, and only if'. If this stricter condition was employed instead of the general 'if', then it would be a false statement at this present time. Boston, like all cities, can of course grow and reach Texas, and engulf completely at one point the Alamo. Then, and only then, the condition 'if, and only if' also would hold true in the statement.

(2) If the Alamo is in Houston, then the Alamo is not in Texas.

False.

As the Alamo is in Texas, again, there cannot exist any other condition at the present that could override that fact. Should Houston sprawl to reach and enfold completely the Alamo in the future while being decreed outside the territory of Texas, then, and only then, the statement would be true.

(3) If the Alamo is not in Boston, then the Alamo is in Texas.

False.

While we know the Alamo in fact is in Texas, this fact, nevertheless, does not follow from such condition as it not being in Boston. If the Alamo is not in Boston, that means it could be anywhere other than Boston, and does not mean anything more specific for us to infer from it where exactly the Alamo is.

Nice puzzle! I hope I did not commit hair-raising mental flops!

Cheers!

Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . Spoiler . . . . . . None of the statements are true!

If we know that they are all true statements then it is possible to deduce that the Alamo is in Texas (from 1 and 3) but if we do not know which of the statements is true then I don't see that you can deduce anything without further information about what 'the Alamo' is and where Boston and Houston are in relation to Texas. Given that I'm from the UK and don't take much interest in the states I do not know these geographical facts.

However, assuming that 'the Alamo is in Boston' and 'the Alamo is in Houston' are mutually exclusive statements, then the following table can be constructed:

in Texas not in Texas in Boston 1,2,3 2,3 in Houston 1,3 1,2

Where the listed numbers in the table are the true statements.

Hey this feels like a homework assignment rather than a puzzle.

Spoilers

1) True (the Alamo is not in Boston, and the Alamo is in Texas; either is sufficient) 2) True (the Alamo is not in Houston) 3) True (the Alamo is in Texas)

With no knowledge of geography, it is still possible to prove that at least two of them must be true. Therefore the question is ungrammatical, and should read 'Which of the following statements are true?'

: (2) If the Alamo is in Houston, then the Alamo is not in Texas. : (3) If the Alamo is not in Boston, then the Alamo is in Texas.

'r.e.s.'

The correct answer to the question depends on which of a number of controversial semantic theories of English indicative conditionals is correct. Presumably the intended answer takes for granted the common logic textbook assertion that English indicative conditionals are *material* conditionals. (For the record: a material conditional is true whenever its antecedent is false, and whenever its consequent is true, and it is false only when its antecedent is true and its consequent false.)

There is a lot to be said for that standard view, but this very puzzle shows that it has some drawbacks. The only one of the statements that 'sounds true' is (3), even though they all come out true if they're understood as material conditionals.

ObPuzzle: Why is it that arguments with this form sound valid to almost everybody:

P; so P or Q.

and so do these:

P or Q; so if not P then Q

but arguments with this form do not sound valid:

P; so if not P then Q

?

1) False (Boston isn't a city in Texas, as far as I can tell) 2) True (Houston is a city in texas) 3) False (IMO this sort of construction requires the conclusion to follow from the antecedent, not merely be true regardless of it)

I don't think so. 'If Clinton had campaigned for Gore, Gore would have won.'

I know that the consequent doesn't follow logically from the antecedent, but I'm not sure whether the conditional is true.

Damn. For '#1', read '#4'.

I agree it's true. I also agree that the truth function (if any) represented by the 'or' is context sensitive.

Furthermore, my example was not phrased right for what I was trying to show. Mine really should be:

'... either you must take the A, or you must take the #4.'